cgeequb - by-N matrix A and reduce its condition number
SUBROUTINE CGEEQUB(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER INFO, LDA, M, N REAL AMAX, COLCND, ROWCND REAL C(*), R(*) COMPLEX A(LDA,*) SUBROUTINE CGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER*8 INFO, LDA, M, N REAL AMAX, COLCND, ROWCND REAL C(*), R(*) COMPLEX A(LDA,*) F95 INTERFACE SUBROUTINE GEEQUB(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER :: M, N, LDA, INFO REAL, DIMENSION(:) :: R, C COMPLEX, DIMENSION(:,:) :: A REAL :: ROWCND, COLCND, AMAX SUBROUTINE GEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER(8) :: M, N, LDA, INFO REAL, DIMENSION(:) :: R, C COMPLEX, DIMENSION(:,:) :: A REAL :: ROWCND, COLCND, AMAX C INTERFACE #include <sunperf.h> void cgeequb (int m, int n, floatcomplex *a, int lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int *info); void cgeequb_64 (long m, long n, floatcomplex *a, long lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, long *info);
Oracle Solaris Studio Performance Library cgeequb(3P) NAME cgeequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number SYNOPSIS SUBROUTINE CGEEQUB(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER INFO, LDA, M, N REAL AMAX, COLCND, ROWCND REAL C(*), R(*) COMPLEX A(LDA,*) SUBROUTINE CGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER*8 INFO, LDA, M, N REAL AMAX, COLCND, ROWCND REAL C(*), R(*) COMPLEX A(LDA,*) F95 INTERFACE SUBROUTINE GEEQUB(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER :: M, N, LDA, INFO REAL, DIMENSION(:) :: R, C COMPLEX, DIMENSION(:,:) :: A REAL :: ROWCND, COLCND, AMAX SUBROUTINE GEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER(8) :: M, N, LDA, INFO REAL, DIMENSION(:) :: R, C COMPLEX, DIMENSION(:,:) :: A REAL :: ROWCND, COLCND, AMAX C INTERFACE #include <sunperf.h> void cgeequb (int m, int n, floatcomplex *a, int lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int *info); void cgeequb_64 (long m, long n, floatcomplex *a, long lda, float *r, float *c, float *rowcnd, float *colcnd, float *amax, long *info); PURPOSE cgeequb 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 an absolute value of at most the radix. R(i) and C(j) are restricted to be a power of the radix 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. This routine differs from CGEEQU by restricting the scaling factors to a power of the radix. Baring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitured are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). ARGUMENTS M (input) M is INTEGER The number of rows of the matrix A. M >= 0. N (input) N is INTEGER The number of columns of the matrix A. N >= 0. A (input) A is COMPLEX array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). R (output) R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A. C (output) C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND (output) ROWCND is 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) COLCND is 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 scal- ing by C. AMAX (output) AMAX is 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) INFO is 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 7 Nov 2015 cgeequb(3P)