wc.image: Image plot of the cross-wavelet power spectrum and wavelet...
In WaveletComp: Computational Wavelet Analysis
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
This function plots the cross-wavelet power image, or alternatively the wavelet
coherence image, of two time series, which are provided by an object of class
"analyze.coherency".
The vertical axis shows the Fourier periods. The horizontal axis shows time step counts, but can
be easily transformed into a calendar axis if dates are provided in either row names or a variable
named "date" in the data frame at hand. Both axes can be relabeled.
In particular, an option is given to individualize the period and/or time axis
by specifying tick marks and labels.
An option is given to raise cross-wavelet power (or wavelet coherence) values
to any (positive) exponent before plotting in order to accentuate the contrast of the image.
The color levels can be defined according to quantiles of values
or according to equidistant breakpoints (covering the interval
from 0 to maximum level), with the number of levels as a further
parameter. A user-defined maximum level can be applied to cross-wavelet power images.
In addition, there is an option to adopt an individual color palette.
Further plot design options concern: plot of the cone of
influence, plot of contour lines to border areas of significance, plot of
the ridge, and plot of arrows (optional: "smoothed" arrows computed
from smoothing filters as defined in analyze.coherency) to reflect
phase differences.
For that matter, the significance level of contour lines can be
defined separately. The plot of the ridge can be restricted to a high-level region
("high" according to a given level of plotted values).
In particular, the area to be filled with arrows can be determined in several ways:
to reflect significance (at a given level) with respect to cross-wavelet power, wavelet
coherence, or individual wavelet power, and/or to flag a high-value region.
Furthermore, there is an option to clear out the area where the p-values of
cross-wavelet power (coherence, respectively) exceed a given
level.
Finally, there is an option to format and insert a color legend (a
right-hand vertical color bar) and to set the plot title. For
further processing of the plot, graphical parameters of plot
regions are provided as output.
The name and parts of the layout were inspired by a similar function developed by
Huidong Tian and Bernard Cazelles (archived R package WaveletCo).
The code for the arrow design to reflect phase differences
has been adopted from Huidong Tian.
Usage
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wc.image(WC,
which.image = "wp", exponent = 1,
plot.coi = TRUE,
plot.contour = TRUE, siglvl.contour = 0.1, col.contour = "white",
plot.ridge = FALSE, lvl = 0, col.ridge = "black",
plot.arrow = TRUE, use.sAngle = FALSE,
p = 1,
which.arrow.sig = which.image,
siglvl.arrow = 0.05, col.arrow = "black",
clear.area = FALSE,
which.area.sig = which.image, siglvl.area = 0.2,
color.key = "quantile",
n.levels = 100,
color.palette = "rainbow(n.levels, start = 0, end = .7)",
maximum.level = NULL,
useRaster = TRUE, max.contour.segments = 250000,
plot.legend = TRUE,
legend.params = list(width=1.2, shrink = 0.9, mar = 5.1,
n.ticks = 6,
label.digits = 1, label.format = "f",
lab = NULL, lab.line = 2.5),
label.time.axis = TRUE,
show.date = FALSE, date.format = NULL, date.tz = NULL,
timelab = NULL, timetck = 0.02, timetcl = 0.5,
spec.time.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
label.period.axis = TRUE,
periodlab = NULL, periodtck = 0.02, periodtcl = 0.5,
spec.period.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
main = NULL,
lwd = 2, lwd.axis = 1,
graphics.reset = TRUE,
verbose = FALSE)
Arguments
WC
an object of class "analyze.coherency"
which.image
Which image is to be plotted?
"wp" : cross-wavelet power
"wc" : wavelet coherence
Default: "wp".
exponent
Exponent applied to values before plotting in order to accentuate the contrast of the image;
the exponent should be positive.
Default: 1.
plot.coi
Plot cone of influence? Logical. Default: TRUE.
plot.contour
Plot contour lines to border the area of cross-wavelet power (or wavelet coherence,
depending on which.image) significance? Logical.
Default: TRUE.
siglvl.contour
level of cross-wavelet power (or wavelet coherence, depending on which.image)
significance to be applied to the plot of contour lines.
Default: 0.1.
col.contour
color of contour lines. Default: "white".
plot.ridge
Plot the cross-wavelet power (or wavelet coherence, depending on which.image) ridge? Logical.
Default: FALSE.
lvl
minimum level of cross-wavelet power (or wavelet coherence, depending on which.image) for ridge or arrows to be plotted.
