
NAMEzpoequ.f SYNOPSISFunctions/Subroutinessubroutine zpoequ (N, A, LDA, S, SCOND, AMAX, INFO) Function/Subroutine Documentationsubroutine zpoequ (integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)ZPOEQU 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 twonorm). 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. N
Author:
N is INTEGER The order of the matrix A. N >= 0.A A is COMPLEX*16 array, dimension (LDA,N) The NbyN Hermitian positive definite 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.INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, the ith diagonal element is nonpositive. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 114 of file zpoequ.f.
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