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ZPOEQU(l)) ZPOEQU(l)NAMEZPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive def- inite matrix A and reduce its condition number (with respect to the two-norm)SYNOPSISSUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND DOUBLE PRECISION S( * ) COMPLEX*16 A( LDA, * )PURPOSEZPOEQU computes row and column scalings intended to equilibrate a Hermitian positive defi- nite 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.ARGUMENTSN (input) INTEGER The order of the matrix A. N >= 0. A (input) COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be com- puted. Only the diagonal elements of A are referenced. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). S (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) 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 (output) 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 (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.-iLAPACK version 3.015 June 2000 ZPOEQU(l)

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