#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cspcon_(char *uplo, integer *n, complex *ap, integer * ipiv, real *anorm, real *rcond, complex *work, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= CSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). Arguments ========= UPLO (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) COMPLEX array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix. IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSPTRF. ANORM (input) REAL The 1-norm of the original matrix A. RCOND (output) REAL 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 array, dimension (2*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer i__1, i__2; /* Local variables */ static integer kase, i__; extern logical lsame_(char *, char *); static logical upper; static integer ip; extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real *, integer *), xerbla_(char *, integer *); static real ainvnm; extern /* Subroutine */ int csptrs_(char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *); --work; --ipiv; --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*anorm < 0.f) { *info = -5; } if (*info != 0) { i__1 = -(*info); xerbla_("CSPCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.f; if (*n == 0) { *rcond = 1.f; return 0; } else if (*anorm <= 0.f) { return 0; } /* Check that the diagonal matrix D is nonsingular. */ if (upper) { /* Upper triangular storage: examine D from bottom to top */ ip = *n * (*n + 1) / 2; for (i__ = *n; i__ >= 1; --i__) { i__1 = ip; if (ipiv[i__] > 0 && (ap[i__1].r == 0.f && ap[i__1].i == 0.f)) { return 0; } ip -= i__; /* L10: */ } } else { /* Lower triangular storage: examine D from top to bottom. */ ip = 1; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ip; if (ipiv[i__] > 0 && (ap[i__2].r == 0.f && ap[i__2].i == 0.f)) { return 0; } ip = ip + *n - i__ + 1; /* L20: */ } } /* Estimate the 1-norm of the inverse. */ kase = 0; L30: clacon_(n, &work[*n + 1], &work[1], &ainvnm, &kase); if (kase != 0) { /* Multiply by inv(L*D*L') or inv(U*D*U'). */ csptrs_(uplo, n, &c__1, &ap[1], &ipiv[1], &work[1], n, info); goto L30; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.f) { *rcond = 1.f / ainvnm / *anorm; } return 0; /* End of CSPCON */ } /* cspcon_ */