ZPOEQU
November 2006
Purpose
ZPOEQU computes row and column scalings intended to equilibrate a
Hermitian positive definite 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.
Hermitian positive definite 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.
Arguments
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| A |
(input) COMPLEX*16 array, dimension (LDA,N)
The N-by-N Hermitian positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A are referenced. |
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
|
| S |
(output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
|
| SCOND |
(output) DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. |
| AMAX |
(output) DOUBLE PRECISION
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) INTEGER
= 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. |