cpbequ - mitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE CPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*) INTEGER N, KD, LDA, INFO REAL SCOND, AMAX REAL SCALE(*) SUBROUTINE CPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*) INTEGER*8 N, KD, LDA, INFO REAL SCOND, AMAX REAL SCALE(*) F95 INTERFACE SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:,:) :: A INTEGER :: N, KD, LDA, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: SCALE SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: N, KD, LDA, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: SCALE C INTERFACE #include <sunperf.h> void cpbequ(char uplo, int n, int kd, complex *a, int lda, float *scale, float *scond, float *amax, int *info); void cpbequ_64(char uplo, long n, long kd, complex *a, long lda, float *scale, float *scond, float *amax, long *info);
Oracle Solaris Studio Performance Library cpbequ(3P) NAME cpbequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) SYNOPSIS SUBROUTINE CPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*) INTEGER N, KD, LDA, INFO REAL SCOND, AMAX REAL SCALE(*) SUBROUTINE CPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*) INTEGER*8 N, KD, LDA, INFO REAL SCOND, AMAX REAL SCALE(*) F95 INTERFACE SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:,:) :: A INTEGER :: N, KD, LDA, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: SCALE SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: N, KD, LDA, INFO REAL :: SCOND, AMAX REAL, DIMENSION(:) :: SCALE C INTERFACE #include <sunperf.h> void cpbequ(char uplo, int n, int kd, complex *a, int lda, float *scale, float *scond, float *amax, int *info); void cpbequ_64(char uplo, long n, long kd, complex *a, long lda, float *scale, float *scond, float *amax, long *info); PURPOSE cpbequ computes row and column scalings intended to equilibrate a Her- mitian 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 Hermitian 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 cpbequ(3P)