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NAME SPPEQU - compute row and column scalings intended to equili- brate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) SYNOPSIS SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO ) CHARACTER UPLO INTEGER INFO, N REAL AMAX, SCOND REAL AP( * ), S( * ) PURPOSE SPPEQU computes row and column scalings intended to equili- brate a symmetric positive definite matrix A in packed storage 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. ARGUMENTS UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. AP (input) REAL array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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 = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal entry is nonpo- sitive.