R/gsw.R
In gsw: Gibbs Sea Water Functions

Documented in argfix gsw_adiabatic_lapse_rate_from_CT gsw_adiabatic_lapse_rate_ice gsw_alpha gsw_alpha_on_beta gsw_alpha_wrt_t_exact gsw_alpha_wrt_t_ice gsw_beta gsw_beta_const_t_exact gsw_cabbeling gsw_C_from_SP gsw_chem_potential_water_ice gsw_chem_potential_water_t_exact gsw_cp_ice gsw_cp_t_exact gsw_CT_first_derivatives gsw_CT_first_derivatives_wrt_t_exact gsw_CT_freezing gsw_CT_freezing_first_derivatives gsw_CT_freezing_first_derivatives_poly gsw_CT_freezing_poly gsw_CT_from_enthalpy gsw_CT_from_entropy gsw_CT_from_pt gsw_CT_from_rho gsw_CT_from_t gsw_CT_maxdensity gsw_CT_second_derivatives gsw_deltaSA_from_SP gsw_dilution_coefficient_t_exact gsw_dynamic_enthalpy gsw_enthalpy gsw_enthalpy_CT_exact gsw_enthalpy_diff gsw_enthalpy_first_derivatives gsw_enthalpy_first_derivatives_CT_exact gsw_enthalpy_ice gsw_enthalpy_second_derivatives gsw_enthalpy_second_derivatives_CT_exact gsw_enthalpy_t_exact gsw_entropy_first_derivatives gsw_entropy_from_pt gsw_entropy_from_t gsw_entropy_ice gsw_entropy_second_derivatives gsw_Fdelta gsw_frazil_properties gsw_frazil_properties_potential gsw_frazil_properties_potential_poly gsw_frazil_ratios_adiabatic gsw_frazil_ratios_adiabatic_poly gsw_geo_strf_dyn_height gsw_geo_strf_dyn_height_1 gsw_geo_strf_dyn_height_pc gsw_gibbs gsw_gibbs_ice gsw_grav gsw_Helmholtz_energy_ice gsw_ice_fraction_to_freeze_seawater gsw_internal_energy gsw_internal_energy_ice gsw_IPV_vs_fNsquared_ratio gsw_kappa gsw_kappa_const_t_ice gsw_kappa_ice gsw_kappa_t_exact gsw_latentheat_evap_CT gsw_latentheat_evap_t gsw_latentheat_melting gsw_melting_ice_equilibrium_SA_CT_ratio gsw_melting_ice_equilibrium_SA_CT_ratio_poly gsw_melting_ice_into_seawater gsw_melting_ice_SA_CT_ratio gsw_melting_ice_SA_CT_ratio_poly gsw_melting_seaice_into_seawater gsw_Nsquared gsw_O2sol gsw_O2sol_SP_pt gsw_p_from_z gsw_pot_enthalpy_from_pt_ice gsw_pot_enthalpy_from_pt_ice_poly gsw_pot_enthalpy_ice_freezing gsw_pot_enthalpy_ice_freezing_first_derivatives gsw_pot_enthalpy_ice_freezing_first_derivatives_poly gsw_pot_enthalpy_ice_freezing_poly gsw_pot_rho_t_exact gsw_pressure_coefficient_ice gsw_pressure_freezing_CT gsw_pt0_from_t gsw_pt0_from_t_ice gsw_pt_first_derivatives gsw_pt_from_CT gsw_pt_from_entropy gsw_pt_from_pot_enthalpy_ice gsw_pt_from_pot_enthalpy_ice_poly gsw_pt_from_t gsw_pt_from_t_ice gsw_pt_second_derivatives gsw_rho gsw_rho_alpha_beta gsw_rho_first_derivatives gsw_rho_first_derivatives_wrt_enthalpy gsw_rho_ice gsw_rho_second_derivatives gsw_rho_second_derivatives_wrt_enthalpy gsw_rho_t_exact gsw_SAAR gsw_SA_freezing_from_CT gsw_SA_freezing_from_CT_poly gsw_SA_freezing_from_t gsw_SA_freezing_from_t_poly gsw_SA_from_rho gsw_SA_from_SP gsw_SA_from_SP_Baltic gsw_SA_from_Sstar gsw_seaice_fraction_to_freeze_seawater gsw_sigma0 gsw_sigma1 gsw_sigma2 gsw_sigma3 gsw_sigma4 gsw_sound_speed gsw_sound_speed_ice gsw_sound_speed_t_exact gsw_specvol gsw_specvol_alpha_beta gsw_specvol_anom_standard gsw_specvol_first_derivatives gsw_specvol_first_derivatives_wrt_enthalpy gsw_specvol_ice gsw_specvol_second_derivatives gsw_specvol_second_derivatives_wrt_enthalpy gsw_specvol_t_exact gsw_SP_from_C gsw_SP_from_SA gsw_SP_from_SK gsw_SP_from_SR gsw_SP_from_Sstar gsw_spiciness0 gsw_spiciness1 gsw_spiciness2 gsw_SP_salinometer gsw_SR_from_SP gsw_Sstar_from_SA gsw_Sstar_from_SP gsw_t_deriv_chem_potential_water_t_exact gsw_t_freezing gsw_t_freezing_first_derivatives gsw_t_freezing_first_derivatives_poly gsw_t_from_CT gsw_t_from_pt0_ice gsw_thermobaric gsw_Turner_Rsubrho gsw_z_from_p

# vim:textwidth=80:expandtab:shiftwidth=4:softtabstop=4

## Please see ../README_developer.md for the scheme used in adding functions
## here. Generally the functions will be added to Part 4.


## PART 1: document the package and the 'gsw' dataset

#' R implementation of Thermodynamic Equation Of Seawater - 2010 (TEOS-10)
#'
#' @description
#' Provides an R interface to the TEOS-10 / GSW (Gibbs Sea Water) library,
#' partly for use by the \code{oce} package (see \url{https://dankelley.github.io/oce/})
#' and partly for general use. It is assumed that users are familiar with
#' the science and methodology of GSW, and that the package vignette
#' (obtained by typing \code{vignette("gsw")} in an R window) provides
#' enough orientation to get users started with the \code{gsw} functions.
#'
#' @details
#' \code{gsw} was developed using open-source methodologies, on
#' the GitHub site (\url{https://github.com/TEOS-10/GSW-R}), which
#' is part of a set of sites dedicated to GSW formulations in
#' various languages.
#'
#' The \code{gsw} system is to link R functions with the C version of
#' the TEOS-10 library.  The R function names are chosen to match
#' those of the Matlab version of GSW, and the function arguments
#' also match with one exception: in \code{gsw}, longitude
#' and latitude are indicated with their full names, whereas in
#' Matlab they are indicated with \code{long} and \code{lat};
#' since R permits abbreviated function arguments, the shortened
#' names can be used in \code{gsw} as well.
#'
#' The documentation for the \code{gsw} functions focuses mainly
#' on the arguments and return values, relying on links to the
#' TEOS-10 webpages for details.
#'
#' See \url{http://www.teos-10.org/pubs/gsw/html/gsw_contents.html}
#' for a list of the TEOS-10 functions and
#' \url{https://teos-10.github.io/GSW-R/reference/index.html}
#' for a list of the functions implemented in the present package.
#'
#' Each function is tested during the building of the package,
#' which means that results are guaranteed to match those of
#' the equivalent Matlab functions to at least 8 digits.
#'
#' A significant difference from the Matlab case is in the inspection
#' of the dimensions of arguments. The Matlab library has rules
#' for expanding some arguments to match others. For example,
#' if Practical Salinity is a matrix and pressure is a single value,
#' then that single pressure is used throughout a calculation of
#' Absolute Salinity. This convenience is only partly mimicked in the
#' present package.  Since the underlying C code works on vectors,
#' the R functions in \code{gsw} start by transforming the arguments accordingly.
#' This involves using \code{\link{rep}} on each argument to get something
#' with length matching the first argument, and, after the computation
#' is complete, converting the return value into a matrix, if the first
#' argument was a matrix. There are some exceptions to this, however.
#' For example, \code{\link{gsw_SA_from_SP}} and similar functions
#' can handle the case in which the \code{SA} argument is a matrix and
#' \code{longitude} and \code{latitude} are vectors sized to match.
#' This can be handy with gridded datasets. However, the careful
#' analyst will probably prefer to avoid this and other conveniences,
#' supplying properly-matched arguments from the outset.
#'
#' @docType package
#' @name gsw
NULL

#' Global SA lookup file
#'
#' @description
#' This dataset is not intended for users, but rather for internal use
#' within the \code{gsw} package. The dataset stores the 1.4M lookup
#' table defined in the 8.3M file \code{src/gsw_saar_data.c} in the C
#' library. (The .c file exceeds CRAN limitations on size.)
#'
#' @details
#' The data are designed to replace C elements defined as below
#' in \code{src/gsw_saar_data.c}:
#' \preformatted{
#'     static int	gsw_nx=91, gsw_ny=45, gsw_nz=45;
#'     static double	longs_ref[91];
#'     static double	lats_ref[45];
#'     static double	p_ref[45];
#'     static double	ndepth_ref[4095];
#'     static double	saar_ref[184275];
#'     static double	delta_sa_ref[184275];
#' }
#'
#' R storage is in a list named \code{saar}, with elements named
#' as in the C code, i.e. \code{gsw_nx} etc.
#'
#' C storage for these variables is allocated as needed,
#' and the data are inserted, when \code{gsw} is launched.
#' Thus, the existing C library code "knows" about the data
#' as local storage, which keeps alterations to the C library to
#' a minimum.
#'
#' The \code{saar} dataset was created by the following R code. The
#' netcdf file used in this code comes from the GSW-Fortran
#' repository (at commit \code{baa0c09ffc7ed1f74972a1a2902d8754caa5b4cb})
#' and its md5 value is \code{dacb3f981e8e710ac2e83477701b3905}.
#'\preformatted{
#'   library(ncdf4)
#'   nc <- nc_open("~/git/GSW-Fortran/test/gsw_data_v3_0.nc")
#'   ## Use as.vector() since these will all get handed into C, which does not understand matrices.
#'   p_ref <- as.vector(ncvar_get(nc, "p_ref"))
#'   lats_ref <- as.vector(ncvar_get(nc, "lats_ref"))
#'   longs_ref <- as.vector(ncvar_get(nc, "longs_ref"))
#'   ndepth_ref <- as.vector(ncvar_get(nc, "ndepth_ref"))
#'   ndepth_ref[!is.finite(ndepth_ref)] <- -9e99
#'   saar_ref <- as.vector(ncvar_get(nc, "SAAR_ref"))
#'   saar_ref[!is.finite(saar_ref)] <- -9e99
#'   delta_sa_ref <- as.vector(ncvar_get(nc, "deltaSA_ref"))
#'   delta_sa_ref[!is.finite(delta_sa_ref)] <- -9e99
#'   saar <- list(gsw_nx=gsw_nx, gsw_ny=gsw_ny, gsw_nz=gsw_nz,
#'                longs_ref=longs_ref, lats_ref=lats_ref, p_ref=p_ref, ndepth_ref=ndepth_ref,
#'                saar_ref=saar_ref, delta_sa_ref=delta_sa_ref)
#'   save(saar, file="saar.rda")
#'   tools::resaveRdaFiles("saar.rda")
#'   nc_close(nc)
#'}
#'
#' @docType data
#' @name saar
NULL


## PART 2: utility functions

#' Reshape list elements to match that of the first element
#'
#' This is mainly used within gsw, to ensure that arguments sent
#' to the C functions are of equal length.  This is a convenience,
#' for processing data that often have this condition. For example, a
#' CTD profile is likely to have many values for SP, t, and p,
#' but just a single value for each of longitude and latitude.
#' It is important to call argfix() to handle such cases, because
#' otherwise the underlying C code will be looking past the end of
#' the vectors storing longitude and latitude, which can yield odd
#' results or even segmentation faults.
#'
#' @param list A list of elements, typically arguments that will be used in GSW functions.
#' @return A list with all elements of same shape (length or dimension).
argfix <- function(list)
{
    n <- length(list)
    if (n > 1) {
        length1 <- length(list[[1]])
        for (i in 2:n) {
            if (length(list[[i]]) != length1) {
                list[[i]] <- rep(list[[i]], length.out=length1)
            }
        }
        if (is.matrix(list[[1]])) {
            for (i in 2:n) {
                dim(list[[i]]) <- dim(list[[1]])
            }
        }
    }
    list
}



## PART 3: gsw (Gibbs SeaWater) functions, in alphabetical order (ignoring case)

#' Adiabatic Lapse Rate
#'
#' Note that the unit is K/Pa; multiply by 1e4 to get the more useful K/dbar.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return adiabatic lapse rate (note unconventional unit) [ K/Pa ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' lr <- gsw_adiabatic_lapse_rate_from_CT(SA, CT, p)
#' stopifnot(all.equal(lr*1e7,
#'     c(0.240199646230069, 0.238457486976761, 0.203635157319712,
#'       0.119829566859790, 0.100052760967308, 0.087773070307283)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_adiabatic_lapse_rate_from_CT.html}
gsw_adiabatic_lapse_rate_from_CT <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_adiabatic_lapse_rate_from_CT",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Adiabatic Lapse Rate of Ice
#'
#' Note that the unit is K/Pa; multiply by 1e4 to get the more useful K/dbar.
#'
#' @template teos10template

#' @template ttemplate
#' @template ptemplate
#' @return adiabatic lapse rate (note unconventional unit) [ K/Pa ]
#' @examples
#' t  <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <- c(       10,       50,      125,      250,      600,    1000)
#' lr <- gsw_adiabatic_lapse_rate_ice(t, p)
#' stopifnot(all.equal(lr*1e7, c(0.218777853913651, 0.216559115188599, 0.216867659957613,
#'                               0.216988337914416, 0.217182707402780, 0.218100558740840)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_adiabatic_lapse_rate_ice.html}
gsw_adiabatic_lapse_rate_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_adiabatic_lapse_rate_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Thermal expansion coefficient with respect to Conservative Temperature
#'
#' Thermal expansion coefficient with respect to Conservative Temperature, using
#' the 75-term equation for specific volume.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return thermal expansion coefficient with respect to Conservative Temperature [ 1/K ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' alpha <- gsw_alpha(SA,CT,p)
#' stopifnot(all.equal(alpha*1e3, c(0.324464211877393, 0.322610094680523, 0.281335030247435,
#'                                  0.173529986885424, 0.146898108553385, 0.130265123640082)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_alpha.html}
gsw_alpha <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_alpha",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Thermal expansion coefficient over haline contraction coefficient
#'
#' Thermal expansion coefficient over haline contraction coefficient,
#' using the 75-term equation for specific volume.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return ratio of thermal expansion coefficient to haline contraction coefficient [ (g/kg)/K ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' alpha_on_beta <- gsw_alpha_on_beta(SA,CT,p)
#' stopifnot(all.equal(alpha_on_beta, c(0.452468543022009, 0.449601695030057, 0.387140203094424,
#'                                      0.230778871228268, 0.193747796234162, 0.170946048860385)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_alpha_on_beta.html}
gsw_alpha_on_beta <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_alpha_on_beta",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Thermal expansion coefficient with respect to in-situ temperature
#'
#' Thermal expansion coefficient with respect to in-situ temperature.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return thermal expansion coefficient with respect to in-situ temperature [ 1/K ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <-  c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' alpha_wrt_t_exact <- gsw_alpha_wrt_t_exact(SA,t,p)
#' stopifnot(all.equal(alpha_wrt_t_exact*1e3,
#'     c(0.325601747227247, 0.323448083851267, 0.281413883319329,
#'     0.172825692975230, 0.145569941503599, 0.128362986933288)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_alpha_wrt_t_exact.html}
gsw_alpha_wrt_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_alpha_wrt_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Ice Thermal Expansion Coefficient with Respect to in-situ Temperature
#'
#' Thermal expansion coefficient of ice, with respect to in-situ temperature.
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return thermal expansion coefficient with respect to in-situ temperature [ 1/K ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <-  c(     10,       50,      125,      250,      600,    1000)
#' alpha <- gsw_alpha_wrt_t_ice(t, p)
#' stopifnot(all.equal(alpha*1e3, c(0.154472408751279, 0.153041866100900, 0.153232698269327,
#'                                  0.153297634665747, 0.153387461617896, 0.153938395452558)))
#' @family things related to density
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_alpha_wrt_t_ice.html}
gsw_alpha_wrt_t_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_alpha_wrt_t_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Haline contraction coefficient at constant Conservative Temperature
#'
#' Haline contraction coefficient with respect to Conservative Temperature, using
#' the 75-term equation for specific volume.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return Haline contraction coefficient at constant Conservative Temperature [ kg/g ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' beta <- gsw_beta(SA,CT,p)
#' stopifnot(all.equal(beta, 1e-3*c(0.717521909550091, 0.717657376442386, 0.726169785748549,
#'                                  0.750420924314564, 0.754903052075032, 0.756841573481865)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_beta.html}
gsw_beta <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_beta",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Haline contraction coefficient at constant in-situ temperature
#'
#' Haline contraction coefficient at constant in-situ temperature.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return Haline contraction coefficient at constant in-situ temperature [ kg/g ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' b <- gsw_beta_const_t_exact(SA, t, p)
#' stopifnot(all.equal(b*1e3, c(0.731120837010429, 0.731071779078011, 0.736019128913071,
#'                              0.753810501711847, 0.757259405338257, 0.758649268096996)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_beta_const_t_exact.html}
gsw_beta_const_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_beta_const_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Cabbeling coefficient
#'
#' Cabbeling coefficient (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return Cabbeling coefficient with respect to Conservative Temperature [ 1/(K^2) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' cabbeling <- gsw_cabbeling(SA,CT,p)
#' stopifnot(all.equal(cabbeling*1e4, c(0.086645721047423, 0.086837829466794, 0.092525582052438,
#'                                      0.108884336975401, 0.112971197222338, 0.115483896148927)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_cabbeling.html}
gsw_cabbeling <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_cabbeling",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Electrical Conductivity from Practical Salinity
#'
#' Electrical conductivity (in mS/cm) from Practical Salinity.
#' To convert the return value to conductivity ratio,
#' divide by 42.9140 (the value of conductivity at S=35, T68=15, and
#' p=0).
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template ttemplate
#' @template ptemplate
#' @return electrical conductivity [ mS/cm ]
#' @examples
#' SP <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' C <- gsw_C_from_SP(SP, t, p)
#' stopifnot(all.equal(C, c(56.412599581571186, 56.316185602699953, 50.670369333973944,
#'                          38.134518936104350, 35.056577637635257, 32.986550607990118)))
#' @family things related to salinity
#' @family things related to conductivity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_C_from_SP.html}
gsw_C_from_SP <- function(SP, t, p)
{
    l <- argfix(list(SP=SP, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_C_from_SP",
               SP=as.double(l$SP), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Chemical Potential of Ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return chemical potential [ J/kg ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,      600,      1000)
#' pot <- gsw_chem_potential_water_ice(t, p)
#' stopifnot(all.equal(pot/1e4, c(-1.340648365149857, -1.644921413491445, -1.480991678890353,
#'                                -1.272436055728805, -0.711509477199393, 0.045575390357792)))
#' @family things related to chemical potential
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_chem_potential_water_ice.html}
gsw_chem_potential_water_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_chem_potential_water_ice",
            t=as.double(l$t), p=as.double(l$p), n=as.integer(n),
            rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Chemical Potential of Water in Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return chemical potential [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,       50,      125,      250,      600,      1000)
#' pot <- gsw_chem_potential_water_t_exact(SA, t, p)
#' stopifnot(all.equal(pot, c(-8.545561146284534, -8.008085548342105, -5.103980139874876,
#'                            -0.634067782745442, 3.335566803473286, 7.555434445971858)))
#' @family things related to chemical potential
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_chem_potential_water_t_exact.html}
gsw_chem_potential_water_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_chem_potential_water_t_exact",
            SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p), n=as.integer(n),
            rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific heat to ice
#'
#' Specific heat of ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#'
#' @return specific heat [ J/(K*kg) ]
#'
## @family things related to ice
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' cp <- gsw_cp_ice(t, p)
#' stopifnot(all.equal(cp, c(2017.314262094657, 1997.830122682709, 2002.281331375396,
#'                           2006.127319545421, 2015.676303959609, 2033.308170371559)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_cp_ice.html}
gsw_cp_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_cp_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Isobaric heat capacity
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return heat capacity [ J/(kg*K) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <-  c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' cp_t_exact <- gsw_cp_t_exact(SA, t, p)
#' stopifnot(all.equal(cp_t_exact/1e3, c(4.002888003958537, 4.000980283927373, 3.995546468894633,
#'                                       3.985076769021370, 3.973593843482723, 3.960184084786622)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_cp_t_exact.html}
gsw_cp_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_cp_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' First Derivatives of Conservative Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template pttemplate
#' @return A list containing \code{CT_SA} [ K/(g/kg) ], the derivative of
#' Conservative Temperature with respect to Absolute Salinity,
#' and \code{CT_pt} [ unitless ], the derivative of
#' Conservative Temperature with respect to potential temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' pt <- c(28.7832, 28.4209, 22.7850, 10.2305,  6.8292,  4.3245)
#' r <- gsw_CT_first_derivatives(SA, pt)
#' stopifnot(all.equal(r$CT_SA,
#'     c(-0.041981092877806, -0.041558140199508, -0.034739209004865,
#'       -0.018711103772892, -0.014075941811725, -0.010571716552295)))
#' stopifnot(all.equal(r$CT_pt,
#'     c(1.002814937296636, 1.002554817053239, 1.001645140295163,
#'       1.000003771100520, 0.999716359504731, 0.999474326580093)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_first_derivatives.html}
gsw_CT_first_derivatives <- function(SA, pt)
{
    l <- argfix(list(SA=SA, pt=pt))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_first_derivatives",
            SA=as.double(l$SA), pt=as.double(l$pt),
            n=as.integer(n), CT_SA=double(n), CT_pt=double(n), NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CT_SA[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    ##37 r$CT_pt[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    if (is.matrix(SA)) {
        dim(r$CT_SA) <- dim(SA)
        dim(r$CT_pt) <- dim(SA)
    }
    list(CT_SA=r$CT_SA, CT_pt=r$CT_pt)
}


