zgeequ - by-N matrix A and reduce its condition number
SUBROUTINE ZGEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) DOUBLE COMPLEX A(LDA,*) INTEGER M, N, LDA, INFO DOUBLE PRECISION ROWCND, COLCND, AMAX DOUBLE PRECISION R(*), C(*) SUBROUTINE ZGEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) DOUBLE COMPLEX A(LDA,*) INTEGER*8 M, N, LDA, INFO DOUBLE PRECISION ROWCND, COLCND, AMAX DOUBLE PRECISION R(*), C(*) F95 INTERFACE SUBROUTINE GEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: M, N, LDA, INFO REAL(8) :: ROWCND, COLCND, AMAX REAL(8), DIMENSION(:) :: R, C SUBROUTINE GEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, INFO REAL(8) :: ROWCND, COLCND, AMAX REAL(8), DIMENSION(:) :: R, C C INTERFACE #include <sunperf.h> void zgeequ(int m, int n, doublecomplex *a, int lda, double *r, double *c, double *rowcnd, double *colcnd, double *amax, int *info); void zgeequ_64(long m, long n, doublecomplex *a, long lda, double *r, double *c, double *rowcnd, double *colcnd, double *amax, long *info);
Oracle Solaris Studio Performance Library zgeequ(3P) NAME zgeequ - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number SYNOPSIS SUBROUTINE ZGEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) DOUBLE COMPLEX A(LDA,*) INTEGER M, N, LDA, INFO DOUBLE PRECISION ROWCND, COLCND, AMAX DOUBLE PRECISION R(*), C(*) SUBROUTINE ZGEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) DOUBLE COMPLEX A(LDA,*) INTEGER*8 M, N, LDA, INFO DOUBLE PRECISION ROWCND, COLCND, AMAX DOUBLE PRECISION R(*), C(*) F95 INTERFACE SUBROUTINE GEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: M, N, LDA, INFO REAL(8) :: ROWCND, COLCND, AMAX REAL(8), DIMENSION(:) :: R, C SUBROUTINE GEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, INFO REAL(8) :: ROWCND, COLCND, AMAX REAL(8), DIMENSION(:) :: R, C C INTERFACE #include <sunperf.h> void zgeequ(int m, int n, doublecomplex *a, int lda, double *r, double *c, double *rowcnd, double *colcnd, double *amax, int *info); void zgeequ_64(long m, long n, doublecomplex *a, long lda, double *r, double *c, double *rowcnd, double *colcnd, double *amax, long *info); PURPOSE zgeequ computes row and column scalings intended to equilibrate an M- by-N 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. A (input) The M-by-N matrix whose equilibration factors are to be com- puted. LDA (input) The leading dimension of the array A. LDA >= max(1,M). 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 zgeequ(3P)