zlaqgb(l) [redhat man page]
ZLAQGB(l) ) ZLAQGB(l) NAME
ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C SYNOPSIS
SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED ) CHARACTER EQUED INTEGER KL, KU, LDAB, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND DOUBLE PRECISION C( * ), R( * ) COMPLEX*16 AB( LDAB, * ) PURPOSE
ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vec- tors R and C. ARGUMENTS
M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. AB (input/output) COMPLEX*16 array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. LDAB (input) INTEGER The leading dimension of the array AB. LDA >= KL+KU+1. R (output) DOUBLE PRECISION array, dimension (M) The row scale factors for A. C (output) DOUBLE PRECISION array, dimension (N) The column scale factors for A. ROWCND (output) DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i). COLCND (output) DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i). AMAX (input) DOUBLE PRECISION Absolute value of largest matrix entry. EQUED (output) CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmulti- plied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). PARAMETERS
THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. LAPACK version 3.0 15 June 2000 ZLAQGB(l)
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zlaqgb.f(3) LAPACK zlaqgb.f(3) NAME
zlaqgb.f - SYNOPSIS
Functions/Subroutines subroutine zlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. Function/Subroutine Documentation subroutine zlaqgb (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, characterEQUED) ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. Purpose: ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. LDAB LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1. R R is DOUBLE PRECISION array, dimension (M) The row scale factors for A. C C is DOUBLE PRECISION array, dimension (N) The column scale factors for A. ROWCND ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i). COLCND COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i). AMAX AMAX is DOUBLE PRECISION Absolute value of largest matrix entry. EQUED EQUED is CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). Internal Parameters: THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Definition at line 160 of file zlaqgb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 zlaqgb.f(3)