sppequ - metric positive definite matrix A in packed storage and reduce its con- dition number (with respect to the two-norm)
SUBROUTINE SPPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER N, INFO REAL SCOND, AMAX REAL A(*), SCALE(*) SUBROUTINE SPPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER*8 N, INFO REAL SCOND, AMAX REAL A(*), SCALE(*) F95 INTERFACE SUBROUTINE PPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: A, SCALE SUBROUTINE PPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: A, SCALE C INTERFACE #include <sunperf.h> void sppequ(char uplo, int n, float *a, float *scale, float *scond, float *amax, int *info); void sppequ_64(char uplo, long n, float *a, float *scale, float *scond, float *amax, long *info);
Oracle Solaris Studio Performance Library sppequ(3P) NAME sppequ - compute row and column scalings intended to equilibrate a sym- metric positive definite matrix A in packed storage and reduce its con- dition number (with respect to the two-norm) SYNOPSIS SUBROUTINE SPPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER N, INFO REAL SCOND, AMAX REAL A(*), SCALE(*) SUBROUTINE SPPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER*8 N, INFO REAL SCOND, AMAX REAL A(*), SCALE(*) F95 INTERFACE SUBROUTINE PPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: A, SCALE SUBROUTINE PPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: A, SCALE C INTERFACE #include <sunperf.h> void sppequ(char uplo, int n, float *a, float *scale, float *scond, float *amax, int *info); void sppequ_64(char uplo, long n, float *a, float *scale, float *scond, float *amax, long *info); PURPOSE sppequ computes row and column scalings intended to equilibrate a sym- metric positive definite matrix A in packed storage and reduce its con- dition 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 condition number over all possible diagonal scalings. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. A (input) REAL array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. SCALE (output) REAL array, dimension (N) 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 sppequ(3P)