CSYEQUB
Purpose
CSYEQUB computes row and column scalings intended to equilibrate a
symmetric 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.
symmetric 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
| UPLO |
(input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| A |
(input) COMPLEX array, dimension (LDA,N)
The N-by-N symmetric 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) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
|
| SCOND |
(output) REAL
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) REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix should be scaled. |
| WORK |
(workspace) COMPLEX array, dimension (3*N)
|
| 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. |
Further Details
Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf