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SPOEQU(l)) SPOEQU(l)SPOEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)NAMESUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) INTEGER INFO, LDA, N REAL AMAX, SCOND REAL A( LDA, * ), S( * )SYNOPSISSPOEQU computes row and column scalings intended to equilibrate a symmetric 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 condi- tion number over all possible diagonal scalings.PURPOSEN (input) INTEGER The order of the matrix A. N >= 0. A (input) REAL array, dimension (LDA,N) The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). S (output) REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. 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. AMAX (output) REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to under- flow, the matrix should be scaled. INFO (output) INTEGER = 0: successful exit < 0: if INFO =ARGUMENTS, 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 SPOEQU(l)

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