#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cpocon_(char *uplo, integer *n, complex *a, integer *lda, real *anorm, real *rcond, complex *work, real *rwork, 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 ======= CPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF. 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 = '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. A (input) COMPLEX array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM (input) REAL The 1-norm (or infinity-norm) of the Hermitian 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) RWORK (workspace) REAL array, dimension (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 a_dim1, a_offset, i__1; real r__1, r__2; /* Builtin functions */ double r_imag(complex *); /* Local variables */ static integer kase; static real scale; extern logical lsame_(char *, char *); static logical upper; extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real *, integer *); static integer ix; extern integer icamax_(integer *, complex *, integer *); static real scalel; extern doublereal slamch_(char *); static real scaleu; extern /* Subroutine */ int xerbla_(char *, integer *); static real ainvnm; extern /* Subroutine */ int clatrs_(char *, char *, char *, char *, integer *, complex *, integer *, complex *, real *, real *, integer *), csrscl_(integer *, real *, complex *, integer *); static char normin[1]; static real smlnum; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --work; --rwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } else if (*anorm < 0.f) { *info = -5; } if (*info != 0) { i__1 = -(*info); xerbla_("CPOCON", &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; } smlnum = slamch_("Safe minimum"); /* Estimate the 1-norm of inv(A). */ kase = 0; *(unsigned char *)normin = 'N'; L10: clacon_(n, &work[*n + 1], &work[1], &ainvnm, &kase); if (kase != 0) { if (upper) { /* Multiply by inv(U'). */ clatrs_("Upper", "Conjugate transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scalel, &rwork[1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(U). */ clatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scaleu, &rwork[1], info); } else { /* Multiply by inv(L). */ clatrs_("Lower", "No transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scalel, &rwork[1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(L'). */ clatrs_("Lower", "Conjugate transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scaleu, &rwork[1], info); } /* Multiply by 1/SCALE if doing so will not cause overflow. */ scale = scalel * scaleu; if (scale != 1.f) { ix = icamax_(n, &work[1], &c__1); i__1 = ix; if (scale < ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(& work[ix]), dabs(r__2))) * smlnum || scale == 0.f) { goto L20; } csrscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.f) { *rcond = 1.f / ainvnm / *anorm; } L20: return 0; /* End of CPOCON */ } /* cpocon_ */