/* Subroutine */ int strsna_(char *job, char *howmny, logical *select, integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, integer *ldvr, real *s, real *sep, integer *mm, integer *m, real * work, integer *ldwork, integer *iwork, integer *info) { /* System generated locals */ integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, work_dim1, work_offset, i__1, i__2; real r__1, r__2; /* Local variables */ integer i__, j, k, n2; real cs; integer nn, ks; real sn, mu, eps, est; integer kase; real cond; logical pair; integer ierr; real dumm, prod; integer ifst; real lnrm; integer ilst; real rnrm, prod1, prod2; real scale, delta; integer isave[3]; logical wants; real dummy[1]; real bignum; logical wantbh; logical somcon; real smlnum; logical wantsp; /* -- LAPACK routine (version 3.2) -- */ /* November 2006 */ /* Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. */ /* Purpose */ /* ======= */ /* STRSNA estimates reciprocal condition numbers for specified */ /* eigenvalues and/or right eigenvectors of a real upper */ /* quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q */ /* orthogonal). */ /* T must be in Schur canonical form (as returned by SHSEQR), that is, */ /* block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each */ /* 2-by-2 diagonal block has its diagonal elements equal and its */ /* off-diagonal elements of opposite sign. */ /* Arguments */ /* ========= */ /* JOB (input) CHARACTER*1 */ /* Specifies whether condition numbers are required for */ /* eigenvalues (S) or eigenvectors (SEP): */ /* = 'E': for eigenvalues only (S); */ /* = 'V': for eigenvectors only (SEP); */ /* = 'B': for both eigenvalues and eigenvectors (S and SEP). */ /* HOWMNY (input) CHARACTER*1 */ /* = 'A': compute condition numbers for all eigenpairs; */ /* = 'S': compute condition numbers for selected eigenpairs */ /* specified by the array SELECT. */ /* SELECT (input) LOGICAL array, dimension (N) */ /* If HOWMNY = 'S', SELECT specifies the eigenpairs for which */ /* condition numbers are required. To select condition numbers */ /* for the eigenpair corresponding to a real eigenvalue w(j), */ /* corresponding to a complex conjugate pair of eigenvalues w(j) */ /* and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be */ /* If HOWMNY = 'A', SELECT is not referenced. */ /* N (input) INTEGER */ /* The order of the matrix T. N >= 0. */ /* T (input) REAL array, dimension (LDT,N) */ /* The upper quasi-triangular matrix T, in Schur canonical form. */ /* LDT (input) INTEGER */ /* The leading dimension of the array T. LDT >= max(1,N). */ /* VL (input) REAL array, dimension (LDVL,M) */ /* If JOB = 'E' or 'B', VL must contain left eigenvectors of T */ /* (or of any Q*T*Q**T with Q orthogonal), corresponding to the */ /* eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* must be stored in consecutive columns of VL, as returned by */ /* SHSEIN or STREVC. */ /* If JOB = 'V', VL is not referenced. */ /* LDVL (input) INTEGER */ /* The leading dimension of the array VL. */ /* LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N. */ /* VR (input) REAL array, dimension (LDVR,M) */ /* If JOB = 'E' or 'B', VR must contain right eigenvectors of T */ /* (or of any Q*T*Q**T with Q orthogonal), corresponding to the */ /* eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* must be stored in consecutive columns of VR, as returned by */ /* SHSEIN or STREVC. */ /* If JOB = 'V', VR is not referenced. */ /* LDVR (input) INTEGER */ /* The leading dimension of the array VR. */ /* LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N. */ /* S (output) REAL array, dimension (MM) */ /* If JOB = 'E' or 'B', the reciprocal condition numbers of the */ /* selected eigenvalues, stored in consecutive elements of the */ /* array. For a complex conjugate pair of eigenvalues two */ /* consecutive elements of S are set to the same value. Thus */ /* S(j), SEP(j), and the j-th columns of VL and VR all */ /* correspond to the same eigenpair (but not in general the */ /* j-th eigenpair, unless all eigenpairs are selected). */ /* If JOB = 'V', S is not referenced. */ /* SEP (output) REAL array, dimension (MM) */ /* If JOB = 'V' or 'B', the estimated reciprocal condition */ /* numbers of the selected eigenvectors, stored in consecutive */ /* elements of the array. For a complex eigenvector two */ /* consecutive elements of SEP are set to the same value. If */ /* the eigenvalues cannot be reordered to compute SEP(j), SEP(j) */ /* is set to 0; this can only occur when the true value would be */ /* very small anyway. */ /* If JOB = 'E', SEP is not referenced. */ /* MM (input) INTEGER */ /* The number of elements in the arrays S (if JOB = 'E' or 'B') */ /* and/or SEP (if JOB = 'V' or 'B'). MM >= M. */ /* M (output) INTEGER */ /* The number of elements of the arrays S and/or SEP actually */ /* used to store the estimated condition numbers. */ /* If HOWMNY = 'A', M is set to N. */ /* WORK (workspace) REAL array, dimension (LDWORK,N+6) */ /* If JOB = 'E', WORK is not referenced. */ /* LDWORK (input) INTEGER */ /* The leading dimension of the array WORK. */ /* LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N. */ /* IWORK (workspace) INTEGER array, dimension (2*(N-1)) */ /* If JOB = 'E', IWORK is not referenced. */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* Further Details */ /* =============== */ /* The reciprocal of the condition number of an eigenvalue lambda is */ /* defined as */ /* S(lambda) = |v'*u| / (norm(u)*norm(v)) */ /* where u and v are the right and left eigenvectors of T corresponding */ /* to lambda; v' denotes the conjugate-transpose of v, and norm(u) */ /* denotes the Euclidean norm. These reciprocal condition numbers always */ /* lie between zero (very badly conditioned) and one (very well */ /* conditioned). If n = 1, S(lambda) is defined to be 1. */ /* An approximate error bound for a computed eigenvalue W(i) is given by */ /* EPS * norm(T) / S(i) */ /* where EPS is the machine precision. */ /* The reciprocal of the condition number of the right eigenvector u */ /* corresponding to lambda is defined as follows. Suppose */ /* T = ( lambda c ) */ /* ( 0 T22 ) */ /* Then the reciprocal condition number is */ /* SEP( lambda, T22 ) = sigma-min( T22 - lambda*I ) */ /* where sigma-min denotes the smallest singular value. We approximate */ /* the smallest singular value by the reciprocal of an estimate of the */ /* one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is */ /* defined to be abs(T(1,1)). */ /* An approximate error bound for a computed right eigenvector VR(i) */ /* is given by */ /* EPS * norm(T) / SEP(i) */ /* ===================================================================== */ /* Decode and test the input parameters */ /* Parameter adjustments */ --select; t_dim1 = *ldt; t_offset = 1 + t_dim1; t -= t_offset; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1; vr -= vr_offset; --s; --sep; work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; --iwork; /* Function Body */ wantbh = lsame_(job, "B"); wants = lsame_(job, "E") || wantbh; wantsp = lsame_(job, "V") || wantbh; somcon = lsame_(howmny, "S"); *info = 0; if (! wants && ! wantsp) { *info = -1; } else if (! lsame_(howmny, "A") && ! somcon) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*ldt < max(1,*n)) { *info = -6; } else if (*ldvl < 1 || wants && *ldvl < *n) { *info = -8; } else if (*ldvr < 1 || wants && *ldvr < *n) { *info = -10; } else { /* Set M to the number of eigenpairs for which condition numbers */ /* are required, and test MM. */ if (somcon) { *m = 0; pair = FALSE_; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (pair) { pair = FALSE_; } else { if (k < *n) { if (t[k + 1 + k * t_dim1] == 0.f) { if (select[k]) { ++(*m); } } else { pair = TRUE_; if (select[k] || select[k + 1]) { *m += 2; } } } else { if (select[*n]) { ++(*m); } } } } } else { *m = *n; } if (*mm < *m) { *info = -13; } else if (*ldwork < 1 || wantsp && *ldwork < *n) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("STRSNA", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (somcon) { if (! select[1]) { return 0; } } if (wants) { s[1] = 1.f; } if (wantsp) { sep[1] = (r__1 = t[t_dim1 + 1], dabs(r__1)); } return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = slamch_("S") / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); ks = 0; pair = FALSE_; i__1 = *n; for (k = 1; k <= i__1; ++k) { /* Determine whether T(k,k) begins a 1-by-1 or 2-by-2 block. */ if (pair) { pair = FALSE_; goto L60; } else { if (k < *n) { pair = t[k + 1 + k * t_dim1] != 0.f; } } /* Determine whether condition numbers are required for the k-th */ /* eigenpair. */ if (somcon) { if (pair) { if (! select[k] && ! select[k + 1]) { goto L60; } } else { if (! select[k]) { goto L60; } } } ++ks; if (wants) { /* Compute the reciprocal condition number of the k-th */ /* eigenvalue. */ if (! pair) { /* Real eigenvalue. */ prod = sdot_(n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); rnrm = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); lnrm = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); s[ks] = dabs(prod) / (rnrm * lnrm); } else { /* Complex eigenvalue. */ prod1 = sdot_(n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); prod1 += sdot_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], &c__1); prod2 = sdot_(n, &vl[ks * vl_dim1 + 1], &c__1, &vr[(ks + 1) * vr_dim1 + 1], &c__1); prod2 -= sdot_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1, &vr[ks * vr_dim1 + 1], &c__1); r__1 = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); r__2 = snrm2_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1); rnrm = slapy2_(&r__1, &r__2); r__1 = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); r__2 = snrm2_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1); lnrm = slapy2_(&r__1, &r__2); cond = slapy2_(&prod1, &prod2) / (rnrm * lnrm); s[ks] = cond; s[ks + 1] = cond; } } if (wantsp) { /* Estimate the reciprocal condition number of the k-th */ /* eigenvector. */ /* Copy the matrix T to the array WORK and swap the diagonal */ /* block beginning at T(k,k) to the (1,1) position. */ slacpy_("Full", n, n, &t[t_offset], ldt, &work[work_offset], ldwork); ifst = k; ilst = 1; strexc_("No Q", n, &work[work_offset], ldwork, dummy, &c__1, & ifst, &ilst, &work[(*n + 1) * work_dim1 + 1], &ierr); if (ierr == 1 || ierr == 2) { /* Could not swap because blocks not well separated */ scale = 1.f; est = bignum; } else { /* Reordering successful */ if (work[work_dim1 + 2] == 0.f) { /* Form C = T22 - lambda*I in WORK(2:N,2:N). */ i__2 = *n; for (i__ = 2; i__ <= i__2; ++i__) { work[i__ + i__ * work_dim1] -= work[work_dim1 + 1]; } n2 = 1; nn = *n - 1; } else { /* Triangularize the 2 by 2 block by unitary */ /* transformation U = [ cs i*ss ] */ /* [ i*ss cs ]. */ /* such that the (1,1) position of WORK is complex */ /* eigenvalue lambda with positive