(Only effective if plot.ridge = TRUE or, when setting p = 0 or p = 2, if plot.arrow = TRUE.)
Default: 0.
col.ridge
ridge color. Default: "black".
plot.arrow
Plot arrows depicting the phase difference? Logical.
Default: TRUE.
use.sAngle
Use smoothed version of phase difference? Logical.
Default: FALSE.
p
Which area should be filled with arrows displaying phase differences?
(Only effective if plot.arrow = TRUE.)
[0 :] Select the area w.r.t. power (or coherence, depending on which.image.
The value of lvl is the threshold.
Set lvl = 0 to plot arrows over the entire area.
[1 :] Select the area w.r.t. significance as specified in which.arrow.sig.
The value of siglvl.arrow is the threshold.
[2 :] Intersection of both areas above.
Default: 1.
which.arrow.sig
Which spectrum (and corresponding p-values) should be used to restrict the plot
of arrows according to significance?
"wp" : cross-wavelet power
"wc" : wavelet coherence
"wt" : individual wavelet power
Default: which.image.
siglvl.arrow
level of significance for arrows to be plotted.
(Only effective if plot.arrow = TRUE and p = 1 or p = 2.)
Default: 0.05.
col.arrow
arrow color. Default: "black".
clear.area
Clear out an area where p-values are above a certain level? Logical.
(Here, p-values will refer to the spectrum defined by which.area.sig and significance level siglvl.area, see below.)
Default: FALSE.
which.area.sig
Which power spectrum (and corresponding p-values) should be used to clear the outer area?
(Only effective if clear.area = TRUE)
"wp" : cross-wavelet power
"wc" : wavelet coherence
"wt" : individual wavelet power
Default: which.image.
siglvl.area
level of significance for the area to be cleared out.
(Only effective if clear.area = TRUE.)
Default: 0.2.
color.key
How to assign colors to power and coherence levels? Two options:
"interval" or "i" : equidistant breakpoints
(from 0 through maximum value)
"quantile" or "q" : quantiles
Default: "quantile".
n.levels
Number of color levels. Default: 100.
color.palette
Definition of color levels. (The color palette will be assigned to levels in reverse order!)
Default: "rainbow(n.levels, start = 0, end = .7)".
maximum.level
Maximum plot level of cross-wavelet power considered; only effective in case of equidistant breakpoints (color.key equaling "i").
Default: NULL (referring to maximum level observed).
Wavelet coherence has maximum plot level 1 by definition.
useRaster
Use a bitmap raster instead of polygons to plot the image? Logical.
Default: TRUE.
max.contour.segments
limit on the number of segments in a single contour line, positive integer.
Default: 250000 (options(...) default settings: 25000).
plot.legend
Plot color legend (a vertical bar of colors and breakpoints)? Logical.
Default: TRUE.
legend.params
a list of parameters for the plot of the color legend; parameter values can be set selectively
(style in parts adopted from image.plot in the R package fields by Douglas Nychka):
[width:] width of legend bar.
Default: 1.2.
[shrink:] a vertical shrinkage factor.
Default: 0.9.
[mar:] right margin of legend bar.
Default: 5.1.
[n.ticks:] number of ticks for labels.
Default: 6.
[label.digits:] digits of labels.
Default: 1.
[label.format:] format of labels.
Default: "f".
[lab:] axis label.
Default: NULL.
[lab.line:] line (in user coordinate units) where to put the axis label.
Default: 2.5.
label.time.axis
Label the time axis? Logical.
Default: TRUE.
show.date
Show calendar dates? (Effective only if dates are available as row names or by variable
date in the data frame which has been analyzed.) Logical.
Default: FALSE.
date.format
the format of calendar date given as a character string, e.g. "%Y-%m-%d", or equivalently "%F";
see strptime for a list of implemented date conversion specifications. Explicit information given here will overturn any specification
stored in WC. If unspecified, date formatting is attempted according to as.Date.
Default: NULL.
date.tz
a character string specifying the time zone of calendar date; see strptime. Explicit information given here will overturn
any specification stored in WC. If unspecified, "" (the local time zone) is used.
Default: NULL.
timelab
Time axis label.
Default: "index"; in case of a calendar axis: "calendar date".
timetck
length of tick marks on the time axis as a fraction of the smaller of the width or height of the plotting region; see par.
