#include "blaswrap.h" /* zppt03.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" /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static integer c__1 = 1; /* Subroutine */ int zppt03_(char *uplo, integer *n, doublecomplex *a, doublecomplex *ainv, doublecomplex *work, integer *ldwork, doublereal *rwork, doublereal *rcond, doublereal *resid) { /* System generated locals */ integer work_dim1, work_offset, i__1, i__2, i__3; doublecomplex z__1; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer i__, j, jj; static doublereal eps; extern logical lsame_(char *, char *); static doublereal anorm; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhpmv_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); extern doublereal dlamch_(char *), zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); static doublereal ainvnm; extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, doublereal *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZPPT03 computes the residual for a Hermitian packed matrix times its inverse: norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), where EPS is the machine epsilon. Arguments ========== UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The number of rows and columns of the matrix A. N >= 0. A (input) COMPLEX*16 array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix. AINV (input) COMPLEX*16 array, dimension (N*(N+1)/2) The (Hermitian) inverse of the matrix A, stored as a packed triangular matrix. WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N) LDWORK (input) INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N). RWORK (workspace) DOUBLE PRECISION array, dimension (N) RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV). RESID (output) DOUBLE PRECISION norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) ===================================================================== Quick exit if N = 0. Parameter adjustments */ --a; --ainv; work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; --rwork; /* Function Body */ if (*n <= 0) { *rcond = 1.; *resid = 0.; return 0; } /* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */ eps = dlamch_("Epsilon"); anorm = zlanhp_("1", uplo, n, &a[1], &rwork[1]); ainvnm = zlanhp_("1", uplo, n, &ainv[1], &rwork[1]); if (anorm <= 0. || ainvnm <= 0.) { *rcond = 0.; *resid = 1. / eps; return 0; } *rcond = 1. / anorm / ainvnm; /* UPLO = 'U': Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and expand it to a full matrix, then multiply by A one column at a time, moving the result one column to the left. */ if (lsame_(uplo, "U")) { /* Copy AINV */ jj = 1; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { zcopy_(&j, &ainv[jj], &c__1, &work[(j + 1) * work_dim1 + 1], & c__1); i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + (i__ + 1) * work_dim1; d_cnjg(&z__1, &ainv[jj + i__ - 1]); work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L10: */ } jj += j; /* L20: */ } jj = (*n - 1) * *n / 2 + 1; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n + (i__ + 1) * work_dim1; d_cnjg(&z__1, &ainv[jj + i__ - 1]); work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L30: */ } /* Multiply by A */ i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { z__1.r = -1., z__1.i = -0.; zhpmv_("Upper", n, &z__1, &a[1], &work[(j + 1) * work_dim1 + 1], & c__1, &c_b1, &work[j * work_dim1 + 1], &c__1); /* L40: */ } z__1.r = -1., z__1.i = -0.; zhpmv_("Upper", n, &z__1, &a[1], &ainv[jj], &c__1, &c_b1, &work[*n * work_dim1 + 1], &c__1); /* UPLO = 'L': Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1) and multiply by A, moving each column to the right. */ } else { /* Copy AINV */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ * work_dim1 + 1; d_cnjg(&z__1, &ainv[i__ + 1]); work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L50: */ } jj = *n + 1; i__1 = *n; for (j = 2; j <= i__1; ++j) { i__2 = *n - j + 1; zcopy_(&i__2, &ainv[jj], &c__1, &work[j + (j - 1) * work_dim1], & c__1); i__2 = *n - j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + (j + i__ - 1) * work_dim1; d_cnjg(&z__1, &ainv[jj + i__]); work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L60: */ } jj = jj + *n - j + 1; /* L70: */ } /* Multiply by A */ for (j = *n; j >= 2; --j) { z__1.r = -1., z__1.i = -0.; zhpmv_("Lower", n, &z__1, &a[1], &work[(j - 1) * work_dim1 + 1], & c__1, &c_b1, &work[j * work_dim1 + 1], &c__1); /* L80: */ } z__1.r = -1., z__1.i = -0.; zhpmv_("Lower", n, &z__1, &a[1], &ainv[1], &c__1, &c_b1, &work[ work_dim1 + 1], &c__1); } /* Add the identity matrix to WORK . */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * work_dim1; i__3 = i__ + i__ * work_dim1; z__1.r = work[i__3].r + 1., z__1.i = work[i__3].i + 0.; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L90: */ } /* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) */ *resid = zlange_("1", n, n, &work[work_offset], ldwork, &rwork[1]); *resid = *resid * *rcond / eps / (doublereal) (*n); return 0; /* End of ZPPT03 */ } /* zppt03_ */