imaginary part. (2,2) */ /* position of WORK is the complex eigenvalue lambda */ /* with negative imaginary part. */ mu = sqrt((r__1 = work[(work_dim1 << 1) + 1], dabs(r__1))) * sqrt((r__2 = work[work_dim1 + 2], dabs(r__2))); delta = slapy2_(&mu, &work[work_dim1 + 2]); cs = mu / delta; sn = -work[work_dim1 + 2] / delta; /* Form */ /* [ mu ] */ /* [ mu ] */ /* where C' is conjugate transpose of complex matrix C, */ /* and RWORK is stored starting in the N+1-st column of */ /* WORK. */ i__2 = *n; for (j = 3; j <= i__2; ++j) { work[j * work_dim1 + 2] = cs * work[j * work_dim1 + 2] ; work[j + j * work_dim1] -= work[work_dim1 + 1]; } work[(work_dim1 << 1) + 2] = 0.f; work[(*n + 1) * work_dim1 + 1] = mu * 2.f; i__2 = *n - 1; for (i__ = 2; i__ <= i__2; ++i__) { work[i__ + (*n + 1) * work_dim1] = sn * work[(i__ + 1) * work_dim1 + 1]; } n2 = 2; nn = *n - 1 << 1; } /* Estimate norm(inv(C')) */ est = 0.f; kase = 0; L50: slacn2_(&nn, &work[(*n + 2) * work_dim1 + 1], &work[(*n + 4) * work_dim1 + 1], &iwork[1], &est, &kase, isave); if (kase != 0) { if (kase == 1) { if (n2 == 1) { /* Real eigenvalue: solve C'*x = scale*c. */ i__2 = *n - 1; slaqtr_(&c_true, &c_true, &i__2, &work[(work_dim1 << 1) + 2], ldwork, dummy, &dumm, &scale, &work[(*n + 4) * work_dim1 + 1], &work[(* n + 6) * work_dim1 + 1], &ierr); } else { /* Complex eigenvalue: solve */ /* C'*(p+iq) = scale*(c+id) in real arithmetic. */ i__2 = *n - 1; slaqtr_(&c_true, &c_false, &i__2, &work[( work_dim1 << 1) + 2], ldwork, &work[(*n + 1) * work_dim1 + 1], &mu, &scale, &work[(* n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], &ierr); } } else { if (n2 == 1) { /* Real eigenvalue: solve C*x = scale*c. */ i__2 = *n - 1; slaqtr_(&c_false, &c_true, &i__2, &work[( work_dim1 << 1) + 2], ldwork, dummy, & dumm, &scale, &work[(*n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], & ierr); } else { /* Complex eigenvalue: solve */ /* C*(p+iq) = scale*(c+id) in real arithmetic. */ i__2 = *n - 1; slaqtr_(&c_false, &c_false, &i__2, &work[( work_dim1 << 1) + 2], ldwork, &work[(*n + 1) * work_dim1 + 1], &mu, &scale, &work[(* n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], &ierr); } } goto L50; } } sep[ks] = scale / dmax(est,smlnum); if (pair) { sep[ks + 1] = sep[ks]; } } if (pair) { ++ks; } L60: ; } return 0; /* End of STRSNA */ } /* strsna_ */
/* Subroutine */ int sget39_(real *rmax, integer *lmax, integer *ninfo, integer *knt) { /* Initialized data */ static integer idim[6] = { 4,5,5,5,5,5 }; static integer ival[150] /* was [5][5][6] */ = { 3,0,0,0,0,1,1,-1,0,0, 3,2,1,0,0,4,3,2,2,0,0,0,0,0,0,1,0,0,0,0,2,2,0,0,0,3,3,4,0,0,4,2,2, 3,0,1,1,1,1,5,1,0,0,0,0,2,4,-2,0,0,3,3,4,0,0,4,2,2,3,0,1,1,1,1,1, 1,0,0,0,0,2,1,-1,0,0,9,8,1,0,0,4,9,1,2,-1,2,2,2,2,2,9,0,0,0,0,6,4, 0,0,0,3,2,1,1,0,5,1,-1,1,0,2,2,2,2,2,4,0,0,0,0,2,2,0,0,0,1,4,4,0, 0,2,4,2,2,-1,2,2,2,2,2 }; /* System generated locals */ integer i__1, i__2; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal), cos(doublereal), sin(doublereal); /* Local variables */ real b[10], d__[20]; integer i__, j, k, n; real t[100] /* was [10][10] */, w, x[20], y[20], vm1[5], vm2[5], vm3[5], vm4[5], vm5[3], dum[1], eps; integer ivm1, ivm2, ivm3, ivm4, ivm5, ndim, info; real dumm; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); real norm, work[10], scale, domin, resid; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); extern doublereal sasum_(integer *, real *, integer *); extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); real xnorm; extern /* Subroutine */ int slabad_(real *, real *); extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); real bignum; extern integer