#include "blaswrap.h" /* dget38.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__400 = 400; /* Subroutine */ int dget38_(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 q[400] /* was [20][20] */, s, t[400] /* was [20][ 20] */, v, wi[20], wr[20], val[3], eps, sep, sin__, tol, tmp[400] /* was [20][20] */; static integer ndim, iscl, info, kmin, itmp, ipnt[20]; static doublereal vmax, qsav[400] /* was [20][20] */, tsav[400] /* was [20][20] */, tnrm, qtmp[400] /* was [20][20] */, work[1200] , stmp, vmul, ttmp[400] /* was [20][20] */, tsav1[400] /* was [20][20] */; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *), dhst01_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *); static doublereal sepin; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); static doublereal vimin, tolin, vrmin; static integer iwork[400]; 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 *); static integer iselec[20]; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); static logical select[20]; static doublereal bignum; extern /* Subroutine */ int dorghr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dhseqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *), dtrsen_(char *, char *, logical *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, integer *); static doublereal septmp, smlnum, result[2]; /* 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 }; static cilist io___14 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DGET38 tests DTRSEN, a routine for estimating condition numbers of a cluster of eigenvalues and/or its associated right invariant subspace The test matrices are read from a file with logical unit number NIN. Arguments ========== RMAX (output) DOUBLE PRECISION array, dimension (3) Values of the largest test ratios. RMAX(1) = largest residuals from DHST01 or comparing different calls to DTRSEN 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 DTRSEN 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 DTRSEN 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(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)); do_lio(&c__3, &c__1, (char *)&ndim, (ftnlen)sizeof(integer)); e_rsle(); if (n == 0) { return 0; } io___8.ciunit = *nin; s_rsle(&io___8); i__1 = ndim; for (i__ = 1; i__ <= i__1; ++i__) { do_lio(&c__3, &c__1, (char *)&iselec[i__ - 1], (ftnlen)sizeof(integer) ); } e_rsle(); i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___11.ciunit = *nin; s_rsle(&io___11); 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: */ } io___14.ciunit = *nin; s_rsle(&io___14); do_lio(&c__5, &c__1, (char *)&sin__, (ftnlen)sizeof(doublereal)); do_lio(&c__5, &c__1, (char *)&sepin, (ftnlen)sizeof(doublereal)); e_rsle(); tnrm = dlange_("M", &n, &n, tmp, &c__20, work); 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); /* L30: */ } if (tnrm == 0.) { vmul = 1.; } dlacpy_("F", &n, &n, t, &c__20, tsav, &c__20); /* Compute Schur form */ 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 L160; } /* Generate orthogonal matrix */ dlacpy_("L", &n, &n, t, &c__20, q, &c__20); i__1 = 1200 - n; dorghr_(&n, &c__1, &n, q, &c__20, work, &work[n], &i__1, &info); /* Compute Schur form */ dhseqr_("S", "V", &n, &c__1, &n, t, &c__20, wr, wi, q, &c__20, work, & c__1200, &info); if (info != 0) { lmax[2] = *knt; ++ninfo[2]; goto L160; } /* Sort, select eigenvalues */ i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { ipnt[i__ - 1] = i__; select[i__ - 1] = FALSE_; /* L40: */ } dcopy_(&n, wr, &c__1, wrtmp, &c__1); dcopy_(&n, wi, &c__1, witmp, &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]; } /* L50: */ } wrtmp[kmin - 1] = wrtmp[i__ - 1]; witmp[kmin - 1] = witmp[i__ - 1]; wrtmp[i__ - 1] = vrmin; witmp[i__ - 1] = vimin; itmp = ipnt[i__ - 1]; ipnt[i__ - 1] = ipnt[kmin - 1]; ipnt[kmin - 1] = itmp; /* L60: */ } i__1 = ndim; for (i__ = 1; i__ <= i__1; ++i__) { select[ipnt[iselec[i__ - 1] - 1] - 1] = TRUE_; /* L70: */ } /* Compute condition numbers */ dlacpy_("F", &n, &n, q, &c__20, qsav, &c__20); dlacpy_("F", &n, &n, t, &c__20, tsav1, &c__20); dtrsen_("B", "V", select, &n, t, &c__20, q, &c__20, wrtmp, witmp, &m, &s, &sep, work, &c__1200, iwork, &c__400, &info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L160; } septmp = sep / vmul; stmp = s; /* Compute residuals */ dhst01_(&n, &c__1, &n, tsav, &c__20, t, &c__20, q, &c__20, work, & c__1200, result); vmax = max(result[0],result[1]); if (vmax > rmax[1]) { rmax[1] = vmax; if (ninfo[1] == 0) { lmax[1] = *knt; } } /* Compare condition number for eigenvalue cluster taking its condition number into account Computing MAX */ d__1 = (doublereal) n * 2. * eps * tnrm; v = max(d__1,smlnum); if (tnrm == 0.) { v = 1.; } if (v > septmp) { tol = 1.; } else { tol = v / septmp; } if (v > sepin) { tolin = 1.; } else { tolin = v / sepin; } /* 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__ - tolin) > stmp + tol) { vmax = 1. / eps; } else if (sin__ - tolin > stmp + tol) { vmax = (sin__ - tolin) / (stmp + tol); } else if (sin__ + tolin < eps * (stmp - tol)) { vmax = 1. / eps; } else if (sin__ + tolin < stmp - tol) { vmax = (stmp - tol) / (sin__ + tolin); } else { vmax = 1.; } if (vmax > rmax[2]) { rmax[2] = vmax; if (ninfo[2] == 0) { lmax[2] = *knt; } } /* Compare condition numbers for invariant subspace taking its condition number into account */ if (v > septmp * stmp) { tol = septmp; } else { tol = v / stmp; } if (v > sepin * sin__) { tolin = sepin; } else { tolin = v / sin__; } /* 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 - tolin) > septmp + tol) { vmax = 1. / eps; } else if (sepin - tolin > septmp + tol) { vmax = (sepin - tolin) / (septmp + tol); } else if (sepin + tolin < eps * (septmp - tol)) { vmax = 1. / eps; } else if (sepin + tolin < septmp - tol) { vmax = (septmp - tol) / (sepin + tolin); } else { vmax = 1.; } if (vmax > rmax[2]) { rmax[2] = vmax; if (ninfo[2] == 0) { lmax[2] = *knt; } } /* Compare condition number for eigenvalue cluster without taking its condition number into account */ if (sin__ <= (doublereal) (n << 1) * eps && stmp <= (doublereal) (n << 1) * eps) { vmax = 1.; } else if (eps * sin__ > stmp) { vmax = 1. / eps; } else if (sin__ > stmp) { vmax = sin__ / stmp; } else if (sin__ < eps * stmp) { vmax = 1. / eps; } else if (sin__ < stmp) { vmax = stmp / sin__; } else { vmax = 1.; } if (vmax > rmax[3]) { rmax[3] = vmax; if (ninfo[3] == 0) { lmax[3] = *knt; } } /* Compare condition numbers for invariant subspace without taking its condition number into account */ if (sepin <= v && septmp <= v) { vmax = 1.; } else if (eps * sepin > septmp) { vmax = 1. / eps; } else if (sepin > septmp) { vmax = sepin / septmp; } else if (sepin < eps * septmp) { vmax = 1. / eps; } else if (sepin < septmp) { vmax = septmp / sepin; } else { vmax = 1.; } if (vmax > rmax[3]) { rmax[3] = vmax; if (ninfo[3] == 0) { lmax[3] = *knt; } } /* Compute eigenvalue condition number only and compare Update Q */ vmax = 0.; dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20); dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20); septmp = -1.; stmp = -1.; dtrsen_("E", "V", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp, witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, & info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L160; } if (s != stmp) { vmax = 1. / eps; } if (-1. != septmp) { vmax = 1. / eps; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = n; for (j = 1; j <= i__2; ++j) { if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) { vmax = 1. / eps; } if (qtmp[i__ + j * 20 - 21] != q[i__ + j * 20 - 21]) { vmax = 1. / eps; } /* L80: */ } /* L90: */ } /* Compute invariant subspace condition number only and compare Update Q */ dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20); dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20); septmp = -1.; stmp = -1.; dtrsen_("V", "V", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp, witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, & info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L160; } if (-1. != stmp) { vmax = 1. / eps; } if (sep != septmp) { vmax = 1. / eps; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = n; for (j = 1; j <= i__2; ++j) { if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) { vmax = 1. / eps; } if (qtmp[i__ + j * 20 - 21] != q[i__ + j * 20 - 21]) { vmax = 1. / eps; } /* L100: */ } /* L110: */ } /* Compute eigenvalue condition number only and compare Do not update Q */ dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20); dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20); septmp = -1.; stmp = -1.; dtrsen_("E", "N", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp, witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, & info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L160; } if (s != stmp) { vmax = 1. / eps; } if (-1. != septmp) { vmax = 1. / eps; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = n; for (j = 1; j <= i__2; ++j) { if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) { vmax = 1. / eps; } if (qtmp[i__ + j * 20 - 21] != qsav[i__ + j * 20 - 21]) { vmax = 1. / eps; } /* L120: */ } /* L130: */ } /* Compute invariant subspace condition number only and compare Do not update Q */ dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20); dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20); septmp = -1.; stmp = -1.; dtrsen_("V", "N", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp, witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, & info); if (info != 0) { lmax[3] = *knt; ++ninfo[3]; goto L160; } if (-1. != stmp) { vmax = 1. / eps; } if (sep != septmp) { vmax = 1. / eps; } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = n; for (j = 1; j <= i__2; ++j) { if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) { vmax = 1. / eps; } if (qtmp[i__ + j * 20 - 21] != qsav[i__ + j * 20 - 21]) { vmax = 1. / eps; } /* L140: */ } /* L150: */ } if (vmax > rmax[1]) { rmax[1] = vmax; if (ninfo[1] == 0) { lmax[1] = *knt; } } L160: ; } goto L10; /* End of DGET38 */ } /* dget38_ */