void LapackLuDense::prepare() { double time_start=0; if (CasadiOptions::profiling && CasadiOptions::profilingBinary) { time_start = getRealTime(); // Start timer profileWriteEntry(CasadiOptions::profilingLog, this); } prepared_ = false; // Get the elements of the matrix, dense format input(0).get(mat_); if (equilibriate_) { // Calculate the col and row scaling factors double colcnd, rowcnd; // ratio of the smallest to the largest col/row scaling factor double amax; // absolute value of the largest matrix element int info = -100; dgeequ_(&ncol_, &nrow_, getPtr(mat_), &ncol_, getPtr(r_), getPtr(c_), &colcnd, &rowcnd, &amax, &info); if (info < 0) throw CasadiException("LapackQrDense::prepare: " "dgeequ_ failed to calculate the scaling factors"); if (info>0) { stringstream ss; ss << "LapackLuDense::prepare: "; if (info<=ncol_) ss << (info-1) << "-th row (zero-based) is exactly zero"; else ss << (info-1-ncol_) << "-th col (zero-based) is exactly zero"; userOut() << "Warning: " << ss.str() << endl; if (allow_equilibration_failure_) userOut() << "Warning: " << ss.str() << endl; else casadi_error(ss.str()); } // Equilibrate the matrix if scaling was successful if (info!=0) dlaqge_(&ncol_, &nrow_, getPtr(mat_), &ncol_, getPtr(r_), getPtr(c_), &colcnd, &rowcnd, &amax, &equed_); else equed_ = 'N'; } // Factorize the matrix int info = -100; dgetrf_(&ncol_, &ncol_, getPtr(mat_), &ncol_, getPtr(ipiv_), &info); if (info != 0) throw CasadiException("LapackLuDense::prepare: " "dgetrf_ failed to factorize the Jacobian"); // Success if reached this point prepared_ = true; if (CasadiOptions::profiling && CasadiOptions::profilingBinary) { double time_stop = getRealTime(); // Stop timer profileWriteTime(CasadiOptions::profilingLog, this, 0, time_stop-time_start, time_stop-time_start); profileWriteExit(CasadiOptions::profilingLog, this, time_stop-time_start); } }
/* Main function to be called */ void errbars (int numparams, double *p, struct kslice *ks, double **covar) { int ii, ij, ik; lapack_int n, lda, info, worksize; char c; double *fish, *work, *rscale, *cscale; double row, col, amax; int *piv; c = 'U'; fish = malloc(numparams*numparams*sizeof(double)); piv = malloc(numparams*numparams*sizeof(int)); rscale = malloc(numparams*sizeof(double)); cscale = malloc(numparams*sizeof(double)); /* compute fisher information matrix */ fisher(numparams, p, ks, fish); n = numparams; lda = numparams; dgeequ_(&n, &n, fish, &lda, rscale, cscale, &row, &col, &amax, &info); /* for (ii=0; ii<numparams; ii++) for (ij=0; ij<numparams; ij++) fish[ii*numparams+ij] *= rscale[ii]*cscale[ij]; */ n = numparams; lda = numparams; dgetrf_(&n, &n, fish, &lda, piv, &info); // printf("\tLU decomp status: %d\n", info); worksize = 32*n; work = malloc(worksize*sizeof(double)); dgetri_(&n, fish, &lda, piv, work, &worksize, &info); // printf("\tInversion status: %d\n", info); /* for (ii=0; ii<numparams; ii++) for (ij=0; ij<numparams; ij++) fish[ii*numparams+ij] *= rscale[ij]*cscale[ii]; */ /* compute inverse of fisher information matrix */ /* for (ii=0; ii<numparams; ii++) { for (ij=0; ij<numparams; ij++) printf("%d\t%d\t%e\n", ii, ij, (fish[ii*numparams+ij])); printf("\n"); } */ /* return */ *covar = fish; /* free local memory */ free(work); free(piv); free(rscale); free(cscale); }
/* Subroutine */ int derrge_(char *path, integer *nunit) { /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ doublereal a[16] /* was [4][4] */, b[4]; integer i__, j; doublereal w[12], x[4]; char c2[2]; doublereal r1[4], r2[4], af[16] /* was [4][4] */; integer ip[4], iw[4], info; doublereal anrm, ccond, rcond; extern /* Subroutine */ int dgbtf2_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), dgetf2_(integer *, integer *, doublereal *, integer *, integer *, integer *), dgbcon_(char *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgecon_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), alaesm_(char *, logical *, integer *), dgbequ_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *) , dgbrfs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgbtrf_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), dgeequ_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dgerfs_(char *, integer * , integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgetrf_(integer *, integer *, doublereal *, integer *, integer *, integer *), dgetri_(integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), dgbtrs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dgetrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DERRGE tests the error exits for the DOUBLE PRECISION routines */ /* for general matrices. */ /* Arguments */ /* ========= */ /* PATH (input) CHARACTER*3 */ /* The LAPACK path name for the routines to be tested. */ /* NUNIT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { a[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j); af[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j); /* L10: */ } b[j - 1] = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; w[j - 1] = 0.; x[j - 1] = 0.; ip[j - 1] = j; iw[j - 1] = j; /* L20: */ } infoc_1.ok = TRUE_; if (lsamen_(&c__2, c2, "GE")) { /* Test error exits of the routines that use the LU decomposition */ /* of a general matrix. */ /* DGETRF */ s_copy(srnamc_1.srnamt, "DGETRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetrf_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetrf_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgetrf_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETF2 */ s_copy(srnamc_1.srnamt, "DGETF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetf2_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetf2_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgetf2_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETRI */ s_copy(srnamc_1.srnamt, "DGETRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info); chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgetri_(&c__2, a, &c__1, ip, w, &c__12, &info); chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETRS */ s_copy(srnamc_1.srnamt, "DGETRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; dgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGERFS */ s_copy(srnamc_1.srnamt, "DGERFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGECON */ s_copy(srnamc_1.srnamt, "DGECON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGEEQU */ s_copy(srnamc_1.srnamt, "DGEEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } else if (lsamen_(&c__2, c2, "GB")) { /* Test error exits of the routines that use the LU decomposition */ /* of a general band matrix. */ /* DGBTRF */ s_copy(srnamc_1.srnamt, "DGBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBTF2 */ s_copy(srnamc_1.srnamt, "DGBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBTRS */ s_copy(srnamc_1.srnamt, "DGBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBRFS */ s_copy(srnamc_1.srnamt, "DGBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, & c__2, x, &c__2, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; dgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, & c__2, x, &c__2, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; dgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__2, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 14; dgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, & c__2, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBCON */ s_copy(srnamc_1.srnamt, "DGBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBEQU */ s_copy(srnamc_1.srnamt, "DGBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of DERRGE */ } /* derrge_ */
