qfrm_cpp: Internal C++ functions
In qfratio: Moments and Distributions of Ratios of Quadratic Forms Using Recursion

p_A1B1_Ed

R Documentation

Internal C++ functions

Description

These are internal C++ functions called from corresponding R functions when use_cpp = TRUE. Direct access by the user is not assumed. All parameters are assumed to be appropriately structured.

Usage

p_A1B1_Ed(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

p_A1B1_El(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

p_A1B1_Ec(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

d_A1I1_Ed(quantile, LA, m, thr_margin = 100)

p_imhof_Ed(
  quantile,
  A,
  B,
  mu,
  autoscale_args,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  limit
)

d_broda_Ed(
  quantile,
  A,
  B,
  mu,
  autoscale_args,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  limit
)

d_butler_Ed(
  quantile,
  A,
  B,
  mu,
  order_spa,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  maxiter
)

p_butler_Ed(
  quantile,
  A,
  B,
  mu,
  order_spa,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  maxiter
)

Ap_int_E(A, mu, p_ = 1, thr_margin = 100, tol_zero = 2.2e-14)

ABpq_int_E(A, LB, mu, p_ = 1, q_ = 1, thr_margin = 100, tol_zero = 2.2e-14)

ABDpqr_int_E(
  A,
  LB,
  D,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  thr_margin = 100,
  tol_zero = 2.2e-14
)

ApIq_int_cE(A, p_ = 1, q_ = 1, thr_margin = 100)

ApIq_int_nE(A, mu, p_ = 1, q_ = 1, thr_margin = 100)

ApIq_npi_cE(
  LA,
  bA,
  p_ = 1,
  q_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100
)

ApIq_npi_nEd(
  LA,
  bA,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 1L
)

ApBq_int_E(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  tol_zero = 2.2e-14
)

ApBq_npi_Ed(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_int_cEd(
  A,
  LB,
  bB,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  tol_zero = 2.2e-14
)

ApBIqr_int_nEd(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_npi_Ed(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

IpBDqr_gen_Ed(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_int_Ed(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_npi_Ed(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApIq_npi_nEc(
  LA,
  bA,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 1L
)

ApBq_npi_Ec(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_int_nEc(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_npi_Ec(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

IpBDqr_gen_Ec(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_int_Ec(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_npi_Ec(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApIq_npi_nEl(
  LA,
  bA,
  mu,
  p_ = 1L,
  q_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 1L
)

ApBq_npi_El(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_int_nEl(
  A,
  LB,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBIqr_npi_El(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

IpBDqr_gen_El(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_int_El(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

ApBDqr_npi_El(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)

rqfpE(nit, A, B, D, p_, q_, r_, mu, Sigma)

Arguments

`quantile`	Scalar of quantile `q`, passed as `double`
`A`, `B`, `D`	Argument matrices passed as `Eigen::Matrix`. Symmetry is assumed.
`mu`	Mean vector `\bm{\mu}` for `\mathbf{x}` passed as `Eigen::Array`. For `d_broda_Ed()`, assumed to be rotated by the eigenvectors of `\mathbf{A} - q \mathbf{B}`
`m`	Integer to specify the order of polynomials at which the series expression is truncated. Passed as `Eigen::Index` (aka `std::ptrdiff_t` or `long long int`)
`stop_on_error`	`bool` to specify whether execution is stopped upon error in numerical integration or root finding
`thr_margin`	Optional argument to adjust the threshold for scaling. See “Scaling” in `d1_i`.
`nthreads`	`int` to specify the number of threads in OpenMP-enabled functions. See “Multithreading” in `qfrm`.
`tol_zero`	Tolerance against which numerical zero is determined
`LA`, `LB`	Eigenvalues of the argument matrices passed as `Eigen::Array`
`autoscale_args`	Factor to which the largest absolute eigenvalue of `\mathbf{A} - q \mathbf{B}` is scaled, passed as `double`
`epsrel`, `epsabs`, `limit`, `maxiter`	Optional arguments passed to `gsl_integration_qagi()` or `gsl_root_test_delta()`
`order_spa`	`int` to specify order of saddlepoint approximation
`p_`, `q_`, `r_`	Exponents for `\mathbf{A}`, `\mathbf{B}`, and `\mathbf{D}`. Passed as `double` or `long double`.
`bA`, `bB`, `bD`	Scaling coefficients for `\mathbf{A}`, `\mathbf{B}`, and `\mathbf{D}`. Passed as `double` or `long double`.
`error_bound`	`bool` to specify whether the error bound is returned
`nit`	`int` to specify the number of iteration or sample size
`Sigma`	Covariance matrix `\mathbf{\Sigma}` for `\mathbf{x}`. Passed as `Eigen::Matrix`.