#' Derivatives of Conservative Temperature with Respect to or at
#' Constant in-situ Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return A list containing \code{CT_SA_wrt_t} [ K/(g/kg) ], the derivative of
#' Conservative Temperature with respect to Absolute Salinity at constant
#' temperature and pressure, \code{CT_t_wrt_t} [ unitless], the derivative of
#' Conservative Temperature with respect to temperature at constant
#' Absolute Salinity and pressure, and \code{CT_p_wrt_t}, the derivative
#' of Conservative Temperature with respect to pressure at constant Absolute
#' Salinity and temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_CT_first_derivatives_wrt_t_exact(SA, t, p)
#' stopifnot(all.equal(r$CT_SA_wrt_t,
#'     c(-0.041988694538987, -0.041596549088952, -0.034853545749326,
#'       -0.019067140454607, -0.015016439826591, -0.012233725491373)))
#' stopifnot(all.equal(r$CT_t_wrt_t,
#'     c(1.002752642867571, 1.002243118597902, 1.000835702767227,
#'       0.998194915250648, 0.995219303532390, 0.991780205482695)))
#' stopifnot(all.equal(r$CT_p_wrt_t/1e-7,
#'     c(-0.241011880838437, -0.239031676279078, -0.203649928441505,
#'       -0.119370679226136, -0.099140832825342, -0.086458168643579)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_first_derivatives_wrt_t_exact.html}
gsw_CT_first_derivatives_wrt_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_first_derivatives_wrt_t_exact",
            SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
            n=as.integer(n),
            CT_SA_wrt_t=double(n), CT_t_wrt_t=double(n), CT_p_wrt_t=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CT_SA_wrt_t[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    ##37 r$CT_t_wrt_t[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    ##37 r$CT_p_wrt_t[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$CT_SA_wrt_t) <- dim
        dim(r$CT_t_wrt_t) <- dim
        dim(r$CT_p_wrt_t) <- dim
    }
    list(CT_SA_wrt_t=r$CT_SA_wrt_t, CT_t_wrt_t=r$CT_t_wrt_t, CT_p_wrt_t=r$CT_p_wrt_t)
}


#' Conservative Temperature of Freezing Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @param saturation_fraction saturation fraction of dissolved air in seawater
#' @return Conservative Temperature at freezing of seawater [ degC ].
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- 1
#' CT <- gsw_CT_freezing(SA, p, saturation_fraction)
#' stopifnot(all.equal(CT, c(-1.899683776424096, -1.940791867869104, -2.006240664432488,
#'                           -2.092357761318778, -2.359300831770506, -2.677162675412748)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_freezing.html}
gsw_CT_freezing <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_freezing",
               SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}

#' First Derivatives of Conservative Temperature for Freezing Water
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return A list containing \code{CTfreezing_SA} [ K/(g/kg) ], the derivative of
#' Conservative Temperature with respect to Absolute Salinity at constant
#' potential temperature, and \code{CTfreezing_p} [ unitless], the derivative of
#' Conservative Temperature with respect to pressure at constant
#' Absolute Salinity.
#' @examples
#' SA <- c(                 34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(                       10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- c(      1,     0.8,     0.6,     0.5,     0.4,       0)
#' r <- gsw_CT_freezing_first_derivatives(SA, p, saturation_fraction)
#' stopifnot(all.equal(r$CTfreezing_SA,
#'     c(-0.058193253897272, -0.058265158334170, -0.058345661671901,
#'      -0.058373842446463, -0.058534544740846, -0.058730846361252)))
#' stopifnot(all.equal(r$CTfreezing_p/1e-7,
#'     c(-0.765300390432684, -0.766942996466485, -0.769892679988284,
#'       -0.774561011527902, -0.787769143040504, -0.802771548245855)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_freezing_first_derivatives.html}
gsw_CT_freezing_first_derivatives <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_freezing_first_derivatives",
            SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
            n=as.integer(n), CTfreezing_SA=double(n), CTfreezing_p=double(n), NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CTfreezing_SA[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    ##37 r$CTfreezing_p[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$CTfreezing_SA) <- dim
        dim(r$CTfreezing_p) <- dim
    }
    list(CTfreezing_SA=r$CTfreezing_SA, CTfreezing_p=r$CTfreezing_p)
}


#' First Derivatives of Conservative Temperature for Freezing Water (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return A list containing \code{CTfreezing_SA} [ K/(g/kg) ], the derivative of
#' Conservative Temperature with respect to Absolute Salinity at constant
#' potential temperature, and \code{CTfreezing_p} [ unitless], the derivative of
#' Conservative Temperature with respect to pressure at constant
#' Absolute Salinity.
#' @examples
#' SA <- c(                 34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(                       10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- c(      1,     0.8,     0.6,     0.5,     0.4,       0)
#' r <- gsw_CT_freezing_first_derivatives_poly(SA, p, saturation_fraction)
#' stopifnot(all.equal(r$CTfreezing_SA,
#'     c(-0.058191181082769, -0.058263310660779, -0.058343573188907,
#'      -0.058370514075271, -0.058528023214462, -0.058722959729433)))
#' stopifnot(all.equal(r$CTfreezing_p/1e-7,
#'     c(-0.765690732336706, -0.767310677213890, -0.770224214219328,
#'      -0.774843488962665, -0.787930403016584, -0.802821704643775)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_freezing_first_derivatives_poly.html}
gsw_CT_freezing_first_derivatives_poly <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_freezing_first_derivatives_poly",
            SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
            n=as.integer(n), CTfreezing_SA=double(n), CTfreezing_p=double(n), NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CTfreezing_SA[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    ##37 r$CTfreezing_p[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$CTfreezing_SA) <- dim
        dim(r$CTfreezing_p) <- dim
    }
    list(CTfreezing_SA=r$CTfreezing_SA, CTfreezing_p=r$CTfreezing_p)
}


#' Conservative Temperature Freezing Point (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @param saturation_fraction saturation fraction of dissolved air in seawater
#' @return Conservative Temperature at freezing of seawater [ degC ].
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- 1
#' CT_freezing <- gsw_CT_freezing(SA, p, saturation_fraction)
#' stopifnot(all.equal(CT_freezing, c(-1.899683776424096, -1.940791867869104, -2.006240664432488,
#'                                    -2.092357761318778, -2.359300831770506, -2.677162675412748)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_freezing_poly.html}
gsw_CT_freezing_poly <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_freezing_poly",
               SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Conservative Temperature from Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template htemplate
#' @template ptemplate
#' @return Conservative Temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' h <- c(1.15103e5, 1.14014e5, 0.92180e5, 0.43255e5, 0.33087e5, 0.26970e5)
#' p <- c(       10,        50,       125,       250,       600,      1000)
#' pt <- c(28.7832, 28.4209, 22.7850, 10.2305,  6.8292,  4.3245)
#' CT <- gsw_CT_from_enthalpy(SA, h, p)
#' stopifnot(all.equal(CT, c(28.809854569021972, 28.439026483379287, 22.786196534098817,
#'                           10.226106994920777, 6.827159682675204, 4.323428660306681)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_from_enthalpy.html}
gsw_CT_from_enthalpy <- function(SA, h, p)
{
    l <- argfix(list(SA=SA, h=h, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_from_enthalpy",
               SA=as.double(l$SA), h=as.double(l$h), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$h) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Conservative Temperature from Entropy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template entropytemplate
#' @return Conservative Temperature [ degC ]
#' @examples
#' SA <- c(      34.7118,  34.8915,  35.0256,  34.8472, 34.7366, 34.7324)
#' entropy <- c(400.3892, 395.4378, 319.8668, 146.7910, 98.6471, 62.7919)
#' CT <- gsw_CT_from_entropy(SA, entropy)
#' stopifnot(all.equal(CT, c(28.809902787278070, 28.439199226786918, 22.786199266954270,
#'                           10.226197672488652, 6.827196739780282, 4.323602945446461)))
#' @family things related to entropy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_from_entropy.html}
gsw_CT_from_entropy <- function(SA, entropy)
{
    l <- argfix(list(SA=SA, entropy=entropy))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_from_entropy",
               SA=as.double(l$SA), entropy=as.double(l$entropy),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$entropy)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Conservative Temperature from Potential Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template pttemplate
#' @return Conservative Temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' pt <- c(28.7832, 28.4209, 22.7850, 10.2305,  6.8292,  4.3245)
#' CT <- gsw_CT_from_pt(SA, pt)
#' stopifnot(all.equal(CT, c(28.809923015982083, 28.439144260767169, 22.786246608464264,
#'                           10.226165605435785, 6.827183417643142,  4.323565182322069)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_from_pt.html}
gsw_CT_from_pt <- function(SA, pt)
{
    l <- argfix(list(SA=SA, pt=pt))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_from_pt",
               SA=as.double(l$SA), pt=as.double(l$pt),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Conservative Temperature from Density, Absolute Salinity and Pressure
#'
#' @template teos10template
#'
#' @template rhotemplate
#' @template SAtemplate
#' @template ptemplate
#' @return A list containing two estimates of Conservative Temperature:
#' \code{CT} and \code{CT_multiple}, each in [ degC ].
#' @examples
#' rho <- c(1021.8484, 1022.2647, 1024.4207, 1027.7841, 1029.8287, 1031.9916)
#' SA <- c(   34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' p <- c(         10,        50,       125,       250,       600,      1000)
#' r <- gsw_CT_from_rho(rho, SA, p)
#' stopifnot(all.equal(r$CT, c(28.784377302226968, 28.432402127485858, 22.808745445250068,
#'                             10.260169334807866, 6.887336649146716, 4.404594162282834)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_from_rho.html}
gsw_CT_from_rho <- function(rho, SA, p)
{
    l <- argfix(list(rho=rho, SA=SA, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_from_rho",
            rho=as.double(l$rho), SA=as.double(l$SA), p=as.double(l$p),
            n=as.integer(n), CT=double(n), CT_multiple=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CT[!is.finite(l$rho) | !is.finite(l$SA) | !is.finite(l$p)] <- NA
    ##37 r$CT_multiple[!is.finite(l$rho) | !is.finite(l$SA) | !is.finite(l$p)] <- NA
    if (is.matrix(rho)) {
        dim <- dim(rho)
        dim(r$CT) <- dim
        dim(r$CT_multiple) <- dim
    }
    ## NaN is coming out as 9e15 in the doc test case
    r$CT[r$CT > 1e15] <- NA
    r$CT_multiple[r$CT_multiple > 1e15] <- NA
    list(CT=r$CT, CT_multiple=r$CT_multiple)
}


#' Convert from temperature to conservative temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return Conservative Temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <-  c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' CT <- gsw_CT_from_t(SA, t, p)
#' stopifnot(all.equal(CT, c(28.809919826700281, 28.439227816091140, 22.786176893078498,
#'                           10.226189266620782, 6.827213633479988, 4.323575748610455)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_from_t.html}
gsw_CT_from_t <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_from_t",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA

    ## FIXME: May-11 on my work machine...I don't think this is actually
    ## needed, since W31 catches the NA value. But how, then, did I get the
    ## error reported at https://github.com/TEOS-10/GSW-R/issues/37?
    ## I found that problem on my home machine ... is there a difference? (The
    ## CPUs are definitely different.)

    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Conservative Temperature at Maximum Density
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return Conservative Temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' CT <- gsw_CT_maxdensity(SA, p)
#' stopifnot(all.equal(CT, c(-3.731407240089855, -3.861137427731664, -4.060390602245942,
#'                           -4.306222571955388, -5.089240667106197, -6.028034316992341)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_maxdensity.html}
gsw_CT_maxdensity <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_CT_maxdensity",
               SA=as.double(l$SA), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Second Derivatives of Conservative Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template pttemplate
#' @return A list containing \code{CT_SA_SA} [ K/(g/kg)^2 ], the second derivative of
#' Conservative Temperature with respect to Absolute Salinity at constant
#' potential temperature, and \code{CT_SA_pt} [ 1/(g/kg) ], the derivative of
#' Conservative Temperature with respect to potential temperature and
#' Absolute Salinity, and \code{CT_pt_pt} [ 1/degC ], the second derivative of
#' Conservative Temperature with respect to potential temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' pt <- c(28.7832, 28.4209, 22.7850, 10.2305,  6.8292,  4.3245)
#' r <- gsw_CT_second_derivatives(SA, pt)
#' stopifnot(all.equal(r$CT_SA_SA/1e-3, c(-0.060718502077064, -0.062065324400873, -0.084017055354742,
#'                                        -0.148436050120131, -0.171270386500246, -0.189920754900116)))
#' stopifnot(all.equal(r$CT_SA_pt, c(-0.001197415000869, -0.001198309530139, -0.001226523296082,
#'                                   -0.001335896286481, -0.001380492698572, -0.001417751669135)))
#' stopifnot(all.equal(r$CT_pt_pt/1e-3, c(0.123012754427146, 0.124662008871271, 0.140829458783443,
#'                                        0.140646803448166, 0.113684095615077, 0.082286843477998)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_CT_second_derivatives.html}
gsw_CT_second_derivatives <- function(SA, pt)
{
    l <- argfix(list(SA=SA, pt=pt))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_CT_second_derivatives",
            SA=as.double(l$SA), pt=as.double(l$pt),
            n=as.integer(n),
            CT_SA_SA=double(n), CT_SA_pt=double(n), CT_pt_pt=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 r$CT_SA_SA[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    ##37 r$CT_SA_pt[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    ##37 r$CT_pt_pt[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$CT_SA_SA) <- dim
        dim(r$CT_SA_pt) <- dim
        dim(r$CT_pt_pt) <- dim
    }
    list(CT_SA_SA=r$CT_SA_SA, CT_SA_pt=r$CT_SA_pt, CT_pt_pt=r$CT_pt_pt)
}


#' Absolute Salinity Anomaly from Practical Salinity
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return deltaSA Absolute Salinity Anomaly  [ g/kg ]
#' @examples
#' SP =   c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p =    c(     10,      50,     125,     250,     600,    1000)
#' lat =  c(      4,       4,       4,       4,       4,       4)
#' long = c(    188,     188,     188,     188,     188,     188)
#' deltaSA = gsw_deltaSA_from_SP(SP,p,long,lat)
#' stopifnot(all.equal(deltaSA, c(0.000167203365230, 0.000268836122231, 0.000665803155705,
#'                                0.002706154619403, 0.005652977406832,  0.009444734661606)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_deltaSA_from_SP.html}
gsw_deltaSA_from_SP <- function(SP, p, longitude, latitude)
{
    if (missing(SP)) stop("must supply SP")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    l <- argfix(list(SP=SP, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_deltaSA_from_SP",
               SP=as.double(l$SP), p=as.double(l$p),
               longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Dilution coefficient
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return dilution coefficient [ (J/kg)(kg/g) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' dc <- gsw_dilution_coefficient_t_exact(SA, t, p)
#' stopifnot(all.equal(dc, c(79.140034211532040, 79.104983526833820, 77.503312016847389,
#'                           73.535062653715272, 72.483378545466564, 71.760667498673087)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_dilution_coefficient_t_exact.html}
gsw_dilution_coefficient_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_dilution_coefficient_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Dynamic enthalpy of seawater (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return dynamic enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <-c( 28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' de <- gsw_dynamic_enthalpy(SA, CT, p)
#' stopifnot(all.equal(de/1000, c(0.097864698087770, 0.489161476686235, 1.220512192086506,
#'                                2.433731199531144, 5.833880057399701, 9.711443860944032)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy.html}
gsw_dynamic_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_dynamic_enthalpy",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific enthalpy of seawater (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return specific enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <-c( 28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' e <- gsw_enthalpy(SA, CT, p)
#' stopifnot(all.equal(e/1e5, c(1.151031813559086, 1.140146926828028, 0.921800138366058,
#'                              0.432553713026279, 0.330871609742468, 0.269706841603465)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy.html}
gsw_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_enthalpy",
               SA=as.double(l$SA), t=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Seawater Specific Enthalpy in terms of Conservative Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return specific enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' e <- gsw_enthalpy_CT_exact(SA, CT, p)
#' stopifnot(all.equal(e/1e5, c(1.151031813321767, 1.140146925586514, 0.921800131787836,
#'                              0.432553712315790, 0.330871615358722, 0.269706848807403)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_CT_exact.html}
gsw_enthalpy_CT_exact <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_enthalpy_ct_exact",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific Enthalpy Difference with Pressure
#'
#' Specific enthalpy difference [ J/kg ].
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @param p_shallow pressure at a shallower depth [ dbar ]
#' @param p_deep pressure at a deeper depth [ dbar ]
#'
#' @return specific enthalpy difference [ J/kg ]
#'
#' @family things related to enthalpy
#' @examples
#' SA <- c(  34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(  28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p_shallow <- c(10,      50,     125,     250,     600,    1000)
#' p_deep <- c(  110,     150,     225,     350,     700,    1100)
#' ed <- gsw_enthalpy_diff(SA, CT, p_shallow, p_deep)
#' stopifnot(all.equal(ed/1e2, c(9.784180644568052, 9.780195056105020, 9.759587700515114,
#'                               9.727552719534447, 9.708223170174454, 9.687871289079633)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_diff.html}
gsw_enthalpy_diff <- function(SA, CT, p_shallow, p_deep)
{
    l <- argfix(list(SA=SA, CT=CT, p_shallow=p_shallow, p_deep=p_deep))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_enthalpy_diff",
               SA=as.double(l$SA), CT=as.double(l$CT), p_shallow=as.double(l$p_shallow),
               p_deep=as.double(l$p_deep),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p_shallow) | !is.finite(l$p_deep)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' First Derivatives of Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#'
#' @return a list containing \code{h_SA} [ (J/kg)/(g/kg) ], the derivative
#' of enthalpy wrt Absolute Salinity, and \code{h_CT} [ (J/kg)/degC ],
#' the derivative of enthalpy wrt Conservative Temperature.
#'
#' @family things related to enthalpy
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' d <- gsw_enthalpy_first_derivatives(SA, CT, p)
#' stopifnot(all.equal(d$h_SA, c(-0.070223912348929, -0.351159768365102, -0.887025065692568,
#'                               -1.829602387915694, -4.423463748270238, -7.405100077558673)))
#' stopifnot(all.equal(d$h_CT/1e3, c(3.991899705530481, 3.992025640520101, 3.992210365030743,
#'                                   3.992284150250490, 3.992685389122658, 3.993014168534175)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_first_derivatives.html}
gsw_enthalpy_first_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_enthalpy_first_derivatives",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            h_SA=double(n), h_CT=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 r$h_SA[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    ##37 r$h_CT[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$h_SA) <- dim
        dim(r$h_CT) <- dim
    }
    list(h_SA=r$h_SA, h_CT=r$h_CT)
}


#' First Derivatives of Enthalpy wrt CT
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#'
#' @return a list containing \code{h_SA} [ (J/kg)/(g/kg) ], the derivative
#' of enthalpy wrt Absolute Salinity, and \code{h_CT} [ (J/kg)/degC ],
#' the derivative of enthalpy wrt Conservative Temperature.
#'
#' @section Bugs:
#' The HTML documentation suggests that this function returns 3 values, but
#' there are only 2 returned values in the C code used here (and the matlab code
#' on which that is based). Also, the d/dSA check values given the HTML are not
#' reproduced by the present function. This was reported on Mar 18, 2017
#' as https://github.com/TEOS-10/GSW-Matlab/issues/7.
#' See https://github.com/TEOS-10/GSW-R/issues/34
#'
#' @family things related to enthalpy
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' d <- gsw_enthalpy_first_derivatives_CT_exact(SA, CT, p)
#' stopifnot(all.equal(d$h_SA, c(-0.070224183838619, -0.351159869043798, -0.887036550157504,
#'                               -1.829626251448858, -4.423522691827955, -7.405211691293971)))
#' stopifnot(all.equal(d$h_CT/1e3, c(3.991899712269790, 3.992025674159605, 3.992210402650973,
#'                                   3.992283991748418, 3.992685275917238, 3.993014370250710)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_first_derivatives_CT_exact.html}
gsw_enthalpy_first_derivatives_CT_exact <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_enthalpy_first_derivatives_CT_exact",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            h_SA=double(n), h_CT=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$h_SA[bad] <- NA
    ##37 r$h_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$h_SA) <- dim
        dim(r$h_CT) <- dim
    }
    list(h_SA=r$h_SA, h_CT=r$h_CT)
}


#' Ice Specific Enthalpy
#'
#' Specific enthalpy of ice [ J/kg ]. Note that this is a negative quantity.
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#'
#' @return specific enthalpy [ J/kg ]
#'
#' @family things related to enthalpy
## @family things related to ice
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' se <- gsw_enthalpy_ice(t, p)
#' stopifnot(all.equal(se/1e5, c(-3.554414597446597, -3.603380857687490, -3.583089884253586,
#'                               -3.558998379233944, -3.494811024956881, -3.402784319238127)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_ice.html}
gsw_enthalpy_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_enthalpy_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Second Derivatives of Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{h_SA_SA} [ (J/kg)/(g/kg)^2 ], the second derivative of
#' enthalpy with respect to Absolute Salinity, \code{h_SA_CT} [ (J/kg)/(K*g/kg) ], the derivative of
#' enthalpy with respect to Absolute Salinity and Conservative Temperature,
#' and \code{h_CT_CT} [ (J/kg)/degC^2 ], the second derivative of
#' enthalpy with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_enthalpy_second_derivatives(SA, CT, p)
#' stopifnot(all.equal(r$h_SA_SA, c(0.000080922482023, 0.000404963500641, 0.001059800046742,
#'                                  0.002431088963823, 0.006019611828423, 0.010225411250217)))
#' stopifnot(all.equal(r$h_SA_CT, c(0.000130004715129, 0.000653614489248, 0.001877220817849,
#'                                  0.005470392103793, 0.014314756132297, 0.025195603327700)))
#' stopifnot(all.equal(r$h_CT_CT, c(0.000714303909834, 0.003584401249266, 0.009718730753139,
#'                                  0.024064471995224, 0.061547884081343, 0.107493969308119)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_second_derivatives.html}
gsw_enthalpy_second_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_enthalpy_second_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            h_SA_SA=double(n), h_SA_CT=double(n), h_CT_CT=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$h_SA_SA[bad] <- NA
    ##37 r$h_SA_CT[bad] <- NA
    ##37 r$h_CT_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$h_SA_SA) <- dim
        dim(r$h_SA_CT) <- dim
        dim(r$h_CT_CT) <- dim
    }
    list(h_SA_SA=r$h_SA_SA, h_SA_CT=r$h_SA_CT, h_CT_CT=r$h_CT_CT)
}


#' Second Derivatives of Enthalpy (exact)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{h_SA_SA} [ (J/kg)/(g/kg)^2 ], the second derivative of
#' enthalpy with respect to Absolute Salinity, \code{h_SA_CT} [ (J/kg)/(K*g/kg) ], the derivative of
#' enthalpy with respect to Absolute Salinity and Conservative Temperature,
#' and \code{h_CT_CT} [ (J/kg)/degC^2 ], the second derivative of
#' enthalpy with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_enthalpy_second_derivatives_CT_exact(SA, CT, p)
#' stopifnot(all.equal(r$h_SA_SA, c(0.000082767011576, 0.000414469343141, 0.001089580017293,
#'                                  0.002472193425998, 0.006103171596320, 0.010377465312463)))
#' stopifnot(all.equal(r$h_SA_CT, c(0.000130320164426, 0.000655016236924, 0.001879127443985,
#'                                  0.005468695168037, 0.014315709000526, 0.025192691262061)))
#' stopifnot(all.equal(r$h_CT_CT, c(0.000714365642428, 0.003584965089168, 0.009733337653703,
#'                                  0.024044402143825, 0.061449390733344, 0.107333638394904)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_second_derivatives_CT_exact.html}
gsw_enthalpy_second_derivatives_CT_exact <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_enthalpy_second_derivatives_CT_exact", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            h_SA_SA=double(n), h_SA_CT=double(n), h_CT_CT=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$h_SA_SA[bad] <- NA
    ##37 r$h_SA_CT[bad] <- NA
    ##37 r$h_CT_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$h_SA_SA) <- dim
        dim(r$h_SA_CT) <- dim
        dim(r$h_CT_CT) <- dim
    }
    list(h_SA_SA=r$h_SA_SA, h_SA_CT=r$h_SA_CT, h_CT_CT=r$h_CT_CT)
}


#' Seawater Specific Enthalpy in terms of in-situ Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return specific enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' e <- gsw_enthalpy_t_exact(SA, t, p)
#' stopifnot(all.equal(e/1e5, c(1.151032604783763, 1.140148036012021, 0.921799209310966,
#'                              0.432553283808897, 0.330872159700175, 0.269705880448018)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_enthalpy_t_exact.html}
gsw_enthalpy_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_enthalpy_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' First Derivatives of Entropy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#'
#' @return a list containing \code{eta_SA} [ (J/(kg*degC) / (g/kg) ],
#' the derivative of entropy wrt Absolute Salinity, and \code{eta_CT} [ (J/(kg*degC^2) ],
#' the derivative of entropy wrt Conservative Temperature.
#'
#' @family things related to entropy
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' d <- gsw_entropy_first_derivatives(SA, CT)
#' stopifnot(all.equal(d$eta_SA, c(-0.263286800711655, -0.263977276574528, -0.255367497912925,
#'                                 -0.238066586439561, -0.234438260606436, -0.232820684341694)))
#' stopifnot(all.equal(d$eta_CT, c(13.221031210083824, 13.236911191313675, 13.489004628681361,
#'                                 14.086599016583795, 14.257729576432077, 14.386429945649411)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_entropy_first_derivatives.html}
gsw_entropy_first_derivatives <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_entropy_first_derivatives",
            SA=as.double(l$SA), CT=as.double(l$CT),
            n=as.integer(n),
            eta_SA=double(n), eta_CT=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT)
    ##37 r$eta_SA[bad] <- NA
    ##37 r$eta_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$eta_SA) <- dim
        dim(r$eta_CT) <- dim
    }
    list(eta_SA=r$eta_SA, eta_CT=r$eta_CT)
}


#' Specific Entropy ito Absolute Salinity and Potential Temperature
#'
#' Calculates specific entropy in terms of Absolute Salinity and
#' Potential Temperature.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template pttemplate
#' @return specific entropy [ J/(kg*degC) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' pt <- c(28.7832, 28.4210, 22.7850, 10.2305,  6.8292,  4.3245)
#' e <- gsw_entropy_from_pt(SA, pt)
#' stopifnot(all.equal(e/1e2, c(4.003894674443156, 3.954383994925507, 3.198674385897981,
#'                              1.467905482842553, 0.986469100565646, 0.627913567234252)))
#' @family things related to entropy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_entropy_from_pt.html}
gsw_entropy_from_pt <- function(SA, pt)
{
    l <- argfix(list(SA=SA, pt=pt))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_entropy_from_pt",
               SA=as.double(l$SA), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$pt)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific Entropy i.t.o. Absolute Salinity, Temperature, and Pressure
#'
#' Calculates specific entropy in terms of Absolute Salinity, in-situ
#' temperature and pressure.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return specific entropy [ J/(kg*K) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' e <- gsw_entropy_from_t(SA, t, p)
#' stopifnot(all.equal(e/1e2, c(4.003894252787245, 3.954381784340642, 3.198664981986740,
#'                              1.467908815899072, 0.986473408657975, 0.627915087346090)))
#' @family things related to entropy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_entropy_from_t.html}
gsw_entropy_from_t <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_entropy_from_t", NAOK=TRUE, PACKAGE="gsw",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Second Derivatives of Entropy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return A list containing \code{eta_SA_SA} [ (J/(K*kg))/(g/kg)^2 ], the second derivative of
#' entropy with respect to Absolute Salinity, \code{eta_SA_CT} [ (J/(K*kg))/(K*g/kg) ], the derivative of
#' entropy with respect to Absolute Salinity and Conservative Temperature,
#' and \code{eta_CT_CT} [ (J/(K*kg))/K^2 ], the second derivative of
#' entropy with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' r <- gsw_entropy_second_derivatives(SA, CT)
#' stopifnot(all.equal(r$eta_SA_SA, c(-0.007627718929669, -0.007591969960708, -0.007528186784540,
#'                                    -0.007455177590576, -0.007441108287466, -0.007414368396280)))
#' stopifnot(all.equal(r$eta_SA_CT, c(-0.001833104216751, -0.001819473824306, -0.001580843823414,
#'                                    -0.000930111408561, -0.000717011215195, -0.000548410546830)))
#' stopifnot(all.equal(r$eta_CT_CT, c(-0.043665023731109, -0.043781336189326, -0.045506114440888,
#'                                    -0.049708939454018, -0.050938690879443, -0.051875017843472)))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_entropy_second_derivatives.html}
gsw_entropy_second_derivatives <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_entropy_second_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT),
            n=as.integer(n),
            eta_SA_SA=double(n), eta_SA_CT=double(n), eta_CT_CT=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT)
    ##37 r$h_SA_SA[bad] <- NA
    ##37 r$h_CT_CT[bad] <- NA
    ##37 r$h_CT_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$eta_SA_SA) <- dim
        dim(r$eta_SA_CT) <- dim
        dim(r$eta_CT_CT) <- dim
    }
    list(eta_SA_SA=r$eta_SA_SA, eta_SA_CT=r$eta_SA_CT, eta_CT_CT=r$eta_CT_CT)
}


#' Ratio of Absolute to Preformed Salinity, minus 1
#'
#' @template teos10template
#'
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return (S/Sstar)-1 [ unitless ]
#' @examples
#' p <- c(         10,   50,  125,  250,  600, 1000)
#' latitude <- c(   4,    4,    4,    4,    4,    4)
#' longitude <- c(188,  188,  188,  188,  188,  188)
#' r <- gsw_Fdelta(p, longitude, latitude)
#' stopifnot(all.equal(r/1e-3, c(0.006472309923452, 0.010352848168433, 0.025541937543450,
#'                               0.104348729347986, 0.218678084205081, 0.365415366571266)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Fdelta.html}
gsw_Fdelta <- function(p, longitude, latitude)
{
    l <- argfix(list(p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_Fdelta", NAOK=TRUE, PACKAGE="gsw",
               p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(p))
        dim(rval) <- dim(p)
    rval
}


#' Entropy of ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return entropy [ J/(kg*degC) ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,      600,      1000)
#' e <- gsw_entropy_ice(t, p)
#' stopifnot(all.equal(e/1e3, c(-1.303663820598987, -1.324090218294577, -1.319426394193644,
#'                              -1.315402956671801, -1.305426590579231, -1.287021035328113)))
#' @family things related to entropy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_entropy_ice.html}
gsw_entropy_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_entropy_ice",
            t=as.double(l$t), p=as.double(l$p), n=as.integer(n),
            rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Properties of Frazil ice
#'
#' Calculation of Absolute Salinity, Conservative Temperature, and ice mass fraction
#' based on bulk Absolute Salinity, bulk enthalpy, and pressure
#'
#' @template teos10template
#'
#' @template SAbulktemplate
#' @template hbulktemplate
#' @template ptemplate
#' @return a list containing \code{SA_final}, \code{h_final} and \code{w_Ih_final}.
#' @examples
#' SA_bulk <- c(  34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' h_bulk <- c( -4.5544e4, -4.6033e4, -4.5830e4, -4.5589e4, -4.4948e4, -4.4027e4)
#' p <- c(             10,        50,       125,       250,       600,      1000)
#' r <- gsw_frazil_properties(SA_bulk, h_bulk, p)
#' stopifnot(all.equal(r$SA_final, c(39.111030663000442, 39.407625769681573, 39.595789974885108,
#'                                   39.481230045372889, 39.591177095552503, 39.826467709177123)))
#' stopifnot(all.equal(r$CT_final, c(-2.156311126114311, -2.204672298963783, -2.273689262333450,
#'                                   -2.363714136353600, -2.644541000680772, -2.977651291726651)))
#' stopifnot(all.equal(r$w_Ih_final, c(0.112480560814322, 0.114600300867556, 0.115421108602301,
#'                                     0.117372990660305, 0.122617649983886, 0.127906590822347)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_frazil_properties.html}
gsw_frazil_properties <- function(SA_bulk, h_bulk, p)
{
    l <- argfix(list(SA_bulk=SA_bulk, h_bulk=h_bulk, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_frazil_properties",
            SA_bulk=as.double(l$SA_bulk), h_bulk=as.double(l$h_bulk), p=as.double(l$p),
            n=as.integer(n),
            SA_final=double(n), CT_final=double(n), w_Ih_final=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA_bulk) | !is.finite(l$h_bulk) | !is.finite(l$p)
    ##37 r$SA_final[bad] <- NA
    ##37 r$CT_final[bad] <- NA
    ##37 r$t_Ih_final[bad] <- NA
    if (is.matrix(SA_bulk)) {
        dim <- dim(SA_bulk)
        dim(r$SA_final) <- dim
        dim(r$CT_final) <- dim
        dim(r$t_Ih_final) <- dim
    }
    list(SA_final=r$SA_final, CT_final=r$CT_final, w_Ih_final=r$w_Ih_final)
}


#' Properties of Frazil ice i.t.o. potential enthalpy
#'
#' Calculation of Absolute Salinity, Conservative Temperature, and ice mass fraction
#' based on bulk Absolute Salinity, bulk potential enthalpy, and pressure
#'
#' @template teos10template
#'
#' @template SAbulktemplate
#' @template h_pot_bulktemplate
#' @template ptemplate
#' @return a list containing \code{SA_final}, \code{h_final} and \code{w_Ih_final}.
#' @examples
#' SA_bulk <- c(     34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' h_pot_bulk <- c(-4.5544e4, -4.6033e4, -4.5830e4, -4.5589e4, -4.4948e4, -4.4027e4)
#' p <- c(                 10,        50,       125,       250,       600,      1000)
#' r <- gsw_frazil_properties_potential(SA_bulk, h_pot_bulk, p)
#' stopifnot(all.equal(r$SA_final, c(39.098258701462051, 39.343217598625756, 39.434254585716296,
#'                                   39.159536295126657, 38.820511558004590, 38.542322667924459)))
#' stopifnot(all.equal(r$CT_final, c(-2.155553336670014, -2.200844802695826, -2.264077329325076,
#'                                   -2.344567015865174, -2.598559540430464, -2.900814843304696)))
#' stopifnot(all.equal(r$w_Ih_final, c(0.112190640891586, 0.113150826758543, 0.111797588975174,
#'                                     0.110122251260246, 0.105199838799201, 0.098850365110330)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_frazil_properties_potential.html}
gsw_frazil_properties_potential <- function(SA_bulk, h_pot_bulk, p)
{
    l <- argfix(list(SA_bulk=SA_bulk, h_pot_bulk=h_pot_bulk, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_frazil_properties_potential",
            SA_bulk=as.double(l$SA_bulk), h_pot_bulk=as.double(l$h_pot_bulk), p=as.double(l$p),
            n=as.integer(n),
            SA_final=double(n), CT_final=double(n), w_Ih_final=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA_bulk) | !is.finite(l$h_pot_bulk) | !is.finite(l$p)
    ##37 r$SA_final[bad] <- NA
    ##37 r$CT_final[bad] <- NA
    ##37 r$t_Ih_final[bad] <- NA
    if (is.matrix(SA_bulk)) {
        dim <- dim(SA_bulk)
        dim(r$SA_final) <- dim
        dim(r$CT_final) <- dim
        dim(r$t_Ih_final) <- dim
    }
    list(SA_final=r$SA_final, CT_final=r$CT_final, w_Ih_final=r$w_Ih_final)
}


#' Properties of Frazil ice i.t.o. potential enthalpy (polynomial version)
#'
#' Calculation of Absolute Salinity, Conservative Temperature, and ice mass fraction
#' based on bulk Absolute Salinity, bulk potential enthalpy, and pressure
#'
#' @template teos10template
#'
#' @template SAbulktemplate
#' @template h_pot_bulktemplate
#' @template ptemplate
#' @return a list containing \code{SA_final}, \code{h_final} and \code{w_Ih_final}.
#' @examples
#' SA_bulk <- c(     34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' h_pot_bulk <- c(-4.5544e4, -4.6033e4, -4.5830e4, -4.5589e4, -4.4948e4, -4.4027e4)
#' p <- c(                10,        50,       125,       250,       600,      1000)
#' r <- gsw_frazil_properties_potential_poly(SA_bulk, h_pot_bulk, p)
#' stopifnot(all.equal(r$SA_final, c(39.098264696022831, 39.343217436835218, 39.434244243586633,
#'                                   39.159511498029801, 38.820458704205542, 38.542256756176229)))
#' stopifnot(all.equal(r$CT_final, c(-2.155537691991377, -2.200841508940901, -2.264094318382661,
#'                                   -2.344613208230164, -2.598663953454472, -2.900948531145453)))
#' stopifnot(all.equal(r$w_Ih_final, c(0.112190777010854, 0.113150823111566, 0.111797356032850,
#'                                     0.110121687760246, 0.105198620534670, 0.098848824039493)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_frazil_properties_potential_poly.html}
gsw_frazil_properties_potential_poly <- function(SA_bulk, h_pot_bulk, p)
{
    l <- argfix(list(SA_bulk=SA_bulk, h_pot_bulk=h_pot_bulk, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_frazil_properties_potential_poly",
            SA_bulk=as.double(l$SA_bulk), h_pot_bulk=as.double(l$h_pot_bulk), p=as.double(l$p),
            n=as.integer(n),
            SA_final=double(n), CT_final=double(n), w_Ih_final=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA_bulk) | !is.finite(l$h_pot_bulk) | !is.finite(l$p)
    ##37 r$SA_final[bad] <- NA
    ##37 r$CT_final[bad] <- NA
    ##37 r$t_Ih_final[bad] <- NA
    if (is.matrix(SA_bulk)) {
        dim <- dim(SA_bulk)
        dim(r$SA_final) <- dim
        dim(r$CT_final) <- dim
        dim(r$t_Ih_final) <- dim
    }
    list(SA_final=r$SA_final, CT_final=r$CT_final, w_Ih_final=r$w_Ih_final)
}


#' Ratios of SA, CT and p changes when Frazil Ice Forms
#'
#' Ratios of changes in \code{SA}, \code{CT} and \code{p} that occur
#' when frazil ice forms due to changes in pressure upon
#' the mixture of seawater and ice.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template w_Ihtemplate
#' @return a list containing \code{dSA_dCT_frazil}, \code{dSA_dP_frazil} and \code{dCT_dP_frazil}.
#' @examples
#' SA <- c(  34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' p <- c(        10,        50,       125,       250,       600,      1000)
#' w_Ih <- c(    0.9,      0.84,       0.4,      0.25,      0.05,      0.01)
#' r <- gsw_frazil_ratios_adiabatic(SA, p, w_Ih)
#' stopifnot(all.equal(r$dSA_dCT_frazil,
#'     c(3.035152370800401, 1.932548405396193, 0.613212115809003,
#'      0.516103092738565, 0.436656742034200, 0.425827266533876)))
#' stopifnot(all.equal(r$dSA_dP_frazil/1e-6,
#'     c(-0.197406834470366, -0.133213926580032, -0.045580136143659,
#'      -0.038806356507548, -0.033541272953744, -0.033350141194082)))
#' stopifnot(all.equal(r$dCT_dP_frazil/1e-7,
#'     c(-0.650401727338347, -0.689317412221414, -0.743301297684333,
#'      -0.751910946738026, -0.768138213038669, -0.783184728059898)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_frazil_ratios_adiabatic.html}
gsw_frazil_ratios_adiabatic <- function(SA, p, w_Ih)
{
    l <- argfix(list(SA=SA, p=p, w_Ih=w_Ih))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_frazil_ratios_adiabatic",
            SA=as.double(l$SA), p=as.double(l$p), w_Ih=as.double(l$w_Ih),
            n=as.integer(n),
            dSA_dCT_frazil=double(n), dSA_dP_frazil=double(n), dCT_dP_frazil=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$w_Ih)
    ##37 r$dSA_dCT_frazil[bad] <- NA
    ##37 r$dSA_dP_frazil[bad] <- NA
    ##37 r$dCT_dP_frazil[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$dSA_dCT_frazil) <- dim
        dim(r$dSA_dP_frazil) <- dim
        dim(r$dCT_dP_frazil) <- dim
    }
    list(dSA_dCT_frazil=r$dSA_dCT_frazil, dSA_dP_frazil=r$dSA_dP_frazil, dCT_dP_frazil=r$dCT_dP_frazil)
}


#' Ratios of SA, CT and p changes when Frazil Ice Forms (polynomial form)
#'
#' Ratios of changes in \code{SA}, \code{CT} and \code{p} that occur
#' when frazil ice forms due to changes in pressure upon
#' the mixture of seawater and ice.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template w_Ihtemplate
#' @return a list containing \code{dSA_dCT_frazil}, \code{dSA_dP_frazil} and \code{dCT_dP_frazil}.
#' @examples
#' SA <- c(  34.7118,   34.8915,   35.0256,   34.8472,   34.7366,   34.7324)
#' p <- c(        10,        50,       125,       250,       600,      1000)
#' w_Ih <- c(    0.9,      0.84,       0.4,      0.25,      0.05,      0.01)
#' r <- gsw_frazil_ratios_adiabatic_poly(SA, p, w_Ih)
#' stopifnot(all.equal(r$dSA_dCT_frazil,
#'     c(3.035308957896530, 1.932631198810934, 0.613220785586734,
#'      0.516106221687200, 0.436657158542033, 0.425827675768018)))
#' stopifnot(all.equal(r$dSA_dP_frazil/1e-6,
#'     c(-0.197512213108610, -0.133280971893621, -0.045599951957139,
#'       -0.038820466574251, -0.033548047632788, -0.033352365425407)))
#' stopifnot(all.equal(r$dCT_dP_frazil/1e-7,
#'     c(-0.650715350062703, -0.689634794137768, -0.743613932027895,
#'      -0.752179782823459, -0.768292629045686, -0.783236208526200)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_frazil_ratios_adiabatic_poly.html}
gsw_frazil_ratios_adiabatic_poly <- function(SA, p, w_Ih)
{
    l <- argfix(list(SA=SA, p=p, w_Ih=w_Ih))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_frazil_ratios_adiabatic_poly",
            SA=as.double(l$SA), p=as.double(l$p), w_Ih=as.double(l$w_Ih),
            n=as.integer(n),
            dSA_dCT_frazil=double(n), dSA_dP_frazil=double(n), dCT_dP_frazil=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$w_Ih)
    ##37 r$dSA_dCT_frazil[bad] <- NA
    ##37 r$dSA_dP_frazil[bad] <- NA
    ##37 r$dCT_dP_frazil[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$dSA_dCT_frazil) <- dim
        dim(r$dSA_dP_frazil) <- dim
        dim(r$dCT_dP_frazil) <- dim
    }
    list(dSA_dCT_frazil=r$dSA_dCT_frazil, dSA_dP_frazil=r$dSA_dP_frazil, dCT_dP_frazil=r$dCT_dP_frazil)
}


#' Gravitational Acceleration
#'
#' @template teos10template
#'
#' @template latitudetemplate
#' @template ptemplate
#' @return gravitational acceleration [ m/s^2 ]
#' @examples
#' lat <- c(-90, -60, -30, 0)
#' grav <- gsw_grav(lat)
#' stopifnot(all.equal(grav, c(9.832186205884799, 9.819178859991149,
#'                             9.793249257048750, 9.780327000000000)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_grav.html}
gsw_grav <- function(latitude, p=0)
{
    l <- argfix(list(latitude=latitude, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_grav",
               latitude=as.double(l$latitude), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$latitude) | !is.finite(l$p)] <- NA
    if (is.matrix(latitude))
        dim(rval) <- dim(latitude)
    rval
}


#' Geostrophic Dynamic Height Anomaly
#'
#' @description
#' This calculates a geopotential anomaly, called either the
#' dynamic height anomaly or the geostrophic streamfunction
#' in the TEOS-10 document listed as [1] below; users should
#' read that and the references therein for more details on
#' the definition and its calculation here.
#'
#' To get the column-integrated value in meters, take the first
#' value of the returned vector and divide by
#' 9.7963\eqn{m/s^2}{m/s^2}. Note that this yields an integral
#' with the top measured pressure (not zero) as an upper limit.
#'
#' @details
#'
#' Because of the scheme used in the underlying C code, the
#' pressures must be in order, and must not have any repeats.
#' Also, there must be at least 4 pressure values. Violating
#' any of these three restrictions yields an error.
#'
#' If \code{p_ref} exceeds the largest \code{p} value, a vector
#' of zeros is returned, in accordance with the underlying C code.
#'
#' Note the alteration of the test-value tolerance from a much smaller
#' default. This is required because the test values derive from the
#' GSW-Matlab code, which uses a different interpolation scheme than
#' the GSW-C code, upon which GSW-R relies.  See References 2 and 3 for
#' more on this topic.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template p_reftemplate
#' @return A vector containing geopotential anomaly in
#' \eqn{m^2/s^2}{m^2/s^2} for each level. For more on the units, see [2].
#'
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' p_ref <- 500
#' dh <- gsw_geo_strf_dyn_height(SA, CT, p, p_ref)
#' # NOTE: see Details for the reason for the coarse tolerance.
#' stopifnot(all.equal(dh,
#'     c(12.172172845782585, 9.797739925848624, 6.070940749148281,
#'       3.042891445395256, -1.078872239804912, -4.656953829254061),
#'     tolerance=0.02))
#'
#' @references
#' 1. \url{http://www.teos-10.org/pubs/gsw/html/gsw_geo_strf_dyn_height.html}
#' 2. \url{https://github.com/TEOS-10/GSW-R/issues/47}
#' 3. Barker, Paul M., and Trevor J. McDougall.
#' "Two Interpolation Methods Using Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials."
#' Journal of Atmospheric and Oceanic Technology 37, no. 4 (April 2020): 605–19.
gsw_geo_strf_dyn_height <- function(SA, CT, p, p_ref=0)
{
    if (missing(SA) || missing(CT) || missing(p)) stop("must supply SA, CT, and p")
    if (!is.vector(SA)) stop("SA must be a vector")
    if (!is.vector(CT)) stop("CT must be a vector")
    if (!is.vector(p)) stop("p must be a vector")
    if (length(SA) != length(CT)) stop("SA and CT must be of the same length")
    if (length(CT) != length(p)) stop("CT and p must be of the same length")
    n <- length(SA)
    if (n < 4L)
        stop("must have at least 4 levels")
    if (any(diff(order(p)) != 1L))
        stop("pressures must be in order")
    if (any(diff(p) == 0))
        stop("repeated pressures are not permitted")
    rval <- .C("wrap_gsw_geo_strf_dyn_height", NAOK=TRUE, PACKAGE="gsw",
               SA=as.double(SA), CT=as.double(CT), p=as.double(p), p_ref=as.double(p_ref[1]),
               n=as.integer(n), rval=double(n))$rval
    rval
}