If timetck >= 0.5, timetck is interpreted as a fraction of the length of the time axis, so if timetck = 1
(and timetcl = NULL), vertical grid lines will be drawn.
Setting timetck = NA is to use timetcl = -0.5 (which is the R default setting of tck and tcl).
Default here: 0.02.
timetcl
length of tick marks on the time axis as a fraction of the height of a line of text; see par.
With timetcl = -0.5 (which is the R default setting of tcl), ticks will be drawn outward.
Default here: 0.5.
spec.time.axis
a list of tick mark and label specifications for individualized time axis labeling
(only effective if label.time.axis = TRUE):
[at:] locations of tick marks (when NULL, default plotting will be applied).
Valid tick marks can be provided as numerical values or as dates. Dates are used only in the case show.date = TRUE, however,
and date formats should conform to as.Date or the format given in date.format.
Default: NULL.
[labels:] either a logical value specifying whether annotations at the tick marks are the tick marks themselves,
or any vector of labels. If labels is non-logical, at should be of same length.
Default: TRUE.
[las:] the style of axis labels, see par.
Default: 1 (always horizontal).
[hadj:] adjustment of labels horizontal to the reading direction, see axis.
Default: NA (centering is used).
[padj:] adjustment of labels perpendicular to the reading direction (this can be a vector of adjustments for each label),
see axis.
Default: NA (centering is used).
Mismatches will result in a reset to default plotting.
label.period.axis
Label the (Fourier) period axis? Logical.
Default: TRUE.
periodlab
(Fourier) period axis label.
Default: "period".
periodtck
length of tick marks on the period axis as a fraction of the smaller of the width or height
of the plotting region; see par. If periodtck >= 0.5, periodtck is interpreted as a fraction
of the length of the period axis, so if periodtck = 1 (and periodtcl = NULL), horizontal grid lines will be drawn.
Setting periodtck = NA is to use periodtcl = -0.5 (which is the R default setting of tck and tcl).
Default here: 0.02.
periodtcl
length of tick marks on the period axis as a fraction of the height of a line of text; see par.
With periodtcl = -0.5 (which is the R default setting of tcl) ticks will be drawn outward.
Default here: 0.5.
spec.period.axis
a list of tick mark and label specifications for individualized period axis labeling
(only effective if label.period.axis = TRUE):
[at:] locations of tick marks (when NULL, default plotting will be applied). Valid tick marks can be provided as
numerical and positive values only.
Default: NULL.
[labels:] either a logical value specifying whether annotations at the tick marks are the tick marks themselves,
or any vector of labels. If labels is non-logical, at should be of same length.
Default: TRUE.
[las:] the style of axis labels, see par.
Default: 1 (always horizontal).
[hadj:] adjustment of labels horizontal to the reading direction, see axis.
Default: NA (centering is used).
[padj:] adjustment of labels perpendicular to the reading direction (this can be a vector of adjustments for each label),
see axis.
Default: NA (centering is used).
Mismatches will result in a reset to default plotting.
main
an overall title for the plot.
Default: NULL.
lwd
line width of contour lines and ridge.
Default: 2.
lwd.axis
line width of axes (image and legend bar).
Default: 1.
graphics.reset
Reset graphical parameters? Logical.
Default: TRUE
verbose
Print verbose output on the screen? Logical.
Default: FALSE.
Value
A list of class graphical parameters with the following elements:
op
original graphical parameters
image.plt
image plot region
legend.plt
legend plot region
Author(s)
Angi Roesch and Harald Schmidbauer; credits are also due to Huidong Tian, and Bernard Cazelles.
References
Aguiar-Conraria L., and Soares M.J., 2011.
Business cycle synchronization and the Euro: A wavelet analysis.
Journal of Macroeconomics 33 (3), 477–489.
Aguiar-Conraria L., and Soares M.J., 2011.
The Continuous Wavelet Transform: A Primer.
NIPE Working Paper Series 16/2011.
Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008.
Wavelet analysis of ecological time series.
Oecologia 156, 287–304.
Liu P.C., 1994.
Wavelet spectrum analysis and ocean wind waves.
In: Foufoula-Georgiou E., and Kumar P., (eds.), Wavelets in Geophysics, Academic Press, San Diego, 151–166.
Tian, H., and Cazelles, B., 2012. WaveletCo.
Available at https://cran.r-project.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.
Torrence C., and Compo G.P., 1998.
A practical guide to wavelet analysis.