/* Subroutine */ int ddrvge_(logical *dotype, integer *nn, integer *nval, integer *nrhs, doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a, doublereal *afac, doublereal *asav, doublereal *b, doublereal *bsav, doublereal *x, doublereal *xact, doublereal *s, doublereal *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"; static char facts[1*3] = "F" "N" "E"; static char equeds[1*4] = "N" "R" "C" "B"; /* Format strings */ static char fmt_9999[] = "(1x,a,\002, N =\002,i5,\002, type \002,i2,\002" ", test(\002,i2,\002) =\002,g12.5)"; static char fmt_9997[] = "(1x,a,\002, FACT='\002,a1,\002', TRANS='\002,a" "1,\002', N=\002,i5,\002, EQUED='\002,a1,\002', type \002,i2,\002" ", test(\002,i1,\002)=\002,g12.5)"; static char fmt_9998[] = "(1x,a,\002, FACT='\002,a1,\002', TRANS='\002,a" "1,\002', N=\002,i5,\002, type \002,i2,\002, test(\002,i1,\002)" "=\002,g12.5)"; /* System generated locals */ address a__1[2]; integer i__1, i__2, i__3, i__4, i__5[2]; doublereal d__1; char ch__1[2]; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ extern /* Subroutine */ int debchvxx_(doublereal *, char *); integer i__, k, n; doublereal *errbnds_c__, *errbnds_n__; integer k1, nb, in, kl, ku, nt, n_err_bnds__; extern doublereal dla_rpvgrw__(integer *, integer *, doublereal *, integer *, doublereal *, integer *); integer lda; char fact[1]; integer ioff, mode; doublereal amax; char path[3]; integer imat, info; doublereal *berr; char dist[1]; doublereal rpvgrw_svxx__; char type__[1]; integer nrun; extern /* Subroutine */ int dget01_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *), dget02_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer ifact; extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer nfail, iseed[4], nfact; extern doublereal dget06_(doublereal *, doublereal *); extern /* Subroutine */ int dget07_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, logical *, doublereal *, doublereal *); extern logical lsame_(char *, char *); char equed[1]; integer nbmin; doublereal rcond, roldc; integer nimat; doublereal roldi; extern /* Subroutine */ int dgesv_(integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); doublereal anorm; integer itran; logical equil; doublereal roldo; char trans[1]; integer izero, nerrs, lwork; logical zerot; char xtype[1]; extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), aladhd_(integer *, char *); extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *), dlaqge_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, char *); logical prefac; doublereal colcnd, rcondc; logical nofact; integer iequed; extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *); doublereal rcondi; extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *, integer *, integer *, integer *), dgetri_(integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), alasvm_(char *, integer *, integer *, integer *, integer *); doublereal cndnum, anormi, rcondo, ainvnm; extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *); logical trfcon; doublereal anormo, rowcnd; extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), dgesvx_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, char *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer * , integer *), dlatms_(integer *, integer * , char *, integer *, char *, doublereal *, integer *, doublereal * , doublereal *, integer *, integer *, char *, doublereal *, integer *, doublereal *, integer *), xlaenv_(integer *, integer *), derrvx_(char *, integer *); doublereal result[7], rpvgrw; extern /* Subroutine */ int dgesvxx_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, char *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___55 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___62 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___63 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___64 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___65 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___66 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___67 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___68 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___74 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___75 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___76 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___77 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___78 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___79 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___80 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___81 = { 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 */ /* ======= */ /* DDRVGE tests the driver routines DGESV, -SVX, and -SVXX. */ /* Note that this file is used only when the XBLAS are available, */ /* otherwise ddrvge.f defines this subroutine. */ /* 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 column dimension N. */ /* NRHS (input) INTEGER */ /* The number of right hand side vectors to be generated for */ /* each linear system. */ /* 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. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */ /* AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */ /* ASAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */ /* B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */ /* BSAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */ /* X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */ /* XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */ /* S (workspace) DOUBLE PRECISION array, dimension (2*NMAX) */ /* WORK (workspace) DOUBLE PRECISION array, dimension */ /* (NMAX*max(3,NRHS)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (2*NRHS+NMAX) */ /* IWORK (workspace) INTEGER array, dimension (2*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; --s; --xact; --x; --bsav; --b; --asav; --afac; --a; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "GE", (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) { derrvx_(path, nout); } infoc_1.infot = 0; /* Set the block size and minimum block size for testing. */ nb = 1; nbmin = 2; xlaenv_(&c__1, &nb); xlaenv_(&c__2, &nbmin); /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 11; 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 L80; } /* Skip types 5, 6, or 7 if the matrix size is too small. */ zerot = imat >= 5 && imat <= 7; if (zerot && n < imat - 4) { goto L80; } /* Set up parameters with DLATB4 and generate a test matrix */ /* with DLATMS. */ dlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, & cndnum, dist); rcondc = 1. / cndnum; s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)32, (ftnlen)6); dlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, & anorm, &kl, &ku, "No packing", &a[1], &lda, &work[1], & info); /* Check error code from DLATMS. */ if (info != 0) { alaerh_(path, "DLATMS", &info, &c__0, " ", &n, &n, &c_n1, & c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L80; } /* For types 5-7, zero one or more columns of the matrix to */ /* test that INFO is returned correctly. */ if (zerot) { if (imat == 5) { izero = 1; } else if (imat == 6) { izero = n; } else { izero = n / 2 + 1; } ioff = (izero - 1) * lda; if (imat < 7) { i__3 = n; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff + i__] = 0.; /* L20: */ } } else { i__3 = n - izero + 1; dlaset_("Full", &n, &i__3, &c_b20, &c_b20, &a[ioff + 1], & lda); } } else { izero = 0; } /* Save a copy of the matrix A in ASAV. */ dlacpy_("Full", &n, &n, &a[1], &lda, &asav[1], &lda); for (iequed = 1; iequed <= 4; ++iequed) { *(unsigned char *)equed = *(unsigned char *)&equeds[iequed - 1]; if (iequed == 1) { nfact = 3; } else { nfact = 1; } i__3 = nfact; for (ifact = 1; ifact <= i__3; ++ifact) { *(unsigned char *)fact = *(unsigned char *)&facts[ifact - 1]; prefac = lsame_(fact, "F"); nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); if (zerot) { if (prefac) { goto L60; } rcondo = 0.; rcondi = 0.; } else if (! nofact) { /* Compute the condition number for comparison with */ /* the value returned by DGESVX (FACT = 'N' reuses */ /* the condition number from the previous iteration */ /* with FACT = 'F'). */ dlacpy_("Full", &n, &n, &asav[1], &lda, &afac[1], & lda); if (equil || iequed > 1) { /* Compute row and column scale factors to */ /* equilibrate the matrix A. */ dgeequ_(&n, &n, &afac[1], &lda, &s[1], &s[n + 1], &rowcnd, &colcnd, &amax, &info); if (info == 0 && n > 0) { if (lsame_(equed, "R")) { rowcnd = 0.; colcnd = 1.; } else if (lsame_(equed, "C")) { rowcnd = 1.; colcnd = 0.; } else if (lsame_(equed, "B")) { rowcnd = 0.; colcnd = 0.; } /* Equilibrate the matrix. */ dlaqge_(&n, &n, &afac[1], &lda, &s[1], &s[n + 1], &rowcnd, &colcnd, &amax, equed); } } /* Save the condition number of the non-equilibrated */ /* system for use in DGET04. */ if (equil) { roldo = rcondo; roldi = rcondi; } /* Compute the 1-norm and infinity-norm of A. */ anormo = dlange_("1", &n, &n, &afac[1], &lda, &rwork[ 1]); anormi = dlange_("I", &n, &n, &afac[1], &lda, &rwork[ 1]); /* Factor the matrix A. */ dgetrf_(&n, &n, &afac[1], &lda, &iwork[1], &info); /* Form the inverse of A. */ dlacpy_("Full", &n, &n, &afac[1], &lda, &a[1], &lda); lwork = *nmax * max(3,*nrhs); dgetri_(&n, &a[1], &lda, &iwork[1], &work[1], &lwork, &info); /* Compute the 1-norm condition number of A. */ ainvnm = dlange_("1", &n, &n, &a[1], &lda, &rwork[1]); if (anormo <= 0. || ainvnm <= 0.) { rcondo = 1.; } else { rcondo = 1. / anormo / ainvnm; } /* Compute the infinity-norm condition number of A. */ ainvnm = dlange_("I", &n, &n, &a[1], &lda, &rwork[1]); if (anormi <= 0. || ainvnm <= 0.) { rcondi = 1.; } else { rcondi = 1. / anormi / ainvnm; } } for (itran = 1; itran <= 3; ++itran) { for (i__ = 1; i__ <= 7; ++i__) { result[i__ - 1] = 0.; } /* Do for each value of TRANS. */ *(unsigned char *)trans = *(unsigned char *)&transs[ itran - 1]; if (itran == 1) { rcondc = rcondo; } else { rcondc = rcondi; } /* Restore the matrix A. */ dlacpy_("Full", &n, &n, &asav[1], &lda, &a[1], &lda); /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)32, (ftnlen) 6); dlarhs_(path, xtype, "Full", trans, &n, &n, &kl, &ku, nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); *(unsigned char *)xtype = 'C'; dlacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], &lda); if (nofact && itran == 1) { /* --- Test DGESV --- */ /* Compute the LU factorization of the matrix and */ /* solve the system. */ dlacpy_("Full", &n, &n, &a[1], &lda, &afac[1], & lda); dlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "DGESV ", (ftnlen)32, ( ftnlen)6); dgesv_(&n, nrhs, &afac[1], &lda, &iwork[1], &x[1], &lda, &info); /* Check error code from DGESV . */ if (info != izero) { alaerh_(path, "DGESV ", &info, &izero, " ", & n, &n, &c_n1, &c_n1, nrhs, &imat, & nfail, &nerrs, nout); goto L50; } /* Reconstruct matrix from factors and compute */ /* residual. */ dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, & iwork[1], &rwork[1], result); nt = 1; if (izero == 0) { /* Compute residual of the computed solution. */ dlacpy_("Full", &n, nrhs, &b[1], &lda, &work[ 1], &lda); dget02_("No transpose", &n, &n, nrhs, &a[1], & lda, &x[1], &lda, &work[1], &lda, & rwork[1], &result[1]); /* Check solution from generated exact solution. */ dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &result[2]); nt = 3; } /* Print information about the tests that did not */ /* pass the threshold. */ i__4 = nt; for (k = 1; k <= i__4; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___55.ciunit = *nout; s_wsfe(&io___55); do_fio(&c__1, "DGESV ", (ftnlen)6); do_fio(&c__1, (char *)&n, (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; } /* L30: */ } nrun += nt; } /* --- Test DGESVX --- */ if (! prefac) { dlaset_("Full", &n, &n, &c_b20, &c_b20, &afac[1], &lda); } dlaset_("Full", &n, nrhs, &c_b20, &c_b20, &x[1], &lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT = 'F' and */ /* EQUED = 'R', 'C', or 'B'. */ dlaqge_(&n, &n, &a[1], &lda, &s[1], &s[n + 1], & rowcnd, &colcnd, &amax, equed); } /* Solve the system and compute the condition number */ /* and error bounds using DGESVX. */ s_copy(srnamc_1.srnamt, "DGESVX", (ftnlen)32, (ftnlen) 6); dgesvx_(fact, trans, &n, nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], equed, &s[1], &s[n + 1], &b[ 1], &lda, &x[1], &lda, &rcond, &rwork[1], & rwork[*nrhs + 1], &work[1], &iwork[n + 1], & info); /* Check the error code from DGESVX. */ if (info == n + 1) { goto L50; } if (info != izero) { /* Writing concatenation */ i__5[0] = 1, a__1[0] = fact; i__5[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2); alaerh_(path, "DGESVX", &info, &izero, ch__1, &n, &n, &c_n1, &c_n1, nrhs, &imat, &nfail, & nerrs, nout); goto L50; } /* Compare WORK(1) from DGESVX with the computed */ /* reciprocal pivot growth factor RPVGRW */ if (info != 0) { rpvgrw = dlantr_("M", "U", "N", &info, &info, & afac[1], &lda, &work[1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = dlange_("M", &n, &info, &a[1], &lda, &work[1]) / rpvgrw; } } else { rpvgrw = dlantr_("M", "U", "N", &n, &n, &afac[1], &lda, &work[1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = dlange_("M", &n, &n, &a[1], &lda, & work[1]) / rpvgrw; } } result[6] = (d__1 = rpvgrw - work[1], abs(d__1)) / max(work[1],rpvgrw) / dlamch_("E"); if (! prefac) { /* Reconstruct matrix from factors and compute */ /* residual. */ dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, & iwork[1], &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } if (info == 0) { trfcon = FALSE_; /* Compute residual of the computed solution. */ dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1] , &lda); dget02_(trans, &n, &n, nrhs, &asav[1], &lda, &x[1] , &lda, &work[1], &lda, &rwork[(*nrhs << 1) + 1], &result[1]); /* Check solution from generated exact solution. */ if (nofact || prefac && lsame_(equed, "N")) { dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &result[2]); } else { if (itran == 1) { roldc = roldo; } else { roldc = roldi; } dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &roldc, &result[2]); } /* Check the error bounds from iterative */ /* refinement. */ dget07_(trans, &n, nrhs, &asav[1], &lda, &b[1], & lda, &x[1], &lda, &xact[1], &lda, &rwork[ 1], &c_true, &rwork[*nrhs + 1], &result[3] ); } else { trfcon = TRUE_; } /* Compare RCOND from DGESVX with the computed value */ /* in RCONDC. */ result[5] = dget06_(&rcond, &rcondc); /* Print information