Chi-square distribution Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with v degrees of free

This function is used to calculate number of chunks (including partial, non-complete chunks) in some set. It expects that ChunkSize>=1, TaskSize>=0. A

Fast kernel -- ALGLIB routine -- 19.01.2010 Bochkanov Sergey *************************************************************************/

Dense solver for A*X=B with N*N complex A given by its LU decomposition, and N*M matrices X and B (multiple right sides). "Slow-but-feature-rich"

Dense solver. Same as RMatrixMixedSolveM(), but for complex matrices. Algorithm features: * automatic detection of degenerate cases * condition numbe

Complex dense solver for A*X=B with N*N complex matrix A, N*M complex matrices X and B. "Slow-but-feature-rich" version which provides

1-dimensional complex convolution. For given A/B returns conv(A,B) (non-circular). Subroutine can automatically choose between three implementations:

1-dimensional circular complex convolution. For given S/R returns conv(S,R) (circular). Algorithm has linearithmic complexity for any M/N. IMPORTANT

1-dimensional real convolution. Analogous to ConvC1D(), see ConvC1D() comments for more details. INPUT PARAMETERS A - array[0..M-1] - real f

1-dimensional circular real convolution. Analogous to ConvC1DCircular(), see ConvC1DCircular() comments for more details. INPUT PARAMETERS S -

Tail(S, 5) *************************************************************************/

Tail(S, 6) *************************************************************************/

Tail(S, 7) *************************************************************************/

Tail(S, 8) *************************************************************************/

Tail(S, 9) *************************************************************************/

Covariance matrix ! COMMERCIAL EDITION OF ALGLIB: ! ! Commercial Edition of ALGLIB includes following important improvements ! of this functi

Internal subroutine. Returns maximum count of RFS iterations as function of: 1. machine epsilon 2. task size. 3. norm-2 condition number -- ALGLIB

Complete elliptic integral of the second kind Approximates the integral pi/2 - | | 2 E(m) = |

Complete elliptic integral of the first kind Approximates the integral pi/2 - | | | dt K(m)

Complementary error function 1 - erf(x) = inf. - 2 | | 2

1-dimensional real inverse FFT. Algorithm has O(N*logN) complexity for any N (composite or prime). INPUT PARAMETERS F - array[0..floor(N/2)]

1-dimensional Fast Hartley Transform. Algorithm has O(N*logN) complexity for any N (composite or prime). INPUT PARAMETERS A - array[0..N-1]

* this function copies Hermitian transpose of lower part of * diagonal block A0 to its upper part Block is specified by offset and size. * * [

* this function copies Hermitian transpose of offdiagonal block BL to * its symmetric counterpart BU (see below). Block BL is specified by * offsets

* this function copies lower part of diagonal block A0 to its upper part * Block is specified by offset and size. * * [ . ] * [

* this function copies offdiagonal block BL to its symmetric counterpart * BU (see below). Block BL is specified by offsets (offset0,offset1) * and

Controls whether events will be forwarded to listeners_. Set to false in death test child processes.

Frees all allocated memory chunks */

Frees all allocated memory chunks */

Recurrent subroutine for a InternalComplexLinTranspose Write A^T to B, where: * A is m*n complex matrix stored in array A as pairs of real/image valu

Twiddle factors calculation -- ALGLIB -- Copyright 01.05.2009 by Bochkanov Sergey ************************************************************

This subroutine applies complex codelet FFT to input/output array A. INPUT PARAMETERS: A - array, must be large enough for plan to wo

This subroutine applies complex "integrated" codelet FFT to input/output array A. "Integrated" codelet differs from "normal" one in following ways:

This subroutine applies complex reference FFT to input/output array A. VERY SLOW OPERATION, do not use it in real life plans :) INPUT PARAMETERS:

This subroutine applies complex Bluestein's FFT to input/output array A. INPUT PARAMETERS: Plan - transformation plan A -

Recurrent function called by FTComplexFFTPlan() and other functions. It recursively builds transformation plan INPUT PARAMETERS: N -

This function returns EXACT estimate of the space requirements for N-point FFT. Internals of this function are highly dependent on details of differen

This subroutine precomputes data for complex Rader's FFT and writes them to array PrecR[] at specified offset. It is responsibility of the caller

This subroutine applies complex Rader's FFT to input/output array A. INPUT PARAMETERS: A - array, must be large enough for plan to wo

Linear transpose: transpose complex matrix stored in 1-dimensional array -- ALGLIB -- Copyright 01.05.2009 by Bochkanov Sergey ***************

Returns Gauss and Gauss-Kronrod nodes/weights for Gauss-Legendre quadrature with N points. GKQLegendreCalc (calculation) or GKQLegendreTbl

Returns Gauss and Gauss-Kronrod nodes for quadrature with N points. Reduction to tridiagonal eigenproblem is used. INPUT PARAMETERS: N

Returns Gauss and Gauss-Kronrod nodes for quadrature with N points using pre-calculated table. Nodes/weights were computed with accuracy up to

Stub function. -- ALGLIB routine -- 14.06.2013 Bochkanov Sergey *************************************************************************

Stub function. -- ALGLIB routine -- 14.06.2013 Bochkanov Sergey *************************************************************************

Dense solver for A*X=B with N*N Hermitian positive definite matrix A given by its Cholesky decomposition and N*M complex matrices X and B. This is

Dense solver for A*X=B, with N*N Hermitian positive definite matrix A and N*M complex matrices X and B. "Slow-but-feature-rich" version of the

HQRNDState initialization with seed values -- ALGLIB -- Copyright 02.12.2009 by Bochkanov Sergey *********************************************

Continued fraction expansion #1 for incomplete beta integral Cephes Math Library, Release 2.8: June, 2000 Copyright 1984, 1995, 2000 by Stephen L. M

Continued fraction expansion #2 for incomplete beta integral Cephes Math Library, Release 2.8: June, 2000 Copyright 1984, 1995, 2000 by Stephen L. M

This function returns (A div B) rounded up; it expects that A>0, B>0, but does not check it. *********************************************************

Inverse of Normal CDF Returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to

* this function checks that diagonal block A0 is Hermitian. * Block A0 is specified by its offset and size. * * [ . ] * [ A0

* this function checks difference between offdiagonal blocks BL and BU * (see below). Block BL is specified by offsets (offset0,offset1) and * size

Returns true iff this is NAN (not a number).

* this function checks that diagonal block A0 is symmetric. * Block A0 is specified by its offset and size. * * [ . ] * [ A0

* this function checks difference between offdiagonal blocks BL and BU * (see below). Block BL is specified by offsets (offset0,offset1) and * size

Resizes X and: * preserves old contents of X * fills new elements by zeros -- ALGLIB -- Copyright 20.03.2009 by Bochkanov Sergey *************