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  Linear algebra routines - Based on EBK&NVS Library for Turbo/Object Pascal
by Nikolai V. Shokhirev and Eugene B. Krissinel
ŠNikolai V. Shokhirev, 2002-2007


Nikolai Shokhirev <>
Eugene B. Krissinel <>˜krissinel/)


2002.02.02 - created
2004.12.22 - extended
2007.07.07 - added Slice as FArr2D property, extended comments, other cleanup
2007.07.11 - TriDiagSLE was generalised for an arbitrary [Lo,..,Hi] arrays
2007.07.15 - Added DelphiCodeToDoc comments

Constant Description
RS_IterMaxError 'Lim Mismatch';
RS_LimMismatch 'Lim Mismatch';
RS_NotSquare 'Matrix is not square';

Function Description
BiDiagMt d, e -> M
BiDiagSLE Bi-diagonal SLE
ChBandSolve Solution of the equation L*LT*S = G by the Cholesky method
CholBandDec Cholesky decomposition of the band matrix H[1..p+1,1..N].
CholDecomp Perturbated Cholesky Decomposition -
Cholesky Cholesky Decomposition A = L*LT
ChSolve Solution of L*LT*X = B by the Cholesky method
CJacobi Jacoby diagonalization of Hermitian matrix
DecompSolve Solution of linear system a*x = b
diag Diagonalization of the real symmetric matrix a[Lo..Hi,Lo..Hi] .
diagc Diagonalization of Hermitian matrix a = ar + i*ai.
FastInverse Fast Inversion of the matrix A by the Gauss-Jordan elimination algorithm
FastSolve solution of a set of linear equations a*x = b
FMMDecomp PURPOSE: Decomposes a matrix by Gaussian elimination and estimates the condition
FMMSolve PURPOSE: Solution of linear system, a*x = b - translation from FORTRAN
GaussJordan solution of a set of linear equations by the Gauss Jordan elimination with partial pivoting
GJSolve Direct use of GaussJordan for solving m*x =b
GramSchmidt Gram-Schmidt Orthonormalization of vectors
householder Householder reduction (m >= n) extracted from xsvd
htribk This subroutine forms the eigenvectors of a complex Hermitian matrix
htridi This subroutine reduces a complex hermitian matrix to a real symmetric
Jacobi Diagonalization of real symmetric matrix by JACOBI method
JacobiC 1-Based variant of Jacobi diagonalization of Hermitian matrix
LBandSolve Cholesky L - Solution of L*Y = B (for given B)
LSolve Solution of L*Y = B;
LTBandSolve Cholesky LT - Solution of LT*X = Y (for given Y)
LTSolve Solution of LT*X = Y L[j,i], j >= i
MaskSolve solution of a set of linear equations by the Gauss Jordan elimination with partial pivoting
OrderSVD Singular Value Decomposition - translation from FORTRAN
QRDecomp QR-decomposition of the n x n matrix M: M = Q*R
QRSolve solution of the equation Q*R*X = B
SortSVD Descending singular value sorting with sorting of U and V
SortVal Quick sort, Functionally the same as SortVal0
SortVal0 Simple sort algorithm of the vector d[Lo..Hi] and corresponding columns
SortValC Simple sort algorithm of the first m components of vector d[Lo..Hi]
SVD A is a rectangular D1xD2 matrix: A[L1..H1,L2..H2]
SVD_ used in SVD, based om FMMSVD
tqli QL algorithm with implicit shifts for a real tridiaginal symmetric matrix.
tred2 Householder (tridiagonal) reduction of a real, symmetric matrix a.
TriDiagMt a, b, c -> M
TriDiagSLE Tri-diagonal SLE
xsvd Singular Value Decomposition (m >= n)

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ŠNikolai V. Shokhirev, 2001-2007
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