#include "blaswrap.h" /* dget37.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Table of constant values */ static integer c__3 = 3; static integer c__1 = 1; static integer c__5 = 5; static integer c__20 = 20; static integer c__1200 = 1200; static integer c__0 = 0; /* Subroutine */ int dget37_(doublereal *rmax, integer *lmax, integer *ninfo, integer *knt, integer *nin) { /* System generated locals */ integer i__1, i__2; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), e_rsle(void); /* Local variables */ static integer i__, j, m, n; static doublereal s[20], t[400] /* was [20][20] */, v, le[400] /* was [20][20] */, re[400] /* was [20][20] */, wi[20], wr[20], val[3], dum[1], eps, sep[20], sin__[20], tol, tmp[400] /* was [20][20] */; static integer ifnd, icmp, iscl, info, lcmp[3], kmin; static doublereal wiin[20], vmax, tnrm, wrin[20], work[1200], vmul, stmp[ 20]; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal sepin[20]; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); static doublereal vimin, tolin, vrmin; static integer iwork[40]; static doublereal witmp[20], wrtmp[20]; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); static logical select[20]; static doublereal bignum; extern /* Subroutine */ int dhseqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *), dtrevc_(char *, char *, logical *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *), dtrsna_(char *, char *, logical *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, integer *); static doublereal septmp[20], smlnum; /* Fortran I/O blocks */ static cilist io___5 = { 0, 0, 0, 0, 0 }; static cilist io___8 = { 0, 0, 0, 0, 0 }; static cilist io___11 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DGET37 tests DTRSNA, a routine for estimating condition numbers of eigenvalues and/or right eigenvectors of a matrix. The test matrices are read from a file with logical unit number NIN. Arguments ========== RMAX (output) DOUBLE PRECISION array, dimension (3) Value of the largest test ratio. RMAX(1) = largest ratio comparing different calls to DTRSNA RMAX(2) = largest error in reciprocal condition numbers taking their conditioning into account RMAX(3) = largest error in reciprocal condition numbers not taking their conditioning into account (may be larger than RMAX(2)) LMAX (output) INTEGER array, dimension (3) LMAX(i) is example number where largest test ratio RMAX(i) is achieved. Also: If DGEHRD returns INFO nonzero on example i, LMAX(1)=i If DHSEQR returns INFO nonzero on example i, LMAX(2)=i If DTRSNA returns INFO nonzero on example i, LMAX(3)=i NINFO (output) INTEGER array, dimension (3) NINFO(1) = No. of times DGEHRD returned INFO nonzero NINFO(2) = No. of times DHSEQR returned INFO nonzero NINFO(3) = No. of times DTRSNA returned INFO nonzero KNT (output) INTEGER Total number of examples tested. NIN (input) INTEGER Input logical unit number ===================================================================== Parameter adjustments */ --ninfo; --lmax; --rmax; /* Function Body */ eps = dlamch_("P"); smlnum = dlamch_("S") / eps; bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); /* EPSIN = 2**(-24) = precision to which input data computed */ eps = max(eps,5.9605e-8); rmax[1] = 0.; rmax[2] = 0.; rmax[3] = 0.; lmax[1] = 0; lmax[2] = 0; lmax[3] = 0; *knt = 0; ninfo[1] = 0; ninfo[2] = 0; ninfo[3] = 0; val[0] = sqrt(smlnum); val[1] = 1.; val[2] = sqrt(bignum); /* Read input data until N=0. Assume input eigenvalues are sorted