csyequb-f(3)

csyequb.f –

Synopsis

Functions/Subroutines

subroutine csyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
CSYEQUB

Function/Subroutine Documentation

subroutine csyequb (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, complex, dimension( * )WORK, integerINFO)

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.

Parameters:

UPLO

 UPLO is 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 is INTEGER
 The order of the matrix A. N >= 0.

 A is 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

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

 S is REAL array, dimension (N)
 If INFO = 0, S contains the scale factors for A.

SCOND

 SCOND is 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

 AMAX is 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

 WORK is COMPLEX array, dimension (3*N)

INFO

 INFO is 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

References:

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

Definition at line 137 of file csyequb.f.

Author

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