about the tests that did not pass */ /* the threshold. */ if (! trfcon) { for (k = k1; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___61.ciunit = *nout; s_wsfe(&io___61); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___62.ciunit = *nout; s_wsfe(&io___62); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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 *)&k, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(doublereal)); e_wsfe(); } ++nfail; } /* L40: */ } nrun = nrun + 7 - k1; } else { if (result[0] >= *thresh && ! prefac) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___63.ciunit = *nout; s_wsfe(&io___63); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___64.ciunit = *nout; s_wsfe(&io___64); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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__1, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[0], (ftnlen) sizeof(doublereal)); e_wsfe(); } ++nfail; ++nrun; } if (result[5] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___65.ciunit = *nout; s_wsfe(&io___65); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&c__6, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[5], (ftnlen) sizeof(doublereal)); e_wsfe(); } else { io___66.ciunit = *nout; s_wsfe(&io___66); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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__6, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[5], (ftnlen) sizeof(doublereal)); e_wsfe(); } ++nfail; ++nrun; } if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___67.ciunit = *nout; s_wsfe(&io___67); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___68.ciunit = *nout; s_wsfe(&io___68); do_fio(&c__1, "DGESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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; } } /* --- Test DGESVXX --- */ /* Restore the matrices A and B. */ dlacpy_("Full", &n, &n, &asav[1], &lda, &a[1], &lda); dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &b[1], &lda); if (! prefac) { dlaset_("Full", &n, &n, &c_b20, &c_b20, &afac[1], &lda); } dlaset_("Full", &n, nrhs, &c_b20, &c_b20, &x[1], &lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT = 'F' and */ /* EQUED = 'R', 'C', or 'B'. */ dlaqge_(&n, &n, &a[1], &lda, &s[1], &s[n + 1], & rowcnd, &colcnd, &amax, equed); } /* Solve the system and compute the condition number */ /* and error bounds using DGESVXX. */ s_copy(srnamc_1.srnamt, "DGESVXX", (ftnlen)32, ( ftnlen)7); n_err_bnds__ = 3; dalloc3(); dgesvxx_(fact, trans, &n, nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], equed, &s[1], &s[n + 1], &b[ 1], &lda, &x[1], &lda, &rcond, &rpvgrw_svxx__, berr, &n_err_bnds__, errbnds_n__, errbnds_c__, &c__0, &c_b20, &work[1], &iwork[ n + 1], &info); free3(); /* Check the error code from DGESVXX. */ if (info == n + 1) { goto L50; } if (info != izero) { /* Writing concatenation */ i__5[0] = 1, a__1[0] = fact; i__5[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2); alaerh_(path, "DGESVXX", &info, &izero, ch__1, &n, &n, &c_n1, &c_n1, nrhs, &imat, &nfail, & nerrs, nout); goto L50; } /* Compare rpvgrw_svxx from DGESVXX with the computed */ /* reciprocal pivot growth factor RPVGRW */ if (info > 0 && info < n + 1) { rpvgrw = dla_rpvgrw__(&n, &info, &a[1], &lda, & afac[1], &lda); } else { rpvgrw = dla_rpvgrw__(&n, &n, &a[1], &lda, &afac[ 1], &lda); } result[6] = (d__1 = rpvgrw - rpvgrw_svxx__, abs(d__1)) / max(rpvgrw_svxx__,rpvgrw) / dlamch_("E"); if (! prefac) { /* Reconstruct matrix from factors and compute */ /* residual. */ dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, & iwork[1], &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } if (info == 0) { trfcon = FALSE_; /* Compute residual of the computed solution. */ dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1] , &lda); dget02_(trans, &n, &n, nrhs, &asav[1], &lda, &x[1] , &lda, &work[1], &lda, &rwork[(*nrhs << 1) + 1], &result[1]); /* Check solution from generated exact solution. */ if (nofact || prefac && lsame_(equed, "N")) { dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &result[2]); } else { if (itran == 1) { roldc = roldo; } else { roldc = roldi; } dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &roldc, &result[2]); } } else { trfcon = TRUE_; } /* Compare RCOND from DGESVXX with the computed value */ /* in RCONDC. */ result[5] = dget06_(&rcond, &rcondc); /* Print information about the tests that did not pass */ /* the threshold. */ if (! trfcon) { for (k = k1; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___74.ciunit = *nout; s_wsfe(&io___74); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___75.ciunit = *nout; s_wsfe(&io___75); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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 *)&k, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(doublereal)); e_wsfe(); } ++nfail; } /* L45: */ } nrun = nrun + 7 - k1; } else { if (result[0] >= *thresh && ! prefac) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___76.ciunit = *nout; s_wsfe(&io___76); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___77.ciunit = *nout; s_wsfe(&io___77); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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__1, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[0], (ftnlen) sizeof(doublereal)); e_wsfe(); } ++nfail; ++nrun; } if (result[5] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___78.ciunit = *nout; s_wsfe(&io___78); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&c__6, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[5], (ftnlen) sizeof(doublereal)); e_wsfe(); } else { io___79.ciunit = *nout; s_wsfe(&io___79); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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__6, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[5], (ftnlen) sizeof(doublereal)); e_wsfe(); } ++nfail; ++nrun; } if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___80.ciunit = *nout; s_wsfe(&io___80); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___81.ciunit = *nout; s_wsfe(&io___81); do_fio(&c__1, "DGESVXX", (ftnlen)7); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, trans, (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: ; } L60: ; } /* L70: */ } L80: ; } /* L90: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); /* Test Error Bounds from DGESVXX */ debchvxx_(thresh, path); return 0; /* End of DDRVGE */ } /* ddrvge_ */
CASADI_LINEARSOLVER_LAPACKLU_EXPORT void dgeequ_casadi(int *m, int *n, double *a, int *lda, double *r, double *c, double *colcnd, double *rowcnd, double *amax, int *info) { dgeequ_(m, n, a, lda, r, c, colcnd, rowcnd, amax, info); }