Bulletin of the American Meteorological Society 79 (1), 61–78.
Veleda D., Montagne R., and Araujo M., 2012.
Cross-Wavelet Bias Corrected by Normalizing Scales.
Journal of Atmospheric and Oceanic Technology 29, 1401–1408.
See Also
analyze.coherency, wc.avg, wc.sel.phases, wc.phasediff.image,
wt.image, wt.avg,
wt.sel.phases, wt.phase.image, reconstruct
Examples
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## Not run:
## The following example is modified from Veleda et al., 2012:
series.length <- 3*128*24
x1 <- periodic.series(start.period = 1*24, length = series.length)
x2 <- periodic.series(start.period = 2*24, length = series.length)
x3 <- periodic.series(start.period = 4*24, length = series.length)
x4 <- periodic.series(start.period = 8*24, length = series.length)
x5 <- periodic.series(start.period = 16*24, length = series.length)
x6 <- periodic.series(start.period = 32*24, length = series.length)
x7 <- periodic.series(start.period = 64*24, length = series.length)
x8 <- periodic.series(start.period = 128*24, length = series.length)
x <- x1 + x2 + x3 + x4 + 3*x5 + x6 + x7 + x8 + rnorm(series.length)
y <- x1 + x2 + x3 + x4 - 3*x5 + x6 + 3*x7 + x8 + rnorm(series.length)
matplot(data.frame(x, y), type = "l", lty = 1, xaxs = "i", col = 1:2,
xlab = "index", ylab = "",
main = "hourly series with periods of 1, 2, 4, 8, 16, 32, 64, 128 days",
sub = "(out of phase at period 16, different amplitudes at period 64)")
legend("topright", legend = c("x","y"), col = 1:2, lty = 1)
## The following dates refer to the local time zone
## (possibly allowing for daylight saving time):
my.date <- seq(as.POSIXct("2014-10-14 00:00:00", format = "%F %T"),
by = "hour",
length.out = series.length)
my.data <- data.frame(date = my.date, x = x, y = y)
## Computation of cross-wavelet power and wavelet coherence, x over y:
## a natural choice of 'dt' in the case of hourly data is 'dt = 1/24',
## resulting in one time unit equaling one day.
## This is also the time unit in which periods are measured.
my.wc <- analyze.coherency(my.data, c("x","y"),
loess.span = 0,
dt = 1/24, dj = 1/20,
window.size.t = 1, window.size.s = 1/2,
lowerPeriod = 1/4,
make.pval = TRUE, n.sim = 10)
## Plot of cross-wavelet power spectrum,
## with color breakpoints according to quantiles:
wc.image(my.wc,
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (quantiles)"),
periodlab = "period (days)")
## Note:
## The default time axis shows an index of given points in time,
## which is the count of hours in our example.
## By default, arrows are plotted which show the phase differences
## of x over y at respective significant periods.
## (Please see our guide booklet for further explanation.)
## The same plot, but with equidistant color breakpoints:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
periodlab = "period (days)")
## The same plot, but adopting a palette of gray colors,
## omitting the arrows:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
plot.arrow = FALSE,
periodlab = "period (days)")
## The same plot, now with ridge of power:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
plot.arrow = FALSE,
plot.ridge = TRUE, col.ridge = "red",
periodlab = "period (days)")
## The plot, turning back to arrows, now in yellow color:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)")
## Alternate styles of the time axis:
## The plot with time elapsed in days, starting from 0 and proceeding
## in steps of 50 days (50*24 hours), instead of the (default) time index:
index.ticks <- seq(1, series.length, by = 50*24)
index.labels <- (index.ticks-1)/24
## Insert your specification of time axis:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)", timelab = "time elapsed (days)",
spec.time.axis = list(at = index.ticks, labels = index.labels))
## The plot with (automatically produced) calendar axis:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
show.date = TRUE, date.format = "%F %T")
## Individualizing your calendar axis (works with show.date = TRUE)...
## How to obtain, for example, monthly date ticks and labels:
## The sequence of tick positions:
monthly.ticks <- seq(as.POSIXct("2014-11-01 00:00:00", format = "%F %T"),
as.POSIXct("2015-11-01 00:00:00", format = "%F %T"),
by = "month")