#' Geostrophic Dynamic Height Anomaly (provisional version)
#'
#' @description
#' This calculates a geopotential anomaly, called either the
#' dynamic height anomaly or the geostrophic streamfunction
#' in the TEOS-10 document listed as [1] below.
#'
#' To get the column-integrated value in meters, take the first
#' value of the returned vector and divide by
#' 9.7963\eqn{m/s^2}{m/s^2}. Note that this yields an integral
#' with the top measured pressure (not zero) as an upper limit.
#'
#' @details
#'
#' Because of the scheme used in the underlying C code, the
#' pressures must be in order, and must not have any repeats.
#' Also, there must be at least 4 pressure values. Violating
#' any of these restrictions yields an error.
#'
#' If \code{p_ref} exceeds the largest \code{p} value, a vector
#' of zeros is returned, in accordance with the underlying C code.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template p_reftemplate
#' @param max_dp numeric value indicating the maximum tolerated pressure
#' separation between levels. If any pressure step exceeds \code{max_dp}, then
#' a uniform grid is constructed with \code{max_dp} as the interval.
#' @param interp_method integer specifying interpolation scheme (1 for linear, 2 for pchip)
#' @return A vector containing geopotential anomaly in
#' \eqn{m^2/s^2}{m^2/s^2} for each level. For more on the units, see [2].
#'
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' p_ref <- 1000
#' dh <- gsw_geo_strf_dyn_height_1(SA, CT, p, p_ref, 1, 2)
#' ## FIXME: The following test values fail.
#' ## all.equal(dh, c(17.039204557769487, 14.665853784722286, 10.912861136923812,
#' ##                 7.567928838774945, 3.393524055565328, 0))
#' @references
#' 1. \url{http://www.teos-10.org/pubs/gsw/html/gsw_geo_strf_dyn_height.html}
#'
#' 2. Talley et al., 2011. Descriptive Physical Oceanography, Edition 6, Elsevier.
gsw_geo_strf_dyn_height_1 <- function(SA, CT, p, p_ref=0, max_dp=1, interp_method=2)
{
    if (missing(SA) || missing(CT) || missing(p)) stop("must supply SA, CT, and p")
    if (!is.vector(SA)) stop("SA must be a vector")
    if (!is.vector(CT)) stop("CT must be a vector")
    if (!is.vector(p)) stop("p must be a vector")
    if (length(SA) != length(CT)) stop("SA and CT must be of the same length")
    if (length(CT) != length(p)) stop("CT and p must be of the same length")
    n <- length(SA)
    if (n < 4L)
        stop("must have at least 4 levels")
    if (any(diff(order(p)) != 1L))
        stop("pressures must be in order")
    if (any(diff(p) == 0))
        stop("repeated pressures are not permitted")
    rval <- .C("wrap_gsw_geo_strf_dyn_height_1", NAOK=TRUE, PACKAGE="gsw",
               SA=as.double(SA), CT=as.double(CT), p=as.double(p), p_ref=as.double(p_ref[1]),
               max_dp=as.double(max_dp), interp_method=as.integer(interp_method),
               n=as.integer(n), rval=double(n))$rval
    rval
}



#' Geostrophic Dynamic Height Anomaly (Piecewise-Constant Profile)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template delta_ptemplate
#' @return A list containing \code{dyn_height}, the dynamic height anomaly [ m^2/s^2 ], and
#' \code{p_mid} [ dbar ], the pressures at the layer centres. Note that the dynamic height
#' anomaly unit, also known as a "dynamic meter", corresponds to approximately 1.02 metres of sealevel height
#' (see e.g. Talley et al., 2011. Descriptive Physical Oceanography, Edition 6.
#' Elsevier).
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' delta_p <- c(10,      40,      75,     125,     350,     400)
#' r <- gsw_geo_strf_dyn_height_pc(SA, CT, delta_p)
#' stopifnot(all.equal(r$dyn_height, c(-0.300346215853487, -1.755165998114308, -4.423531083131365,
#'                                     -6.816659136254657, -9.453175257818430, -12.721009624991439)))
#' stopifnot(all.equal(r$p_mid/1e2, c(0.050000000000000, 0.300000000000000, 0.875000000000000,
#'                                    1.875000000000000, 4.250000000000000, 8.000000000000000)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_geo_strf_dyn_height.html}
gsw_geo_strf_dyn_height_pc <- function(SA, CT, delta_p)
{
    if (missing(SA) || missing(CT) || missing(delta_p)) stop("must supply SA, CT, and delta_p")
    if (!is.vector(SA)) stop("SA must be a vector")
    if (!is.vector(CT)) stop("CT must be a vector")
    if (!is.vector(delta_p)) stop("delta_p must be a vector")
    if (any(delta_p <= 0)) stop("each delta_p value must be positive")
    if (length(SA) != length(CT)) stop("SA and CT must be of the same length")
    if (length(CT) != length(delta_p)) stop("CT and delta_p must be of the same length")
    n <- length(SA)
    r <- .C("wrap_gsw_geo_strf_dyn_height_pc", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(SA), CT=as.double(CT), delta_p=as.double(delta_p),
            n=as.integer(n), dyn_height=double(n), p_mid=double(n))
    list(dyn_height=r$dyn_height, p_mid=r$p_mid)
}


#' Gibbs Energy of Seawater, and its Derivatives
#'
#' @template teos10template
#'
#' @param ns An integer, the order of the \code{SA} derivative. Must be 0, 1, or 2.
#' @param nt An integer, the order of the \code{t} derivative. Must be 0, 1, or 2.
#' @param np An integer, the order of the \code{p} derivative. Must be 0, 1, or 2.
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return Gibbs energy [ J/kg ] if \code{ns}=\code{nt}=\code{np}=0. Derivative of energy
#' with respect to \code{SA} [ J/kg/(g/kg)^ns ] if \code{ns} is nonzero and \code{nt}=\code{np}=0,
#' etc. Note that derivatives with respect to pressure are in units with Pa, not dbar.
#' @section Caution:
#' The TEOS-10 webpage for \code{gsw_gibbs} does not provide test values, so
#' the present R version should be considered untested.
#' @examples
#' library(gsw)
#' p <- seq(0, 100, 1)
#' SA <- rep(35, length(p))
#' t <- rep(-5, length(p))
#' ## Check the derivative wrt pressure. Note the unit change
#' E <- gsw_gibbs(0, 0, 0, SA, t, p)
#' # Estimate derivative from linear fit (try plotting: it is very linear)
#' m <- lm(E ~ p)
#' print(summary(m))
#' plot(p, E)
#' abline(m)
#' dEdp1 <- coef(m)[2]
#' # Calculate derivative ... note we multiply by 1e4 to get from 1/Pa to 1/dbar
#' dEdp2 <- 1e4 * gsw_gibbs(0, 0, 1, SA[1], t[1], p[1])
#' ## Ratio
#' dEdp1 / dEdp2
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_gibbs.html}
gsw_gibbs <- function(ns, nt, np, SA, t, p=0)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_gibbs",
               as.integer(ns[1]), as.integer(nt[1]), as.integer(np[1]),
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$ns) | !is.finite(nt) | !is.finite(np) | !is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Gibbs Energy of Ice, and its Derivatives
#'
#' @template teos10template
#'
#' @param nt An integer, the order of the \code{t} derivative. Must be 0, 1, or 2.
#' @param np An integer, the order of the \code{p} derivative. Must be 0, 1, or 2.
#' @template ttemplate
#' @template ptemplate
#' @return Gibbs energy [ J/kg ] if \code{ns}=\code{nt}=\code{np}=0. Derivative of energy
#' with respect to \code{t} [ J/kg/(degC)^nt ] if \code{nt} is nonzero,
#' etc. Note that derivatives with respect to pressure are in units with Pa, not dbar.
#' @section Caution:
#' The TEOS-10 webpage for \code{gsw_gibbs_ice} does not provide test values, so
#' the present R version should be considered untested.
#' @examples
#' library(gsw)
#' p <- seq(0, 100, 1)
#' t <- rep(-5, length(p))
#' ## Check the derivative wrt pressure. Note the unit change
#' E <- gsw_gibbs_ice(0, 0, t, p)
#' # Estimate derivative from linear fit (try plotting: it is very linear)
#' m <- lm(E ~ p)
#' print(summary(m))
#' plot(p, E)
#' abline(m)
#' dEdp1 <- coef(m)[2]
#' # Calculate derivative ... note we multiply by 1e4 to get from 1/Pa to 1/dbar
#' dEdp2 <- 1e4 * gsw_gibbs_ice(0, 1, t[1], p[1])
#' ## Ratio
#' dEdp1 / dEdp2
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_gibbs_ice.html}
gsw_gibbs_ice <- function(nt, np, t, p=0)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_gibbs_ice",
               as.integer(nt[1]), as.integer(np[1]),
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$nt) | !is.finite(l$np) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Helmholtz Energy of Ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return Helmholtz energy if ice [ J/kg ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,       600,     1000)
#' e <- gsw_Helmholtz_energy_ice(t, p)
#' stopifnot(all.equal(e/1e4, c(-1.362572315008330, -1.710375005915343, -1.628083272702224,
#'                              -1.555573047498573, -1.375469831393882, -1.053585607014677)))
#' @family things related to energy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Helmholtz_energy_ice.html}
gsw_Helmholtz_energy_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_Helmholtz_energy_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n),
               NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


##> #' Hill Ratio
##> #'
##> #' @template teos10template
##> #'
##> #' @template ttemplate
##> #' @return Hill ratio [ unitless ]
##> #' @examples
##> #' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
##> #' r <- gsw_hill_ratio_at_SP2(t)
##> #' all.equal(r4, c(-1.362572315008330, -1.710375005915343, -1.628083272702224,
##> #'                 -1.555573047498573, -1.375469831393882, -1.053585607014677))
##> #' @references
##> #' \url{http://www.teos-10.org/pubs/gsw/html/gsw_hill_ratio_at_sp2.html}
##> gsw_hill_ratio_at_SP2 <- function(t)
##> {
##>     l <- argfix(list(t=t))
##>     n <- length(l[[1]])
##>     rval <- .C("wrap_gsw_hill_ratio_at_SP2",
##>                t=as.double(l$t),
##>                n=as.integer(n), rval=double(n),
##>                NAOK=TRUE, PACKAGE="gsw")$rval
##>     if (is.matrix(t))
##>         dim(rval) <- dim(t)
##>     rval
##> }


#' Ice Fraction to Cool Seawater to Freezing
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template t_Ihtemplate
#' @return a list containing \code{SA_freeze}, \code{CT_freeze} and \code{w_Ih}.
#' @examples
#' SA <- c(   34.7118,  34.8915,  35.0256,  34.8472,  34.7366, 34.7324)
#' CT <- c(   28.7856,  28.4329,  22.8103,  10.2600,   6.8863,  4.4036)
#' p <- c(         10,       50,      125,      250,      600,    1000)
#' t_Ih <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' r <- gsw_ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih)
#' stopifnot(all.equal(r$SA_freeze, c(25.823952352620722, 26.120495895535438, 27.460572941868072,
#'                                    30.629978769577168, 31.458222332943784, 32.121170316796444)))
#' stopifnot(all.equal(r$CT_freeze, c(-1.389936216242376, -1.437013334134283, -1.569815847128818,
#'                                    -1.846419165657020, -2.166786673735941, -2.522730879078756)))
#' stopifnot(all.equal(r$w_Ih, c(0.256046867272203, 0.251379393389925, 0.215985652155336,
#'                               0.121020375537284, 0.094378196687535, 0.075181377710828)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_ice_fraction_to_freeze_seawater.html}
gsw_ice_fraction_to_freeze_seawater <- function(SA, CT, p, t_Ih)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, t_Ih=t_Ih))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_ice_fraction_to_freeze_seawater",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), t_Ih=as.double(l$t_Ih),
            n=as.integer(n), SA_freeze=double(n), CT_freeze=double(n), w_Ih=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$t_Ih)
    ##37 r$h_SA_freeze[bad] <- NA
    ##37 r$h_CT_freeze[bad] <- NA
    ##37 r$w_Ih[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$SA_freeze) <- dim
        dim(r$CT_freeze) <- dim
        dim(r$w_Ih) <- dim
    }
    list(SA_freeze=r$SA_freeze, CT_freeze=r$CT_freeze, w_Ih=r$w_Ih)
}


#' Specific Internal Energy of Seawater (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return specific internal energy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' e <- gsw_internal_energy(SA, CT, p)
#' stopifnot(all.equal(e/1e5, c(1.148091576956162, 1.134013145527675, 0.909571141498779,
#'                              0.408593072177020, 0.273985276460357, 0.175019409258405)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_internal_energy.html}
gsw_internal_energy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_internal_energy",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific Internal Energy of Ice (75-term equation)
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return specific internal energy [ J/kg ]
#' @examples
#' t_Ih <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' e <- gsw_internal_energy_ice(t_Ih, p)
#' stopifnot(all.equal(e/1e5, c(-3.556606992432442, -3.609926216929878, -3.597799043634774,
#'                              -3.587312078410920, -3.561207060376329, -3.512700418975375)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_internal_energy_ice.html}
gsw_internal_energy_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_internal_energy_ice",
               t=(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Ratio of vert. gradient of pot. density to vert grad of locally-referenced pot density
#'
#' Note that the C library had to be patched to get this working; a new
#' version of the library will address the bug directly.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @param p_ref reference pressure [ dbar ]
#' @return list containing IPV_vs_fNsquared_ratio [ unitless ] and mid-point pressure p_mid [ dbar ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' p_ref <- 0
#' r <- gsw_IPV_vs_fNsquared_ratio(SA, CT, p, p_ref)
#' stopifnot(all.equal(r$IPV_vs_fNsquared_ratio,
#'     c(0.999742244888022, 0.996939883468178, 0.986141997098021,
#'       0.931595598713477, 0.861224354872028)))
#' stopifnot(all.equal(r$p_mid, c(30, 87.5, 187.5, 425, 800)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_IPV_vs_fNsquared_ratio.html}
gsw_IPV_vs_fNsquared_ratio <- function(SA, CT, p, p_ref=0)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, p_ref=p_ref))
    n <- length(l[[1]])
    ## note: only use p_ref[1] since the C-library code says it must be constant
    r <- .C("wrap_gsw_IPV_vs_fNsquared_ratio",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), p_ref=as.double(l$p_ref[1]),
            n=as.integer(n),
            ratio=double(n-1), p_mid=double(n-1), NAOK=TRUE, PACKAGE="gsw")
    bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$p_ref)
    if (any(bad))
        warning("gsw_IPV_vs_fNsquared_ratio() has some NA inputs ... these are not handled well\n")
    if (is.matrix(SA))
        stop("gsw_IPV_vs_fNsquared_ratio() cannot handle matrix SA")
    list(IPV_vs_fNsquared_ratio=r$ratio, p_mid=r$p_mid)
}


#' Isentropic Compressibility of Seawater (75-term equation)
#'
#' Isentropic Compressibility of Seawater (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return isentropic compressibility [ 1/Pa ] (not 1/dbar)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <-c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' kappa <- gsw_kappa(SA, CT, p)
#' stopifnot(all.equal(kappa*1e9, c(0.411343648791300, 0.411105416128094, 0.416566236026610,
#'                                  0.435588650838751, 0.438782500588955, 0.439842289994702)))
#' @family things related to compressibility
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_kappa.html}
gsw_kappa <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_kappa",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}

#' Isothermal Compressibility of Ice
#'
#' Calculate isothermal compressibility of ice, in 1/Pa.
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return isothermal compressibility of ice [ 1/Pa ] (not 1/dbar)
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,       600,     1000)
#' kappa <- gsw_kappa_const_t_ice(t, p)
#' stopifnot(all.equal(kappa*1e9, c(0.115874753261484, 0.115384948953145, 0.115442212717850,
#'                                  0.115452884634531, 0.115454824232421, 0.115619994536961)))
#' @family things related to compressibility
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_kappa_const_t_ice.html}
gsw_kappa_const_t_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_kappa_const_t_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Isentropic Compressibility of Ice
#'
#' Calculate isentropic compressibility of ice, in 1/Pa.
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return isentropic compressibility of ice [ 1/Pa ] (not 1/dbar)
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,       600,     1000)
#' kappa <- gsw_kappa_ice(t, p)
#' stopifnot(all.equal(kappa*1e9, c(0.112495239053936, 0.112070687842183, 0.112119091047584,
#'                                  0.112126504739297, 0.112123513812840, 0.112262589530974)))
#' @family things related to compressibility
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_kappa_ice.html}
gsw_kappa_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_kappa_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Isentropic compressibility of seawater (exact)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return isentropic compressibility [ 1/Pa ] (not 1/dbar)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <-c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' kappa <- gsw_kappa(SA, CT, p)
#' stopifnot(all.equal(kappa*1e9,
#'     c(0.411343648791300, 0.411105416128094, 0.416566236026610,
#'      0.435588650838751, 0.438782500588955, 0.439842289994702)))
#' @family things related to compressibility
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_kappa_t_exact.html}
gsw_kappa_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_kappa_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Latent heat of evaporation
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return latent heat of evaporation [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' lh  <- gsw_latentheat_evap_CT(SA, CT)
#' stopifnot(all.equal(lh/1e6, c(2.429947107462561, 2.430774073049213, 2.444220372158452,
#'                               2.474127109232524, 2.482151446148560, 2.488052297193594)))
#' @family things related to latent heat
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_latentheat_evap_CT.html}
gsw_latentheat_evap_CT <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_latentheat_evap_CT",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Latent heat of evaporation
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @return latent heat of evaporation [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' lh = gsw_latentheat_evap_t(SA, t)
#' stopifnot(all.equal(lh/1e6, c(2.429882982734836, 2.430730236218543, 2.444217294049004,
#'                               2.474137411322517, 2.482156276375029, 2.488054617630297)))
#' @family things related to latent heat
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_latentheat_evap_t.html}
gsw_latentheat_evap_t <- function(SA, t)
{
    l <- argfix(list(SA=SA, t=t))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_latentheat_evap_t",
               SA=as.double(l$SA), t=as.double(l$t),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Latent Heat of Melting
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return latent heat of freezing [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' lh <- gsw_latentheat_melting(SA, p)
#' stopifnot(all.equal(lh/1e5, c(3.299496680271213, 3.298613352397986, 3.297125622834541,
#'                               3.294973895330757, 3.288480445559747, 3.280715862416388)))
#' @family things related to latent heat
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_latentheat_melting.html}
gsw_latentheat_melting <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_latentheat_melting",
               SA=as.double(l$SA), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate properties related to ice melting in seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template w_Ihtemplate
#' @template t_Ihtemplate
#' @return a list containing \code{SA_final}, \code{CT_final} and \code{w_Ih_final}.
#' @examples
#' SA <- c(  34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(   4.7856,  2.4329,  1.8103,  1.2600,  0.6886,  0.4403)
#' p <- c(        10,      50,     125,     250,     600,    1000)
#' w_Ih <- c( 0.0560, 0.02513, 0.02159, 0.01210, 0.00943, 0.00751)
#' t_Ih <- c(-4.7856, -4.4329, -3.8103, -4.2600, -3.8863, -3.4036)
#' r <- gsw_melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih)
#' stopifnot(all.equal(r$SA_final, c(32.767939199999994, 34.014676604999998, 34.269397295999994,
#'                                   34.425548880000001, 34.409033862000001, 34.471559675999998)))
#' stopifnot(all.equal(r$CT_final, c(-0.298448911022612, 0.215263001418312, -0.074341719211557,
#'                                   0.207796293045473, -0.123785388299875, -0.202531182809225)))
#' stopifnot(all.equal(r$w_Ih_final, rep(0, 6)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_ice_into_seawater.html}
gsw_melting_ice_into_seawater <- function(SA, CT, p, w_Ih, t_Ih)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, w_Ih=w_Ih, t_Ih=t_Ih))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_melting_ice_into_seawater",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), w_Ih=as.double(l$w_Ih), t_Ih=as.double(l$t_Ih),
            n=as.integer(n), SA_final=double(n), CT_final=double(n), w_Ih_final=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$w_Ih) | !is.finite(l$t_Ih)
    ##37 r$SA_final[bad] <- NA
    ##37 r$CT_final[bad] <- NA
    ##37 r$t_Ih_final[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$SA_final) <- dim
        dim(r$CT_final) <- dim
        dim(r$t_Ih_final) <- dim
    }
    list(SA_final=r$SA_final, CT_final=r$CT_final, w_Ih_final=r$w_Ih_final)
}


#' Calculate properties related to seaice melting in seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @param w_seaice mass fraction (seaice) / (water + seaice)
#' @param SA_seaice Absolute Salinity of seaice
#' @param t_seaice temperature of seaice
#' @return a list containing \code{SA_final} and \code{CT_final}.
#' @examples
#' SA <- c(      34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(       4.7856,  2.4329,  1.8103,  1.2600,  0.6886,  0.4403)
#' p <- c(            10,      50,     125,     250,     600,    1000)
#' w_seaice <- c( 0.0560, 0.02513, 0.02159, 0.01210, 0.00943, 0.00751)
#' SA_seaice <- c(     5,     4.8,     3.5,     2.5,       1,     0.4)
#' t_seaice <- c(-4.7856, -4.4329, -3.8103, -4.2600, -3.8863, -3.4036)
#' r <- gsw_melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice)
#' stopifnot(all.equal(r$SA_final, c(33.047939199999995, 34.135300604999998, 34.344962295999999,
#'                                   34.455798880000003, 34.418463862000003, 34.474563675999995)))
#' stopifnot(all.equal(r$CT_final, c(-0.018822367305381, 0.345095540241769, 0.020418581143151,
#'                                   0.242672380976922, -0.111078380121959, -0.197363471215418)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_seaice_into_seawater.html}
gsw_melting_seaice_into_seawater <- function(SA, CT, p, w_seaice, SA_seaice, t_seaice)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, w_seaice=w_seaice, SA_seaice=SA_seaice, t_seaice=t_seaice))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_melting_seaice_into_seawater",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            w_seaice=as.double(l$w_seaice), SA_seaice=as.double(l$SA_seaice), t_seaice=as.double(l$t_seaice),
            n=as.integer(n), SA_final=double(n), CT_final=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$w_seaice) | !is.finite(l$SA_seaice) | !is.finite(l$t_seaice)
    ##37 r$SA_final[bad] <- NA
    ##37 r$CT_final[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$SA_final) <- dim
        dim(r$CT_final) <- dim
    }
    list(SA_final=r$SA_final, CT_final=r$CT_final)
}