int jmi_linear_solver_solve(jmi_block_residual_t * block){ int n_x = block->n; int info; int i; /* int j; */ char trans; jmi_linear_solver_t* solver = block->solver; jmi_t * jmi = block->jmi; /* If needed, reevaluate and factorize Jacobian */ if (solver->cached_jacobian != 1) { /*printf("** Computing factorization in jmi_linear_solver_solve for block %d\n",block->index);*/ /* TODO: this code should be merged with the code used in kinsol interface module. A regularization strategy for simple cases singular jac should be introduced. */ info = block->F(jmi,NULL,solver->factorization,JMI_BLOCK_EVALUATE_JACOBIAN); if(info) { if(block->init) { jmi_log_node(jmi->log, logError, "Error", "Failed in Jacobian calculation for <block: %d>", block->index); } else { jmi_log_node(jmi->log, logWarning, "Warning", "Failed in Jacobian calculation for <block: %d>", block->index); } return -1; } if((n_x>1) && block->jmi->options.use_jacobian_equilibration_flag) { double rowcnd, colcnd, amax; dgeequ_(&n_x, &n_x, solver->factorization, &n_x, solver->rScale, solver->cScale, &rowcnd, &colcnd, &amax, &info); if(info == 0) { dlaqge_(&n_x, &n_x, solver->factorization, &n_x, solver->rScale, solver->cScale, &rowcnd, &colcnd, &amax, &solver->equed); } else solver->equed = 'N'; } /* printf("Jacobian: \n"); for (i=0;i<n_x;i++) { for (j=0;j<n_x;j++) { printf("%e, ", solver->factorization[i + j*n_x]); } printf("\n"); }*/ dgetrf_(&n_x, &n_x, solver->factorization, &n_x, solver->ipiv, &info); if(info) { if(block->init) { jmi_log_node(jmi->log, logError, "Error", "Singular Jacobian detected for <block: %d>", block->index); } else { jmi_log_node(jmi->log, logWarning, "Warning", "Singular Jacobian detected for <block: %d>", block->index); } return -1; } /*printf("Factorization: \n"); for (i=0;i<n_x;i++) { for (j=0;j<n_x;j++) { printf("%e, ", solver->factorization[i + j*n_x]); } printf("\n"); }*/ if (block->jacobian_variability == JMI_CONSTANT_VARIABILITY || block->jacobian_variability == JMI_PARAMETER_VARIABILITY) { solver->cached_jacobian = 1; } } /* Compute right hand side at initial x*/ /* TESTING ONLY! setting x to zero leads to invalid arguments to the function in case of bounds */ /*for (i=0;i<n_x;i++) { block->x[i] = 0.; } */ info = block->F(block->jmi,block->initial, block->res, JMI_BLOCK_EVALUATE); if(info) { if(block->init) { jmi_log_node(jmi->log, logError, "Error", "Failed to evaluate equations in <block: %d>", block->index); } else { jmi_log_node(jmi->log, logWarning, "Warning", "Failed to evaluate equations in <block: %d>", block->index); } return -1; } if((solver->equed == 'R') || (solver->equed == 'B')) { for (i=0;i<n_x;i++) { block->res[i] *= solver->rScale[i]; } } /* Do back-solve */ trans = 'N'; /* No transposition */ i = 1; /* One rhs to solve for */ dgetrs_(&trans, &n_x, &i, solver->factorization, &n_x, solver->ipiv, block->res, &n_x, &info); if(info) { /* can only be "bad param" -> internal error */ jmi_log_node(jmi->log, logError, "Error", "Internal error when solving <block: %d>", block->index); return -1; } if((solver->equed == 'C') || (solver->equed == 'B')) { for (i=0;i<n_x;i++) { block->x[i] = block->initial[i] + block->res[i] * solver->cScale[i]; } } else { for (i=0;i<n_x;i++) { block->x[i] = block->initial[i] + block->res[i] ; } } /* Write solution back to model */ block->F(block->jmi,block->x, NULL, JMI_BLOCK_WRITE_BACK); return info==0? 0: -1; }
/* Subroutine */ int dchkeq_(doublereal *thresh, integer *nout) { /* Format strings */ static char fmt_9999[] = "(1x,\002All tests for \002,a3,\002 routines pa" "ssed the threshold\002)"; static char fmt_9998[] = "(\002 DGEEQU failed test with value \002,d10" ".3,\002 exceeding\002,\002 threshold \002,d10.3)"; static char fmt_9997[] = "(\002 DGBEQU failed test with value \002,d10" ".3,\002 exceeding\002,\002 threshold \002,d10.3)"; static char fmt_9996[] = "(\002 DPOEQU failed test with value \002,d10" ".3,\002 exceeding\002,\002 threshold \002,d10.3)"; static char fmt_9995[] = "(\002 DPPEQU failed test with value \002,d10" ".3,\002 exceeding\002,\002 threshold \002,d10.3)"; static char fmt_9994[] = "(\002 DPBEQU failed test with value \002,d10" ".3,\002 exceeding\002,\002 threshold \002,d10.3)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8; doublereal d__1, d__2, d__3; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); double pow_di(doublereal *, integer *); integer pow_ii(integer *, integer *), s_wsle(cilist *), e_wsle(void), s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ doublereal a[25] /* was [5][5] */, c__[5]; integer i__, j, m, n; doublereal r__[5], ab[65] /* was [13][5] */, ap[15]; integer kl; logical ok; integer ku; doublereal eps, pow[11]; integer info; char path[3]; doublereal norm, rpow[11], ccond, rcond, rcmin, rcmax, ratio; extern doublereal dlamch_(char *); extern /* Subroutine */ int dgbequ_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dgeequ_( integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *) , dpbequ_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dpoequ_(integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dppequ_(char *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer * ); doublereal reslts[5]; /* Fortran I/O blocks */ static cilist io___25 = { 0, 0, 0, 0, 0 }; static cilist io___26 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___27 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___28 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___29 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___30 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___31 = { 0, 0, 0, fmt_9994, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU */ /* Arguments */ /* ========= */ /* THRESH (input) DOUBLE PRECISION */ /* Threshold for testing routines. Should be between 2 and 10. */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "EQ", (ftnlen)2, (ftnlen)2); eps = dlamch_("P"); for (i__ = 1; i__ <= 5; ++i__) { reslts[i__ - 1] = 0.; /* L10: */ } for (i__ = 1; i__ <= 11; ++i__) { i__1 = i__ - 1; pow[i__ - 1] = pow_di(&c_b7, &i__1); rpow[i__ - 1] = 1. / pow[i__ - 1]; /* L20: */ } /* Test DGEEQU */ for (n = 0; n <= 5; ++n) { for (m = 0; m <= 5; ++m) { for (j = 1; j <= 5; ++j) { for (i__ = 1; i__ <= 5; ++i__) { if (i__ <= m && j <= n) { i__1 = i__ + j; a[i__ + j * 5 - 6] = pow[i__ + j] * pow_ii(&c_n1, & i__1); } else { a[i__ + j * 5 - 6] = 0.; } /* L30: */ } /* L40: */ } dgeequ_(&m, &n, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info); if (info != 0) { reslts[0] = 1.; } else { if (n != 0 && m != 0) { /* Computing MAX */ d__2 = reslts[0], d__3 = (d__1 = (rcond - rpow[m - 1]) / rpow[m - 1], abs(d__1)); reslts[0] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[0], d__3 = (d__1 = (ccond - rpow[n - 1]) / rpow[n - 1], abs(d__1)); reslts[0] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[0], d__3 = (d__1 = (norm - pow[n + m]) / pow[n + m], abs(d__1)); reslts[0] = max(d__2,d__3); i__1 = m; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = reslts[0], d__3 = (d__1 = (r__[i__ - 1] - rpow[ i__ + n]) / rpow[i__ + n], abs(d__1)); reslts[0] = max(d__2,d__3); /* L50: */ } i__1 = n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ d__2 = reslts[0], d__3 = (d__1 = (c__[j - 1] - pow[n - j]) / pow[n - j], abs(d__1)); reslts[0] = max(d__2,d__3); /* L60: */ } } } /* L70: */ } /* L80: */ } /* Test with zero rows and columns */ for (j = 1; j <= 5; ++j) { a[j * 5 - 2] = 0.; /* L90: */ } dgeequ_(&c__5, &c__5, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info); if (info != 4) { reslts[0] = 1.; } for (j = 1; j <= 5; ++j) { a[j * 5 - 2] = 1.; /* L100: */ } for (i__ = 1; i__ <= 5; ++i__) { a[i__ + 14] = 0.; /* L110: */ } dgeequ_(&c__5, &c__5, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info); if (info != 9) { reslts[0] = 1.; } reslts[0] /= eps; /* Test DGBEQU */ for (n = 0; n <= 5; ++n) { for (m = 0; m <= 5; ++m) { /* Computing MAX */ i__2 = m - 1; i__1 = max(i__2,0); for (kl = 0; kl <= i__1; ++kl) { /* Computing