#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zppcon_(char *uplo, integer *n, doublecomplex *ap, doublereal *anorm, doublereal *rcond, doublecomplex *work, doublereal *rwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. Purpose ======= ZPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian 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))). 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. 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 = -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; doublereal d__1, d__2; /* Builtin functions */ double d_imag(doublecomplex *); /* Local variables */ static integer ix, kase; static doublereal scale; extern logical lsame_(char *, char *); static integer isave[3]; static logical upper; extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); static doublereal scalel, scaleu; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal ainvnm; extern integer izamax_(integer *, doublecomplex *, integer *); extern /* Subroutine */ int zdrscl_(integer *, doublereal *, doublecomplex *, integer *); static char normin[1]; static doublereal smlnum; extern /* Subroutine */ int zlatps_(char *, char *, char *, char *, integer *, doublecomplex *, doublecomplex *, doublereal *, doublereal *, integer *); --rwork; --work; --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.) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPPCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { *rcond = 1.; return 0; } else if (*anorm == 0.) { return 0; } smlnum = dlamch_("Safe minimum"); /* Estimate the 1-norm of the inverse. */ kase = 0; *(unsigned char *)normin = 'N'; L10: zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave); if (kase != 0) { if (upper) { /* Multiply by inv(U'). */ zlatps_("Upper", "Conjugate transpose", "Non-unit", normin, n, & ap[1], &work[1], &scalel, &rwork[1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(U). */ zlatps_("Upper", "No transpose", "Non-unit", normin, n, &ap[1], & work[1], &scaleu, &rwork[1], info); } else { /* Multiply by inv(L). */ zlatps_("Lower", "No transpose", "Non-unit", normin, n, &ap[1], & work[1], &scalel, &rwork[1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(L'). */ zlatps_("Lower", "Conjugate transpose", "Non-unit", normin, n, & ap[1], &work[1], &scaleu, &rwork[1], info); } /* Multiply by 1/SCALE if doing so will not cause overflow. */ scale = scalel * scaleu; if (scale != 1.) { ix = izamax_(n, &work[1], &c__1); i__1 = ix; if (scale < ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(& work[ix]), abs(d__2))) * smlnum || scale == 0.) { goto L20; } zdrscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } L20: return 0; /* End of ZPPCON */ } /* zppcon_ */