/* 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 */ integer i__, j, k, m, n; doublecomplex z__[3]; integer in, kl, ku, ix, lda; doublereal cond; integer mode, koff, imat, info; char path[3], dist[1]; integer irhs, nrhs; char norm[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); doublereal rcond; integer nimat; doublereal anorm; integer itran; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); char trans[1]; 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 *); 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 *); doublereal rcondc, rcondi; extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *), alasum_(char *, integer *, integer *, integer *, integer *); doublereal rcondo, ainvnm; 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 *); 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 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --af; --a; --nsval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ 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)32, (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)32, (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)32, (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)32, (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)32, (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_ */
/* Subroutine */ int zchkgb_(logical *dotype, integer *nm, integer *mval, integer *nn, integer *nval, integer *nnb, integer *nbval, integer * nns, integer *nsval, doublereal *thresh, logical *tsterr, doublecomplex *a, integer *la, doublecomplex *afac, integer *lafac, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(\002 *** In ZCHKGB, LA=\002,i5,\002 is too sm" "all for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU=\002" ",i4,/\002 ==> Increase LA to at least \002,i5)"; static char fmt_9998[] = "(\002 *** In ZCHKGB, LAFAC=\002,i5,\002 is too" " small for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU" "=\002,i4,/\002 ==> Increase LAFAC to at least \002,i5)"; static char fmt_9997[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, KL=" "\002,i5,\002, KU=\002,i5,\002, NB =\002,i4,\002, type \002,i1" ",\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9996[] = "(\002 TRANS='\002,a1,\002', N=\002,i5,\002, " "KL=\002,i5,\002, KU=\002,i5,\002, NRHS=\002,i3,\002, type \002,i" "1,\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9995[] = "(\002 NORM ='\002,a1,\002', N=\002,i5,\002, " "KL=\002,i5,\002, KU=\002,i5,\002,\002,10x,\002 type \002,i1,\002" ", test(\002,i1,\002)=\002,g12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10, i__11; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ integer i__, j, k, m, n, i1, i2, nb, im, in, kl, ku, lda, ldb, inb, ikl, nkl, iku, nku, ioff, mode, koff, imat, info; char path[3], dist[1]; integer irhs, nrhs; char norm[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); doublereal rcond; extern /* Subroutine */ int zgbt01_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, doublereal *); integer nimat, klval[4]; extern /* Subroutine */ int zgbt02_(char *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *), zgbt05_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer * , doublereal *, doublereal *, doublereal *); doublereal anorm; integer itran; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); integer kuval[4]; char trans[1]; integer izero, nerrs; logical zerot; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *); integer ldafac; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); doublereal rcondc; extern doublereal zlangb_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *); doublereal rcondi; extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); doublereal cndnum, anormi, rcondo; extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *); doublereal ainvnm; logical trfcon; doublereal anormo; extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrge_(char *, integer *), zgbrfs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgbtrf_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zgbtrs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal result[7]; /* Fortran I/O blocks */ static cilist io___25 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___26 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___59 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9995, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZCHKGB tests ZGBTRF, -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. */ /* NM (input) INTEGER */ /* The number of values of M contained in the vector MVAL. */ /* MVAL (input) INTEGER array, dimension (NM) */ /* The values of the matrix row dimension M. */ /* 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 column dimension N. */ /* NNB (input) INTEGER */ /* The number of values of NB contained in the vector NBVAL. */ /* NBVAL (input) INTEGER array, dimension (NBVAL) */ /* The values of the blocksize NB. */ /* 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 (LA) */ /* LA (input) INTEGER */ /* The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX */ /* where KLMAX is the largest entry in the local array KLVAL, */ /* KUMAX is the largest entry in the local array KUVAL and */ /* NMAX is the largest entry in the input array NVAL. */ /* AFAC (workspace) COMPLEX*16 array, dimension (LAFAC) */ /* LAFAC (input) INTEGER */ /* The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX */ /* where KLMAX is the largest entry in the local array KLVAL, */ /* KUMAX is the largest entry in the local array KUVAL and */ /* NMAX is the largest entry in the input array NVAL. */ /* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* 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,NMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* IWORK (workspace) INTEGER array, dimension (NMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --afac; --a; --nsval; --nbval; --nval; --mval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "GB", (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; /* Initialize the first value for the lower and upper bandwidths. */ klval[0] = 0; kuval[0] = 0; /* Do for each value of M in MVAL */ i__1 = *nm; for (im = 1; im <= i__1; ++im) { m = mval[im]; /* Set values to use for the lower bandwidth. */ klval[1] = m + (m + 1) / 4; /* KLVAL( 2 ) = MAX( M-1, 0 ) */ klval[2] = (m * 3 - 1) / 4; klval[3] = (m + 1) / 4; /* Do for each value of N in NVAL */ i__2 = *nn; for (in = 1; in <= i__2; ++in) { n = nval[in]; *(unsigned char *)xtype = 'N'; /* Set values to use for the upper bandwidth. */ kuval[1] = n + (n + 1) / 4; /* KUVAL( 2 ) = MAX( N-1, 0 ) */ kuval[2] = (n * 3 - 1) / 4; kuval[3] = (n + 1) / 4; /* Set limits on the number of loop iterations. */ /* Computing MIN */ i__3 = m + 1; nkl = min(i__3,4); if (n == 0) { nkl = 2; } /* Computing MIN */ i__3 = n + 1; nku = min(i__3,4); if (m == 0) { nku = 2; } nimat = 8; if (m <= 0 || n <= 0) { nimat = 1; } i__3 = nkl; for (ikl = 1; ikl <= i__3; ++ikl) { /* Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This */ /* order makes it easier to skip redundant values for small */ /* values of M. */ kl = klval[ikl - 1]; i__4 = nku; for (iku = 1; iku <= i__4; ++iku) { /* Do for KU = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This */ /* order makes it easier to skip redundant values for */ /* small values of N. */ ku = kuval[iku - 1]; /* Check that A and AFAC are big enough to generate this */ /* matrix. */ lda = kl + ku + 1; ldafac = (kl << 1) + ku + 1; if (lda * n > *la || ldafac * n > *lafac) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } if (n * (kl + ku + 1) > *la) { io___25.ciunit = *nout; s_wsfe(&io___25); do_fio(&c__1, (char *)&(*la), (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer) ); i__5 = n * (kl + ku + 1); do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof( integer)); e_wsfe(); ++nerrs; } if (n * ((kl << 1) + ku + 1) > *lafac) { io___26.ciunit = *nout; s_wsfe(&io___26); do_fio(&c__1, (char *)&(*lafac), (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer) ); i__5 = n * ((kl << 1) + ku + 1); do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof( integer)); e_wsfe(); ++nerrs; } goto