Generate and return the Probability Density Function (PDF) of the Raised Cosine distribution for an input x
within the support of the distribution \(x \in [\mu  \sigma, \mu + \sigma]\).
More...
Generate and return the Probability Density Function (PDF) of the Raised Cosine distribution for an input x
within the support of the distribution \(x \in [\mu  \sigma, \mu + \sigma]\).
See the documentation of pm_distCosRaised for more information on the Raised Cosine distribution.
 Parameters

[in]  x  : The input scalar or array of the same shape as other array like arguments, of

type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the value at which the PDF must be computed.

[in]  mu  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind the input argument x , containing the location parameter of the distribution.
(optional, default = \(0.\)) 
[in]  sigma  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as x , containing the scale parameter of the distribution.
(optional, default = \(1.\)) 
 Returns
pdf
: The output scalar or array of the same shape as any input arraylike argument, of the same type and kind the input argument x
, containing the PDF of the distribution.
Possible calling interfaces ⛓
Generate and return the Probability Density Function (PDF) of the Raised Cosine distribution for an i...
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition
0. < sigma
must hold for the corresponding input arguments.
The condition x >= mu  sigma
must hold for the corresponding input arguments.
The condition x <= mu + sigma
must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1
.

The
pure
procedure(s) documented herein become impure
when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1
.
By default, these procedures are pure
in release
build and impure
in debug
and testing
builds.
 See also
 setCosRaisedPDF
Example usage ⛓
15 integer(IK),
parameter :: NP
= 5_IK
16 real(RKG), dimension(NP) :: mu, sigma, PDF
18 type(display_type) :: disp
22 call disp%show(
"!%%%%%%%%%%%%%%%%%%")
23 call disp%show(
"! The standard PDF.")
24 call disp%show(
"!%%%%%%%%%%%%%%%%%%")
28 call setLogSpace(sigma, logx1
= log(
0.1_RKG), logx2
= log(
10._RKG))
31 call disp%show(
"PDF(1) = getCosRaisedPDF(0._RKG)")
38 call disp%show(
"PDF(1:5) = getCosRaisedPDF([real(RKG) :: 1., .5, 0., .5, 1.])")
53 call disp%show(
"PDF(1) = getCosRaisedPDF(mu(1), mu(1))")
60 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
61 call disp%show(
"! PDF with a scale parameter.")
62 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
68 call disp%show(
"PDF(1) = getCosRaisedPDF(0._RKG, sigma = sigma(1))")
75 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
76 call disp%show(
"! PDF with a mean and a standard deviation.")
77 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
85 call disp%show(
"PDF(1:2) = getCosRaisedPDF(mu(1) .subadd. sigma(1) / 2, mu(1), sigma(1))")
86 PDF(
1:
2)
= getCosRaisedPDF(mu(
1) .subadd. sigma(
1)
/ 2, mu(
1), sigma(
1))
92 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
93 call disp%show(
"! A vector of PDF at different points with the same mean and standard deviation.")
94 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
102 call disp%show(
"PDF(1:NP) = getCosRaisedPDF(getLinSpace(mu(1)  sigma(1), mu(1) + sigma(1), count = NP), mu(1), sigma(1))")
109 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
110 call disp%show(
"! A vector of PDF at the same point but with different means and standard deviations.")
111 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
119 call disp%show(
"PDF(1:NP) = getCosRaisedPDF(mu(1:NP), mu(1:NP), sigma(1:NP))")
126 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
127 call disp%show(
"! A vector of PDF at different points with different means and a standard deviations.")
128 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
136 call disp%show(
"PDF(1:NP) = getCosRaisedPDF(mu(1:NP), mu(1:NP), sigma(1:NP))")
147 integer(IK) :: fileUnit, i, j
148 real(RKG) :: point(
1000), PDF(
4), mu(
4), sigma(
4)
149 open(newunit
= fileUnit, file
= "getCosRaisedPDF.RK.txt")
150 call setLinSpace(point, x1
= 4._RKG, x2
= +4._RKG)
151 sigma
= [
+3._RKG,
+1._RKG,
+.
3_RKG,
1._RKG]
152 mu
= [
+0._RKG,
+0._RKG,
+0._RKG,
2._RKG]
153 do i
= 1,
size(point)
155 if(point(i) .inrange. (mu(j) .subadd. sigma(j)))
then
161 write(fileUnit,
"(5(g0,:,' '))") point(i), PDF
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Return the linSpace output argument with size(linSpace) elements of evenlyspaced values over the int...
Return the logSpace output argument with size(logSpace) elements of logarithmicallyevenlyspaced val...
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
This module contains procedures and generic interfaces for assessing whether particular value(s) or a...
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind typeparameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in CFortran Interoperati...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
This module contains procedures and generic interfaces for evaluating the mathematical operator acti...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
14+0.0000000000000000,
+0.50000000000000000,
+1.0000000000000000,
+0.50000000000000000,
+0.0000000000000000
52+5.0000000000000293,
+5.0000000000000293
66+0.0000000000000000,
+5.0000000000000293,
+9.9999999999999964,
+5.0000000000000293,
+0.0000000000000000
755.0000000000000000,
2.5000000000000000,
+0.0000000000000000,
+2.5000000000000000,
+5.0000000000000000
77+0.10000000000000003,
+0.31622776601683800,
+1.0000000000000004,
+3.1622776601683813,
+10.000000000000002
80+9.9999999999999964,
+3.1622776601683786,
+0.99999999999999956,
+0.31622776601683772,
+0.99999999999999978E1
895.0000000000000000,
2.5000000000000000,
+0.0000000000000000,
+2.5000000000000000,
+5.0000000000000000
91+0.10000000000000003,
+0.31622776601683800,
+1.0000000000000004,
+3.1622776601683813,
+10.000000000000002
94+9.9999999999999964,
+3.1622776601683786,
+0.99999999999999956,
+0.31622776601683772,
+0.99999999999999978E1
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"X ( real/imaginary components )"
17 ,
"IK" :
"X ( integervalued )"
18 ,
"RK" :
"X ( realvalued )"
20legends = [
r"$\mu = 0.0,~\sigma = 3.0$"
21 ,
r"$\mu = 0.0,~\sigma = 1.0$"
22 ,
r"$\mu = 0.0,~\sigma = 0.3$"
23 ,
r"$\mu = 2.,~\sigma = 1.0$"
26for kind
in [
"IK",
"CK",
"RK"]:
28 pattern =
"*." + kind +
".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
32 df = pd.read_csv(fileList[0], delimiter =
" ")
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
38 plt.plot( df.values[:, 0]
41 , linewidth = linewidth
44 plt.plot( df.values[:, 1]
47 , linewidth = linewidth
51 plt.plot( df.values[:, 0]
54 , linewidth = linewidth
61 plt.xticks(fontsize = fontsize  2)
62 plt.yticks(fontsize = fontsize  2)
63 ax.set_xlabel(xlab[kind], fontsize = 17)
64 ax.set_ylabel(
"Probability Density Function (PDF)", fontsize = 17)
66 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"")
67 ax.tick_params(axis =
"y", which =
"minor")
68 ax.tick_params(axis =
"x", which =
"minor")
70 plt.savefig(fileList[0].replace(
".txt",
".png"))
72 elif len(fileList) > 1:
74 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
 Test:
 test_pm_distCosRaised
 Todo:
 Very Low Priority: This generic interface can be extended to
complex
arguments.
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.

If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
 Copyright
 Computational Data Science Lab
 Author:
 Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan
Definition at line 196 of file pm_distCosRaised.F90.