dpoequ - metric positive definite matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE DPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER N, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) SUBROUTINE DPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER*8 N, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) F95 INTERFACE SUBROUTINE POEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER :: N, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A SUBROUTINE POEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER(8) :: N, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpoequ(int n, double *a, int lda, double *scale, double *scond, double *amax, int *info); void dpoequ_64(long n, double *a, long lda, double *scale, double *scond, double *amax, long *info);
Oracle Solaris Studio Performance Library dpoequ(3P) NAME dpoequ - compute 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) SYNOPSIS SUBROUTINE DPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER N, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) SUBROUTINE DPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER*8 N, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) F95 INTERFACE SUBROUTINE POEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER :: N, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A SUBROUTINE POEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO) INTEGER(8) :: N, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpoequ(int n, double *a, int lda, double *scale, double *scond, double *amax, int *info); void dpoequ_64(long n, double *a, long lda, double *scale, double *scond, double *amax, long *info); PURPOSE dpoequ 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) The order of the matrix A. N >= 0. A (input) 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) The leading dimension of the array A. LDA >= max(1,N). SCALE (output) If INFO = 0, SCALE contains the scale factors for A. SCOND (output) If INFO = 0, SCALE contains the ratio of the smallest SCALE(i) to the largest SCALE(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by SCALE. 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, the i-th diagonal element is nonpositive. 7 Nov 2015 dpoequ(3P)