isamax_(integer *, real *, integer *); real normtb; extern /* Subroutine */ int slaqtr_(logical *, logical *, integer *, real *, integer *, real *, real *, real *, real *, real *, integer *); real smlnum; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SGET39 tests SLAQTR, a routine for solving the real or */ /* special complex quasi upper triangular system */ /* op(T)*p = scale*c, */ /* or */ /* op(T + iB)*(p+iq) = scale*(c+id), */ /* in real arithmetic. T is upper quasi-triangular. */ /* If it is complex, then the first diagonal block of T must be */ /* 1 by 1, B has the special structure */ /* B = [ b(1) b(2) ... b(n) ] */ /* [ w ] */ /* [ w ] */ /* [ . ] */ /* [ w ] */ /* op(A) = A or A', where A' denotes the conjugate transpose of */ /* the matrix A. */ /* On input, X = [ c ]. On output, X = [ p ]. */ /* [ d ] [ q ] */ /* Scale is an output less than or equal to 1, chosen to avoid */ /* overflow in X. */ /* This subroutine is specially designed for the condition number */ /* estimation in the eigenproblem routine STRSNA. */ /* The test code verifies that the following residual is order 1: */ /* ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| */ /* ----------------------------------------- */ /* max(ulp*(||T||+||B||)*(||x1||+||x2||), */ /* (||T||+||B||)*smlnum/ulp, */ /* smlnum) */ /* (The (||T||+||B||)*smlnum/ulp term accounts for possible */ /* (gradual or nongradual) underflow in x1 and x2.) */ /* Arguments */ /* ========== */ /* RMAX (output) REAL */ /* Value of the largest test ratio. */ /* LMAX (output) INTEGER */ /* Example number where largest test ratio achieved. */ /* NINFO (output) INTEGER */ /* Number of examples where INFO is nonzero. */ /* KNT (output) INTEGER */ /* Total number of examples tested. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. Data statements .. */ /* .. */ /* .. Executable Statements .. */ /* Get machine parameters */ eps = slamch_("P"); smlnum = slamch_("S"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); /* Set up test case parameters */ vm1[0] = 1.f; vm1[1] = sqrt(smlnum); vm1[2] = sqrt(vm1[1]); vm1[3] = sqrt(bignum); vm1[4] = sqrt(vm1[3]); vm2[0] = 1.f; vm2[1] = sqrt(smlnum); vm2[2] = sqrt(vm2[1]); vm2[3] = sqrt(bignum); vm2[4] = sqrt(vm2[3]); vm3[0] = 1.f; vm3[1] = sqrt(smlnum); vm3[2] = sqrt(vm3[1]); vm3[3] = sqrt(bignum); vm3[4] = sqrt(vm3[3]); vm4[0] = 1.f; vm4[1] = sqrt(smlnum); vm4[2] = sqrt(vm4[1]); vm4[3] = sqrt(bignum); vm4[4] = sqrt(vm4[3]); vm5[0] = 1.f; vm5[1] = eps; vm5[2] = sqrt(smlnum); /* Initalization */ *knt = 0; *rmax = 0.f; *ninfo = 0; smlnum /= eps; /* Begin test loop */ for (ivm5 = 1; ivm5 <= 3; ++ivm5) { for (ivm4 = 1; ivm4 <= 5; ++ivm4) { for (ivm3 = 1; ivm3 <= 5; ++ivm3) { for (ivm2 = 1; ivm2 <= 5; ++ivm2) { for (ivm1 = 1; ivm1 <= 5; ++ivm1) { for (ndim = 1; ndim <= 6; ++ndim) { n = idim[ndim - 1]; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = n; for (j = 1; j <= i__2; ++j) { t[i__ + j * 10 - 11] = (real) ival[i__ + ( j + ndim * 5) * 5 - 31] * vm1[ ivm1 - 1]; if (i__ >= j) { t[i__ + j * 10 - 11] *= vm5[ivm5 - 1]; } /* L10: */ } /* L20: */ } w = vm2[ivm2 - 1] * 1.f; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ - 1] = cos((real) i__) * vm3[ivm3 - 1]; /* L30: */ } i__1 = n << 1; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__ - 1] = sin((real) i__) * vm4[ivm4 - 1] ; /* L40: */ } norm = slange_("1", &n, &n, t, &c__10, work); k = isamax_(&n, b, &c__1); normtb = norm + (r__1 = b[k - 1], dabs(r__1)) + dabs(w); scopy_(&n, d__, &c__1, x, &c__1); ++(*knt); slaqtr_(&c_false, &c_true, &n, t, &c__10, dum, & dumm, &scale, x, work, &info); if (info != 0) { ++(*ninfo); } /* || T*x - scale*d || / */ /* max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum) */ scopy_(&n, d__, &c__1, y, &c__1); r__1 = -scale; sgemv_("No transpose", &n, &n, &c_b25, t, &c__10, x, &c__1, &r__1, y, &c__1); xnorm = sasum_(&n, x, &c__1); resid = sasum_(&n, y, &c__1); /* Computing MAX */ r__1 = smlnum, r__2 = smlnum / eps * norm, r__1 = max(r__1,r__2), r__2 = norm * eps * xnorm; domin = dmax(r__1,r__2); resid /= domin; if (resid > *rmax) { *rmax = resid; *lmax = *knt; } scopy_(&n, d__, &c__1, x, &c__1); ++(*knt); slaqtr_(&c_true, &c_true, &n, t, &c__10, dum, & dumm, &scale, x, work, &info); if (info != 0) { ++(*ninfo); } /* || T*x - scale*d || / */ /* max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum) */ scopy_(&n, d__, &c__1, y, &c__1); r__1 = -scale; sgemv_("Transpose", &n, &n, &c_b25, t, &c__10, x, &c__1, &r__1, y, &c__1); xnorm = sasum_(&n, x, &c__1); resid = sasum_(&n, y, &c__1); /* Computing MAX */ r__1 = smlnum, r__2 = smlnum / eps * norm, r__1 = max(r__1,r__2), r__2 = norm * eps * xnorm; domin = dmax(r__1,r__2); resid /= domin; if (resid > *rmax) { *rmax = resid; *lmax = *knt; } i__1 = n << 1; scopy_(&i__1, d__, &c__1, x, &c__1); ++(*knt); slaqtr_(&c_false, &c_false, &n, t, &c__10, b, &w, &scale, x, work, &info); if (info != 0) { ++(*ninfo); } /* ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| / */ /* max(ulp*(||T||+||B||)*(||x1||+||x2||), */ /* smlnum/ulp * (||T||+||B||), smlnum ) */ i__1 = n << 1; scopy_(&i__1, d__, &c__1, y, &c__1); y[0] = sdot_(&n, b, &c__1, &x[n], &c__1) + scale * y[0]; i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { y[i__ - 1] = w * x[i__ + n - 1] + scale * y[ i__ - 1]; /* L50: */ } sgemv_("No transpose", &n, &n, &c_b25, t, &c__10, x, &c__1, &c_b59, y, &c__1); y[n] = sdot_(&n, b, &c__1, x, &c__1) - scale * y[ n]; i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { y[i__ + n - 1] = w * x[i__ - 1] - scale * y[ i__ + n - 1]; /* L60: */ } sgemv_("No transpose", &n, &n, &c_b25, t, &c__10, &x[n], &c__1, &c_b25, &y[n], &c__1); i__1 = n << 1; resid = sasum_(&i__1, y, &c__1); /* Computing MAX */ i__1 = n << 1; r__1 = smlnum, r__2 = smlnum / eps * normtb, r__1 = max(r__1,r__2), r__2 = eps * (normtb * sasum_(&i__1, x, &c__1)); domin = dmax(r__1,r__2); resid /= domin; if (resid > *rmax) { *rmax = resid; *lmax = *knt; } i__1 = n << 1; scopy_(&i__1, d__, &c__1, x, &c__1); ++(*knt); slaqtr_(&c_true, &c_false, &n, t, &c__10, b, &w, & scale, x, work, &info); if (info != 0) { ++(*ninfo); } /* ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| / */ /* max(ulp*(||T||+||B||)*(||x1||+||x2||), */ /* smlnum/ulp * (||T||+||B||), smlnum ) */ i__1 = n << 1; scopy_(&i__1, d__, &c__1, y, &c__1); y[0] = b[0] * x[n] - scale * y[0]; i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { y[i__ - 1] = b[i__ - 1] * x[n] + w * x[i__ + n - 1] - scale * y[i__ - 1]; /* L70: */ } sgemv_("Transpose", &n, &n, &c_b25, t, &c__10, x, &c__1, &c_b25, y, &c__1); y[n] = b[0] * x[0] + scale * y[n]; i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { y[i__ + n - 1] = b[i__ - 1] * x[0] + w * x[ i__ - 1] + scale * y[i__ + n - 1]; /* L80: */ } sgemv_("Transpose", &n, &n, &c_b25, t, &c__10, &x[ n], &c__1, &c_b59, &y[n], &c__1); i__1 = n << 1; resid = sasum_(&i__1, y, &c__1); /* Computing MAX */ i__1 = n << 1; r__1 = smlnum, r__2 = smlnum / eps * normtb, r__1 = max(r__1,r__2), r__2 = eps * (normtb * sasum_(&i__1, x, &c__1)); domin = dmax(r__1,r__2); resid /= domin; if (resid > *rmax) { *rmax = resid; *lmax = *knt; } /* L90: */ } /* L100: */ } /* L110: */ } /* L120: */ } /* L130: */ } /* L140: */ } return 0; /* End of SGET39 */ } /* sget39_ */