#include "blaswrap.h" /* zchkgt.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" /* Common Block Declarations */ struct { integer infot, nunit; logical ok, lerr; } infoc_; #define infoc_1 infoc_ struct { char srnamt[6]; } srnamc_; #define srnamc_1 srnamc_ /* Table of constant values */ static integer c__3 = 3; static integer c__0 = 0; static integer c_n1 = -1; static integer c__1 = 1; static integer c__2 = 2; static integer c__7 = 7; static doublereal c_b63 = 1.; static doublereal c_b64 = 0.; /* Subroutine */ int zchkgt_(logical *dotype, integer *nn, integer *nval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, doublecomplex *a, doublecomplex *af, doublecomplex *b, doublecomplex * x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 0,0,0,1 }; static char transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(12x,\002N =\002,i5,\002,\002,10x,\002 type" " \002,i2,\002, test(\002,i2,\002) = \002,g12.5)"; static char fmt_9997[] = "(\002 NORM ='\002,a1,\002', N =\002,i5,\002" ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) = \002,g12." "5)"; static char fmt_9998[] = "(\002 TRANS='\002,a1,\002', N =\002,i5,\002, N" "RHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) = \002,g" "12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static integer i__, j, k, m, n; static doublecomplex z__[3]; static integer in, kl, ku, ix, lda; static doublereal cond; static integer mode, koff, imat, info; static char path[3], dist[1]; static integer irhs, nrhs; static char norm[1], type__[1]; static integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); static integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); static doublereal rcond; static integer nimat; static doublereal anorm; static integer itran; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); static char trans[1]; static integer izero, nerrs; extern /* Subroutine */ int zgtt01_(integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex * , doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zgtt02_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zgtt05_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); static logical zerot; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static doublereal rcondc, rcondi; extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *), alasum_(char *, integer *, integer *, integer *, integer *); static doublereal rcondo, ainvnm; static logical trfcon; extern /* Subroutine */ int zerrge_(char *, integer *); extern doublereal zlangt_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *); extern /* Subroutine */ int zlagtm_(char *, integer *, integer *, doublereal *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern doublereal dzasum_(integer *, doublecomplex *, integer *); extern /* Subroutine */ int zgtcon_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *), zlarnv_(integer *, integer *, integer *, doublecomplex *); static doublereal result[7]; extern /* Subroutine */ int zgtrfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex * , doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgttrf_(integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, integer *), zgttrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___29 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___39 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9998, 0 }; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZCHKGT tests ZGTTRF, -TRS, -RFS, and -CON Arguments ========= DOTYPE (input) LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. NN (input) INTEGER The number of values of N contained in the vector NVAL. NVAL (input) INTEGER array, dimension (NN) The values of the matrix dimension N. NNS (input) INTEGER The number of values of NRHS contained in the vector NSVAL. NSVAL (input) INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS. THRESH (input) DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. TSTERR (input) LOGICAL Flag that indicates whether error exits are to be tested. A (workspace) COMPLEX*16 