spoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm
SUBROUTINE SPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER INFO, LDA, N REAL AMAX, SCOND REAL A(LDA,*), S(*) SUBROUTINE SPOEQUB_64 (N, A, LDA, S, SCOND, AMAX, INFO) INTEGER*8 INFO, LDA, N REAL AMAX, SCOND REAL A(LDA,*), S(*) F95 INTERFACE SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, INFO REAL, DIMENSION(:) :: S REAL :: SCOND, AMAX SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, INFO REAL, DIMENSION(:) :: S REAL :: SCOND, AMAX C INTERFACE #include <sunperf.h> void spoequb (int n, float *a, int lda, float *s, float *scond, float *amax, int *info); void spoequb_64 (long n, float *a, long lda, float *s, float *scond, float *amax, long *info);
Oracle Solaris Studio Performance Library spoequb(3P) NAME spoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm SYNOPSIS SUBROUTINE SPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER INFO, LDA, N REAL AMAX, SCOND REAL A(LDA,*), S(*) SUBROUTINE SPOEQUB_64 (N, A, LDA, S, SCOND, AMAX, INFO) INTEGER*8 INFO, LDA, N REAL AMAX, SCOND REAL A(LDA,*), S(*) F95 INTERFACE SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, INFO REAL, DIMENSION(:) :: S REAL :: SCOND, AMAX SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, INFO REAL, DIMENSION(:) :: S REAL :: SCOND, AMAX C INTERFACE #include <sunperf.h> void spoequb (int n, float *a, int lda, float *s, float *scond, float *amax, int *info); void spoequb_64 (long n, float *a, long lda, float *s, float *scond, float *amax, long *info); PURPOSE spoequb computes row and column scalings intended to equilibrate a sym- metric positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condi- tion number over all possible diagonal scalings. ARGUMENTS N (input) N is INTEGER The order of the matrix A. N >= 0. A (input) A is REAL array, dimension (LDA,N) The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). S (output) S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. 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, the i-th diagonal element is nonpositive. 7 Nov 2015 spoequb(3P)