## Observe that the following specification may produce an error:
## 'seq(as.Date("2014-11-01"), as.Date("2015-11-01"), by = "month")'
## Time of the day is missing here!
## The sequence of labels (e.g. information on month and year only):
monthly.labels <- strftime(monthly.ticks, format = "%b %Y")
## Insert your specification of time axis as parameter to wc.image:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
show.date = TRUE, date.format = "%F %T",
spec.time.axis = list(at = monthly.ticks, labels = monthly.labels,
las = 2))
## Note:
## The monthly ticks specify the midpoints of the colored cells and
## match the location of corresponding (default) time index ticks.
## A cross-wavelet power plot with individualized period axis and exponent
## to accentuate contrast in the image:
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
spec.period.axis = list(at = c(1,2,4,8,16,32,64,128)))
## An option to switch to the corresponding frequency axis:
my.periods <- c(1,2,4,8,16,32,64,128)
my.frequencies <- paste("1/",my.periods, sep = "")
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "frequency (per day)",
spec.period.axis = list(at = my.periods, labels = my.frequencies))
## Adding, for example, horizontal lines at period ticks...
## There is an option to add further objects to the image plot region,
## by setting 'graphics.reset = FALSE'
## (but recall previous par settings after plotting):
op <- par(no.readonly = TRUE)
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette="gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "frequency (per day)",
spec.period.axis = list(at = my.periods, labels = my.frequencies),
timelab = "",
show.date = TRUE, date.format = "%F %T",
graphics.reset = FALSE)
abline(h = log2(my.periods))
year2015 <- as.POSIXct("2015-01-01 00:00:00", format = "%F %T")
abline(v = year2015)
axis(1, at = year2015, labels = 2015, padj = 1)
par(op)
## For further axis plotting options:
## Please see the examples in our guide booklet,
## URL http://www.hs-stat.com/projects/WaveletComp/WaveletComp_guided_tour.pdf.
## Plot of wavelet coherence of x over y,
## with color breakpoints according to quantiles:
wc.image(my.wc, which.image = "wc",
main = "wavelet coherence, x over y",
legend.params = list(lab = "wavelet coherence levels (quantiles)",
lab.line = 3.5, label.digits = 3),
periodlab = "period (days)")
## Plot of wavelet coherence, but with equidistant color breakpoints:
wc.image(my.wc, which.image = "wc", color.key = "i",
main = "wavelet coherence, x over y",
legend.params = list(lab = "wavelet coherence levels (equidistant)"),
periodlab = "period (days)")
## End(Not run)
WaveletComp documentation built on May 2, 2019, 6:33 a.m.
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Description Usage Arguments Value Author(s) References See Also Examples
Description
This function plots the cross-wavelet power image, or alternatively the wavelet
coherence image, of two time series, which are provided by an object of class
"analyze.coherency".
The vertical axis shows the Fourier periods. The horizontal axis shows time step counts, but can
be easily transformed into a calendar axis if dates are provided in either row names or a variable
named "date" in the data frame at hand. Both axes can be relabeled.
In particular, an option is given to individualize the period and/or time axis
by specifying tick marks and labels.
An option is given to raise cross-wavelet power (or wavelet coherence) values to any (positive) exponent before plotting in order to accentuate the contrast of the image.
The color levels can be defined according to quantiles of values or according to equidistant breakpoints (covering the interval from 0 to maximum level), with the number of levels as a further parameter. A user-defined maximum level can be applied to cross-wavelet power images. In addition, there is an option to adopt an individual color palette.
Further plot design options concern: plot of the cone of
influence, plot of contour lines to border areas of significance, plot of
the ridge, and plot of arrows (optional: "smoothed" arrows computed
from smoothing filters as defined in analyze.coherency) to reflect
phase differences.
For that matter, the significance level of contour lines can be defined separately. The plot of the ridge can be restricted to a high-level region ("high" according to a given level of plotted values). In particular, the area to be filled with arrows can be determined in several ways: to reflect significance (at a given level) with respect to cross-wavelet power, wavelet coherence, or individual wavelet power, and/or to flag a high-value region. Furthermore, there is an option to clear out the area where the p-values of cross-wavelet power (coherence, respectively) exceed a given level.
Finally, there is an option to format and insert a color legend (a right-hand vertical color bar) and to set the plot title. For further processing of the plot, graphical parameters of plot regions are provided as output.
The name and parts of the layout were inspired by a similar function developed by
Huidong Tian and Bernard Cazelles (archived R package WaveletCo).