#' Calculate d(SA)/d(CT) for Ice Melting in near-freezing Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return ratio of change in \code{SA} to change in \code{CT} [ g/kg/degC ].
#' @examples
#' SA <- c(   34.7118,  34.8915,  35.0256,  34.8472,  34.7366, 34.7324)
#' p <- c(         10,       50,      125,      250,      600,    1000)
#' r <- gsw_melting_ice_equilibrium_SA_CT_ratio(SA, p)
#' stopifnot(all.equal(r, c(0.420209509196985, 0.422511693121631, 0.424345503216433,
#'                          0.422475836091426, 0.422023427778221, 0.423037622331042)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_ice_equilibrium_SA_CT_ratio.html}
gsw_melting_ice_equilibrium_SA_CT_ratio <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_melting_ice_equilibrium_SA_CT_ratio",
               SA=as.double(l$SA), p=as.double(l$p),
               n=as.integer(n), rval=double(n),
               NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate d(SA)/d(CT) for Ice Melting in near-freezing Seawater (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return ratio of change in \code{SA} to change in \code{CT} [ g/kg/degC ].
#' @examples
#' SA <- c(   34.7118,  34.8915,  35.0256,  34.8472,  34.7366, 34.7324)
#' p <- c(         10,       50,      125,      250,      600,    1000)
#' r <- gsw_melting_ice_equilibrium_SA_CT_ratio_poly(SA, p)
#' stopifnot(all.equal(r, c(0.420209444587263, 0.422511664682796, 0.424345538275708,
#'                          0.422475965003649, 0.422023755182266, 0.423038080717229)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_ice_equilibrium_SA_CT_ratio_poly.html}
gsw_melting_ice_equilibrium_SA_CT_ratio_poly <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_melting_ice_equilibrium_SA_CT_ratio_poly",
               SA=as.double(l$SA), p=as.double(l$p),
               n=as.integer(n), rval=double(n),
               NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate d(SA)/d(CT) for Ice Melting in Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template t_Ihtemplate
#' @return ratio of change in \code{SA} to change in \code{CT} [ g/kg/degC ].
#' @examples
#' SA <- c(   34.7118,  34.8915,  35.0256,  34.8472,  34.7366, 34.7324)
#' CT <- c(    3.7856,   3.4329,   2.8103,   1.2600,   0.6886,  0.4403)
#' p <- c(         10,       50,      125,      250,      600,    1000)
#' t_Ih <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' r <- gsw_melting_ice_SA_CT_ratio(SA, CT, p, t_Ih)
#' stopifnot(all.equal(r, c(0.373840909022490, 0.371878514972099, 0.377104664622191,
#'                          0.382777696796156, 0.387133845152000, 0.393947316026914)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_ice_SA_CT_ratio.html}
gsw_melting_ice_SA_CT_ratio <- function(SA, CT, p, t_Ih)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, t_Ih=t_Ih))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_melting_ice_SA_CT_ratio",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), t_Ih=as.double(l$t_Ih),
               n=as.integer(n), rval=double(n),
               NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$t_Ih)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate d(SA)/d(CT) for Ice Melting in Seawater (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template t_Ihtemplate
#' @return ratio of change in \code{SA} to change in \code{CT} [ g/kg/degC ].
#' @examples
#' SA <- c(   34.7118,  34.8915,  35.0256,  34.8472,  34.7366, 34.7324)
#' CT <- c(    3.7856,   3.4329,   2.8103,   1.2600,   0.6886,  0.4403)
#' p <- c(         10,       50,      125,      250,      600,    1000)
#' t_Ih <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' r <- gsw_melting_ice_SA_CT_ratio_poly(SA, CT, p, t_Ih)
#' stopifnot(all.equal(r, c(0.373840908629278, 0.371878512745054, 0.377104658031030,
#'                          0.382777681212224, 0.387133812279563, 0.393947267481204)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_melting_ice_SA_CT_ratio_poly.html}
gsw_melting_ice_SA_CT_ratio_poly <- function(SA, CT, p, t_Ih)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, t_Ih=t_Ih))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_melting_ice_SA_CT_ratio_poly",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), t_Ih=as.double(l$t_Ih),
               n=as.integer(n), rval=double(n),
               NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$t_Ih)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate Brunt Vaisala Frequency squared
#'
#' The result is computed based on first-differencing a computed density with
#' respect pressure, and this can yield noisy results with CTD data that
#' have not been smoothed and decimated. It also yields infinite values,
#' for repeated adjacent pressure (e.g. this occurs twice with the \code{ctd}
#' dataset provided in the \CRANpkg{oce} package).
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template latitudetemplate
#' @return list containing N2 [ 1/s^2 ] and mid-point pressure p_mid [ dbar ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' latitude <- 4
#' r <- gsw_Nsquared(SA, CT, p, latitude=4)
#' stopifnot(all.equal(r$N2*1e3, c(0.060843209693499, 0.235723066151305, 0.216599928330380,
#'                                 0.012941204313372, 0.008434782795209)))
#' stopifnot(all.equal(r$p_mid, c(30, 87.5, 187.5, 425, 800)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Nsquared.html}
gsw_Nsquared <- function(SA, CT, p, latitude=0)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, latitude=latitude))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_Nsquared",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), latitude=as.double(l$latitude),
            n=as.integer(n), n2=double(n-1), p_mid=double(n-1), NAOK=TRUE, PACKAGE="gsw")
    bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$latitude)
    if (any(bad))
        warning("gsw_Nsquared() has some NA inputs ... these are not handled well\n")
    if (is.matrix(SA))
        stop("gsw_Nsquared() cannot handle matrix SA")
    list(N2=r$n2, p_mid=r$p_mid)
}

#' Oxygen Solubility in Seawater (GSW variables)
#'
#' Computes oxygen concentration for seawater that is equilibrium with
#' vapour-saturated air at standard atmospheric pressure (101.325 kPa,
#' i.e. for sea pressure of 0dbar).  The formula, not created by the SCOR/IAPSO
#' Working Group 127 nor approved by the IOC, is stated in the TEOS-10
#' documentation to be from Benson and Krause (1984), as fitted by
#' Garcia and Gordon (1992, 1993). That formulation is framed in UNESCO-era
#' water properties, so longitude and latitude are needed here, to convert
#' to these quantities from Absolute Salinity and Conservative Temperature;
#' see also \code{\link{gsw_O2sol_SP_pt}}, which is formulated in UNESCO
#' terms.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Oxygen solubility in micro-moles per kg.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' latitude <- c(4,       4,       4,       4,       4,       4)
#' longitude <- c(188,  188,     188,     188,     188,     188)
#' O2sol <- gsw_O2sol(SA,CT,p,longitude,latitude)
#' stopifnot(all.equal(O2sol/100, c(1.949651126384804, 1.958728907684003,
#'             2.148922307892045, 2.738656506758550, 2.955109771828408,
#'             3.133584919106894)))
#' @family things related to oxygen
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_O2sol.html}
gsw_O2sol <- function(SA, CT, p, longitude, latitude)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(CT)) stop("must supply CT")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    l <- argfix(list(SA=SA, CT=CT, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_o2sol",
        SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
        longitude=as.double(l$longitude), latitude=as.double(l$latitude),
        n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}

#' Oxygen Solubility in Seawater (UNESCO variables)
#'
#' Computes oxygen concentration for seawater that is equilibrium with
#' vapour-saturated air at standard atmospheric pressure (101.325 kPa,
#' i.e. for sea pressure of 0dbar).  The formula, not created by the SCOR/IAPSO
#' Working Group 127 nor approved by the IOC, is stated in the TEOS-10
#' documentation to be from Benson and Krause (1984), as fitted by
#' Garcia and Gordon (1992, 1993). That formulation is framed in UNESCO-era
#' water properties; see \code{\link{gsw_O2sol}} for the corresponding
#' computation in GSW variables.
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template pttemplate
#' @return Oxygen solubility in micro-moles per kg.
#' @examples
#' SP <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' pt <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' O2sol <- gsw_O2sol_SP_pt(SP, pt)
#' stopifnot(all.equal(O2sol/100, c(1.946825431692940, 1.956135062814438,
#'             2.146559360234014, 2.735652832698713, 2.951580761415903,
#'             3.129598716631408)))
#' @family things related to oxygen
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_O2sol_SP_pt.html}
gsw_O2sol_SP_pt <- function(SP, pt)
{
    if (missing(SP)) stop("must supply SP")
    if (missing(pt)) stop("must supply pt")
    l <- argfix(list(SP=SP, pt=pt))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_o2sol_SP_pt",
        SP=as.double(l$SP), pt=as.double(l$pt),
        n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}

#' Pressure from height (75-term equation)
#'
#' @template teos10template
#'
#' @param z height, zero at surface (but note last 2 args) and positive upwards [ m ]
#' @template latitudetemplate
#' @return sea pressure [ dbar ]
#' @param geo_strf_dyn_height vector of same length as \code{z} and \code{latitude},
#' indicating dynamic height [ m^2/s^2 ].
#' If not supplied, this defaults to a vector of 0 values, with length matching that
#' of \code{z}.
#' @param sea_surface_geopotential vector of same length as \code{z} and \code{latitude},
#' indicating geopotential at zero sea pressure [ m^2/s^2 ].
#' If not supplied, this defaults to a vector of 0 values, with length matching that
#' of \code{z}.
#' @examples
#' z <- -c(10, 50, 125, 250, 600, 1000)
#' latitude <- 4
#' p <- gsw_p_from_z(z, latitude)
#' stopifnot(all.equal(p/1e3, c(0.010055726724518, 0.050283543374874, 0.125731858435610,
#'                              0.251540299593468, 0.604210012340727, 1.007990337692001)))
#' @family things related to depth
#'
#' @section Historical Note:
#' The \code{geo_strf_dyn_height} and \code{sea_surface_geopotential}
#' parameters were added in GSW-R version 1.0-6.
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_p_from_z.html}
gsw_p_from_z <- function(z, latitude, geo_strf_dyn_height, sea_surface_geopotential)
{
    if (missing(geo_strf_dyn_height))
        geo_strf_dyn_height <- rep(0.0, length(z))
    if (missing(sea_surface_geopotential))
        sea_surface_geopotential <- rep(0.0, length(z))
    l <- argfix(list(z=z,
                     latitude=latitude,
                     geo_strf_dyn_height=geo_strf_dyn_height,
                     sea_surface_geopotential=sea_surface_geopotential))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_p_from_z",
               z=as.double(l$z), latitude=as.double(l$latitude),
               geo_strf_dyn_height=as.double(l$geo_strf_dyn_height),
               sea_surface_geopotential=as.double(l$sea_surface_geopotential),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    if (is.matrix(z))
        dim(rval) <- dim(z)
    rval
}


#' Potential Enthalpy of Ice
#'
#' @template teos10template
#'
#' @template pt0_icetemplate
#' @return potential enthalpy [ J/kg ]
#' @examples
#' pt0_ice <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' e <- gsw_pot_enthalpy_from_pt_ice(pt0_ice)
#' stopifnot(all.equal(e/1e5, c(-3.555459449611868, -3.608607069998877, -3.596153890859193,
#'                              -3.585123178806596, -3.557490528226009, -3.507198313847837)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_from_pt_ice.html}
gsw_pot_enthalpy_from_pt_ice <- function(pt0_ice)
{
    l <- argfix(list(pt0_ice=pt0_ice))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pot_enthalpy_from_pt_ice",
               pt0_ice=as.double(l$pt0_ice),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$pt0_ice)] <- NA
    if (is.matrix(pt0_ice))
        dim(rval) <- dim(pt0_ice)
    rval
}


#' Potential Enthalpy of Ice (Polynomial version)
#'
#' @template teos10template
#'
#' @template pt0_icetemplate
#' @return potential enthalpy [ J/kg ]
#' @examples
#' pt0_ice <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' e <- gsw_pot_enthalpy_from_pt_ice_poly(pt0_ice)
#' stopifnot(all.equal(e/1e5, c(-3.555459482216265, -3.608607100959428, -3.596153924697033,
#'                              -3.585123214031169, -3.557490561327994, -3.507198320793373)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_from_pt_ice_poly.html}
gsw_pot_enthalpy_from_pt_ice_poly <- function(pt0_ice)
{
    l <- argfix(list(pt0_ice=pt0_ice))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pot_enthalpy_from_pt_ice_poly",
               pt0_ice=as.double(l$pt0_ice),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$pt0_ice)] <- NA
    if (is.matrix(pt0_ice))
        dim(rval) <- dim(pt0_ice)
    rval
}


#' Potential Enthalpy of Ice at Freezing Point
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return potential enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' saturation_fraction = 1
#' e <- gsw_pot_enthalpy_ice_freezing(SA, p, saturation_fraction)
#' \dontrun{
#' stopifnot(all.equal(e/1e5, c(-3.373409558967978, -3.374434164002012, -3.376117536928847,
#'                              -3.378453698871986, -3.385497832886802, -3.393768587631489)))
#'}
#' @section Bugs:
#' 1. The C source underlying this function lacks an argument, \code{saturation_fraction},
#' which is present in the Matlab source, and so that argument is ignored here.
#'
#' 2. The R code does not reproduce the check values stated at
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_ice_freezing.html}. Those
#' values are incorporated in the test provided in \dQuote{Examples}, so that test
#' is not performed during build tests.  See https://github.com/TEOS-10/GSW-R/issues/27.
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_ice_freezing.html}
gsw_pot_enthalpy_ice_freezing <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pot_enthalpy_ice_freezing",
               SA=as.double(l$SA), p=as.double(l$p), # saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential Enthalpy of Ice at Freezing Point (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return potential enthalpy [ J/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' saturation_fraction = 1
#' e <- gsw_pot_enthalpy_ice_freezing_poly(SA, p, saturation_fraction)
#' stopifnot(all.equal(e/1e5, c(-3.373370858777002, -3.374395733068549, -3.376079507278181,
#'                              -3.378416106344322, -3.385460970578123, -3.393731732645173)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_ice_freezing_poly.html}
gsw_pot_enthalpy_ice_freezing_poly <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pot_enthalpy_ice_freezing_poly",
               SA=as.double(l$SA), p=as.double(l$p), # saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' First Derivatives of Potential Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return A list containing \code{pot_enthalpy_ice_freezing_SA} [ (J/kg)/(g/kg) ], the derivative of
#' potential enthalpy with respect to Absolute Salinity,
#' and \code{pot_enthalpy_ice_freezing_p} [ unitless ], the derivative of
#' Conservative Temperature with respect to potential temperature. (Note that the second
#' quantity is denoted \code{pot_enthalpy_ice_freezing_P} in the documentation for the Matlab function.)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_pot_enthalpy_ice_freezing_first_derivatives(SA, p)
#' stopifnot(all.equal(r$pot_enthalpy_ice_freezing_SA/1e2,
#'       c(-1.183484968590718, -1.184125268891200, -1.184619267864844,
#'       -1.184026131143674, -1.183727706650925, -1.183814873741961)))
#' stopifnot(all.equal(r$pot_enthalpy_ice_freezing_p/1e-3,
#'       c(-0.202880939983260, -0.203087335312542, -0.203473018454630,
#'       -0.204112435106666, -0.205889571619502, -0.207895691215823)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_ice_freezing_first_derivatives.html}
gsw_pot_enthalpy_ice_freezing_first_derivatives <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_pot_enthalpy_ice_freezing_first_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), p=as.double(l$p),
            n=as.integer(n),
            pot_enthalpy_ice_freezing_SA=double(n), pot_enthalpy_ice_freezing_p=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p)
    ##37 r$pot_enthalpy_ice_freezing_SA[bad] <- NA
    ##37 r$pot_enthalpy_ice_freezing_p[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$pot_enthalpy_ice_freezing_SA) <- dim(SA)
        dim(r$pot_enthalpy_ice_freezing_p) <- dim(SA)
    }
    list(pot_enthalpy_ice_freezing_SA=r$pot_enthalpy_ice_freezing_SA, pot_enthalpy_ice_freezing_p=r$pot_enthalpy_ice_freezing_p)
}


#' First Derivatives of Potential Enthalpy (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @return A list containing \code{pot_enthalpy_ice_freezing_SA} [ (J/kg)/(g/kg) ], the derivative of
#' potential enthalpy with respect to Absolute Salinity,
#' and \code{pot_enthalpy_ice_freezing_p} [ unitless ], the derivative of
#' Conservative Temperature with respect to potential temperature. (Note that the second
#' quantity is denoted \code{pot_enthalpy_ice_freezing_P} in the documentation for the Matlab function.)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p)
#' stopifnot(all.equal(r$pot_enthalpy_ice_freezing_SA/1e2,
#'       c(-1.183498006918154, -1.184135169530602, -1.184626138334419,
#'       -1.184032656542549, -1.183727371435808, -1.183805326863513)))
#' stopifnot(all.equal(r$pot_enthalpy_ice_freezing_p/1e-3,
#'       c(-0.202934280214689, -0.203136950111241, -0.203515960539503,
#'       -0.204145112153220, -0.205898365024147, -0.207885289186464)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_enthalpy_ice_freezing_first_derivatives_poly.html}
gsw_pot_enthalpy_ice_freezing_first_derivatives_poly <- function(SA, p)
{
    l <- argfix(list(SA=SA, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_pot_enthalpy_ice_freezing_first_derivatives_poly", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), p=as.double(l$p),
            n=as.integer(n),
            pot_enthalpy_ice_freezing_SA=double(n), pot_enthalpy_ice_freezing_p=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p)
    ##37 r$pot_enthalpy_ice_freezing_SA[bad] <- NA
    ##37 r$pot_enthalpy_ice_freezing_p[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$pot_enthalpy_ice_freezing_SA) <- dim(SA)
        dim(r$pot_enthalpy_ice_freezing_p) <- dim(SA)
    }
    list(pot_enthalpy_ice_freezing_SA=r$pot_enthalpy_ice_freezing_SA, pot_enthalpy_ice_freezing_p=r$pot_enthalpy_ice_freezing_p)
}


#' Potential density
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @param p_ref reference pressure [ dbar ]
#' @return potential density [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' p_ref  <- 0
#' prho <- gsw_pot_rho_t_exact(SA,t,p,p_ref)
#' stopifnot(all.equal(prho/1e3, c(1.021798145811089, 1.022052484416980, 1.023893583651958,
#'                                 1.026667621124443, 1.027107230868492, 1.027409631264134)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pot_rho_t_exact.html}
gsw_pot_rho_t_exact <- function(SA, t, p, p_ref)
{
    l <- argfix(list(SA=SA, t=t, p=p, p_ref=p_ref))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pot_rho_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p), pref=as.double(l$p_ref),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p) | !is.finite(l$p_ref)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Pressure Coefficient for Ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return specific internal energy [ Pa/degC ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' pc <- gsw_pressure_coefficient_ice(t, p)
#' stopifnot(all.equal(pc/1e6, c(1.333098059787838, 1.326359005133730, 1.327354133828322,
#'                               1.327793888831923, 1.328549609231685, 1.331416733490227)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pressure_coefficient_ice.html}
gsw_pressure_coefficient_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pressure_coefficient_ice",
               t=(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Pressure at which Seawater Freezes
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template saturation_fractiontemplate
#' @return pressure at which freezing will occur [ dbar ]
#' @examples
#' SA <- c(                 34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(                 -1.8996, -1.9407, -2.0062, -2.0923, -2.3593, -2.6771)
#' saturation_fraction <- c(       1,    0.8,     0.6,     0.5,     0.4,       0)
#' p <- gsw_pressure_freezing_CT(SA, CT, saturation_fraction)
#' stopifnot(all.equal(p/1e3, c(0.009890530270710, 0.050376026585933, 0.125933117050624,
#'                              0.251150973076077, 0.601441775836021, 1.002273338145043)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pressure_freezing_CT.html}
gsw_pressure_freezing_CT <- function(SA, CT, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, CT=CT, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pressure_freezing_CT", NAOK=TRUE, PACKAGE="gsw",
               SA=as.double(l$SA), CT=as.double(l$CT), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential temperature referenced to the surface
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return potential temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' pt0 <- gsw_pt0_from_t(SA, t, p)
#' stopifnot(all.equal(pt0, c(28.783196819670632, 28.420983342398962, 22.784930399117108,
#'                            10.230523661095731, 6.829230224409661, 4.324510571845719)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt0_from_t.html}
gsw_pt0_from_t <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt0_from_t",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential Temperature of Ice Referenced to the Surface
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return potential temperature [ degC ]
#' @examples
#' t  <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <- c(       10,       50,      125,      250,      600,    1000)
#' pt0 <- gsw_pt0_from_t_ice(t, p)
#' stopifnot(all.equal(pt0, c(-10.787787898205298, -13.443730926050607, -12.837427056999708,
#'                            -12.314321615760905, -11.017040858094250, -8.622907355083088)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt0_from_t_ice.html}
gsw_pt0_from_t_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt0_from_t_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' First Derivatives of Potential Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return A list containing \code{pt_SA} [ K/(g/kg) ], the derivative of
#' potential temperature with respect to Absolute Salinity,
#' and \code{pt_CT} [ unitless ], the derivative of potential temperature
#' with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' r <- gsw_pt_first_derivatives(SA, CT)
#' stopifnot(all.equal(r$pt_SA, c(0.041863223165431, 0.041452303483011, 0.034682095247246,
#'                                0.018711079068408, 0.014079958329844, 0.010577326129948)))
#' stopifnot(all.equal(r$pt_CT, c(0.997192967140242, 0.997451686508335, 0.998357568277750,
#'                                0.999996224076267, 1.000283719083268, 1.000525947028218)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_first_derivatives.html}
gsw_pt_first_derivatives <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_pt_first_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT),
            n=as.integer(n),
            pt_SA=double(n), pt_CT=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT)
    ##37 r$pt_SA[bad] <- NA
    ##37 r$pt_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$pt_SA) <- dim(SA)
        dim(r$pt_CT) <- dim(SA)
    }
    list(pt_SA=r$pt_SA, pt_CT=r$pt_CT)
}


