Contents
cpbequ - compute row and column scalings intended to equili-
brate a Hermitian 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);
cpbequ computes row and column scalings intended to equili-
brate a Hermitian positive definite band matrix A and reduce
its condition number (with respect to the two-norm). S con-
tains 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 diago-
nal scalings.
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 smal-
lest 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 under-
flow, the matrix should be scaled.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: if INFO = i, the i-th diagonal element is
nonpositive.