L130; } i__5 = nimat; for (imat = 1; imat <= i__5; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L120; } /* Skip types 2, 3, or 4 if the matrix size is too */ /* small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L120; } if (! zerot || ! dotype[1]) { /* Set up parameters with ZLATB4 and generate a */ /* test matrix with ZLATMS. */ zlatb4_(path, &imat, &m, &n, type__, &kl, &ku, & anorm, &mode, &cndnum, dist); /* Computing MAX */ i__6 = 1, i__7 = ku + 2 - n; koff = max(i__6,i__7); i__6 = koff - 1; for (i__ = 1; i__ <= i__6; ++i__) { i__7 = i__; a[i__7].r = 0., a[i__7].i = 0.; /* L20: */ } s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, ( ftnlen)6); zlatms_(&m, &n, dist, iseed, type__, &rwork[1], & mode, &cndnum, &anorm, &kl, &ku, "Z", &a[ koff], &lda, &work[1], &info); /* Check the error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, " ", &m, &n, &kl, &ku, &c_n1, &imat, &nfail, & nerrs, nout); goto L120; } } else if (izero > 0) { /* Use the same matrix for types 3 and 4 as for */ /* type 2 by copying back the zeroed out column. */ i__6 = i2 - i1 + 1; zcopy_(&i__6, &b[1], &c__1, &a[ioff + i1], &c__1); } /* For types 2, 3, and 4, zero one or more columns of */ /* the matrix to test that INFO is returned correctly. */ izero = 0; if (zerot) { if (imat == 2) { izero = 1; } else if (imat == 3) { izero = min(m,n); } else { izero = min(m,n) / 2 + 1; } ioff = (izero - 1) * lda; if (imat < 4) { /* Store the column to be zeroed out in B. */ /* Computing MAX */ i__6 = 1, i__7 = ku + 2 - izero; i1 = max(i__6,i__7); /* Computing MIN */ i__6 = kl + ku + 1, i__7 = ku + 1 + (m - izero); i2 = min(i__6,i__7); i__6 = i2 - i1 + 1; zcopy_(&i__6, &a[ioff + i1], &c__1, &b[1], & c__1); i__6 = i2; for (i__ = i1; i__ <= i__6; ++i__) { i__7 = ioff + i__; a[i__7].r = 0., a[i__7].i = 0.; /* L30: */ } } else { i__6 = n; for (j = izero; j <= i__6; ++j) { /* Computing MAX */ i__7 = 1, i__8 = ku + 2 - j; /* Computing MIN */ i__10 = kl + ku + 1, i__11 = ku + 1 + (m - j); i__9 = min(i__10,i__11); for (i__ = max(i__7,i__8); i__ <= i__9; ++i__) { i__7 = ioff + i__; a[i__7].r = 0., a[i__7].i = 0.; /* L40: */ } ioff += lda; /* L50: */ } } } /* These lines, if used in place of the calls in the */ /* loop over INB, cause the code to bomb on a Sun */ /* SPARCstation. */ /* ANORMO = ZLANGB( 'O', N, KL, KU, A, LDA, RWORK ) */ /* ANORMI = ZLANGB( 'I', N, KL, KU, A, LDA, RWORK ) */ /* Do for each blocksize in NBVAL */ i__6 = *nnb; for (inb = 1; inb <= i__6; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the LU factorization of the band matrix. */ if (m > 0 && n > 0) { i__9 = kl + ku + 1; zlacpy_("Full", &i__9, &n, &a[1], &lda, &afac[ kl + 1], &ldafac); } s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, ( ftnlen)6); zgbtrf_(&m, &n, &kl, &ku, &afac[1], &ldafac, & iwork[1], &info); /* Check error code from ZGBTRF. */ if (info != izero) { alaerh_(path, "ZGBTRF", &info, &izero, " ", & m, &n, &kl, &ku, &nb, &imat, &nfail, & nerrs, nout); } trfcon = FALSE_; /* + TEST 1 */ /* Reconstruct matrix from factors and compute */ /* residual. */ zgbt01_(&m, &n, &kl, &ku, &a[1], &lda, &afac[1], & ldafac, &iwork[1], &work[1], result); /* Print information about the tests so far that */ /* did not pass the threshold. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___45.ciunit = *nout; s_wsfe(&io___45); do_fio(&c__1, (char *)&m, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&kl, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nb, (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; /* Skip the remaining tests if this is not the */ /* first block size or if M .ne. N. */ if (inb > 1 || m != n) { goto L110; } anormo = zlangb_("O", &n, &kl, &ku, &a[1], &lda, & rwork[1]); anormi = zlangb_("I", &n, &kl, &ku, &a[1], &lda, & rwork[1]); if (info == 0) { /* Form the inverse of A so we can get a good */ /* estimate of CNDNUM = norm(A) * norm(inv(A)). */ ldb = max(1,n); zlaset_("Full", &n, &n, &c_b61, &c_b62, &work[ 1], &ldb); s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, ( ftnlen)6); zgbtrs_("No transpose", &n, &kl, &ku, &n, & afac[1], &ldafac, &iwork[1], &work[1], &ldb, &info); /* Compute the 1-norm condition number of A. */ ainvnm = zlange_("O", &n, &n, &work[1], &ldb, &rwork[1]); if (anormo <= 0. || ainvnm <= 0.) { rcondo = 1.; } else { rcondo = 1. / anormo / ainvnm; } /* Compute the infinity-norm condition number of */ /* A. */ ainvnm = zlange_("I", &n, &n, &work[1], &ldb, &rwork[1]); if (anormi <= 0. || ainvnm <= 0.) { rcondi = 1.; } else { rcondi = 1. / anormi / ainvnm; } } else { /* Do only the condition estimate if INFO.NE.0. */ trfcon = TRUE_; rcondo = 0.; rcondi = 0.; } /* Skip the solve tests if the matrix is singular. */ if (trfcon) { goto L90; } i__9 = *nns; for (irhs = 1; irhs <= i__9; ++irhs) { nrhs = nsval[irhs]; *(unsigned char *)xtype = 'N'; for (itran = 1; itran <= 3; ++itran) { *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]; if (itran == 1) { rcondc = rcondo; *(unsigned char *)norm = 'O'; } else { rcondc = rcondi; *(unsigned char *)norm = 'I'; } /* + TEST 2: */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen) 6, (ftnlen)6); zlarhs_(path, xtype, " ", trans, &n, &n, & kl, &ku, &nrhs, &a[1], &lda, & xact[1], &ldb, &b[1], &ldb, iseed, &info); *(unsigned char *)xtype = 'C'; zlacpy_("Full", &n, &nrhs, &b[1], &ldb, & x[1], &ldb); s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen) 6, (ftnlen)6); zgbtrs_(trans, &n, &kl, &ku, &nrhs, &afac[ 1], &ldafac, &iwork[1], &x[1], & ldb, &info); /* Check error code from ZGBTRS. */ if (info != 0) { alaerh_(path, "ZGBTRS", &info, &c__0, trans, &n, &n, &kl, &ku, & c_n1, &imat, &nfail, &nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &ldb, & work[1], &ldb); zgbt02_(trans, &m, &n, &kl, &ku, &nrhs, & a[1], &lda, &x[1], &ldb, &work[1], &ldb, &result[1]); /* + TEST 3: */ /* Check solution from generated exact */ /* solution. */ zget04_(&n, &nrhs, &x[1], &ldb, &xact[1], &ldb, &rcondc, &result[2]); /* + TESTS 4, 5, 6: */ /* Use iterative refinement to improve the */ /* solution. */ s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen) 6, (ftnlen)6); zgbrfs_(trans, &n, &kl, &ku, &nrhs, &a[1], &lda, &afac[1], &ldafac, &iwork[ 1], &b[1], &ldb, &x[1], &ldb, & rwork[1], &rwork[nrhs + 1], &work[ 1], &rwork[(nrhs << 1) + 1], & info); /* Check error code from ZGBRFS. */ if (info != 0) { alaerh_(path, "ZGBRFS", &info, &c__0, trans, &n, &n, &kl, &ku, & nrhs, &imat, &nfail, &nerrs, nout); } zget04_(&n, &nrhs, &x[1], &ldb, &xact[1], &ldb, &rcondc, &result[3]); zgbt05_(trans, &n, &kl, &ku, &nrhs, &a[1], &lda, &b[1], &ldb, &x[1], &ldb, & xact[1], &ldb, &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___59.ciunit = *nout; s_wsfe(&io___59); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kl, ( ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&ku, ( 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; } /* L60: */ } nrun += 5; /* L70: */ } /* L80: */ } /* + TEST 7: */ /* Get an estimate of RCOND = 1/CNDNUM. */ L90: for (itran = 1; itran <= 2; ++itran) { if (itran == 1) { anorm = anormo; rcondc = rcondo; *(unsigned char *)norm = 'O'; } else { anorm = anormi; rcondc = rcondi; *(unsigned char *)norm = 'I'; } s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, ( ftnlen)6); zgbcon_(norm, &n, &kl, &ku, &afac[1], &ldafac, &iwork[1], &anorm, &rcond, &work[1], &rwork[1], &info); /* Check error code from ZGBCON. */ if (info != 0) { alaerh_(path, "ZGBCON", &info, &c__0, norm, &n, &n, &kl, &ku, &c_n1, & imat, &nfail, &nerrs, nout); } result[6] = dget06_(&rcond, &rcondc); /* Print information about the tests that did */ /* not pass the threshold. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___61.ciunit = *nout; s_wsfe(&io___61); do_fio(&c__1, norm, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&kl, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&ku, (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; /* L100: */ } L110: ; } L120: ; } L130: ; } /* L140: */ } /* L150: */ } /* L160: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKGB */ } /* zchkgb_ */