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| Package: NORMT3 | ||
| Title: Evaluates complex erf, erfc and density of sum of Gaussian and Student's t | ||
| Version: 1.0-1 | ||
| Date: 209-02-137 | ||
| Title: Evaluates complex erf, erfc, Faddeeva, and density of sum of | ||
| Gaussian and Student's t | ||
| Version: 1.0-2 | ||
| Date: 17/03/2010 | ||
| Author: Guy Nason <g.p.nason@bristol.ac.uk> | ||
| Maintainer: Guy Nason <g.p.nason@bristol.ac.uk> | ||
| Description: Evaluates the probability density function of the sum of the | ||
| Gaussian and Student's t density on 3 degrees of freedom. | ||
| Evaluates the p.d.f. of the sphered Student's t density function. | ||
| Also evaluates the erf and erfc functions on complex-valued arguments. | ||
| License: GPL (>= 2) | ||
| Packaged: Fri Feb 13 14:50:55 2009; ripley | ||
| Depends: R (>= 2.0) | ||
| Description: Evaluates the probability density function of the sum of | ||
| the Gaussian and Student's t density on 3 degrees of freedom. | ||
| Evaluates the p.d.f. of the sphered Student's t density | ||
| function. Also evaluates the erf, and erfc functions on | ||
| complex-valued arguments. Thanks to Krishna Myneni the function | ||
| is calculates the Faddeeva function also! | ||
| License: GPL-2 | ||
| Packaged: 2012-10-29 08:57:20 UTC; ripley | ||
| Repository: CRAN | ||
| Date/Publication: 2012-10-29 08:57:20 |
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| fd5fe172ef3ae16f4cc83501ea3215dd *DESCRIPTION | ||
| 9fdfeb11f7ddba6f3aab9aaa6b1ac5dd *NAMESPACE | ||
| adef3a419005deb8c91bade7964cb31c *R/dnormt3.R | ||
| dce3e8bb5f353fda3d700bdba01f4651 *R/dst.R | ||
| 33717d45906e412719aa2035088377f4 *R/erf.R | ||
| 2b2c7491f277ea56529f7dc734267509 *R/erfc.R | ||
| b9b9b1afbe458bdac0b8e34ad1e7163e *R/firstlib.R | ||
| 411d2dcce18a3bef73c4577aea757ed2 *R/ic1.R | ||
| a96ad4f75bd8fb4c9386afb8366caa78 *R/is1.R | ||
| 2544c29d1fdb284e4b8e0b7faa257080 *R/normt3ip.R | ||
| ea867ba161640aaa7004b538e0982f03 *R/wofz.R | ||
| 69ea61dec509d31c2a8954e2e56596a6 *man/dnormt3.Rd | ||
| e607dd933db78b0e85db55bf365174f5 *man/dst.Rd | ||
| 90037f89dc17dab9a589590bc90a910c *man/erf.Rd | ||
| 48cb03b2e588846b870566ec6b8ed0f7 *man/erfc.Rd | ||
| f28360e4fcdb9b5801cd25324b6dd2b1 *man/ic1.Rd | ||
| 335b5adaf6aff4553056ca6fbf699dca *man/is1.Rd | ||
| b6f6de285b52f88e67c8f850033e3768 *man/normt3ip.Rd | ||
| 11b45690e9d2298505aba5446c28f75f *man/wofz.Rd | ||
| 46c60069216c8375f3caa9b8f7ef8b6e *src/IPerfcvec.c | ||
| 3897cb5687a7258aa7f64e824657a414 *src/IPwofzvec.c | ||
| 6b033d6d3f308a67c31739db00f4d6de *src/toms680-1.f |
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| # Default NAMESPACE created by R | ||
| # Remove the previous line if you edit this file | ||
|
|
||
| # Export all names | ||
| exportPattern(".") |
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| "wofz" <- | ||
| function(z){ | ||
|
|
||
| ans <- .C("IPwofzvec", | ||
| x=as.double(Re(z)), | ||
| y=as.double(Im(z)), | ||
| ansx=as.double(Re(z)), | ||
| ansy=as.double(Im(z)), | ||
| n = as.integer(length(z)), | ||
| error = as.integer(0), | ||
| PACKAGE="NORMT3") | ||
| if (ans$error != 0) | ||
| stop(paste("Error code from TOMS 680 was ", ans$error)) | ||