#' Potential temperature from Conservative Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' pt <- gsw_pt_from_CT(SA, CT)
#' stopifnot(all.equal(pt, c(28.783177048624573, 28.420955597191984, 22.784953468087107,
#'                           10.230534394434429, 6.829216587061605, 4.324534835990236)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_CT.html}
gsw_pt_from_CT <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_CT",
               SA=as.double(l$SA), t=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential Temperature from Entropy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template entropytemplate
#' @return potential temperature [ degC ]
#' @examples
#' SA <- c(      34.7118,  34.8915,  35.0256,  34.8472, 34.7366, 34.7324)
#' entropy <- c(400.3892, 395.4378, 319.8668, 146.7910, 98.6471, 62.7919)
#' pt <- gsw_pt_from_entropy(SA, entropy)
#' stopifnot(all.equal(pt, c(28.783179828078666, 28.420954825949291, 22.784952736245351,
#'                           10.230532066931868, 6.829213325916900, 4.324537782985845)))
#' @family things related to entropy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_entropy.html}
gsw_pt_from_entropy <- function(SA, entropy)
{
    l <- argfix(list(SA=SA, entropy=entropy))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_entropy",
               SA=as.double(l$SA), entropy=as.double(l$entropy),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$entropy)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential Temperature from Potential Enthalpy of Ice
#'
#' @template teos10template
#'
#' @template pot_enthalpy_icetemplate
#' @return potential temperature [ degC ]
#' @examples
#' pot_enthalpy_ice <- c(-3.5544e5, -3.6033e5, -3.5830e5, -3.5589e5, -3.4948e5, -3.4027e5)
#' pt <- gsw_pt_from_pot_enthalpy_ice(pot_enthalpy_ice)
#' stopifnot(all.equal(pt, c(-10.733087588125384, -13.167397822300588, -12.154205899172704,
#'                           -10.956202704066083, -7.794963180206421, -3.314905214262531)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_pot_enthalpy_ice.html}
gsw_pt_from_pot_enthalpy_ice <- function(pot_enthalpy_ice)
{
    l <- argfix(list(pot_enthalpy_ice=pot_enthalpy_ice))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_pot_enthalpy_ice",
               pot_enthalpy_ice=as.double(l$pot_enthalpy_ice),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$pot_enthalpy_ice)] <- NA
    if (is.matrix(pot_enthalpy_ice))
        dim(rval) <- dim(pot_enthalpy_ice)
    rval
}


#' Potential Temperature from in-situ Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @param p_ref reference pressure [ dbar ]
#' @return potential temperature [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' p_ref <- 0
#' pt <- gsw_pt_from_t(SA, t, p, p_ref)
#' stopifnot(all.equal(pt, c(28.783196819670632, 28.420983342398962, 22.784930399117108,
#'                           10.230523661095731, 6.829230224409661, 4.324510571845719)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_t.html}
gsw_pt_from_t <- function(SA, t, p, p_ref=0)
{
    l <- argfix(list(SA=SA, t=t, p=p, p_ref=p_ref))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_t",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p), p_ref=as.double(l$p_ref),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p) | !is.finite(l$p_ref)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential Temperature from Potential Enthalpy of Ice (Polynomial version)
#'
#' @template teos10template
#'
#' @template pot_enthalpy_icetemplate
#' @return potential temperature [ degC ]
#' @examples
#' pot_enthalpy_ice <- c(-3.5544e5, -3.6033e5, -3.5830e5, -3.5589e5, -3.4948e5, -3.4027e5)
#' pt <- gsw_pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice)
#' stopifnot(all.equal(pt, c(-10.733085986035007, -13.167396204945987, -12.154204137867396,
#'                           -10.956201046447006, -7.794963341294590, -3.314907552013722)))
#' @family things related to enthalpy
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_pot_enthalpy_ice_poly.html}
gsw_pt_from_pot_enthalpy_ice_poly <- function(pot_enthalpy_ice)
{
    l <- argfix(list(pot_enthalpy_ice=pot_enthalpy_ice))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_pot_enthalpy_ice_poly",
               pot_enthalpy_ice=as.double(l$pot_enthalpy_ice),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$pot_enthalpy_ice)] <- NA
    if (is.matrix(pot_enthalpy_ice))
        dim(rval) <- dim(pot_enthalpy_ice)
    rval
}


#' Potential Temperature of Ice from in-situ Temperature
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @param p_ref reference pressure [ dbar ]
#' @return potential temperature [ degC ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <- c(      10,       50,      125,      250,      600,    1000)
#' p_ref <- 0 # not actually needed, since 0 is the default
#' pt <- gsw_pt_from_t_ice(t, p, p_ref)
#' stopifnot(all.equal(pt, c(-10.787787898205272, -13.443730926050661, -12.837427056999676,
#'                           -12.314321615760921, -11.017040858094234, -8.622907355083147)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_from_t_ice.html}
gsw_pt_from_t_ice <- function(t, p, p_ref=0)
{
    l <- argfix(list(t=t, p=p, p_ref=p_ref))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_pt_from_t_ice",
               t=as.double(l$t), p=as.double(l$p), p_ref=as.double(l$p_ref),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p) | !is.finite(l$p_ref)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Second Derivatives of Potential Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return A list containing \code{pt_SA_SA} [ K/(g/kg)^2 ], the second derivative of
#' potential temperature with respect to Absolute Salinity at constant
#' potential temperature, and \code{pt_SA_pt} [ 1/(g/kg) ], the derivative of
#' potential temperature with respect to Conservative Temperature and
#' Absolute Salinity, and \code{pt_pt_pt} [ 1/degC ], the second derivative of
#' potential temperature with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' r <- gsw_pt_second_derivatives(SA, CT)
#' stopifnot(all.equal(r$pt_SA_SA/1e-3,
#'     c(0.160307058371208, 0.160785497957769, 0.168647220588324,
#'       0.198377949876584, 0.210181899321236, 0.220018966513329)))
#' stopifnot(all.equal(r$pt_SA_CT,
#'     c(0.001185581323691, 0.001187068518686, 0.001217629686266,
#'       0.001333254154015, 0.001379674342678, 0.001418371539325)))
#' stopifnot(all.equal(r$pt_CT_CT/1e-3,
#'     c(-0.121979811279463, -0.123711264754503, -0.140136818504977,
#'       -0.140645384127949, -0.113781055410824, -0.082417269009484)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_pt_second_derivatives.html}
gsw_pt_second_derivatives <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_pt_second_derivatives",
            SA=as.double(l$SA), CT=as.double(l$CT),
            n=as.integer(n),
            pt_SA_SA=double(n), pt_SA_CT=double(n), pt_CT_CT=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT)
    ##37 r$pt_SA_SA[bad] <- NA
    ##37 r$pt_SA_CT[bad] <- NA
    ##37 r$pt_pt_CT[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$pt_SA_SA) <- dim(SA)
        dim(r$pt_SA_CT) <- dim(SA)
        dim(r$pt_pt_CT) <- dim(SA)
    }
    list(pt_SA_SA=r$pt_SA_SA, pt_SA_CT=r$pt_SA_CT, pt_CT_CT=r$pt_CT_CT)
}


#' In-situ density
#'
#' In-situ density, using the 75-term equation for specific volume.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return in-situ density [ kg/m^3 ]
#' @family things related to density
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' rho <- gsw_rho(SA,CT,p)
#' stopifnot(all.equal(rho/1e3, c(1.021839935738108, 1.022262457966867, 1.024427195413316,
#'                                1.027790152759127, 1.029837779000189, 1.032002453224572)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho.html}
gsw_rho <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_rho",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' In-situ density, thermal expansion coefficient and haline contraction coefficient (75-term equation)
#'
#' Calculate the in-situ density, the expansion coefficient (with respect to Conservative Temperature) and
#' the haline contraction coefficient (with respect to Absolute Salinity), using the
#' 75-term equation.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing in-situ density \code{rho} [ kg/m^3 ], thermal expansion
#' coefficient \code{alpha} [ 1/degC ], and haline contraction coefficient
#' \code{beta} [ kg/g ].
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' r <- gsw_rho_alpha_beta(SA, CT, p)
#' stopifnot(all.equal(r$rho/1000, c(1.021839935738108, 1.022262457966867, 1.024427195413316,
#'                                   1.027790152759127, 1.029837779000189, 1.032002453224572)))
#' stopifnot(all.equal(r$alpha*1000, c(0.324638934509245, 0.322655537959731, 0.281145723210171,
#'                                     0.173199716344780, 0.146289673594824, 0.129414845334599)))
#' stopifnot(all.equal(r$beta*1000, c(0.717483987596135, 0.717647512290095, 0.726211643644768,
#'                                    0.750500751749777, 0.755052064788492, 0.757050813384370)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_alpha_beta.html}
gsw_rho_alpha_beta <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_rho_alpha_beta",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n), rho=double(n), alpha=double(n), beta=double(n), NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$rho[bad] <- NA
    ##37 r$alpha[bad] <- NA
    ##37 r$beta[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$alpha) <- dim
        dim(r$beta) <- dim
    }
    list(rho=r$rho, alpha=r$alpha, beta=r$beta)
}


#' Density First Derivatives wrt SA, CT and p (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return list containing drho_dSA [ kg^2/(g m^3) ], drho_dCT [ kg/(K m^3) ] and drho_dp [ kg/(Pa m^3) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_rho_first_derivatives(SA, CT, p)
#' stopifnot(all.equal(r$drho_dSA, c(0.733153791778356, 0.733624109867480, 0.743950957375504,
#'                                   0.771357282286743, 0.777581141431288, 0.781278296628328)))
#' stopifnot(all.equal(r$drho_dCT, c(-0.331729027977015, -0.329838643311336, -0.288013324730644,
#'                                   -0.178012962919839, -0.150654632545556, -0.133556437868984)))
#' stopifnot(all.equal(r$drho_dp, 1e-6*c(0.420302360738476, 0.420251070273888, 0.426773054953941,
#'                                       0.447763615252861, 0.452011501791479, 0.454118117103094)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_first_derivatives.html}
gsw_rho_first_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_rho_first_derivatives",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n), drho_dSA=double(n), drho_dCT=double(n), drho_dp=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 r[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        stop("gsw_rho_first_derivatives() cannot handle matrix SA")
    list(drho_dSA=r$drho_dSA, drho_dCT=r$drho_dCT, drho_dp=r$drho_dp)
}


#' Density First Derivatives wrt enthalpy (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{rho_SA_wrt_h} [ (kg/m^3)/(g/kg) ]
#' and \code{rho_h} [ (kg/m^3)/(J/kg) ].
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_rho_first_derivatives_wrt_enthalpy(SA, CT, p)
#' stopifnot(all.equal(r$rho_SA_wrt_h,
#'     c(0.733147960400929, 0.733595114830609, 0.743886977148835,
#'      0.771275693831993, 0.777414200397148, 0.781030546357425)))
#' stopifnot(all.equal(r$rho_h*1e4,
#'     c(-0.831005413475887, -0.826243794873652, -0.721438289309903,
#'      -0.445892608094272, -0.377326924646647, -0.334475962698187)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_first_derivatives_wrt_enthalpy.html}
gsw_rho_first_derivatives_wrt_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_rho_first_derivatives_wrt_enthalpy",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            rho_SA_wrt_h=double(n), rho_h=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$rho_SA_wrt_h[bad] <- NA
    ##37 r$rho_h[bad] <- NA
    if (is.matrix(SA)) {
        dim  <- dim(SA)
        dim(r$rho_SA_wrt_h)  <- dim
        dim(r$rho_h)  <- dim
    }
    list(rho_SA_wrt_h=r$rho_SA_wrt_h, rho_h=r$rho_h)
}


#' In-situ density of ice
#'
#' In-situ density of ice [kg/m^3]
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#'
#' @return in-situ density [ kg/m^3 ]
#'
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' rho <- gsw_rho_ice(t, p)
#' stopifnot(all.equal(rho, c(918.2879969148962, 918.7043487325120, 918.6962796312690,
#'                            918.7513732275766, 918.9291139833307, 919.0032237449378)))
#' @family things related to density
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_ice.html}
gsw_rho_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_rho_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Second Derivatives of Density
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{rho_SA_SA} [ (kg/m^3)/(g/kg)^2 ], the second derivative of
#' density with respect to Absolute Salinity,
#' \code{rho_SA_CT} [ (g/kg)/(g/kg)/degC ], the derivative of
#' density with respect to Absolute Salinity and Conservative Temperature,
#' and \code{rho_CT_CT} [ (kg/m^3)/degC^2 ], the second derivative of
#' density with respect to Conservative Temperature.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#'
#' r <- gsw_rho_second_derivatives(SA, CT, p)
#'
#' stopifnot(all.equal(r$rho_SA_SA/1e-3, c(0.207364734477357, 0.207415414547223,
#'             0.192903197286004, 0.135809142211237, 0.122627562106076,
#'             0.114042431905783)))
#'
#' stopifnot(all.equal(r$rho_SA_CT, c(-0.001832856561477, -0.001837354806146,
#'             -0.001988065808078, -0.002560181494807, -0.002708939446458,
#'             -0.002798484050141)))
#'
#'stopifnot(all.equal(r$rho_CT_CT, c(-0.007241243828334, -0.007267807914635,
#'            -0.007964270843331, -0.010008164822017, -0.010572200761984,
#'            -0.010939294762200)))
#'
#' all.equal(r$rho_SA_p, 1e-9*c(-0.617330965378778, -0.618403843947729,
#'         -0.655302447133274, -0.764800777480716, -0.792168044875350,
#'         -0.810125648949170))
#'
#' all.equal(r$rho_CT_p, 1e-8*c(-0.116597992537549, -0.117744271236102,
#'         -0.141712549466964, -0.214414626736539, -0.237704139801551,
#'         -0.255296606034074))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_second_derivatives.html}
gsw_rho_second_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_rho_second_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            rho_SA_SA=double(n), rho_SA_CT=double(n), rho_CT_CT=double(n), rho_SA_p=double(n), rho_CT_p=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$rho_SA_SA[bad] <- NA
    ##37 r$rho_SA_CT[bad] <- NA
    ##37 r$rho_CT_CT[bad] <- NA
    ##37 r$rho_SA_p[bad] <- NA
    ##37 r$rho_CT_p[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$rho_SA_SA) <- dim
        dim(r$rho_SA_CT) <- dim
        dim(r$rho_CT_CT) <- dim
        dim(r$rho_SA_p) <- dim
        dim(r$rho_CT_p) <- dim
    }
    list(rho_SA_SA=r$rho_SA_SA, rho_SA_CT=r$rho_SA_CT, rho_CT_CT=r$rho_CT_CT, rho_SA_p=r$rho_SA_p, rho_CT_p=r$rho_CT_p)
}


#' Second Derivatives of Density wrt Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{rho_SA_SA} [ (kg/m^3)/(g/kg)^2 ], the second derivative of
#' density with respect to Absolute Salinity,
#' \code{rho_SA_h} [ (g/kg)/(g/kg)/(J/kg)], the derivative of
#' density with respect to Absolute Salinity and enthalpy,
#' and \code{rho_h_h} [ (kg/m^3)/(J/kg)^2 ], the second derivative of
#' density with respect to enthalpy.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_rho_second_derivatives_wrt_enthalpy(SA, CT, p)
#'
#' stopifnot(all.equal(r$rho_SA_SA/1e-3, c(0.207325714908677, 0.207131960039965,
#'             0.192001360206293, 0.133399974356615, 0.116504845152129,
#'             0.103433221305694)))
#'
#' stopifnot(all.equal(r$rho_SA_h/1e-6, c(-0.459053080088382, -0.460370569872258,
#'             -0.498605615416296, -0.642833108550133, -0.682091962941161,
#'             -0.706793055445909)))
#'
#' stopifnot(all.equal(r$rho_h_h/1e-9, c(-0.454213854637790, -0.455984900239309,
#'             -0.499870030989387, -0.628337767293403, -0.664021595759308,
#'             -0.687367088752173)))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_second_derivatives_wrt_enthalpy.html}
gsw_rho_second_derivatives_wrt_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_rho_second_derivatives_wrt_enthalpy", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            rho_SA_SA=double(n), rho_SA_h=double(n), rho_h_h=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$rho_SA_SA[bad] <- NA
    ##37 r$rho_SA_h[bad] <- NA
    ##37 r$rho_h_h[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$rho_SA_SA) <- dim
        dim(r$rho_SA_h) <- dim
        dim(r$rho_h_h) <- dim
    }
    list(rho_SA_SA=r$rho_SA_SA, rho_SA_h=r$rho_SA_h, rho_h_h=r$rho_h_h)
}


#' In-situ Density of Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return in-situ density [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <-  c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' rho <- gsw_rho_t_exact(SA, t, p)
#' stopifnot(all.equal(rho/1e3, c(1.021840173185531, 1.022262689926782, 1.024427715941676,
#'                                1.027790201811623, 1.029837714725961, 1.032002404116447)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_rho_t_exact.html}
gsw_rho_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_rho_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Absolute Salinity Anomaly Ratio
#'
#' @template teos10template
#'
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return a list containing \code{SAAR}, which is
#' the (unitless) Absolute Salinity Anomaly Ratio, and \code{in_ocean}
#' is set to 1 if \code{SAAR} is nonzero, or to 0 otherwise.
#'
#' @section Bugs:
#' The definition of \code{in_ocean} is incorrect, because the C function named
#' \code{gsw_saar}, which is called by the present R function, does not calculate
#' \code{in_ocean}, as the base Matlab function named \code{gsw_SAAR} does. However,
#' examination of the Matlab code shows that \code{in_ocean} is set to 0 along
#' with \code{SAAR}, whenever the original estimate of the latter is nonfinite.
#' Thus, points that would be signalled as being on the land by the Matlab code
#' are indicated in the same way with the present R function. However, other points
#' may also be indicated as being on land, if \code{SAAR} is simply zero in the
#' first calculation. Whether this poses a problem in practice is an open question,
#' since it seems likely that this function would only be called with oceanic
#' locations, anyway. If problems arise for users, a patch can be written to
#' improve things.
#'
#' @examples
#' p <- c(10, 50, 125, 250, 600, 1000)
#' longitude <- c(188, 188, 188, 188, 188, 188)
#' latitude <- c(4, 4, 4, 4, 4, 4)
#' SAAR <- gsw_SAAR(p, longitude, latitude)
#' stopifnot(all.equal(1e3*SAAR$SAAR, c(0.004794295602143, 0.007668755837570, 0.018919828449091,
#'                                      0.077293264028981, 0.161974583039298, 0.270652408428964)))
#' stopifnot(all.equal(SAAR$in_ocean, rep(1, 6)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SAAR.html}
gsw_SAAR <- function(p, longitude, latitude)
{
    l <- argfix(list(p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_SAAR",
        p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
        n=as.integer(n), SAAR=double(n), inocean=integer(n), NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)
    ##37 r$SAAR[bad] <- NA
    ##37 r$inocean[bad] <- NA
    if (is.matrix(p)) {
        dim(r$SAAR) <- dim(p)
        dim(r$inocean) <- dim(p)
    }
    r$in_ocean <- ifelse(r$SAAR == 0, 0, 1)
    list(SAAR=r$SAAR, in_ocean=r$in_ocean)
}


#' Compute Absolute Salinity at Freezing Conservative Temperature
#'
#' @template teos10template
#'
#' @template CTtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' CT <- c(-0.11901, -0.15608, -0.72138, -1.97738, -2.31728, -2.56764)
#' p <- c(       10,       50,      125,      250,      600,     1000)
#' saturation_fraction <- 1
#' SA <- gsw_SA_freezing_from_CT(CT, p, saturation_fraction)
#' stopifnot(all.equal(SA, c(2.280500648179144, 2.416867651098550, 11.973503162175106,
#'                           32.868973869711390, 34.017513292374431, 32.859871943514150)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_freezing_from_CT.html}
gsw_SA_freezing_from_CT <- function(CT, p, saturation_fraction=1)
{
    l <- argfix(list(CT=CT, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_freezing_from_CT", NAOK=TRUE, PACKAGE="gsw",
               CT=as.double(l$CT), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(CT))
        dim(rval) <- dim(CT)
    rval
}


#' Compute Absolute Salinity at Freezing Point (Polynomial version)
#'
#' @template teos10template
#'
#' @template CTtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' CT <- c(-0.11901, -0.15608, -0.72138, -1.97738, -2.31728, -2.56764)
#' p <- c(       10,       50,      125,      250,      600,     1000)
#' saturation_fraction <- 1
#' SA <- gsw_SA_freezing_from_CT_poly(CT, p, saturation_fraction)
#' stopifnot(all.equal(SA, c(2.281810267792954, 2.418134292641376, 11.971996354752958,
#'                           32.867931280363138, 34.015087798162732, 32.856434894818825)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_freezing_from_CT_poly.html}
gsw_SA_freezing_from_CT_poly <- function(CT, p, saturation_fraction=1)
{
    l <- argfix(list(CT=CT, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_freezing_from_CT_poly", NAOK=TRUE, PACKAGE="gsw",
               CT=as.double(l$CT), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(CT))
        dim(rval) <- dim(CT)
    rval
}


#' Compute Absolute Salinity at Freezing in-situ Temperature
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' t <- c(-0.11901, -0.15608, -0.72138, -1.97738, -2.31728, -2.56764)
#' p <- c(      10,       50,      125,      250,      600,     1000)
#' saturation_fraction <- 1
#' SA <- gsw_SA_freezing_from_t(t, p, saturation_fraction)
#' stopifnot(all.equal(SA, c(2.015798440008186, 2.150742019102164, 11.679080083422074,
#'                           32.844196564019278, 34.138949682974413, 33.100945437175568)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_freezing_from_t.html}
gsw_SA_freezing_from_t <- function(t, p, saturation_fraction=1)
{
    l <- argfix(list(t=t, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_freezing_from_t", NAOK=TRUE, PACKAGE="gsw",
               t=as.double(l$t), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Compute Absolute Salinity at Freezing in-situ Temperature (Polynomial version)
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' t <- c(-0.11901, -0.15608, -0.72138, -1.97738, -2.31728, -2.56764)
#' p <- c(      10,       50,      125,      250,      600,     1000)
#' saturation_fraction <- 1
#' SA <- gsw_SA_freezing_from_t_poly(t, p, saturation_fraction)
#' stopifnot(all.equal(SA, c(2.017072489768256, 2.151989342038462, 11.677649626115608,
#'                           32.843128114999026, 34.136459306273451, 33.097427522625182)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_freezing_from_t_poly.html}
gsw_SA_freezing_from_t_poly <- function(t, p, saturation_fraction=1)
{
    l <- argfix(list(t=t, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_freezing_from_t_poly", NAOK=TRUE, PACKAGE="gsw",
               t=as.double(l$t), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n),
               rval=double(n))$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Compute Absolute Salinity from Density, etc
#'
#' @template teos10template
#'
#' @template rhotemplate
#' @template CTtemplate
#' @template ptemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' rho <- c(1021.8482, 1022.2647, 1024.4207, 1027.7841, 1029.8287, 1031.9916)
#' CT <-c(    28.7856,   28.4329,   22.8103,   10.2600,    6.8863,    4.4036)
#' p <- c(         10,        50,       125,       250,       600,      1000)
#' SA <- gsw_SA_from_rho(rho, CT, p)
#' stopifnot(all.equal(SA, c(34.712080120418108, 34.891723808488869, 35.026202257609505,
#'                           34.847160842234572, 34.736398269039945, 34.732228881079742)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_from_rho.html}
gsw_SA_from_rho <- function(rho, CT, p)
{
    l <- argfix(list(rho=rho, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_from_rho",
               SA=as.double(l$rho), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$rho) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(rho))
        dim(rval) <- dim(rho)
    rval
}


