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DSPTRI(l)) DSPTRI(l)NAMEDSPTRI - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRFSYNOPSISSUBROUTINE DSPTRI( UPLO, N, AP, IPIV, WORK, INFO ) CHARACTER UPLO INTEGER INFO, N INTEGER IPIV( * ) DOUBLE PRECISION AP( * ), WORK( * )PURPOSEDSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF.ARGUMENTSUPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N (input) INTEGER The order of the matrix A. N >= 0. AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the block diagonal matrix D and the multipliers used to obtain the fac- tor U or L as computed by DSPTRF, stored as a packed triangular matrix. On exit, if INFO = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSPTRF. WORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.-iLAPACK version 3.015 June 2000 DSPTRI(l)

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