.TH CPOEQU 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CPOEQU - row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) .SH SYNOPSIS .TP 19 SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) .TP 19 .ti +4 INTEGER INFO, LDA, N .TP 19 .ti +4 REAL AMAX, SCOND .TP 19 .ti +4 REAL S( * ) .TP 19 .ti +4 COMPLEX A( LDA, * ) .SH PURPOSE CPOEQU 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. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 A (input) COMPLEX 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 S (output) REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. .TP 8 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. .TP 8 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, the i-th diagonal element is nonpositive.