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DPPEQU(l)) DPPEQU(l)NAMEDPPEQU - compute row and column scalings intended to equilibrate a symmetric positive def- inite matrix A in packed storage and reduce its condition number (with respect to the two- norm)SYNOPSISSUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO ) CHARACTER UPLO INTEGER INFO, N DOUBLE PRECISION AMAX, SCOND DOUBLE PRECISION AP( * ), S( * )PURPOSEDPPEQU computes row and column scalings intended to equilibrate a symmetric positive defi- nite 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.ARGUMENTSUPLO (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) DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin- ear 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) 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 DPPEQU(l)

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