lexicographically (increasing by real part, then decreasing by imaginary part) */ L10: io___5.ciunit = *nin; s_rsle(&io___5); do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer)); e_rsle(); if (n == 0) { return 0; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___8.ciunit = *nin; s_rsle(&io___8); i__2 = n; for (j = 1; j <= i__2; ++j) { do_lio(&c__5, &c__1, (char *)&tmp[i__ + j * 20 - 21], (ftnlen) sizeof(doublereal)); } e_rsle(); /* L20: */ } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___11.ciunit = *nin; s_rsle(&io___11); do_lio(&c__5, &c__1, (char *)&wrin[i__ - 1], (ftnlen)sizeof( doublereal)); do_lio(&c__5, &c__1, (char *)&wiin[i__ - 1], (ftnlen)sizeof( doublereal)); do_lio(&c__5, &c__1, (char *)&sin__[i__ - 1], (ftnlen)sizeof( doublereal)); do_lio(&c__5, &c__1, (char *)&sepin[i__ - 1], (ftnlen)sizeof( doublereal)); e_rsle(); /* L30: */ } tnrm = dlange_("M", &n, &n, tmp, &c__20, work); /* Begin test */ for (iscl = 1; iscl <= 3; ++iscl) { /* Scale input matrix */ ++(*knt); dlacpy_("F", &n, &n, tmp, &c__20, t, &c__20); vmul = val[iscl - 1]; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { dscal_(&n, &vmul, &t[i__ * 20 - 20], &c__1); /* L40: */ } if (tnrm == 0.) { vmul = 1.; } /* Compute eigenvalues and eigenvectors */ i__1 = 1200 - n; dgehrd_(&n, &c__1, &n, t, &c__20, work, &work[n], &i__1, &info); if (info != 0) { lmax[1] = *knt; ++ninfo[1]; goto L240; } i__1 = n - 2; for (j = 1; j <= i__1; ++j) { i__2 = n; for (i__ = j + 2; i__ <= i__2; ++i__) { t[i__ + j * 20 - 21] = 0.; /* L50: */ } /* L60: */ } /* Compute Schur form */ dhseqr_("S", "N", &n, &c__1, &n, t, &c__20, wr, wi, dum, &c__1, work, &c__1200, &info); if (info != 0) { lmax[2] = *knt; ++ninfo[2]; goto L240; } /* Compute eigenvectors */ dtrevc_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20, &n, &m, work, &info); /* Compute condition numbers */ dtrsna_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20, s, sep, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } /* Sort eigenvalues and condition numbers lexicographically to compare with inputs */ dcopy_(&n, wr, &c__1, wrtmp, &c__1); dcopy_(&n, wi, &c__1, witmp, &c__1); dcopy_(&n, s, &c__1, stmp, &c__1); dcopy_(&n, sep, &c__1, septmp, &c__1); d__1 = 1. / vmul; dscal_(&n, &d__1, septmp, &c__1); i__1 = n - 1; for (i__ = 1; i__ <= i__1; ++i__) { kmin = i__; vrmin = wrtmp[i__ - 1]; vimin = witmp[i__ - 1]; i__2 = n; for (j = i__ + 1; j <= i__2; ++j) { if (wrtmp[j - 1] < vrmin) { kmin = j; vrmin = wrtmp[j - 1]; vimin = witmp[j - 1]; } /* L70: */ } wrtmp[kmin - 1] = wrtmp[i__ - 1]; witmp[kmin - 1] = witmp[i__ - 1]; wrtmp[i__ - 1] = vrmin; witmp[i__ - 1] = vimin; vrmin = stmp[kmin - 1]; stmp[kmin - 1] = stmp[i__ - 1]; stmp[i__ - 1] = vrmin; vrmin = septmp[kmin - 1]; septmp[kmin - 1] = septmp[i__ - 1]; septmp[i__ - 1] = vrmin; /* L80: */ } /* Compare condition numbers for eigenvalues taking their condition numbers into account Computing MAX */ d__1 = (doublereal) n * 2. * eps * tnrm; v = max(d__1,smlnum); if (tnrm == 0.) { v = 1.; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (v > septmp[i__ - 1]) { tol = 1.; } else { tol = v / septmp[i__ - 1]; } if (v > sepin[i__ - 1]) { tolin = 1.; } else { tolin = v / sepin[i__ - 1]; } /* Computing MAX */ d__1 = tol, d__2 = smlnum / eps; tol = max(d__1,d__2); /* Computing MAX */ d__1 = tolin, d__2 = smlnum / eps; tolin = max(d__1,d__2); if (eps * (sin__[i__ - 1] - tolin) > stmp[i__ - 1] + tol) { vmax = 1. / eps; } else if (sin__[i__ - 1] - tolin > stmp[i__ - 1] + tol) { vmax = (sin__[i__ - 1] - tolin) / (stmp[i__ - 1] + tol); } else if (sin__[i__ - 1] + tolin < eps * (stmp[i__ - 1] - tol)) { vmax = 1. / eps; } else if (sin__[i__ - 1] + tolin < stmp[i__ - 1] - tol) { vmax = (stmp[i__ - 1] - tol) / (sin__[i__ - 1] + tolin); } else { vmax = 1.; } if (vmax > rmax[2]) { rmax[2] = vmax; if (ninfo[2] == 0) { lmax[2] = *knt; } } /* L90: */ } /* Compare condition numbers for eigenvectors taking their condition numbers into account */ i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (v > septmp[i__ - 1] * stmp[i__ - 1]) { tol = septmp[i__ - 1]; } else { tol = v / stmp[i__ - 1]; } if (v > sepin[i__ - 1] * sin__[i__ - 1]) { tolin = sepin[i__ - 1]; } else { tolin = v / sin__[i__ - 1]; } /* Computing MAX */ d__1 = tol, d__2 = smlnum / eps; tol = max(d__1,d__2); /* Computing MAX */ d__1 = tolin, d__2 = smlnum / eps; tolin = max(d__1,d__2); if (eps * (sepin[i__ - 1] - tolin) > septmp[i__ - 1] + tol) { vmax = 1. / eps; } else if (sepin[i__ - 1] - tolin > septmp[i__ - 1] + tol) { vmax = (sepin[i__ - 1] - tolin) / (septmp[i__ - 1] + tol); } else if (sepin[i__ - 1] + tolin < eps * (septmp[i__ - 1] - tol)) { vmax = 1. / eps; } else if (sepin[i__ - 1] + tolin < septmp[i__ - 1] - tol) { vmax = (septmp[i__ - 1] - tol) / (sepin[i__ - 1] + tolin); } else { vmax = 1.; } if (vmax > rmax[2]) { rmax[2] = vmax; if (ninfo[2] == 0) { lmax[2] = *knt; } } /* L100: */ } /* Compare condition numbers for eigenvalues without taking their condition numbers into account */ i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (sin__[i__ - 1] <= (doublereal) (n << 1) * eps && stmp[i__ - 1] <= (doublereal) (n << 1) * eps) { vmax = 1.; } else if (eps * sin__[i__ - 1] > stmp[i__ - 1]) { vmax = 1. / eps; } else if (sin__[i__ - 1] > stmp[i__ - 1]) { vmax = sin__[i__ - 1] / stmp[i__ - 1]; } else if (sin__[i__ - 1] < eps * stmp[i__ - 1]) { vmax = 1. / eps; } else if (sin__[i__ - 1] < stmp[i__ - 1]) { vmax = stmp[i__ - 1] / sin__[i__ - 1]; } else { vmax = 1.; } if (vmax > rmax[3]) { rmax[3] = vmax; if (ninfo[3] == 0) { lmax[3] = *knt; } } /* L110: */ } /* Compare condition numbers for eigenvectors without taking their condition numbers into account */ i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (sepin[i__ - 1] <= v && septmp[i__ - 1] <= v) { vmax = 1.; } else if (eps * sepin[i__ - 1] > septmp[i__ - 1]) { vmax = 1. / eps; } else if (sepin[i__ - 1] > septmp[i__ - 1]) { vmax = sepin[i__ - 1] / septmp[i__ - 1]; } else if (sepin[i__ - 1] < eps * septmp[i__ - 1]) { vmax = 1. / eps; } else if (sepin[i__ - 1] < septmp[i__ - 1]) { vmax = septmp[i__ - 1] / sepin[i__ - 1]; } else { vmax = 1.; } if (vmax > rmax[3]) { rmax[3] = vmax; if (ninfo[3] == 0) { lmax[3] = *knt; } } /* L120: */ } /* Compute eigenvalue condition numbers only and compare */ vmax = 0.; dum[0] = -1.; dcopy_(&n, dum, &c__0, stmp, &c__1); dcopy_(&n, dum, &c__0, septmp, &c__1); dtrsna_("Eigcond", "All", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (stmp[i__ - 1] != s[i__ - 1]) { vmax = 1. / eps; } if (septmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } /* L130: */ } /* Compute eigenvector condition numbers only and compare */ dcopy_(&n, dum, &c__0, stmp, &c__1); dcopy_(&n, dum, &c__0, septmp, &c__1); dtrsna_("Veccond", "All", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (stmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } if (septmp[i__ - 1] != sep[i__ - 1]) { vmax = 1. / eps; } /* L140: */ } /* Compute all