cpbequ
cpbequ - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE CPBEQU( UPLO, N, NDIAG, A, LDA, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*)
INTEGER N, NDIAG, LDA, INFO
REAL SCOND, AMAX
REAL SCALE(*)
SUBROUTINE CPBEQU_64( UPLO, N, NDIAG, A, LDA, SCALE, SCOND, AMAX,
* INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*)
INTEGER*8 N, NDIAG, LDA, INFO
REAL SCOND, AMAX
REAL SCALE(*)
SUBROUTINE PBEQU( UPLO, [N], NDIAG, A, [LDA], SCALE, SCOND, AMAX,
* [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, NDIAG, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
SUBROUTINE PBEQU_64( UPLO, [N], NDIAG, A, [LDA], SCALE, SCOND, AMAX,
* [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, NDIAG, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
#include <sunperf.h>
void cpbequ(char uplo, int n, int ndiag, complex *a, int lda, float *scale, float *scond, float *amax, int *info);
void cpbequ_64(char uplo, long n, long ndiag, complex *a, long lda, float *scale, float *scond, float *amax, long *info);
cpbequ computes row and column scalings intended to equilibrate a
Hermitian 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 condition number over all possible diagonal
scalings.
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* UPLO (input)
-
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* N (input)
-
The order of the matrix A. N >= 0.
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* NDIAG (input)
-
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. NDIAG >= 0.
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* A (input)
-
The upper or lower triangle of the Hermitian band matrix A,
stored in the first NDIAG+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).
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* LDA (input)
-
The leading dimension of the array A. LDA >= NDIAG+1.
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* SCALE (output)
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If INFO = 0, SCALE contains the scale factors for A.
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* SCOND (output)
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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.
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* INFO (output)
-