MAX */ i__3 = n - 1; i__2 = max(i__3,0); for (ku = 0; ku <= i__2; ++ku) { for (j = 1; j <= 5; ++j) { for (i__ = 1; i__ <= 13; ++i__) { ab[i__ + j * 13 - 14] = 0.; /* L120: */ } /* L130: */ } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = m; for (i__ = 1; i__ <= i__4; ++i__) { /* Computing MIN */ i__5 = m, i__6 = j + kl; /* Computing MAX */ i__7 = 1, i__8 = j - ku; if (i__ <= min(i__5,i__6) && i__ >= max(i__7,i__8) && j <= n) { i__5 = i__ + j; ab[ku + 1 + i__ - j + j * 13 - 14] = pow[i__ + j] * pow_ii(&c_n1, &i__5); } /* L140: */ } /* L150: */ } dgbequ_(&m, &n, &kl, &ku, ab, &c__13, r__, c__, &rcond, & ccond, &norm, &info); if (info != 0) { if (! (n + kl < m && info == n + kl + 1 || m + ku < n && info == (m << 1) + ku + 1)) { reslts[1] = 1.; } } else { if (n != 0 && m != 0) { rcmin = r__[0]; rcmax = r__[0]; i__3 = m; for (i__ = 1; i__ <= i__3; ++i__) { /* Computing MIN */ d__1 = rcmin, d__2 = r__[i__ - 1]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = r__[i__ - 1]; rcmax = max(d__1,d__2); /* L160: */ } ratio = rcmin / rcmax; /* Computing MAX */ d__2 = reslts[1], d__3 = (d__1 = (rcond - ratio) / ratio, abs(d__1)); reslts[1] = max(d__2,d__3); rcmin = c__[0]; rcmax = c__[0]; i__3 = n; for (j = 1; j <= i__3; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = c__[j - 1]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = c__[j - 1]; rcmax = max(d__1,d__2); /* L170: */ } ratio = rcmin / rcmax; /* Computing MAX */ d__2 = reslts[1], d__3 = (d__1 = (ccond - ratio) / ratio, abs(d__1)); reslts[1] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[1], d__3 = (d__1 = (norm - pow[n + m]) / pow[n + m], abs(d__1)); reslts[1] = max(d__2,d__3); i__3 = m; for (i__ = 1; i__ <= i__3; ++i__) { rcmax = 0.; i__4 = n; for (j = 1; j <= i__4; ++j) { if (i__ <= j + kl && i__ >= j - ku) { ratio = (d__1 = r__[i__ - 1] * pow[ i__ + j] * c__[j - 1], abs( d__1)); rcmax = max(rcmax,ratio); } /* L180: */ } /* Computing MAX */ d__2 = reslts[1], d__3 = (d__1 = 1. - rcmax, abs(d__1)); reslts[1] = max(d__2,d__3); /* L190: */ } i__3 = n; for (j = 1; j <= i__3; ++j) { rcmax = 0.; i__4 = m; for (i__ = 1; i__ <= i__4; ++i__) { if (i__ <= j + kl && i__ >= j - ku) { ratio = (d__1 = r__[i__ - 1] * pow[ i__ + j] * c__[j - 1], abs( d__1)); rcmax = max(rcmax,ratio); } /* L200: */ } /* Computing MAX */ d__2 = reslts[1], d__3 = (d__1 = 1. - rcmax, abs(d__1)); reslts[1] = max(d__2,d__3); /* L210: */ } } } /* L220: */ } /* L230: */ } /* L240: */ } /* L250: */ } reslts[1] /= eps; /* Test DPOEQU */ for (n = 0; n <= 5; ++n) { for (i__ = 1; i__ <= 5; ++i__) { for (j = 1; j <= 5; ++j) { if (i__ <= n && j == i__) { i__1 = i__ + j; a[i__ + j * 5 - 6] = pow[i__ + j] * pow_ii(&c_n1, &i__1); } else { a[i__ + j * 5 - 6] = 0.; } /* L260: */ } /* L270: */ } dpoequ_(&n, a, &c__5, r__, &rcond, &norm, &info); if (info != 0) { reslts[2] = 1.; } else { if (n != 0) { /* Computing MAX */ d__2 = reslts[2], d__3 = (d__1 = (rcond - rpow[n - 1]) / rpow[ n - 1], abs(d__1)); reslts[2] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[2], d__3 = (d__1 = (norm - pow[n * 2]) / pow[n * 2], abs(d__1)); reslts[2] = max(d__2,d__3); i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = reslts[2], d__3 = (d__1 = (r__[i__ - 1] - rpow[i__] ) / rpow[i__], abs(d__1)); reslts[2] = max(d__2,d__3); /* L280: */ } } } /* L290: */ } a[18] = -1.; dpoequ_(&c__5, a, &c__5, r__, &rcond, &norm, &info); if (info != 4) { reslts[2] = 1.; } reslts[2] /= eps; /* Test DPPEQU */ for (n = 0; n <= 5; ++n) { /* Upper triangular packed storage */ i__1 = n * (n + 1) / 2; for (i__ = 1; i__ <= i__1; ++i__) { ap[i__ - 1] = 0.; /* L300: */ } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { ap[i__ * (i__ + 1) / 2 - 1] = pow[i__ * 2]; /* L310: */ } dppequ_("U", &n, ap, r__, &rcond, &norm, &info); if (info != 0) { reslts[3] = 1.; } else { if (n != 0) { /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (rcond - rpow[n - 1]) / rpow[ n - 1], abs(d__1)); reslts[3] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (norm - pow[n * 2]) / pow[n * 2], abs(d__1)); reslts[3] = max(d__2,d__3); i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (r__[i__ - 1] - rpow[i__] ) / rpow[i__], abs(d__1)); reslts[3] = max(d__2,d__3); /* L320: */ } } } /* Lower triangular packed storage */ i__1 = n * (n + 1) / 2; for (i__ = 1; i__ <= i__1; ++i__) { ap[i__ - 1] = 0.; /* L330: */ } j = 1; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { ap[j - 1] = pow[i__ * 2]; j += n - i__ + 1; /* L340: */ } dppequ_("L", &n, ap, r__, &rcond, &norm, &info); if (info != 0) { reslts[3] = 1.; } else { if (n != 0) { /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (rcond - rpow[n - 1]) / rpow[ n - 1], abs(d__1)); reslts[3] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (norm - pow[n * 2]) / pow[n * 2], abs(d__1)); reslts[3] = max(d__2,d__3); i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = reslts[3], d__3 = (d__1 = (r__[i__ - 1] - rpow[i__] ) / rpow[i__], abs(d__1)); reslts[3] = max(d__2,d__3); /* L350: */ } } } /* L360: */ } i__ = 13; ap[i__ - 1] = -1.; dppequ_("L", &c__5, ap, r__, &rcond, &norm, &info); if (info != 4) { reslts[3] = 1.; } reslts[3] /= eps; /* Test DPBEQU */ for (n = 0; n <= 5; ++n) { /* Computing MAX */ i__2 = n - 1; i__1 = max(i__2,0); for (kl = 0; kl <= i__1; ++kl) { /* Test upper triangular storage */ for (j = 1; j <= 5; ++j) { for (i__ = 1; i__ <= 13; ++i__) { ab[i__ + j * 13 - 14] = 0.; /* L370: */ } /* L380: */ } i__2 = n; for (j = 1; j <= i__2; ++j) { ab[kl + 1 + j * 13 - 14] = pow[j * 2]; /* L390: */ } dpbequ_("U", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info); if (info != 0) { reslts[4] = 1.; } else { if (n != 0) { /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (rcond - rpow[n - 1]) / rpow[n - 1], abs(d__1)); reslts[4] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (norm - pow[n * 2]) / pow[n * 2], abs(d__1)); reslts[4] = max(d__2,d__3); i__2 = n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (r__[i__ - 1] - rpow[ i__]) / rpow[i__], abs(d__1)); reslts[4] = max(d__2,d__3); /* L400: */ } } } if (n != 0) { /* Computing MAX */ i__2 = n - 1; ab[kl + 1 + max(i__2,1) * 13 - 14] = -1.; dpbequ_("U", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info); /* Computing MAX */ i__2 = n - 1; if (info != max(i__2,1)) { reslts[4] = 1.; } } /* Test lower triangular storage */ for (j = 1; j <= 5; ++j) { for (i__ = 1; i__ <= 13; ++i__) { ab[i__ + j * 13 - 14] = 0.; /* L410: */ } /* L420: */ } i__2 = n; for (j = 1; j <= i__2; ++j) { ab[j * 13 - 13] = pow[j * 2]; /* L430: */ } dpbequ_("L", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info); if (info != 0) { reslts[4] = 1.; } else { if (n != 0) { /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (rcond - rpow[n - 1]) / rpow[n - 1], abs(d__1)); reslts[4] = max(d__2,d__3); /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (norm - pow[n * 2]) / pow[n * 2], abs(d__1)); reslts[4] = max(d__2,d__3); i__2 = n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ d__2 = reslts[4], d__3 = (d__1 = (r__[i__ - 1] - rpow[ i__]) / rpow[i__], abs(d__1)); reslts[4] = max(d__2,d__3); /* L440: */ } } } if (n != 0) { /* Computing MAX */ i__2 = n - 1; ab[max(i__2,1) * 13 - 13] = -1.; dpbequ_("L", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info); /* Computing MAX */ i__2 = n - 1; if (info != max(i__2,1)) { reslts[4] = 1.; } } /* L450: */ } /* L460: */ } reslts[4] /= eps; ok = reslts[0] <= *thresh && reslts[1] <= *thresh && reslts[2] <= *thresh && reslts[3] <= *thresh && reslts[4] <= *thresh; io___25.ciunit = *nout; s_wsle(&io___25); e_wsle(); if (ok) { io___26.ciunit = *nout; s_wsfe(&io___26); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); } else { if (reslts[0] > *thresh) { io___27.ciunit = *nout; s_wsfe(&io___27); do_fio(&c__1, (char *)&reslts[0], (ftnlen)sizeof(doublereal)); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal)); e_wsfe(); } if (reslts[1] > *thresh) { io___28.ciunit = *nout; s_wsfe(&io___28); do_fio(&c__1, (char *)&reslts[1], (ftnlen)sizeof(doublereal)); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal)); e_wsfe(); } if (reslts[2] > *thresh) { io___29.ciunit = *nout; s_wsfe(&io___29); do_fio(&c__1, (char *)&reslts[2], (ftnlen)sizeof(doublereal)); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal)); e_wsfe(); } if (reslts[3] > *thresh) { io___30.ciunit = *nout; s_wsfe(&io___30); do_fio(&c__1, (char *)&reslts[3], (ftnlen)sizeof(doublereal)); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal)); e_wsfe(); } if (reslts[4] > *thresh) { io___31.ciunit = *nout; s_wsfe(&io___31); do_fio(&c__1, (char *)&reslts[4], (ftnlen)sizeof(doublereal)); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal)); e_wsfe(); } } return 0; /* End of DCHKEQ */ } /* dchkeq_ */
/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer * nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2; doublereal d__1, d__2; /* Local variables */ integer i__, j; doublereal amax; char norm[1]; extern logical lsame_(char *, char *); doublereal rcmin, rcmax, anorm; logical equil; extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dlaqge_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, char *), dgecon_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); doublereal colcnd; logical nofact; extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dgerfs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgetrf_(integer *, integer *, doublereal *, integer *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *); doublereal bignum; extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); integer infequ; logical colequ; extern /* Subroutine */ int dgetrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); doublereal rowcnd; logical notran; doublereal smlnum; logical rowequ; doublereal rpvgrw; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DGESVX uses the LU factorization to compute the solution to a real */ /* system of linear equations */ /* A * X = B, */ /* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */ /* Error bounds on the solution and a condition estimate are also */ /* provided. */ /* Description */ /* =========== */ /* The following steps are performed: */ /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ /* the system: */ /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ /* Whether or not the system will be equilibrated depends on the */ /* scaling of the matrix A, but if equilibration is used, A is */ /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ /* or diag(C)*B (if TRANS = 'T' or 'C'). */ /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */ /* matrix A (after equilibration if FACT = 'E') as */ /* A = P * L * U, */ /* where P is a permutation matrix, L is a unit lower triangular */ /* matrix, and U is upper triangular. */ /* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */ /* returns with INFO = i. Otherwise, the factored form of A is used */ /* to estimate the condition number of the matrix A. If the */ /* reciprocal of the condition number is less than machine precision, */ /* INFO = N+1 is returned as a warning, but the routine still goes on */ /* to solve for X and compute error bounds as described below. */ /* 4. The system of equations is solved for X using the factored form */ /* of A. */ /* 5. Iterative refinement is applied to improve the computed solution */ /* matrix and calculate error bounds and backward error estimates */ /* for it. */ /* 6. If equilibration was used, the matrix X is premultiplied by */ /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ /* that it solves the original system before equilibration. */ /* Arguments */ /* ========= */ /* FACT (input) CHARACTER*1 */ /* Specifies whether or not the factored form of the matrix A is */ /* supplied on entry, and if not, whether the matrix A should be */ /* equilibrated before it is factored. */ /* = 'F': On entry, AF and IPIV contain the factored form of A. */ /* If EQUED is not 'N', the matrix A has been */ /* equilibrated with scaling factors given by R and C. */ /* A, AF, and IPIV are not modified. */ /* = 'N': The matrix A will be copied to AF and factored. */ /* = 'E': The matrix A will be equilibrated if necessary, then */ /* copied to AF and factored. */ /* TRANS (input) CHARACTER*1 */ /* Specifies the form of the system of equations: */ /* = 'N': A * X = B (No transpose) */ /* = 'T': A**T * X = B (Transpose) */ /* = 'C': A**H * X = B (Transpose) */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ /* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */ /* not 'N', then A must have been equilibrated by the scaling */ /* factors in R and/or C. A is not modified if FACT = 'F' or */ /* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ /* EQUED = 'R': A := diag(R) * A */ /* EQUED = 'C': A := A * diag(C) */ /* EQUED = 'B': A := diag(R) * A * diag(C). */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N) */ /* If FACT = 'F', then AF is an input argument and on entry */ /* contains the factors L and U from the factorization */ /* A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then */ /* AF is the factored form of the equilibrated matrix A. */ /* If FACT = 'N', then AF is an output argument and on exit */ /* returns the factors L and U from the factorization A = P*L*U */ /* of the original matrix A. */ /* If FACT = 'E', then AF is an output argument and on exit */ /* returns the factors L and U from the factorization A = P*L*U */ /* of the equilibrated matrix A (see the description of A for */ /* the form of the equilibrated matrix). */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* IPIV (input or output) INTEGER array, dimension (N) */ /* If FACT = 'F', then IPIV is an input argument and on entry */ /* contains the pivot indices from the factorization A = P*L*U */ /* as computed by DGETRF; row i of the matrix was interchanged */ /* with row IPIV(i). */ /* If FACT = 'N', then IPIV is an output argument and on exit */ /* contains the pivot indices from the factorization A = P*L*U */ /* of the original matrix A. */ /* If FACT = 'E', then IPIV is an output argument and on exit */ /* contains the pivot indices from the factorization A = P*L*U */ /* of the equilibrated matrix A. */ /* EQUED (input or output) CHARACTER*1 */ /* Specifies the form of equilibration that was done. */ /* = 'N': No equilibration (always true if FACT = 'N'). */ /* = 'R': Row equilibration, i.e., A has been premultiplied by */ /* diag(R). */ /* = 'C': Column equilibration, i.e., A has been postmultiplied */ /* by diag(C). */ /* = 'B': Both row and column equilibration, i.e., A has been */ /* replaced by diag(R) * A * diag(C). */ /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ /* output argument. */ /* R (input or output) DOUBLE PRECISION array, dimension (N) */ /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ /* is not accessed. R is an input argument if FACT = 'F'; */ /* otherwise, R is an output argument. If FACT = 'F' and */ /* EQUED = 'R' or 'B', each element of R must be positive. */ /* C (input or output) DOUBLE PRECISION array, dimension (N) */ /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ /* is not accessed. C is an input argument if FACT = 'F'; */ /* otherwise, C is an output argument. If FACT = 'F' and */ /* EQUED = 'C' or 'B', each element of C must be positive. */ /* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS right hand side matrix B. */ /* On exit, */ /* if EQUED = 'N', B is not modified; */ /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ /* diag(R)*B; */ /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ /* overwritten by diag(C)*B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */ /* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */ /* to the original system of equations. Note that A and B are */ /* modified on exit if EQUED .ne. 'N', and the solution to the */ /* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */ /* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */ /* and EQUED = 'R' or 'B'. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* The estimate of the reciprocal condition number of the matrix */ /* A after equilibration (if done). If RCOND is less than the */ /* machine precision (in particular, if RCOND = 0), the matrix */ /* is singular to working precision. This condition is */ /* indicated by a return code of INFO > 0. */ /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The estimated forward error bound for each solution vector */ /* X(j) (the j-th column of the solution matrix X). */ /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* is an estimated upper bound for the magnitude of the largest */ /* element in (X(j) - XTRUE) divided by the magnitude of the */ /* largest element in X(j). The estimate is as reliable as */ /* the estimate for RCOND, and is almost always a slight */ /* overestimate of the true error. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The componentwise relative backward error of each solution */ /* vector X(j) (i.e., the smallest relative change in */ /* any element of A or B that makes X(j) an exact solution). */ /* WORK (workspace/output) DOUBLE PRECISION array, dimension (4*N) */ /* On exit, WORK(1) contains the reciprocal pivot growth */ /* factor norm(A)/norm(U). The "max absolute element" norm is */ /* used. If WORK(1) is much less than 1, then the stability */ /* of the LU factorization of the (equilibrated) matrix A */ /* could be poor. This also means that the solution X, condition */ /* estimator RCOND, and forward error bound FERR could be */ /* unreliable. If factorization fails with 0<INFO<=N, then */ /* WORK(1) contains the reciprocal pivot growth factor for the */ /* leading INFO columns of A. */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is */ /* <= N: U(i,i) is exactly zero. The factorization has */ /* been completed, but the factor U is exactly */ /* singular, so the solution and error bounds */ /* could not be computed. RCOND = 0 is returned. */ /* = N+1: U is nonsingular, but RCOND is less than machine */ /* precision, meaning that the matrix is singular */ /* to working precision. Nevertheless, the */ /* solution and error bounds are computed because */ /* there are a number of situations where the */ /* computed solution can be more accurate than the */ /* value of RCOND would suggest. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. 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; --ipiv; --r__; --c__; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --iwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); notran = lsame_(trans, "N"); if (nofact || equil) { *(unsigned char *)equed = 'N'; rowequ = FALSE_; colequ = FALSE_; } else { rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); smlnum = dlamch_("Safe minimum"); bignum = 1. / smlnum; } /* Test the input parameters. */ if (! nofact && ! equil && ! lsame_(fact, "F")) { *info = -1; } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (lsame_(fact, "F") && ! (rowequ || colequ || lsame_(equed, "N"))) { *info = -10; } else { if (rowequ) { rcmin = bignum; rcmax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = r__[j]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = r__[j]; rcmax = max(d__1,d__2); /* L10: */ } if (rcmin <= 0.) { *info = -11; } else if (*n > 0) { rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { rowcnd = 1.; } } if (colequ && *info == 0) { rcmin = bignum; rcmax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = c__[j]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = c__[j]; rcmax = max(d__1,d__2); /* L20: */ } if (rcmin <= 0.) { *info = -12; } else if (*n > 0) { colcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { colcnd = 1.; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -14; } else if (*ldx < max(1,*n)) { *info = -16; } } } if (*info != 0) { i__1 = -(*info); xerbla_("DGESVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ dgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, & amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & colcnd, &amax, equed); rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); } } /* Scale the right hand side. */ if (notran) { if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1]; /* L30: */ } /* L40: */ } } } else if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1]; /* L50: */ } /* L60: */ } } if (nofact || equil) { /* Compute the LU factorization of A. */ dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { /* Compute the reciprocal pivot growth factor of the */ /* leading rank-deficient INFO columns of A. */ rpvgrw = dlantr_("M", "U", "N", info, info, &af[af_offset], ldaf, &work[1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = dlange_("M", n, info, &a[a_offset], lda, &work[1]) / rpvgrw; } work[1] = rpvgrw; *rcond = 0.; return 0; } } /* Compute the norm of the matrix A and the */ /* reciprocal pivot growth factor RPVGRW. */ if (notran) { *(unsigned char *)norm = '1'; } else { *(unsigned char *)norm = 'I'; } anorm = dlange_(norm, n, n, &a[a_offset], lda, &work[1]); rpvgrw = dlantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = dlange_("M", n, n, &a[a_offset], lda, &work[1]) / rpvgrw; } /* Compute the reciprocal of the condition number of A. */ dgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1], info); /* Compute the solution matrix X. */ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ dgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[ 1], &iwork[1], info); /* Transform the solution matrix X to a solution of the original */ /* system. */ if (notran) { if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1]; /* L70: */ } /* L80: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= colcnd; /* L90: */ } } } else if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1]; /* L100: */ } /* L110: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= rowcnd; /* L120: */ } } work[1] = rpvgrw; /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of DGESVX */ } /* dgesvx_ */