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zsyequb.f(3) LAPACK zsyequb.f(3)

zsyequb.f -


subroutine zsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
 
ZSYEQUB

ZSYEQUB
Purpose:
 ZSYEQUB 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
          N is INTEGER
          The order of the matrix A.  N >= 0.
A
          A is COMPLEX*16 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
          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
SCOND
          SCOND is 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
          AMAX is 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.
WORK
          WORK is COMPLEX*16 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 zsyequb.f.

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