array, dimension (NMAX*4) AF (workspace) COMPLEX*16 array, dimension (NMAX*4) B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) WORK (workspace) COMPLEX*16 array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(NMAX)+2*NSMAX) IWORK (workspace) INTEGER array, dimension (NMAX) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --af; --a; --nsval; --nval; --dotype; /* Function Body */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "GT", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { zerrge_(path, nout); } infoc_1.infot = 0; i__1 = *nn; for (in = 1; in <= i__1; ++in) { /* Do for each value of N in NVAL. */ n = nval[in]; /* Computing MAX */ i__2 = n - 1; m = max(i__2,0); lda = max(1,n); nimat = 12; if (n <= 0) { nimat = 1; } i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L100; } /* Set up parameters with ZLATB4. */ zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, & cond, dist); zerot = imat >= 8 && imat <= 10; if (imat <= 6) { /* Types 1-6: generate matrices of known condition number. Computing MAX */ i__3 = 2 - ku, i__4 = 3 - max(1,n); koff = max(i__3,i__4); s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond, &anorm, &kl, &ku, "Z", &af[koff], &c__3, &work[1], & info); /* Check the error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, " ", &n, &n, &kl, & ku, &c_n1, &imat, &nfail, &nerrs, nout); goto L100; } izero = 0; if (n > 1) { i__3 = n - 1; zcopy_(&i__3, &af[4], &c__3, &a[1], &c__1); i__3 = n - 1; zcopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1); } zcopy_(&n, &af[2], &c__3, &a[m + 1], &c__1); } else { /* Types 7-12: generate tridiagonal matrices with unknown condition numbers. */ if (! zerot || ! dotype[7]) { /* Generate a matrix with elements whose real and imaginary parts are from [-1,1]. */ i__3 = n + (m << 1); zlarnv_(&c__2, iseed, &i__3, &a[1]); if (anorm != 1.) { i__3 = n + (m << 1); zdscal_(&i__3, &anorm, &a[1], &c__1); } } else if (izero > 0) { /* Reuse the last matrix by copying back the zeroed out elements. */ if (izero == 1) { i__3 = n; a[i__3].r = z__[1].r, a[i__3].i = z__[1].i; if (n > 1) { a[1].r = z__[2].r, a[1].i = z__[2].i; } } else if (izero == n) { i__3 = n * 3 - 2; a[i__3].r = z__[0].r, a[i__3].i = z__[0].i; i__3 = (n << 1) - 1; a[i__3].r = z__[1].r, a[i__3].i = z__[1].i; } else { i__3 = (n << 1) - 2 + izero; a[i__3].r = z__[0].r, a[i__3].i = z__[0].i; i__3 = n - 1 + izero; a[i__3].r = z__[1].r, a[i__3].i = z__[1].i; i__3 = izero; a[i__3].r = z__[2].r, a[i__3].i = z__[2].i; } } /* If IMAT > 7, set one column of the matrix to 0. */ if (! zerot) { izero = 0; } else if (imat == 8) { izero = 1; i__3 = n; z__[1].r = a[i__3].r, z__[1].i = a[i__3].i; i__3 = n; a[i__3].r = 0., a[i__3].i = 0.; if (n > 1) { z__[2].r = a[1].r, z__[2].i = a[1].i; a[1].r = 0., a[1].i = 0.; } } else if (imat == 9) { izero = n; i__3 = n * 3 - 2; z__[0].r = a[i__3].r, z__[0].i = a[i__3].i; i__3 = (n << 1) - 1; z__[1].r = a[i__3].r, z__[1].i = a[i__3].i; i__3 = n * 3 - 2; a[i__3].r = 0., a[i__3].i = 0.; i__3 = (n << 1) - 1; a[i__3].r = 0., a[i__3].i = 0.; } else { izero = (n + 1) / 2; i__3 = n - 1; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = (n << 1) - 2 + i__; a[i__4].r = 0., a[i__4].i = 0.; i__4 = n - 1 + i__; a[i__4].r = 0., a[i__4].i = 0.; i__4 = i__; a[i__4].r = 0., a[i__4].i = 0.; /* L20: */ } i__3 = n * 3 - 2; a[i__3].r = 0., a[i__3].i = 0.; i__3 = (n << 1) - 1; a[i__3].r = 0., a[i__3].i = 0.; } } /* + TEST 1 Factor A as L*U and compute the ratio norm(L*U - A) / (n * norm(A) * EPS ) */ i__3 = n + (m << 1); zcopy_(&i__3, &a[1], &c__1, &af[1], &c__1); s_copy(srnamc_1.srnamt, "ZGTTRF", (ftnlen)6, (ftnlen)6); zgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &info); /* Check error code from ZGTTRF. */ if (info != izero) { alaerh_(path, "ZGTTRF", &info, &izero, " ", &n, &n, &c__1, & c__1, &c_n1, &imat, &nfail, &nerrs, nout); } trfcon = info != 0; zgtt01_(&n, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &af[m + 1], & af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &work[1], &lda, &rwork[1], result); /* Print the test ratio if it is .GE. THRESH. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___29.ciunit = *nout; s_wsfe(&io___29); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(doublereal)); e_wsfe(); ++nfail; } ++nrun; for (itran = 1; itran <= 2; ++itran) { *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1] ; if (itran == 1) { *(unsigned char *)norm = 'O'; } else { *(unsigned char *)norm = 'I'; } anorm = zlangt_(norm, &n, &a[1], &a[m + 1], &a[n + m + 1]); if (! trfcon) { /* Use ZGTTRS to solve for one column at a time of inv(A), computing the maximum column sum as we go. */ ainvnm = 0.; i__3 = n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = n; for (j = 1; j <= i__4; ++j) { i__5 = j; x[i__5].r = 0., x[i__5].i = 0.; /* L30: */ } i__4 = i__; x[i__4].r = 1., x[i__4].i = 0.; zgttrs_(trans, &n, &c__1, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &x[ 1], &lda, &info); /* Computing MAX */ d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1); ainvnm = max(d__1,d__2); /* L40: */ } /* Compute RCONDC = 1 / (norm(A) * norm(inv(A)) */ if (anorm <= 0. || ainvnm <= 0.) { rcondc = 1.; } else { rcondc = 1. / anorm / ainvnm; } if (itran == 1) { rcondo = rcondc; } else { rcondi = rcondc; } } else { rcondc = 0.; } /* + TEST 7 Estimate the reciprocal of the condition number of the matrix. */ s_copy(srnamc_1.srnamt, "ZGTCON", (ftnlen)6, (ftnlen)6); zgtcon_(norm, &n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &anorm, &rcond, &work[1], & info); /* Check error code from ZGTCON. */ if (info != 0) { alaerh_(path, "ZGTCON", &info, &c__0, norm, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[6] = dget06_(&rcond, &rcondc); /* Print the test ratio if it is .GE. THRESH. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, norm, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; /* L50: */ } /* Skip the remaining tests if the matrix is singular. */ if (trfcon) { goto L100; } i__3 = *nns; for (irhs = 1; irhs <= i__3; ++irhs) { nrhs = nsval[irhs]; /* Generate NRHS random solution vectors. */ ix = 1; i__4 = nrhs; for (j = 1; j <= i__4; ++j) { zlarnv_(&c__2, iseed, &n, &xact[ix]); ix += lda; /* L60: */ } for (itran = 1; itran <= 3; ++itran) { *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]; if (itran == 1) { rcondc = rcondo; } else { rcondc = rcondi; } /* Set the right hand side. */ zlagtm_(trans, &n, &nrhs, &c_b63, &a[1], &a[m + 1], &a[n + m + 1], &xact[1], &lda, &c_b64, &b[1], &lda); /* + TEST 2 Solve op(A) * X = B and compute the residual. */ zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZGTTRS", (ftnlen)6, (ftnlen)6); zgttrs_(trans, &n, &nrhs, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &x[1], &lda, &info); /* Check error code from ZGTTRS. */ if (info != 0) { alaerh_(path, "ZGTTRS", &info, &c__0, trans, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); zgtt02_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], &x[1], &lda, &work[1], &lda, &rwork[1], &result[ 1]); /* + TEST 3 Check solution from generated exact solution. */ zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[2]); /* + TESTS 4, 5, and 6 Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "ZGTRFS", (ftnlen)6, (ftnlen)6); zgtrfs_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &b[1], &lda, &x[1], &lda, & rwork[1], &rwork[nrhs + 1], &work[1], &rwork[( nrhs << 1) + 1], &info); /* Check error code from ZGTRFS. */ if (info != 0) { alaerh_(path, "ZGTRFS", &info, &c__0, trans, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[3]); zgtt05_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[ 1], &rwork[nrhs + 1], &result[4]); /* Print information about the tests that did not pass the threshold. */ for (k = 2; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___44.ciunit = *nout; s_wsfe(&io___44); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } /* L70: */ } nrun += 5; /* L80: */ } /* L90: */ } L100: ; } /* L110: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKGT */ } /* zchkgt_ */