DMGSBV(3)

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

NAME
dmgsbv - Subsidiary to DBVSUP

LIBRARY
SLATEC

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

AUTHOR
Watts, H. A., (SNLA)

DESCRIPTION
********************************************************************** Orthogonalize a set of N double precision 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
DBVSUP

ROUTINES CALLED
DDOT, DPRVEC

COMMON BLOCKS
DML18J, DML5MC

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)
890921 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900328 Added TYPE section. (WRB)
910722 Updated AUTHOR section. (ALS)