|
|
||
| return(complex(real=ans$ansx, im=ans$ansy)) | ||
|
|
||
| } |
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| \name{wofz} | ||
| \alias{wofz} | ||
| \title{Faddeeva function} | ||
| \description{ | ||
| Computes the Faddeeva function of a complex valued argument. This function is | ||
| \deqn{\exp{-z^2}*erfc(-iz)} . | ||
| } | ||
| \usage{ | ||
| wofz(z) | ||
| } | ||
| \arguments{ | ||
| \item{z}{Argument of Faddeeva function} | ||
| } | ||
| \details{ | ||
| Computes the Faddeeva function of a complex valued argument. This function is | ||
| \deqn{\exp{-z^2}*erfc(-iz)} | ||
|
|
||
| This function calls FORTRAN code (algorithm TOMS 680) | ||
| which computes the Faddeeva function. | ||
| } | ||
| \value{ | ||
| The Faddeeva function, w(z) | ||
| } | ||
| \references{ | ||
| Poppe, G.P.M. and Wijers, C.M.J. (1990) More efficient computation of the | ||
| complex error function. \emph{ACM Transactions on Mathematical | ||
| Software}, \bold{16}, 38--46. | ||
| } | ||
| \author{Krishna Myneni, krishna.myneni@ccreweb.org} | ||
|
|
||
|
|
||
| \seealso{\code{\link{erf} \link{erfc}}} | ||
| \examples{ | ||
| options(digits=15) | ||
| wofz(0) | ||
| # | ||
| # Should give 1+0i | ||
| # | ||
| wofz(1) | ||
| # | ||
| # Should give 0.367879441171442+0.607157705841394i | ||
| # | ||
| wofz(complex(re=1, im=1)) | ||
| # | ||
| # Should give 0.304744205256913+0.208218938202832i | ||
| # | ||
| } | ||
| \keyword{math} |
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| #include <math.h> | ||
|
|
||
| /* | ||
| * IPwofzvec - compute Faddeeva function, w(z) on a vector of complex values | ||
| * | ||
| * | ||
| * Input: x + iy (x and y are double vectors containing the real | ||
| and imaginary parts of the complex vector that | ||
| you wish to transform) | ||
| * Output: ansx + i ansy (ansx and ansy are double vectors containing | ||
| the real and imaginary parts of the transformed vector) | ||
| * Other variables: | ||
| * | ||
| * n: Length of each of the vectors x, y, ansx, ansy | ||
| * | ||
| * error: Error code from the routine that computes Faddeva's function | ||
| (computed by TOMS routine 680). Zero means no error. | ||
| */ | ||
|
|
||
| void IPwofzvec(double *x, double *y, double *ansx, double *ansy, int *n, | ||
| int *error) | ||
| { | ||
| int i, flag; | ||
| void IPwofz(); | ||
| void wofz_(); | ||
|
|
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| for(i=0; i< *n; ++i) { | ||
| wofz_( x+i, y+i, ansx+i, ansy+i, &flag); | ||
|
|
||
| if (flag != 0) { | ||
| *error = flag; | ||
| return; | ||
| } | ||
| } | ||
| } | ||
|
|
||
| void IPwofz(double *a, double *b, double *outa, double *outb, int *error) | ||
| { | ||
|
|
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| double d, e; | ||
| void wofz_(); | ||
|
|
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| *error =0l; | ||
|
|
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| /* Want to work out w(ia+b) */ | ||
|
|
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| wofz_( a, b, &d, &e, error); | ||
| if (*error) return; | ||
|
|
||
| *outa = d; | ||
| *outb = e; | ||
| } |
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