#' Convert from Practical Salinity to Absolute Salinity
#'
#' Calculate Absolute Salinity from Practical Salinity, pressure,
#' longitude, and latitude.
#'
#' If SP is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' SP <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' lat <- c(     4,       4,       4,       4,       4,       4)
#' long <- c(  188,     188,     188,     188,     188,     188)
#' SA <- gsw_SA_from_SP(SP, p, long, lat)
#' stopifnot(all.equal(SA, c(34.711778344814114, 34.891522618230098, 35.025544862476920,
#'                           34.847229026189588, 34.736628474576051, 34.732363065590846)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_from_SP.html}
gsw_SA_from_SP <- function(SP, p, longitude, latitude)
{
    if (missing(SP)) stop("must supply SP")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that SP is a matrix defined on lon and lat
    if (is.matrix(SP)) {
        dim <- dim(SP)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(SP=SP, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_from_SP",
               SP=as.double(l$SP), p=as.double(l$p),
               longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SP) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Convert from Practical Salinity to Absolute Salinity (Baltic)
#'
#' Calculate Absolute Salinity from Practical Salinity, pressure,
#' longitude, and latitude.
#'
#' If SP is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' SP <- c( 6.5683, 6.6719, 6.8108, 7.2629, 7.4825, 10.2796)
#' lon <- c(    20,     20,     20,     20,     20,      20)
#' lat <- c(    59,     59,     59,     59,     59,      59)
#' SA <- gsw_SA_from_SP_Baltic(SP, lon, lat)
#' stopifnot(all.equal(SA, c(6.669945432342856, 6.773776430742856, 6.912986138057142,
#'                           7.366094191885713, 7.586183837142856, 10.389520570971428)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_from_SP_Baltic.html}
gsw_SA_from_SP_Baltic <- function(SP, longitude, latitude)
{
    if (missing(SP)) stop("must supply SP")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that SP is a matrix defined on lon and lat
    if (is.matrix(SP)) {
        dim <- dim(SP)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(SP=SP, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_from_SP_Baltic",
               SP=as.double(l$SP), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SP) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Absolute Salinity from Preformed Salinity
#'
#' Calculate Absolute Salinity from Preformed Salinity, pressure,
#' longitude, and latitude.
#'
#' If Sstar is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' @template teos10template
#'
#' @template Sstartemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Absolute Salinity [ g/kg ]
#' @examples
#' Sstar <- c(34.7115, 34.8912, 35.0247, 34.8436, 34.7291, 34.7197)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' lat <- c(     4,       4,       4,       4,       4,       4)
#' long <- c(  188,     188,     188,     188,     188,     188)
#' SA <- gsw_SA_from_Sstar(Sstar, p, long, lat)
#' stopifnot(all.equal(SA, c(34.711724663585905, 34.891561223296009, 35.025594598699882,
#'                           34.847235885385913, 34.736694493054166, 34.732387111902753)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SA_from_Sstar.html}
gsw_SA_from_Sstar <- function(Sstar, p, longitude, latitude)
{
    if (missing(Sstar)) stop("must supply Sstar")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that Sstar is a matrix defined on lon and lat
    if (is.matrix(Sstar)) {
        dim <- dim(Sstar)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(Sstar=Sstar, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SA_from_Sstar",
               Sstar=as.double(l$Sstar), p=as.double(l$p),
               longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$Sstar) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(Sstar))
        dim(rval) <- dim(Sstar)
    rval
}

#' Practical Salinity from Salinometer Reading
#'
#' Calculate Practical Salinity from salinometer readings
#' of conductivity ratio and bath temperature.
#'
#' @template teos10template
#'
#' @param ratio Conductivity ratio [ unitless ].
#' (This is called \code{Rt} in the GSW documentation.)
#' @param temperature Bath temperature [ degC ].
#' (This is called \code{t} in the GSW documentation.)
#' @return Practical salinity on the PSS-77 scale [ unitless ]
#' @examples
#' ratio <- c( 0.9345,  0.95123,  0.91807,  0.8886, 0.8169, 0.6687)
#' temperature <-  c(28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036)
#' SP <- gsw_SP_salinometer(ratio, temperature)
#' stopifnot(all.equal(SP,
#'         c(32.431728787558541, 33.085035719966307, 31.800791917322833,
#'             30.692490757036179, 27.979281308696116, 22.474597460508491)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_salinometer.html}
gsw_SP_salinometer <- function(ratio, temperature)
{
    if (missing(ratio)) stop("must provide ratio")
    if (missing(temperature)) stop("must provide temperature")
    l <- argfix(list(ratio=ratio, temperature=temperature))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SP_salinometer",
        ratio=as.double(l$ratio), temperature=as.double(l$temperature),
        n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    if (is.matrix(ratio))
        dim(rval) <- dim(ratio)
    rval
}

#' Potential density anomaly referenced to 0 dbar
#'
#' This uses the 75-term density equation, and returns
#' potential density referenced to a pressure of 0 dbar,
#' minus 1000 kg/m^3.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential density anomaly [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' sigma0 <- gsw_sigma0(SA,CT)
#' stopifnot(all.equal(sigma0, c(21.797900819337656, 22.052215404397316, 23.892985307893923,
#'                               26.667608665972011, 27.107380455119710, 27.409748977090885)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sigma0.html}
gsw_sigma0 <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sigma0",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential density anomaly referenced to 1000 dbar
#'
#' This uses the 75-term density equation, and returns
#' potential density referenced to a pressure of 1000 dbar,
#' minus 1000 kg/m^3.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential density anomaly [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' sigma1 <- gsw_sigma1(SA,CT)
#' stopifnot(all.equal(sigma1, c(25.955618850310202, 26.213131422420247, 28.125423775188438,
#'                               31.120360038882382, 31.637724222733368, 32.002453224572037)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sigma1.html}
gsw_sigma1 <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sigma1",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential density anomaly referenced to 2000 dbar
#'
#' This uses the 75-term density equation, and returns
#' potential density referenced to a pressure of 2000 dbar,
#' minus 1000 kg/m^3.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential density anomaly [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' sigma2 <- gsw_sigma2(SA,CT)
#' stopifnot(all.equal(sigma2, c(30.023152223799116, 30.283783336283477, 32.265556840289719,
#'                               35.474550881051073, 36.067289438047737, 36.492606494879510)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sigma2.html}
gsw_sigma2 <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sigma2",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential density anomaly referenced to 3000 dbar
#'
#' This uses the 75-term density equation, and returns
#' potential density referenced to a pressure of 3000 dbar,
#' minus 1000 kg/m^3.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential density anomaly with reference pressure 3000 dbar [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' sigma3 <- gsw_sigma3(SA,CT)
#' stopifnot(all.equal(sigma3, c(34.003747849903675, 34.267409891564057, 36.316415829697917,
#'                               39.732367693977039, 40.397934186745033, 40.881795690566832)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sigma3.html}
gsw_sigma3 <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sigma3",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Potential density anomaly referenced to 4000 dbar
#'
#' This uses the 75-term density equation, and returns
#' potential density referenced to a pressure of 4000 dbar,
#' minus 1000 kg/m^3.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return potential density anomaly with reference pressure 4000 dbar [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' sigma4 <- gsw_sigma4(SA,CT)
#' stopifnot(all.equal(sigma4, c(37.900374609834898, 38.166979617032439, 40.280876075282549,
#'                               43.896091033421953, 44.631677245327637, 45.171817312020039)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sigma4.html}
gsw_sigma4 <- function(SA, CT)
{
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sigma4",
               SA=as.double(l$SA), CT=as.double(l$CT),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Sound speed
#'
#' Speed of sound in seawater, using the 75-term equation for specific volume.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return sound speed [ m/s ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' speed <- gsw_sound_speed(SA,CT,p)
#' stopifnot(all.equal(speed/1e3, c(1.542426412426373, 1.542558891663385, 1.530801535436184,
#'                                  1.494551099295314, 1.487622786765276, 1.484271672296205)))
#' @family things related to sound
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sound_speed.html}
gsw_sound_speed <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sound_speed",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Sound speed in ice
#'
#' Speed of sound in ice.
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return sound speed [ m/s ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <- c(      10,       50,      125,      250,      600,    1000)
#' speed <- gsw_sound_speed_ice(t, p)
#' stopifnot(all.equal(speed/1e3, c(3.111311360346254, 3.116492565497544, 3.115833462003452,
#'                                  3.115637032488204, 3.115377253092692, 3.113321384499191)))
## @family things related to ice
#' @family things related to sound
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sound_speed_ice.html}
gsw_sound_speed_ice <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sound_speed_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Sound Speed in Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return sound speed [ m/s ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' sound_speed <- gsw_sound_speed_t_exact(SA,CT,p)
#' stopifnot(all.equal(sound_speed/1e3, c(1.542615803587414, 1.542703534065789, 1.530844979136360,
#'                                        1.494409996920661, 1.487377102518027, 1.483934609078705)))
#' @family things related to sound
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_sound_speed_t_exact.html}
gsw_sound_speed_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_sound_speed_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Specific Volume of Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return Specific volume (1/density)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' specvol <- gsw_specvol(SA, CT, p)
#' stopifnot(all.equal(specvol*1e3,
#'     c(0.978626852431313, 0.978222365701325, 0.976155264597929,
#'       0.972961258011157, 0.971026719344908, 0.968989944622149)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol.html}
gsw_specvol  <- function(SA, CT, p)
{
    1 / gsw_rho(SA, CT, p)
}

#' Specific Volume, alpha, and beta
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return a list holding \code{specvol}, the specific volume [ m^3/kg ], \code{alpha},
#' the thermal expansion coefficient [ 1/degC ], and \code{beta}, the haline contraction
#' coefficient [ kg/g ].
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_specvol_alpha_beta(SA, CT, p)
#' stopifnot(all.equal(r$specvol/1e-3, c(0.978626852431313, 0.978222365701325, 0.976155264597929,
#'                                       0.972961258011157, 0.971026719344908, 0.968989944622149)))
#' stopifnot(all.equal(r$alpha/1e-3, c(0.324638934509245, 0.322655537959731, 0.281145723210171,
#'                                     0.173199716344780, 0.146289673594824, 0.129414845334599)))
#' stopifnot(all.equal(r$beta/1e-3, c(0.717483987596135, 0.717647512290095, 0.726211643644768,
#'                                    0.750500751749777, 0.755052064788492, 0.757050813384370)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_alpha_beta.html}
gsw_specvol_alpha_beta  <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_specvol_alpha_beta",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            specvol=double(n), alpha=double(n), beta=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$specvol[bad] <- NA
    ##37 r$alpha[bad] <- NA
    ##37 r$beta[bad] <- NA
    if (is.matrix(CT)) {
        dim <- dim(CT)
        dim(r$specvol) <- dim
        dim(r$alpha) <- dim
        dim(r$beta) <- dim
    }
    list(specvol=r$specvol, alpha=r$alpha, beta=r$beta)
}


#' Specific volume anomaly [standard] (75-term equation)
#'
#' Note that the TEOS function named \code{specific_volume_anomaly} is not
#' provided in the C library, so it is not provided in R, either.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' a <- gsw_specvol_anom_standard(SA, CT, p)
#' stopifnot(all.equal(a*1e5, c(0.601051894897400, 0.578609769250563, 0.405600538950092,
#'                              0.142190453761838, 0.104335535578967, 0.076383389577725)))
#' @return Specific volume anomaly [ m^3/kg ]
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_anom_standard.html}
gsw_specvol_anom_standard <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_specvol_anom_standard", # FIXME: why the "standard" in name?
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' First Derivatives of Specific Volume
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{v_SA} [ (m^3/kg)/(g/kg) ], the derivative of
#' specific volume with respect to Absolute Salinity, \code{v_CT} [ (m^3/kg)/degC],
#' the derivative of specific volume with respect to Conservative Temperature, and
#' \code{v_p} [ (m^3/kg)/dbar ], the derivative of specific volume with respect
#' to pressure. (Note that the last quantity is denoted \code{v_P} in the
#' documentation for the Matlab function.)
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_specvol_first_derivatives(SA, CT, p)
#' stopifnot(all.equal(r$v_SA/1e-6,
#'     c(-0.702149096451073, -0.702018847212088, -0.708895319156155,
#'       -0.730208155560782, -0.733175729406169, -0.733574625737474)))
#' stopifnot(all.equal(r$v_CT/1e-6,
#'     c(0.317700378655437, 0.315628863649601, 0.274441877830800,
#'       0.168516613901993, 0.142051181824820, 0.125401683814057)))
#' stopifnot(all.equal(r$v_p/1e-12,
#'     c(-0.402527990904794, -0.402146232553089, -0.406663124765787,
#'      -0.423877042622481, -0.426198431093548, -0.426390351853055)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_first_derivatives.html}
gsw_specvol_first_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_specvol_first_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(CT), p=as.double(l$p), n=as.integer(n),
            v_SA=double(n), v_CT=double(n), v_p=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$v_SA[bad] <- NA
    ##37 r$v_CT[bad] <- NA
    ##37 r$v_p[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$v_SA) <- dim
        dim(r$v_CT) <- dim
        dim(r$v_p) <- dim
    }
    list(v_SA=r$v_SA, v_CT=r$v_CT, v_p=r$v_p)
}


#' First Derivatives of Specific Volume wrt Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{v_SA_wrt_h} [ (m^3/kg)/(g/kg) ] and \code{v_h}.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' r <- gsw_specvol_first_derivatives_wrt_enthalpy(SA, CT, p)
#' stopifnot(all.equal(r$v_SA_wrt_h/1e-6,
#'     c(-0.702143511679586, -0.701991101310494, -0.708834353735310,
#'       -0.730130919555592, -0.733018321892082, -0.733342002723321)))
#' stopifnot(all.equal(r$v_h/1e-10,
#'     c(0.795862623587769, 0.790648383268264, 0.687443468257647,
#'       0.422105846942233, 0.355778874334799, 0.314053366403993)))
#' @family things related to enthalpy
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_first_derivatives_wrt_enthalpy.html}
gsw_specvol_first_derivatives_wrt_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_specvol_first_derivatives_wrt_enthalpy", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(CT), p=as.double(l$p), n=as.integer(n),
            v_SA_wrt_h=double(n), v_h=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$v_SA_wrt_h[bad] <- NA
    ##37 r$v_CT_h[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$v_SA_wrt_h) <- dim
        dim(r$v_h) <- dim
    }
    list(v_SA_wrt_h=r$v_SA_wrt_h, v_h=r$v_h)
}


#' Specific Volume of Ice
#'
#' @template teos10template
#'
#' @template ttemplate
#' @template ptemplate
#' @return Specific volume [ m^3/kg ]
#' @examples
#' t <- c(-10.7856, -13.4329, -12.8103, -12.2600,  -10.8863,  -8.4036)
#' p <- c(      10,       50,      125,      250,       600,     1000)
#' v <- gsw_specvol_ice(t, p)
#' stopifnot(all.equal(v, c(0.001088982980677, 0.001088489459509, 0.001088499019939,
#'                          0.001088433747301, 0.001088223220685, 0.001088135464776)))
#' @family things related to density
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_ice.html}
gsw_specvol_ice  <- function(t, p)
{
    l <- argfix(list(t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_specvol_ice",
               t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(t))
        dim(rval) <- dim(t)
    rval
}


#' Second Derivatives of Specific Volume
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{specvol_SA_SA} [ (m^3/kg)/(g/kg)^2 ], the second derivative of
#' specific volume with respect to Absolute Salinity,
#' \code{specvol_SA_CT} [ (m^3/kg)/(g/kg)/degC ], the derivative of
#' specific volume with respect to Absolute Salinity and Conservative Temperature,
#' \code{specvol_CT_CT} [ (m^3/kg)/degC^2 ], the second derivative of
#' specific volume with respect to Conservative Temperature,
#' \code{specvol_SA_p} [ (m^3/kg)/(g/kg)/Pa ], the derivative of specific volume with respect to Absolute
#' Salinity and pressure, and \code{specvol_CT_p} [ (m^3/kg)/K/dbar ], the derivative of specific
#' volume with respect to Conservative Temperature and pressure.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#'
#' r <- gsw_specvol_second_derivatives(SA, CT, p)
#'
#' stopifnot(all.equal(r$specvol_SA_SA/1e-8, c(0.080906777599140,
#'             0.080915086639384, 0.084568844270812, 0.096725108896007,
#'             0.099111765836648, 0.100302277946072)))
#'
#' stopifnot(all.equal(r$specvol_SA_CT/1e-8, c(0.129965332117084,
#'             0.130523053162130, 0.149555815430615, 0.217023290441810,
#'             0.233892039070486, 0.243659989480325)))
#'
#' stopifnot(all.equal(r$specvol_CT_CT/1e-7, c(0.071409582006642,
#'             0.071582962051991, 0.077436153664104, 0.095329736274850,
#'             0.100105336953738, 0.103044572835472)))
#'
#' stopifnot(all.equal(r$specvol_SA_p/1e-14, c(0.116889015000936,
#'             0.116897424150385, 0.121500614193893, 0.136008673596132,
#'             0.139023051292893, 0.140581903529772)))
#'
#' stopifnot(all.equal(r$specvol_CT_p/1e-14, c(0.085542828707964,
#'             0.086723632576213, 0.112156562396990, 0.188269893599500,
#'             0.211615556759369, 0.228609575049911)))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_second_derivatives.html}
gsw_specvol_second_derivatives <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_specvol_second_derivatives", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            specvol_SA_SA=double(n), specvol_SA_CT=double(n), specvol_CT_CT=double(n), specvol_SA_p=double(n), specvol_CT_p=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$specvol_SA_SA[bad] <- NA
    ##37 r$specvol_SA_CT[bad] <- NA
    ##37 r$specvol_CT_CT[bad] <- NA
    ##37 r$specvol_SA_p[bad] <- NA
    ##37 r$specvol_CT_p[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$specvol_SA_SA) <- dim
        dim(r$specvol_SA_CT) <- dim
        dim(r$specvol_CT_CT) <- dim
        dim(r$specvol_SA_p) <- dim
        dim(r$specvol_CT_p) <- dim
    }
    list(specvol_SA_SA=r$specvol_SA_SA, specvol_SA_CT=r$specvol_SA_CT, specvol_CT_CT=r$specvol_CT_CT, specvol_SA_p=r$specvol_SA_p, specvol_CT_p=r$specvol_CT_p)
}


#' Second Derivatives of Specific Volume wrt Enthalpy
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return A list containing \code{specvol_SA_SA} [ (m^3/kg)/(g/kg)^2 ], the second derivative of
#' specific volume with respect to Absolute Salinity,
#' \code{specvol_SA_h} [ (m^3/kg)/(g/kg)/(J/kg) ], the derivative of
#' specific volume with respect to Absolute Salinity and enthalpy,
#' and \code{specvol_h_h} [ (m^3/kg)/(J/kg)^2 ], the second derivative of
#' specific volume with respect to enthalpy.
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#'
#' r <- gsw_specvol_second_derivatives_wrt_enthalpy(SA, CT, p)
#'
#' stopifnot(all.equal(r$specvol_SA_SA/1e-8, c(0.080898741086877,
#'             0.080931595349498, 0.084648485333225, 0.096952812049233,
#'             0.099684475381589, 0.101288447077547)))
#' stopifnot(all.equal(r$specvol_SA_h/1e-12, c(0.325437133570796,
#'             0.327060462851431, 0.375273569184178, 0.545188833073084,
#'             0.589424881889351, 0.616101548209175)))
#' stopifnot(all.equal(r$specvol_h_h/1e-15, c(0.447949998681476, 0.449121446914278,
#'             0.485998151346315, 0.598480711660961, 0.628708349875318,
#'             0.647433212216398)))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_second_derivatives_wrt_enthalpy.html}
gsw_specvol_second_derivatives_wrt_enthalpy <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_specvol_second_derivatives_wrt_enthalpy", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n),
            specvol_SA_SA=double(n), specvol_SA_h=double(n), specvol_h_h=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    ##37 r$specvol_SA_SA[bad] <- NA
    ##37 r$specvol_SA_h[bad] <- NA
    ##37 r$specvol_h_h[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$specvol_SA_SA) <- dim
        dim(r$specvol_SA_h) <- dim
        dim(r$specvol_h_h) <- dim
    }
    list(specvol_SA_SA=r$specvol_SA_SA, specvol_SA_h=r$specvol_SA_h, specvol_h_h=r$specvol_h_h)
}


#' Specific Volume of Seawater
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return Specific volume [ m^3/kg ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' v <- gsw_specvol_t_exact(SA, t, p)
#' stopifnot(all.equal(v*1e3, c(0.978626625025472, 0.978222143734527, 0.976154768597586,
#'                              0.972961211575438, 0.971026779948624, 0.968989990731808)))
#' @family things related to density
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_specvol_t_exact.html}
gsw_specvol_t_exact  <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_specvol_t_exact",
               SA=as.double(l$SA), CT=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Convert from Electrical Conductivity to Practical Salinity
#'
#' @template teos10template
#'
#' @template Ctemplate
#' @template ttemplate
#' @template ptemplate
#' @return Practical Salinity (PSS-78) [ unitless ]
#' @examples
#' C <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' t <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(     10,      50,     125,     250,     600,    1000)
#' SP <- gsw_SP_from_C(C,t,p)
#' stopifnot(all.equal(SP,  c(20.009869599086951, 20.265511864874270, 22.981513062527689,
#'                            31.204503263727982, 34.032315787432829, 36.400308494388170)))
#' @family things related to salinity
#' @family things related to conductivity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_from_C.html}
gsw_SP_from_C <- function(C, t, p)
{
    l <- argfix(list(C=C, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SP_from_C",
               C=as.double(l$C), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$C) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(C))
        dim(rval) <- dim(C)
    rval
}


#' Convert from Absolute Salinity to Practical Salinity
#'
#' Calculate Practical Salinity from Absolute Salinity, pressure,
#' longitude, and latitude.
#'
#' If SP is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' Note: unlike the corresponding Matlab function, this does not
#' return a flag indicating whether the location is in the ocean.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Practical Salinity (PSS-78) [ unitless ]
#' @examples
#' SA <-   c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <-    c(     10,      50,     125,     250,     600,    1000)
#' lat <-  c(      4,       4,       4,       4,       4,       4)
#' long <- c(    188,     188,     188,     188,     188,     188)
#' SP <- gsw_SP_from_SA(SA,p,long,lat)
#' stopifnot(all.equal(SP, c(34.548721553448317, 34.727477488096639, 34.860554877708005,
#'                           34.680971112271791, 34.567971663653388, 34.560036751118204)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_from_SA.html}
gsw_SP_from_SA <- function(SA, p, longitude, latitude)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that SP is a matrix defined on lon and lat
    if (is.matrix(SA)) {
        dim <- dim(SA)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(SA=SA, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_SP_from_SA",
               SA=as.double(l$SA), p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), SP=double(n), NAOK=TRUE, PACKAGE="gsw")$SP
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$longitude)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Calculate Practical Salinity from Knudsen Salinity
#'
#' @param SK Knudsen Salinity [ parts per thousand, ppt ]
#' @return Practical Salinity (PSS-78) [ unitless ]
#' @examples
#' SK <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' SP <- gsw_SP_from_SK(SK)
#' stopifnot(all.equal(SP, c(34.548342096952908, 34.727295637119113, 34.860409847645435,
#'                           34.680755706371187, 34.567658670360110, 34.559651800554022)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_from_SK.html}
gsw_SP_from_SK <- function(SK)
{
    if (missing(SK)) stop("must supply SK")
    n <- length(SK)
    rval <- .C("wrap_gsw_SP_from_SK",
               SA=as.double(SK), n=as.integer(n), SP=double(n), NAOK=TRUE, PACKAGE="gsw")$SP
    if (is.matrix(SK))
        dim(rval) <- dim(SK)
    rval
}