The code for the arrow design to reflect phase differences
has been adopted from Huidong Tian.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | wc.image(WC,
which.image = "wp", exponent = 1,
plot.coi = TRUE,
plot.contour = TRUE, siglvl.contour = 0.1, col.contour = "white",
plot.ridge = FALSE, lvl = 0, col.ridge = "black",
plot.arrow = TRUE, use.sAngle = FALSE,
p = 1,
which.arrow.sig = which.image,
siglvl.arrow = 0.05, col.arrow = "black",
clear.area = FALSE,
which.area.sig = which.image, siglvl.area = 0.2,
color.key = "quantile",
n.levels = 100,
color.palette = "rainbow(n.levels, start = 0, end = .7)",
maximum.level = NULL,
useRaster = TRUE, max.contour.segments = 250000,
plot.legend = TRUE,
legend.params = list(width=1.2, shrink = 0.9, mar = 5.1,
n.ticks = 6,
label.digits = 1, label.format = "f",
lab = NULL, lab.line = 2.5),
label.time.axis = TRUE,
show.date = FALSE, date.format = NULL, date.tz = NULL,
timelab = NULL, timetck = 0.02, timetcl = 0.5,
spec.time.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
label.period.axis = TRUE,
periodlab = NULL, periodtck = 0.02, periodtcl = 0.5,
spec.period.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
main = NULL,
lwd = 2, lwd.axis = 1,
graphics.reset = TRUE,
verbose = FALSE)
|
Arguments
WC |
an object of class | |||||||||
which.image |
Which image is to be plotted?
Default: |
exponent |
Exponent applied to values before plotting in order to accentuate the contrast of the image; the exponent should be positive. Default: |
plot.coi |
Plot cone of influence? Logical. Default: |
plot.contour |
Plot contour lines to border the area of cross-wavelet power (or wavelet coherence,
depending on Default: |
siglvl.contour |
level of cross-wavelet power (or wavelet coherence, depending on Default: |
col.contour |
color of contour lines. Default: |
plot.ridge |
Plot the cross-wavelet power (or wavelet coherence, depending on Default: |
lvl |
minimum level of cross-wavelet power (or wavelet coherence, depending on Default: |
col.ridge |
ridge color. Default: |
plot.arrow |
Plot arrows depicting the phase difference? Logical. Default: |
use.sAngle |
Use smoothed version of phase difference? Logical. Default: |
p |
Which area should be filled with arrows displaying phase differences?
Default: |
which.arrow.sig |
Which spectrum (and corresponding p-values) should be used to restrict the plot of arrows according to significance?
Default: | ||||||||||||
siglvl.arrow |
level of significance for arrows to be plotted. Default: | ||||||||||||
col.arrow |
arrow color. Default: |
clear.area |
Clear out an area where p-values are above a certain level? Logical. (Here, p-values will refer to the spectrum defined by Default: | ||||||||||||
which.area.sig |
Which power spectrum (and corresponding p-values) should be used to clear the outer area?
Default: | ||||||||||||
siglvl.area |
level of significance for the area to be cleared out. Default: |
color.key |
How to assign colors to power and coherence levels? Two options:
Default: | ||||||||||||
n.levels |
Number of color levels. Default: | ||||||||||||
color.palette |
Definition of color levels. (The color palette will be assigned to levels in reverse order!) Default: |
maximum.level |
Maximum plot level of cross-wavelet power considered; only effective in case of equidistant breakpoints ( Default: |
useRaster |
Use a bitmap raster instead of polygons to plot the image? Logical. Default: |
max.contour.segments |
limit on the number of segments in a single contour line, positive integer. Default: |
plot.legend |
Plot color legend (a vertical bar of colors and breakpoints)? Logical. Default: |
legend.params |
a list of parameters for the plot of the color legend; parameter values can be set selectively
(style in parts adopted from
|
label.time.axis |
Label the time axis? Logical. Default: |
show.date |
Show calendar dates? (Effective only if dates are available as row names or by variable
Default: |
date.format |
the format of calendar date given as a character string, e.g. Default: |
date.tz |
a character string specifying the time zone of calendar date; see Default: |
timelab |
Time axis label. Default: |
timetck |
length of tick marks on the time axis as a fraction of the smaller of the width or height of the plotting region; see Default here: |
timetcl |
length of tick marks on the time axis as a fraction of the height of a line of text; see Default here: |
spec.time.axis |
a list of tick mark and label specifications for individualized time axis labeling
(only effective if
Mismatches will result in a reset to default plotting. |
label.period.axis |
Label the (Fourier) period axis? Logical. Default: |
periodlab |
(Fourier) period axis label. Default: |
periodtck |
length of tick marks on the period axis as a fraction of the smaller of the width or height
of the plotting region; see Default here: |
periodtcl |
length of tick marks on the period axis as a fraction of the height of a line of text; see Default here: |
spec.period.axis |
a list of tick mark and label specifications for individualized period axis labeling
(only effective if
Mismatches will result in a reset to default plotting. |
main |
an overall title for the plot. Default: |
lwd |
line width of contour lines and ridge. Default: |
lwd.axis |
line width of axes (image and legend bar). Default: |
graphics.reset |
Reset graphical parameters? Logical. Default: |
verbose |
Print verbose output on the screen? Logical. Default: |
Value
A list of class graphical parameters with the following elements:
op |
original graphical parameters |
image.plt |
image plot region |
legend.plt |
legend plot region |
Author(s)
Angi Roesch and Harald Schmidbauer; credits are also due to Huidong Tian, and Bernard Cazelles.