condition numbers using SELECT and compare */ i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { select[i__ - 1] = TRUE_; /* L150: */ } dcopy_(&n, dum, &c__0, stmp, &c__1); dcopy_(&n, dum, &c__0, septmp, &c__1); dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (septmp[i__ - 1] != sep[i__ - 1]) { vmax = 1. / eps; } if (stmp[i__ - 1] != s[i__ - 1]) { vmax = 1. / eps; } /* L160: */ } /* Compute eigenvalue condition numbers using SELECT and compare */ dcopy_(&n, dum, &c__0, stmp, &c__1); dcopy_(&n, dum, &c__0, septmp, &c__1); dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (stmp[i__ - 1] != s[i__ - 1]) { vmax = 1. / eps; } if (septmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } /* L170: */ } /* Compute eigenvector condition numbers using SELECT and compare */ dcopy_(&n, dum, &c__0, stmp, &c__1); dcopy_(&n, dum, &c__0, septmp, &c__1); dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if (stmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } if (septmp[i__ - 1] != sep[i__ - 1]) { vmax = 1. / eps; } /* L180: */ } if (vmax > rmax[1]) { rmax[1] = vmax; if (ninfo[1] == 0) { lmax[1] = *knt; } } /* Select first real and first complex eigenvalue */ if (wi[0] == 0.) { lcmp[0] = 1; ifnd = 0; i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { if (ifnd == 1 || wi[i__ - 1] == 0.) { select[i__ - 1] = FALSE_; } else { ifnd = 1; lcmp[1] = i__; lcmp[2] = i__ + 1; dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[20], &c__1); dcopy_(&n, &re[(i__ + 1) * 20 - 20], &c__1, &re[40], & c__1); dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[20], &c__1); dcopy_(&n, &le[(i__ + 1) * 20 - 20], &c__1, &le[40], & c__1); } /* L190: */ } if (ifnd == 0) { icmp = 1; } else { icmp = 3; } } else { lcmp[0] = 1; lcmp[1] = 2; ifnd = 0; i__1 = n; for (i__ = 3; i__ <= i__1; ++i__) { if (ifnd == 1 || wi[i__ - 1] != 0.) { select[i__ - 1] = FALSE_; } else { lcmp[2] = i__; ifnd = 1; dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[40], &c__1); dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[40], &c__1); } /* L200: */ } if (ifnd == 0) { icmp = 2; } else { icmp = 3; } } /* Compute all selected condition numbers */ dcopy_(&icmp, dum, &c__0, stmp, &c__1); dcopy_(&icmp, dum, &c__0, septmp, &c__1); dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = icmp; for (i__ = 1; i__ <= i__1; ++i__) { j = lcmp[i__ - 1]; if (septmp[i__ - 1] != sep[j - 1]) { vmax = 1. / eps; } if (stmp[i__ - 1] != s[j - 1]) { vmax = 1. / eps; } /* L210: */ } /* Compute selected eigenvalue condition numbers */ dcopy_(&icmp, dum, &c__0, stmp, &c__1); dcopy_(&icmp, dum, &c__0, septmp, &c__1); dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = icmp; for (i__ = 1; i__ <= i__1; ++i__) { j = lcmp[i__ - 1]; if (stmp[i__ - 1] != s[j - 1]) { vmax = 1. / eps; } if (septmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } /* L220: */ } /* Compute selected eigenvector condition numbers */ dcopy_(&icmp, dum, &c__0, stmp, &c__1); dcopy_(&icmp, dum, &c__0, septmp, &c__1); dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, & c__20, stmp, septmp, &n, &m, work, &n, iwork, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L240; } i__1 = icmp; for (i__ = 1; i__ <= i__1; ++i__) { j = lcmp[i__ - 1]; if (stmp[i__ - 1] != dum[0]) { vmax = 1. / eps; } if (septmp[i__ - 1] != sep[j - 1]) { vmax = 1. / eps; } /* L230: */ } if (vmax > rmax[1]) { rmax[1] = vmax; if (ninfo[1] == 0) { lmax[1] = *knt; } } L240: ; } goto L10; /* End of DGET37 */ } /* dget37_ */