sgbequ (l) - Linux Manuals

sgbequ: computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

Command to display sgbequ manual in Linux: $ man l sgbequ

NAME

SGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

SYNOPSIS

SUBROUTINE SGBEQU(: M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )
: INTEGER INFO, KL, KU, LDAB, M, N
: REAL AMAX, COLCND, ROWCND
: REAL AB( LDAB, * ), C( * ), R( * )

PURPOSE

SGBEQU computes row and column scalings intended to equilibrate an M-by-N 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.

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) REAL array, dimension (LDAB,N): The band matrix A, stored 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).
LDAB (input) INTEGER: The leading dimension of the array AB. LDAB >= KL+KU+1.
R (output) REAL array, dimension (M): If INFO = 0, or INFO > M, R contains the row scale factors for A.
C (output) REAL array, dimension (N): If INFO = 0, C contains the column scale factors for A.
ROWCND (output) REAL: 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.
COLCND (output) REAL: 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.
AMAX (output) REAL: Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
INFO (output) INTEGER: = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero