#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #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 real c_b63 = 1.f; static real c_b64 = 0.f; /* Subroutine */ int cchkgt_(logical *dotype, integer *nn, integer *nval, integer *nns, integer *nsval, real *thresh, logical *tsterr, complex * a, complex *af, complex *b, complex *x, complex *xact, complex *work, real *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; real r__1, r__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 real 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, i__, j, k; extern /* Subroutine */ int alahd_(integer *, char *); static integer m, n; extern /* Subroutine */ int cget04_(integer *, integer *, complex *, integer *, complex *, integer *, real *, real *); static integer nfail, iseed[4]; static complex z__[3]; extern /* Subroutine */ int cgtt01_(integer *, complex *, complex *, complex *, complex *, complex *, complex *, complex *, integer *, complex *, integer *, real *, real *), cgtt02_(char *, integer *, integer *, complex *, complex *, complex *, complex *, integer *, complex *, integer *, real *, real *); static real rcond; extern /* Subroutine */ int cgtt05_(char *, integer *, integer *, complex *, complex *, complex *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, real *); static integer nimat; extern doublereal sget06_(real *, real *); static real anorm; static integer itran; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); static char trans[1]; static integer izero, nerrs; static logical zerot; extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ); static integer in, kl; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static integer ku, ix; extern /* Subroutine */ int cerrge_(char *, integer *); static real rcondc; extern doublereal clangt_(char *, integer *, complex *, complex *, complex *); extern /* Subroutine */ int clagtm_(char *, integer *, integer *, real *, complex *, complex *, complex *, complex *, integer *, real *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), csscal_( integer *, real *, complex *, integer *), cgtcon_(char *, integer *, complex *, complex *, complex *, complex *, integer *, real *, real *, complex *, integer *); static real rcondi; extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); static real rcondo; extern /* Subroutine */ int clarnv_(integer *, integer *, integer *, complex *), clatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char * , complex *, integer *, complex *, integer *); static real ainvnm; extern /* Subroutine */ int cgtrfs_(char *, integer *, integer *, complex *, complex *, complex *, complex *, complex *, complex *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *), cgttrf_(integer *, complex *, complex *, complex *, complex *, integer *, integer *); static logical trfcon; extern doublereal scasum_(integer *, complex *, integer *); extern /* Subroutine */ int cgttrs_(char *, integer *, integer *, complex *, complex *, complex *, complex *, integer *, complex *, integer *, integer *); static real result[7]; static integer lda; /* 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 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CCHKGT tests CGTTRF, -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) REAL 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 array, dimension (NMAX*4) AF (workspace) COMPLEX array, dimension (NMAX*4) B (workspace) COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) COMPLEX array, dimension (NMAX*NSMAX) XACT (workspace) COMPLEX array, dimension (NMAX*NSMAX) WORK (workspace) COMPLEX array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) REAL 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, "Complex 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) { cerrge_(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 CLATB4. */ clatb4_(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, "CLATMS", (ftnlen)6, (ftnlen)6); clatms_(&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 CLATMS. */ if (info != 0) { alaerh_(path, "CLATMS", &info, &c__0, " ", &n, &n, &kl, & ku, &c_n1, &imat, &nfail, &nerrs, nout); goto L100; } izero = 0; if (n > 1) { i__3 = n - 1; ccopy_(&i__3, &af[4], &c__3, &a[1], &c__1); i__3 = n - 1; ccopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1); } ccopy_(&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); clarnv_(&c__2, iseed, &i__3, &a[1]); if (anorm != 1.f) { i__3 = n + (m << 1); csscal_(&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.f, a[i__3].i = 0.f; if (n > 1) { z__[2].r = a[1].r, z__[2].i = a[1].i; a[1].r = 0.f, a[1].i = 0.f; } } 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.f, a[i__3].i = 0.f; i__3 = (n << 1) - 1; a[i__3].r = 0.f, a[i__3].i = 0.f; } 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.f, a[i__4].i = 0.f; i__4 = n - 1 + i__; a[i__4].r = 0.f, a[i__4].i = 0.f; i__4 = i__; a[i__4].r = 0.f, a[i__4].i = 0.f; /* L20: */ } i__3 = n * 3 - 2; a[i__3].r = 0.f, a[i__3].i = 0.f; i__3 = (n << 1) - 1; a[i__3].r = 0.f, a[i__3].i = 0.f; } } /* + TEST 1 Factor A as L*U and compute the ratio norm(L*U - A) / (n * norm(A) * EPS ) */ i__3 = n + (m << 1); ccopy_(&i__3, &a[1], &c__1, &af[1], &c__1); s_copy(srnamc_1.srnamt, "CGTTRF", (ftnlen)6, (ftnlen)6); cgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &info); /* Check error code from CGTTRF. */ if (info != izero) { alaerh_(path, "CGTTRF", &info, &izero, " ", &n, &n, &c__1, & c__1, &c_n1, &imat, &nfail, &nerrs, nout); } trfcon = info != 0; cgtt01_(&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(real)); 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 = clangt_(norm, &n, &a[1], &a[m + 1], &a[n + m + 1]); if (! trfcon) { /* Use CGTTRS to solve for one column at a time of inv(A), computing the maximum column sum as we go. */ ainvnm = 0.f; 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.f, x[i__5].i = 0.f; /* L30: */ } i__4 = i__; x[i__4].r = 1.f, x[i__4].i = 0.f; cgttrs_(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 */ r__1 = ainvnm, r__2 = scasum_(&n, &x[1], &c__1); ainvnm = dmax(r__1,r__2); /* L40: */ } /* Compute RCONDC = 1 / (norm(A) * norm(inv(A)) */ if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } if (itran == 1) { rcondo = rcondc; } else { rcondi = rcondc; } } else { rcondc = 0.f; } /* + TEST 7 Estimate the reciprocal of the condition number of the matrix. */ s_copy(srnamc_1.srnamt, "CGTCON", (ftnlen)6, (ftnlen)6); cgtcon_(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 CGTCON. */ if (info != 0) { alaerh_(path, "CGTCON", &info, &c__0, norm, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[6] = sget06_(&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(real)); 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) { clarnv_(&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. */ clagtm_(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. */ clacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "CGTTRS", (ftnlen)6, (ftnlen)6); cgttrs_(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 CGTTRS. */ if (info != 0) { alaerh_(path, "CGTTRS", &info, &c__0, trans, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } clacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); cgtt02_(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. */ cget04_(&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, "CGTRFS", (ftnlen)6, (ftnlen)6); cgtrfs_(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 CGTRFS. */ if (info != 0) { alaerh_(path, "CGTRFS", &info, &c__0, trans, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[3]); cgtt05_(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(real)); 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 CCHKGT */ } /* cchkgt_ */