.TH DGBEQU 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DGBEQU - row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number .SH SYNOPSIS .TP 19 SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO ) .TP 19 .ti +4 INTEGER INFO, KL, KU, LDAB, M, N .TP 19 .ti +4 DOUBLE PRECISION AMAX, COLCND, ROWCND .TP 19 .ti +4 DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) .SH PURPOSE DGBEQU 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. .br 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. .br .SH ARGUMENTS .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0. .TP 8 KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. .TP 8 KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. .TP 8 AB (input) DOUBLE PRECISION 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). .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. .TP 8 R (output) DOUBLE PRECISION array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A. .TP 8 C (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A. .TP 8 ROWCND (output) 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. .TP 8 COLCND (output) 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. .TP 8 AMAX (output) 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, and i is .br <= M: the i-th row of A is exactly zero .br > M: the (i-M)-th column of A is exactly zero