zgbequ.f (3)  Linux Man Pages
NAME
zgbequ.f 
SYNOPSIS
Functions/Subroutines
subroutine zgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
ZGBEQU
Function/Subroutine Documentation
subroutine zgbequ (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, integerINFO)
ZGBEQU
Purpose:

ZGBEQU computes row and column scalings intended to equilibrate an MbyN band matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.
Parameters:

M
M is INTEGER The number of rows of the matrix A. M >= 0.
NN is INTEGER The number of columns of the matrix A. N >= 0.
KLKL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KUKU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
ABAB is COMPLEX*16 array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=i<=min(m,j+kl).
LDABLDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
RR is DOUBLE PRECISION array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A.
CC is DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A.
ROWCNDROWCND is DOUBLE PRECISION If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.
COLCNDCOLCND is DOUBLE PRECISION If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.
AMAXAMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, and i is <= M: the ith row of A is exactly zero > M: the (iM)th column of A is exactly zero
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Definition at line 154 of file zgbequ.f.
Author
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