MGSBV(3)

SYNOPSIS
SUBROUTINE MGSBV (M, N, A, IA, NIV, IFLAG, S, P, IP, INHOMO, V, W, + WCND)

NAME
mgsbv - Subsidiary to BVSUP

LIBRARY
SLATEC

TYPE
SINGLE PRECISION (MGSBV-S, DMGSBV-D)

AUTHOR
Watts, H. A., (SNLA)

DESCRIPTION
********************************************************************** Orthogonalize a set of N real vectors and determine their rank ********************************************************************** INPUT ********************************************************************** M = Dimension of vectors N = No. of vectors A = Array whose first N cols contain the vectors IA = First dimension of array A (col length) NIV = Number of independent vectors needed INHOMO = 1 Corresponds to having a non-zero particular solution V = Particular solution vector (not included in the pivoting) INDPVT = 1 Means pivoting will not be used ********************************************************************** OUTPUT ********************************************************************** NIV = No. of linear independent vectors in input set A = Matrix whose first NIV cols. contain NIV orthogonal vectors which span the vector space determined by the input vectors IFLAG = 0 success = 1 incorrect input = 2 rank of new vectors less than N P = Decomposition matrix. P is upper triangular and (old vectors) = (new vectors) * P. The old vectors will be reordered due to pivoting The dimension of p must be .GE. N*(N+1)/2. ( N*(2*N+1) when N .NE. NFCC ) IP = Pivoting vector. The dimension of IP must be .GE. N. ( 2*N when N .NE. NFCC ) S = Square of norms of incoming vectors V = Vector which is orthogonal to the vectors of A W = Orthogonalization information for the vector V WCND = Worst case (smallest) norm decrement value of the vectors being orthogonalized (represents a test for linear dependence of the vectors) **********************************************************************

SEE ALSO
BVSUP

ROUTINES CALLED
PRVEC, SDOT

COMMON BLOCKS
ML18JR, ML5MCO

REVISION HISTORY (YYMMDD)
750601 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890921 Realigned order of variables in certain COMMON blocks. (WRB)
891214 Prologue converted to Version 4.0 format. (BAB)
900328 Added TYPE section. (WRB)
910722 Updated AUTHOR section. (ALS)