/* zla_porcond_c.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__1 = 1; doublereal zla_porcond_c__(char *uplo, integer *n, doublecomplex *a, integer * lda, doublecomplex *af, integer *ldaf, doublereal *c__, logical * capply, integer *info, doublecomplex *work, doublereal *rwork, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4; doublereal ret_val, d__1, d__2; doublecomplex z__1; /* Builtin functions */ double d_imag(doublecomplex *); /* Local variables */ integer i__, j; logical up; doublereal tmp; integer kase; extern logical lsame_(char *, char *); integer isave[3]; doublereal anorm; extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *), xerbla_( char *, integer *); doublereal ainvnm; extern /* Subroutine */ int zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); /* -- LAPACK routine (version 3.2.1) -- */ /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ /* -- Jason Riedy of Univ. of California Berkeley. -- */ /* -- April 2009 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley and NAG Ltd. -- */ /* .. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZLA_PORCOND_C Computes the infinity norm condition number of */ /* op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* A (input) COMPLEX*16 array, dimension (LDA,N) */ /* On entry, the N-by-N matrix A */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input) COMPLEX*16 array, dimension (LDAF,N) */ /* The triangular factor U or L from the Cholesky factorization */ /* A = U**T*U or A = L*L**T, as computed by ZPOTRF. */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* C (input) DOUBLE PRECISION array, dimension (N) */ /* The vector C in the formula op(A) * inv(diag(C)). */ /* CAPPLY (input) LOGICAL */ /* If .TRUE. then access the vector C in the formula above. */ /* INFO (output) INTEGER */ /* = 0: Successful exit. */ /* i > 0: The ith argument is invalid. */ /* WORK (input) COMPLEX*16 array, dimension (2*N). */ /* Workspace. */ /* RWORK (input) DOUBLE PRECISION array, dimension (N). */ /* Workspace. */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function Definitions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --c__; --work; --rwork; /* Function Body */ ret_val = 0.; *info = 0; if (*n < 0) { *info = -2; } if (*info != 0) { i__1 = -(*info); xerbla_("ZLA_PORCOND_C", &i__1); return ret_val; } up = FALSE_; if (lsame_(uplo, "U")) { up = TRUE_; } /* Compute norm of op(A)*op2(C). */ anorm = 0.; if (up) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { tmp = 0.; if (*capply) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ j + i__ * a_dim1]), abs(d__2))) / c__[j]; } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ i__ + j * a_dim1]), abs(d__2))) / c__[j]; } } else { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ j + i__ * a_dim1]), abs(d__2)); } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ i__ + j * a_dim1]), abs(d__2)); } } rwork[i__] = tmp; anorm = max(anorm,tmp); } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { tmp = 0.; if (*capply) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ i__ + j * a_dim1]), abs(d__2))) / c__[j]; } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ j + i__ * a_dim1]), abs(d__2))) / c__[j]; } } else { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ i__ + j * a_dim1]), abs(d__2)); } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[ j + i__ * a_dim1]), abs(d__2)); } } rwork[i__] = tmp; anorm = max(anorm,tmp); } } /* Quick return if possible. */ if (*n == 0) { ret_val = 1.; return ret_val; } else if (anorm == 0.) { return ret_val; } /* Estimate the norm of inv(op(A)). */ ainvnm = 0.; kase = 0; L10: zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == 2) { /* Multiply by R. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; } if (up) { zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n, info); } else { zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n, info); } /* Multiply by inv(C). */ if (*capply) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; z__1.r = c__[i__4] * work[i__3].r, z__1.i = c__[i__4] * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; } } } else { /* Multiply by inv(C'). */ if (*capply) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; z__1.r = c__[i__4] * work[i__3].r, z__1.i = c__[i__4] * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; } } if (up) { zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n, info); } else { zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n, info); } /* Multiply by R. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; } } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { ret_val = 1. / ainvnm; } return ret_val; } /* zla_porcond_c__ */