dpbequ - metric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE DPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) SUBROUTINE DPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) F95 INTERFACE SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpbequ(char uplo, int n, int kd, double *a, int lda, double *scale, double *scond, double *amax, int *info); void dpbequ_64(char uplo, long n, long kd, double *a, long lda, double *scale, double *scond, double *amax, long *info);
Oracle Solaris Studio Performance Library dpbequ(3P) NAME dpbequ - compute row and column scalings intended to equilibrate a sym- metric positive definite band matrix A and reduce its condition number (with respect to the two-norm) SYNOPSIS SUBROUTINE DPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) SUBROUTINE DPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDA, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(LDA,*), SCALE(*) F95 INTERFACE SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDA, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: SCALE REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpbequ(char uplo, int n, int kd, double *a, int lda, double *scale, double *scond, double *amax, int *info); void dpbequ_64(char uplo, long n, long kd, double *a, long lda, double *scale, double *scond, double *amax, long *info); PURPOSE dpbequ computes row and column scalings intended to equilibrate a sym- metric positive definite band 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 UPLO (input) = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. A (input) The upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). LDA (input) The leading dimension of the array A. LDA >= KD+1. 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 dpbequ(3P)