cgbequ - by-N band matrix A and reduce its condition number
SUBROUTINE CGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX A(LDA,*) INTEGER M, N, KL, KU, LDA, INFO REAL ROWCND, COLCND, AMAX REAL R(*), C(*) SUBROUTINE CGBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX A(LDA,*) INTEGER*8 M, N, KL, KU, LDA, INFO REAL ROWCND, COLCND, AMAX REAL R(*), C(*) F95 INTERFACE SUBROUTINE GBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX, DIMENSION(:,:) :: A INTEGER :: M, N, KL, KU, LDA, INFO REAL :: ROWCND, COLCND, AMAX REAL, DIMENSION(:) :: R, C SUBROUTINE GBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: M, N, KL, KU, LDA, INFO REAL :: ROWCND, COLCND, AMAX REAL, DIMENSION(:) :: R, C C INTERFACE #include <sunperf.h> void cgbequ(int m, int n, int kl, int ku, complex *a, int lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int *info); void cgbequ_64(long m, long n, long kl, long ku, complex *a, long lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, long *info);
Oracle Solaris Studio Performance Library cgbequ(3P) NAME cgbequ - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number SYNOPSIS SUBROUTINE CGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX A(LDA,*) INTEGER M, N, KL, KU, LDA, INFO REAL ROWCND, COLCND, AMAX REAL R(*), C(*) SUBROUTINE CGBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX A(LDA,*) INTEGER*8 M, N, KL, KU, LDA, INFO REAL ROWCND, COLCND, AMAX REAL R(*), C(*) F95 INTERFACE SUBROUTINE GBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX, DIMENSION(:,:) :: A INTEGER :: M, N, KL, KU, LDA, INFO REAL :: ROWCND, COLCND, AMAX REAL, DIMENSION(:) :: R, C SUBROUTINE GBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: M, N, KL, KU, LDA, INFO REAL :: ROWCND, COLCND, AMAX REAL, DIMENSION(:) :: R, C C INTERFACE #include <sunperf.h> void cgbequ(int m, int n, int kl, int ku, complex *a, int lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int *info); void cgbequ_64(long m, long n, long kl, long ku, complex *a, long lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, long *info); PURPOSE cgbequ 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 num- ber 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) The number of rows of the matrix A. M >= 0. N (input) The number of columns of the matrix A. N >= 0. KL (input) The number of subdiagonals within the band of A. KL >= 0. KU (input) The number of superdiagonals within the band of A. KU >= 0. A (input) 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 A as follows: A(ku+1+i-j,j) = A(i,j) for max(1,j- ku)<=i<=min(m,j+kl). LDA (input) The leading dimension of the array A. LDA >= KL+KU+1. R (output) If INFO = 0, or INFO > M, R contains the row scale factors for A. C (output) If INFO = 0, C contains the column scale factors for A. ROWCND (output) 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) 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 scal- ing by C. AMAX (output) 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) = 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. 7 Nov 2015 cgbequ(3P)