References
Aguiar-Conraria L., and Soares M.J., 2011. Business cycle synchronization and the Euro: A wavelet analysis. Journal of Macroeconomics 33 (3), 477–489.
Aguiar-Conraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.
Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008. Wavelet analysis of ecological time series. Oecologia 156, 287–304.
Liu P.C., 1994. Wavelet spectrum analysis and ocean wind waves. In: Foufoula-Georgiou E., and Kumar P., (eds.), Wavelets in Geophysics, Academic Press, San Diego, 151–166.
Tian, H., and Cazelles, B., 2012. WaveletCo.
Available at https://cran.r-project.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.
Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61–78.
Veleda D., Montagne R., and Araujo M., 2012. Cross-Wavelet Bias Corrected by Normalizing Scales. Journal of Atmospheric and Oceanic Technology 29, 1401–1408.
See Also
analyze.coherency, wc.avg, wc.sel.phases, wc.phasediff.image,
wt.image, wt.avg,
wt.sel.phases, wt.phase.image, reconstruct
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 | ## Not run:
## The following example is modified from Veleda et al., 2012:
series.length <- 3*128*24
x1 <- periodic.series(start.period = 1*24, length = series.length)
x2 <- periodic.series(start.period = 2*24, length = series.length)
x3 <- periodic.series(start.period = 4*24, length = series.length)
x4 <- periodic.series(start.period = 8*24, length = series.length)
x5 <- periodic.series(start.period = 16*24, length = series.length)
x6 <- periodic.series(start.period = 32*24, length = series.length)
x7 <- periodic.series(start.period = 64*24, length = series.length)
x8 <- periodic.series(start.period = 128*24, length = series.length)
x <- x1 + x2 + x3 + x4 + 3*x5 + x6 + x7 + x8 + rnorm(series.length)
y <- x1 + x2 + x3 + x4 - 3*x5 + x6 + 3*x7 + x8 + rnorm(series.length)
matplot(data.frame(x, y), type = "l", lty = 1, xaxs = "i", col = 1:2,
xlab = "index", ylab = "",
main = "hourly series with periods of 1, 2, 4, 8, 16, 32, 64, 128 days",
sub = "(out of phase at period 16, different amplitudes at period 64)")
legend("topright", legend = c("x","y"), col = 1:2, lty = 1)
## The following dates refer to the local time zone
## (possibly allowing for daylight saving time):
my.date <- seq(as.POSIXct("2014-10-14 00:00:00", format = "%F %T"),
by = "hour",
length.out = series.length)
my.data <- data.frame(date = my.date, x = x, y = y)
## Computation of cross-wavelet power and wavelet coherence, x over y:
## a natural choice of 'dt' in the case of hourly data is 'dt = 1/24',
## resulting in one time unit equaling one day.
## This is also the time unit in which periods are measured.
my.wc <- analyze.coherency(my.data, c("x","y"),
loess.span = 0,
dt = 1/24, dj = 1/20,
window.size.t = 1, window.size.s = 1/2,
lowerPeriod = 1/4,
make.pval = TRUE, n.sim = 10)
## Plot of cross-wavelet power spectrum,
## with color breakpoints according to quantiles:
wc.image(my.wc,
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (quantiles)"),
periodlab = "period (days)")
## Note:
## The default time axis shows an index of given points in time,
## which is the count of hours in our example.
## By default, arrows are plotted which show the phase differences
## of x over y at respective significant periods.
## (Please see our guide booklet for further explanation.)
## The same plot, but with equidistant color breakpoints:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
periodlab = "period (days)")
## The same plot, but adopting a palette of gray colors,
## omitting the arrows:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
plot.arrow = FALSE,
periodlab = "period (days)")
## The same plot, now with ridge of power:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
plot.arrow = FALSE,
plot.ridge = TRUE, col.ridge = "red",
periodlab = "period (days)")
## The plot, turning back to arrows, now in yellow color:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)")
## Alternate styles of the time axis:
## The plot with time elapsed in days, starting from 0 and proceeding
## in steps of 50 days (50*24 hours), instead of the (default) time index:
index.ticks <- seq(1, series.length, by = 50*24)
index.labels <- (index.ticks-1)/24
## Insert your specification of time axis:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)", timelab = "time elapsed (days)",
spec.time.axis = list(at = index.ticks, labels = index.labels))
## The plot with (automatically produced) calendar axis:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
show.date = TRUE, date.format = "%F %T")
## Individualizing your calendar axis (works with show.date = TRUE)...
## How to obtain, for example, monthly date ticks and labels:
## The sequence of tick positions:
monthly.ticks <- seq(as.POSIXct("2014-11-01 00:00:00", format = "%F %T"),
as.POSIXct("2015-11-01 00:00:00", format = "%F %T"),
by = "month")
## Observe that the following specification may produce an error:
## 'seq(as.Date("2014-11-01"), as.Date("2015-11-01"), by = "month")'
## Time of the day is missing here!
## The sequence of labels (e.g. information on month and year only):
monthly.labels <- strftime(monthly.ticks, format = "%b %Y")
## Insert your specification of time axis as parameter to wc.image:
wc.image(my.wc, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels (equidistant)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
show.date = TRUE, date.format = "%F %T",
spec.time.axis = list(at = monthly.ticks, labels = monthly.labels,
las = 2))
## Note:
## The monthly ticks specify the midpoints of the colored cells and
## match the location of corresponding (default) time index ticks.
## A cross-wavelet power plot with individualized period axis and exponent
## to accentuate contrast in the image:
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "period (days)",
spec.period.axis = list(at = c(1,2,4,8,16,32,64,128)))
## An option to switch to the corresponding frequency axis:
my.periods <- c(1,2,4,8,16,32,64,128)
my.frequencies <- paste("1/",my.periods, sep = "")
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette = "gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "frequency (per day)",
spec.period.axis = list(at = my.periods, labels = my.frequencies))
## Adding, for example, horizontal lines at period ticks...
## There is an option to add further objects to the image plot region,
## by setting 'graphics.reset = FALSE'
## (but recall previous par settings after plotting):
op <- par(no.readonly = TRUE)
wc.image(my.wc, exponent = 0.5, color.key = "i",
main = "cross-wavelet power spectrum, x over y",
legend.params = list(lab = "cross-wavelet power levels
(raised by exponent 0.5, equidistant levels)"),
color.palette="gray( (1:n.levels)/n.levels )",
col.arrow = "yellow",
periodlab = "frequency (per day)",
spec.period.axis = list(at = my.periods, labels = my.frequencies),
timelab = "",
show.date = TRUE, date.format = "%F %T",
graphics.reset = FALSE)
abline(h = log2(my.periods))
year2015 <- as.POSIXct("2015-01-01 00:00:00", format = "%F %T")
abline(v = year2015)
axis(1, at = year2015, labels = 2015, padj = 1)
par(op)
## For further axis plotting options:
## Please see the examples in our guide booklet,
## URL http://www.hs-stat.com/projects/WaveletComp/WaveletComp_guided_tour.pdf.
## Plot of wavelet coherence of x over y,
## with color breakpoints according to quantiles:
wc.image(my.wc, which.image = "wc",
main = "wavelet coherence, x over y",
legend.params = list(lab = "wavelet coherence levels (quantiles)",
lab.line = 3.5, label.digits = 3),
periodlab = "period (days)")
## Plot of wavelet coherence, but with equidistant color breakpoints:
wc.image(my.wc, which.image = "wc", color.key = "i",
main = "wavelet coherence, x over y",
legend.params = list(lab = "wavelet coherence levels (equidistant)"),
periodlab = "period (days)")
## End(Not run)
|
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