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ZPPCON(l)) ZPPCON(l)NAMEZPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Her- mitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRFSYNOPSISSUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION RWORK( * ) COMPLEX*16 AP( * ), WORK( * )PURPOSEZPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Her- mitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).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) COMPLEX*16 array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. ANORM (input) DOUBLE PRECISION The 1-norm (or infinity-norm) of the Hermitian matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. WORK (workspace) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 ZPPCON(l)

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