#' Calculate Practical Salinity from Reference Salinity
#'
#' @template teos10template
#'
#' @template SRtemplate
#' @return Practical Salinity (PSS-78) [ unitless ]
#' @examples
#' SR <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' SP <- gsw_SP_from_SR(SR)
#' stopifnot(all.equal(SP, c(34.386552667080714, 34.564513505458834, 34.696889296869848,
#'                           34.518231743800094, 34.405762086435850, 34.397799632817147)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_from_SR.html}
gsw_SP_from_SR <- function(SR)
{
    if (missing(SR)) stop("must supply SR")
    n <- length(SR)
    rval <- .C("wrap_gsw_SP_from_SR",
               SA=as.double(SR), n=as.integer(n), SP=double(n), NAOK=TRUE, PACKAGE="gsw")$SP
    if (is.matrix(SR))
        dim(rval) <- dim(SR)
    rval
}

#' Practical Salinity from Preformed Salinity
#'
#' @template teos10template
#'
#' @template Sstartemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Practical Salinity (PSS-78) [ unitless ]
#' @examples
#' Sstar <- c(34.7115, 34.8912, 35.0247, 34.8436, 34.7291, 34.7197)
#' p <- c(         10,      50,     125,     250,     600,    1000)
#' longitude <- 188
#' latitude <- 4
#' SP <- gsw_SP_from_Sstar(Sstar, p, longitude, latitude)
#' stopifnot(all.equal(SP, c(34.548646570969929, 34.727538423586189, 34.860549501859502,
#'                           34.681006826476434, 34.568065697992346, 34.560023926979518)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SP_from_Sstar.html}
gsw_SP_from_Sstar <- function(Sstar, p, longitude, latitude)
{
    if (missing(Sstar)) stop("must supply Sstar")
    l <- argfix(list(Sstar=Sstar, p=p, longitude=longitude, latitude=latitude))
    if (is.null(l$p)) stop("must supply p")
    if (is.null(l$longitude)) stop("must supply longitude")
    if (is.null(l$latitude)) stop("must supply latitude")
    n <- length(Sstar)
    rval <- .C("wrap_gsw_SP_from_Sstar",
               Sstar=as.double(l$Sstar), p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$Sstar) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(Sstar))
        dim(rval) <- dim(Sstar)
    rval
}


#' Sea ice Fraction to Cool Seawater to Freezing
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @template SA_seaicetemplate
#' @template t_seaicetemplate
#' @return a list containing \code{SA_freeze}, \code{CT_freeze} and \code{w_Ih}.
#' @examples
#' SA <- c(      34.7118, 34.8915, 35.0256, 34.8472, 34.7366,  34.7324)
#' CT <- c(      -1.7856, -1.4329, -1.8103, -1.2600, -0.6886,   0.4403)
#' p <- c(            10,      50,     125,     250,     600,     1000)
#' SA_seaice <- c(     5,     4.8,     3.5,     2.5,       1,      0.4)
#' t_seaice <- c(-5.7856, -4.4329, -3.8103, -4.2600, -3.8863,  -3.4036)
#' r <- gsw_seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice)
#' stopifnot(all.equal(r$SA_freeze, c(34.671271207148074, 34.703449677481224, 34.950192062047861,
#'                                    34.525277379661880, 34.077349518029997, 33.501836583274191)))
#' stopifnot(all.equal(r$CT_freeze, c(-1.895419711000293, -1.927935638317893, -1.999943183939312,
#'                                    -2.071677444370745, -2.318866154643864, -2.603185031462614)))
#' stopifnot(all.equal(r$w_seaice, c(0.001364063868629, 0.006249283768465, 0.002391958850970,
#'                                   0.009952101583387, 0.019541106156815, 0.035842627277027)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_seaice_fraction_to_freeze_seawater.html}
gsw_seaice_fraction_to_freeze_seawater <- function(SA, CT, p, SA_seaice, t_seaice)
{
    l <- argfix(list(SA=SA, CT=CT, p=p, SA_seaice=SA_seaice, t_seaice=t_seaice))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_seaice_fraction_to_freeze_seawater", NAOK=TRUE, PACKAGE="gsw",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p), SA_seiace=as.double(l$SA_seaice), t_seaice=as.double(l$t_seaice),
            n=as.integer(n), SA_freeze=double(n), CT_freeze=double(n), w_seaice=double(n))
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p) | !is.finite(l$SA_seaice) | !is.finite(l$t_seaice)
    ##37 r$SA_freeze[bad] <- NA
    ##37 r$CT_freeze[bad] <- NA
    ##37 r$w_freeze[bad] <- NA
    if (is.matrix(SA)) {
        dim <- dim(SA)
        dim(r$SA_freeze) <- dim
        dim(r$CT_freeze) <- dim
        dim(r$w_seaice) <- dim
    }
    list(SA_freeze=r$SA_freeze, CT_freeze=r$CT_freeze, w_seaice=r$w_seaice)
}


#' Calculate Reference Salinity from Practical Salinity
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @return Reference Salinity [ g/kg ]
#' @examples
#' SP <- c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' SR <- gsw_SR_from_SP(SP)
#' stopifnot(all.equal(SR, c(34.711611927085727, 34.891255045714303, 35.024882197714305,
#'                           34.844535778285724, 34.731002934857159, 34.722965211428587)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_SR_from_SP.html}
gsw_SR_from_SP <- function(SP)
{
    if (missing(SP)) stop("must supply SP")
    n <- length(SP)
    rval <- .C("wrap_gsw_SR_from_SP",
               SP=as.double(SP), n=as.integer(n), SR=double(n), NAOK=TRUE, PACKAGE="gsw")$SR
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Seawater Spiciness at p=0 dbar
#'
#' Calculate seawater spiciness referenced to 0 dbar (i.e. the surface).
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return spiciness [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' spiciness <- gsw_spiciness0(SA, CT)
#' stopifnot(all.equal(spiciness, c(5.728998558542941, 5.749940496782486, 4.163547112671111,
#'                                  1.069362556641764, 0.426428274444305, 0.089725188494086)))
#' @family things related to spiciness
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_spiciness0.html}
gsw_spiciness0 <- function(SA, CT)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(CT)) stop("must supply CT")
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_spiciness0",
               SA=as.double(l$SA), CT=as.double(l$CT), n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Seawater Spiciness at p=1000 dbar
#'
#' Calculate seawater spiciness referenced to 1000 dbar.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return spiciness [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' spiciness <- gsw_spiciness1(SA, CT)
#' stopifnot(all.equal(spiciness, c(6.311038322123224, 6.326411175472160, 4.667218659743284,
#'                                  1.351722468726905, 0.628494082166029, 0.224779784908478)))
#' @family things related to spiciness
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_spiciness1.html}
gsw_spiciness1 <- function(SA, CT)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(CT)) stop("must supply CT")
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_spiciness1",
               SA=as.double(l$SA), CT=as.double(l$CT), n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Seawater Spiciness at p=2000 dbar
#'
#' Calculate seawater spiciness referenced to 2000 dbar.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @return spiciness [ kg/m^3 ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' spiciness <- gsw_spiciness2(SA, CT)
#' stopifnot(all.equal(spiciness, c(6.874671751873180, 6.884616399155135, 5.154458892387083,
#'                                  1.624327800598636, 0.823490797424952, 0.355069307641827)))
#' @family things related to spiciness
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_spiciness2.html}
gsw_spiciness2 <- function(SA, CT)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(CT)) stop("must supply CT")
    l <- argfix(list(SA=SA, CT=CT))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_spiciness2",
               SA=as.double(l$SA), CT=as.double(l$CT), n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Convert from Absolute Salinity to Preformed Salinity
#'
#' Calculate Preformed Salinity from Absolute Salinity, pressure,
#' longitude, and latitude.
#'
#' If SA is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Preformed Salinity [ g/kg ]
#' @examples
#' SA <-   c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <-    c(     10,      50,     125,     250,     600,    1000)
#' lat <-  c(      4,       4,       4,       4,       4,       4)
#' long <- c(    188,     188,     188,     188,     188,     188)
#' Sstar <- gsw_Sstar_from_SA(SA,p,long,lat)
#' stopifnot(all.equal(Sstar, c(34.711575335926490, 34.891138777337822, 35.024705401162166,
#'                              34.843564118358302, 34.729005527604883, 34.719712883389462)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Sstar_from_SA.html}
gsw_Sstar_from_SA <- function(SA, p, longitude, latitude)
{
    if (missing(SA)) stop("must supply SA")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that SP is a matrix defined on lon and lat
    if (is.matrix(SA)) {
        dim <- dim(SA)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(SA=SA, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_Sstar_from_SA",
               SA=as.double(l$SA), p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Convert from Practical Salinity to Preformed Salinity
#'
#' Calculate Preformed Salinity from Practical Salinity, pressure,
#' longitude, and latitude.
#'
#' If SP is a matrix and if its dimensions correspond to the
#' lengths of longitude and latitude, then the latter are
#' converted to analogous matrices with \code{\link{expand.grid}}.
#'
#' @template teos10template
#'
#' @template SPtemplate
#' @template ptemplate
#' @template longitudetemplate
#' @template latitudetemplate
#' @return Preformed Salinity [ g/kg ]
#' @examples
#' SP <-   c(34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600)
#' p <-    c(     10,      50,     125,     250,     600,    1000)
#' lat <-  c(      4,       4,       4,       4,       4,       4)
#' long <- c(    188,     188,     188,     188,     188,     188)
#' Sstar <- gsw_Sstar_from_SP(SP,p,long,lat)
#' stopifnot(all.equal(Sstar, c(34.711553680880769, 34.891161395333754, 35.024650265047370,
#'                              34.843593141519356, 34.729033995955525, 34.719675962471783)))
#' @family things related to salinity
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Sstar_from_SP.html}
gsw_Sstar_from_SP <- function(SP, p, longitude, latitude)
{
    if (missing(SP)) stop("must supply SP")
    if (missing(p)) stop("must supply p")
    if (missing(longitude)) stop("must supply longitude")
    if (missing(latitude)) stop("must supply latitude")
    ## check for special case that SP is a matrix defined on lon and lat
    if (is.matrix(SP)) {
        dim <- dim(SP)
        if (length(longitude) == dim[1] && length(latitude) == dim[2]) {
            ll <- expand.grid(longitude=as.vector(longitude), latitude=as.vector(latitude))
            longitude <- ll$longitude
            latitude <- ll$latitude
        }
    }
    l <- argfix(list(SP=SP, p=p, longitude=longitude, latitude=latitude))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_Sstar_from_SP",
               SP=as.double(l$SP), p=as.double(l$p), longitude=as.double(l$longitude), latitude=as.double(l$latitude),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SP) | !is.finite(l$p) | !is.finite(l$longitude) | !is.finite(l$latitude)] <- NA
    if (is.matrix(SP))
        dim(rval) <- dim(SP)
    rval
}


#' Derivative of Chemical Potential of Water in Seawater wrt Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ttemplate
#' @template ptemplate
#' @return derivative [ J/(g*degC) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' t <- c( 28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' d <- gsw_t_deriv_chem_potential_water_t_exact(SA, t, p)
#' stopifnot(all.equal(d, c(-0.428798278908442, -0.423860344327343, -0.345277821010421,
#'                          -0.164446485487145, -0.114228046736087, -0.076990819658255)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_deriv_chem_potential_water_t_exact.html}
gsw_t_deriv_chem_potential_water_t_exact <- function(SA, t, p)
{
    l <- argfix(list(SA=SA, t=t, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_t_deriv_chem_potential_water_t_exact",
               SA=as.double(l$SA), t=as.double(l$t), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$t) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Freezing Temperature of Seawater
#'
#' This uses the C function named \code{gsw_t_freezing_exact}, because the
#' C function named \code{gsw_t_freezing} does not produce check values that
#' match the Matlab function called \code{gsw_t_freezing} (see references
#' for those test values).
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return in-situ freezing temperature (ITS-90) [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(      10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- 1
#' tf <- gsw_t_freezing(SA, p, saturation_fraction)
#' stopifnot(all.equal(tf, c(-1.902730710149803, -1.942908619287183, -2.006861069199743,
#'                           -2.090985086875259, -2.351293130342102, -2.660498762776720)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_freezing.html}
gsw_t_freezing <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_t_freezing",
               SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Derivatives of Freezing Water Properties
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return a list containing \code{tfreezing_SA} [ K/(g/kg) ], the derivative of freezing
#' temperature with Absolute Salinity and
#' \code{tfreezing_p} [ K/dbar ], the derivative with respect to pressure.
#' @examples
#' SA <- c(               34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(                     10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- c(    1,     0.8,     0.6,     0.5,     0.4,       0)
#' derivs <- gsw_t_freezing_first_derivatives(SA, p, saturation_fraction)
#' stopifnot(all.equal(derivs$tfreezing_SA,
#'     c(-0.056811800705787, -0.056856999671114, -0.056903079789292,
#'       -0.056904020028541, -0.056974588411844, -0.057082363270642)))
#' stopifnot(all.equal(derivs$tfreezing_p/1e-7,
#'     c(-0.748468312442338, -0.749793159537290, -0.752225023995510,
#'      -0.756170965034610, -0.767279572670040, -0.779936552091913)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_freezing_first_derivatives.html}
gsw_t_freezing_first_derivatives <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_t_freezing_first_derivatives",
            SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
            n=as.integer(n), tfreezing_SA=double(n), tfreezing_p=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)
    ##37 r$tfreezing_SA[bad] <- NA
    ##37 r$tfreezing_p[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$tfreezing_SA) <- dim(SA)
        dim(r$tfreezing_p) <- dim(SA)
    }
    list(tfreezing_SA=r$tfreezing_SA, tfreezing_p=r$tfreezing_p)
}


#' Derivatives of Freezing Water Properties (Polynomial version)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template ptemplate
#' @template saturation_fractiontemplate
#' @return a list containing \code{tfreezing_SA} [ K/(g/kg) ], the derivative of freezing
#' temperature with Absolute Salinity and
#' \code{tfreezing_p} [ K/dbar ], the derivative with respect to pressure.
#' @examples
#' SA <- c(               34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' p <- c(                     10,      50,     125,     250,     600,    1000)
#' saturation_fraction <- c(    1,     0.8,     0.6,     0.5,     0.4,       0)
#' derivs <- gsw_t_freezing_first_derivatives_poly(SA, p, saturation_fraction)
#' stopifnot(all.equal(derivs$tfreezing_SA,
#'     c(-0.056810211094078, -0.056855567524973, -0.056901968693345,
#'       -0.056903498206432, -0.056975157476629, -0.057083526206200)))
#' stopifnot(all.equal(derivs$tfreezing_p/1e-7,
#'     c(-0.748987354878138, -0.750288853857513, -0.752676389629787,
#'       -0.756549680608529, -0.767482625710990, -0.779985619685683)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_freezing_first_derivatives.html}
gsw_t_freezing_first_derivatives_poly <- function(SA, p, saturation_fraction=1)
{
    l <- argfix(list(SA=SA, p=p, saturation_fraction=saturation_fraction))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_t_freezing_first_derivatives_poly",
            SA=as.double(l$SA), p=as.double(l$p), saturation_fraction=as.double(l$saturation_fraction),
            n=as.integer(n), tfreezing_SA=double(n), tfreezing_p=double(n),
            NAOK=TRUE, PACKAGE="gsw")
    ##37 bad <- !is.finite(l$SA) | !is.finite(l$p) | !is.finite(l$saturation_fraction)
    ##37 r$tfreezing_SA[bad] <- NA
    ##37 r$tfreezing_p[bad] <- NA
    if (is.matrix(SA)) {
        dim(r$tfreezing_SA) <- dim(SA)
        dim(r$tfreezing_p) <- dim(SA)
    }
    list(tfreezing_SA=r$tfreezing_SA, tfreezing_p=r$tfreezing_p)
}


#' In situ temperature from Conservative Temperature
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return in-situ temperature (ITS-90) [ degC ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' t <- gsw_t_from_CT(SA, CT, p)
#' stopifnot(all.equal(t, c(28.785580227725703, 28.432872246163946, 22.810323087627076,
#'                          10.260010752788906, 6.886286301029376, 4.403624452383043)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_from_CT.html}
gsw_t_from_CT <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_t_from_CT",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' In situ Temperature from Potential Temperature at 0dbar
#'
#' @template teos10template
#'
#' @template pt0_icetemplate
#' @template ptemplate
#' @return in-situ temperature (ITS-90) [ degC ]
#' @examples
#' pt0_ice  <- c(-10.7856, -13.4329, -12.8103, -12.2600, -10.8863, -8.4036)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' t <- gsw_t_from_pt0_ice(pt0_ice, p)
#' stopifnot(all.equal(t, c(-10.783412084414074, -13.422068638139141, -12.783170223330448,
#'                          -12.205667526492039, -10.755496924674144, -8.184121042593350)))
## @family things related to ice
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_t_from_pt0_ice.html}
gsw_t_from_pt0_ice <- function(pt0_ice, p)
{
    l <- argfix(list(pt0_ice=pt0_ice, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_t_from_pt0_ice",
               pt0_ice=as.double(l$pt0_ice), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$pt0_ice) | !is.finite(l$p)] <- NA
    if (is.matrix(pt0_ice))
        dim(rval) <- dim(pt0_ice)
    rval
}


#' Thermobaric coefficient (75-term equation)
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return thermobaric coefficient wrt Conservative Temperature [ 1/(K Pa) ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#'
#' tb <- gsw_thermobaric(SA, CT, p)
#'
#' stopifnot(all.equal(tb*1e11,
#'         c(0.141342632944971, 0.142352284525832, 0.163216280125501,
#'             0.226030772122855, 0.246185239871747, 0.261474794884197)))
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_thermobaric.html}
gsw_thermobaric <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_thermobaric",
               SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)] <- NA
    if (is.matrix(SA))
        dim(rval) <- dim(SA)
    rval
}


#' Turner Angle and Density Ratio
#'
#' This uses the 75-term density equation. The values of Turner Angle
#' Tu and density ratio Rrho are calculated at mid-point pressures, \code{p_mid}.
#'
#' @template teos10template
#'
#' @template SAtemplate
#' @template CTtemplate
#' @template ptemplate
#' @return List containing \code{Tu} [ degrees ], \code{Rsubrho} [ unitless ], and \code{p_mid} [ dbar ]
#' @examples
#' SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
#' CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
#' p <-  c(     10,      50,     125,     250,     600,    1000)
#' r <- gsw_Turner_Rsubrho(SA, CT, p)
#' stopifnot(all.equal(r$Tu, c(-2.063858905281147, 41.758435216784427, 47.606966981687535,
#'                             53.710351151706369, 45.527063858211527)))
#' stopifnot(all.equal(r$Rsubrho, 100*c(-0.009304335069039, -0.176564834348709, 0.219627771740757,
#'                                      0.065271424662002, 1.087044054679743)))
#' stopifnot(all.equal(r$p_mid, 100*c(0.300, 0.875, 1.875, 4.250, 8.000)))
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_Turner_Rsubrho.html}
gsw_Turner_Rsubrho <- function(SA, CT, p)
{
    l <- argfix(list(SA=SA, CT=CT, p=p))
    n <- length(l[[1]])
    r <- .C("wrap_gsw_Turner_Rsubrho",
            SA=as.double(l$SA), CT=as.double(l$CT), p=as.double(l$p),
            n=as.integer(n), Tu=double(n-1), Rsubrho=double(n-1), p_mid=double(n-1))
    bad <- !is.finite(l$SA) | !is.finite(l$CT) | !is.finite(l$p)
    if (any(bad))
        warning("gsw_Turner_Rsubrho() has some NA inputs ... these are not handled well\n")
    Tu <- r$Tu
    Rsubrho <- r$Rsubrho
    p_mid <- r$p_mid
    if (is.matrix(SA)) {
        stop("gsw_Turner_Rsubrho() cannot handle matrix SA")
    }
    list(Tu=Tu, Rsubrho=Rsubrho, p_mid=p_mid)
}


#' Height from Pressure
#'
#' Computation of height (above sea level) from pressure, using the 75-term equation for
#' specific volume.
#'
#' @template teos10template
#'
#' @template ptemplate
#' @template latitudetemplate
#' @param geo_strf_dyn_height vector of same length as \code{p} and \code{latitude},
#' indicating dynamic height [ m^2/s^2 ].
#' If not supplied, this defaults to a vector of 0 values, with length matching that
#' of \code{p}.
#' @param sea_surface_geopotential vector of same length as \code{p} and \code{latitude},
#' indicating geopotential at zero sea pressure [ m^2/s^2 ].
#' If not supplied, this defaults to a vector of 0 values, with length matching that
#' of \code{p}.
#'
#' @return height [ m ]
#'
#' @examples
#' z <- gsw_z_from_p(c(10, 50, 125, 250, 600,1000), 4)
#' stopifnot(all.equal(z/1e2, c(-0.099445834469453, -0.497180897012550, -1.242726219409978,
#'                              -2.484700576548589, -5.958253480356214, -9.920919060719987)))
#' @family things related to depth
#'
#' @section Historical Note:
#' The \code{geo_strf_dyn_height} and \code{sea_surface_geopotential}
#' parameters were added in GSW-R version 1.0-6.
#'
#' @references
#' \url{http://www.teos-10.org/pubs/gsw/html/gsw_z_from_p.html}
gsw_z_from_p <- function(p, latitude, geo_strf_dyn_height, sea_surface_geopotential)
{
    if (missing(geo_strf_dyn_height))
        geo_strf_dyn_height <- rep(0.0, length(p))
    if (missing(sea_surface_geopotential))
        sea_surface_geopotential <- rep(0.0, length(p))
    l <- argfix(list(p=p,
                     latitude=latitude,
                     geo_strf_dyn_height=geo_strf_dyn_height,
                     sea_surface_geopotential=sea_surface_geopotential))
    n <- length(l[[1]])
    rval <- .C("wrap_gsw_z_from_p",
               p=as.double(l$p), lat=as.double(l$latitude),
               geo_strf_dyn_height=as.double(l$geo_strf_dyn_height),
               sea_surface_geopotential=as.double(l$sea_surface_geopotential),
               n=as.integer(n), rval=double(n), NAOK=TRUE, PACKAGE="gsw")$rval
    ##37 rval[!is.finite(l$p) | !is.finite(l$latitude)] <- NA
    if (is.matrix(p))
        dim(rval) <- dim(p)
    rval
}