/* Subroutine */ int strsen_(char *job, char *compq, logical *select, integer
*n, real *t, integer *ldt, real *q, integer *ldq, real *wr, real *wi,
integer *m, real *s, real *sep, real *work, integer *lwork, integer *
iwork, integer *liwork, integer *info, ftnlen job_len, ftnlen
compq_len)
{
/* System generated locals */
integer q_dim1, q_offset, t_dim1, t_offset, i__1, i__2;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer k, n1, n2, kk, nn, ks;
static real est;
static integer kase;
static logical pair;
static integer ierr;
static logical swap;
static real scale;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static integer lwmin;
static logical wantq, wants;
static real rnorm;
extern doublereal slange_(char *, integer *, integer *, real *, integer *,
real *, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slacon_(
integer *, real *, real *, integer *, real *, integer *);
static logical wantbh;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen);
static integer liwmin;
extern /* Subroutine */ int strexc_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, integer *,
ftnlen);
static logical wantsp, lquery;
extern /* Subroutine */ int strsyl_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, ftnlen, ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STRSEN reorders the real Schur factorization of a real matrix */
/* A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in */
/* the leading diagonal blocks of the upper quasi-triangular matrix T, */
/* and the leading columns of Q form an orthonormal basis of the */
/* corresponding right invariant subspace. */
/* Optionally the routine computes the reciprocal condition numbers of */
/* the cluster of eigenvalues and/or the invariant subspace. */
/* 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 elemnts equal and its */
/* off-diagonal elements of opposite sign. */
/* Arguments */
/* ========= */
/* JOB (input) CHARACTER*1 */
/* Specifies whether condition numbers are required for the */
/* cluster of eigenvalues (S) or the invariant subspace (SEP): */
/* = 'N': none; */
/* = 'E': for eigenvalues only (S); */
/* = 'V': for invariant subspace only (SEP); */
/* = 'B': for both eigenvalues and invariant subspace (S and */
/* SEP). */
/* COMPQ (input) CHARACTER*1 */
/* = 'V': update the matrix Q of Schur vectors; */
/* = 'N': do not update Q. */
/* SELECT (input) LOGICAL array, dimension (N) */
/* SELECT specifies the eigenvalues in the selected cluster. To */
/* select a real eigenvalue w(j), SELECT(j) must be set to */
/* .TRUE.. To select a complex conjugate pair of eigenvalues */
/* w(j) and w(j+1), corresponding to a 2-by-2 diagonal block, */
/* either SELECT(j) or SELECT(j+1) or both must be set to */
/* .TRUE.; a complex conjugate pair of eigenvalues must be */
/* either both included in the cluster or both excluded. */
/* N (input) INTEGER */
/* The order of the matrix T. N >= 0. */
/* T (input/output) REAL array, dimension (LDT,N) */
/* On entry, the upper quasi-triangular matrix T, in Schur */
/* canonical form. */
/* On exit, T is overwritten by the reordered matrix T, again in */
/* Schur canonical form, with the selected eigenvalues in the */
/* leading diagonal blocks. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= max(1,N). */
/* Q (input/output) REAL array, dimension (LDQ,N) */
/* On entry, if COMPQ = 'V', the matrix Q of Schur vectors. */
/* On exit, if COMPQ = 'V', Q has been postmultiplied by the */
/* orthogonal transformation matrix which reorders T; the */
/* leading M columns of Q form an orthonormal basis for the */
/* specified invariant subspace. */
/* If COMPQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. */
/* LDQ >= 1; and if COMPQ = 'V', LDQ >= N. */
/* WR (output) REAL array, dimension (N) */
/* WI (output) REAL array, dimension (N) */
/* The real and imaginary parts, respectively, of the reordered */
/* eigenvalues of T. The eigenvalues are stored in the same */
/* order as on the diagonal of T, with WR(i) = T(i,i) and, if */
/* T(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) > 0 and */
/* WI(i+1) = -WI(i). Note that if a complex eigenvalue is */
/* sufficiently ill-conditioned, then its value may differ */
/* significantly from its value before reordering. */
/* M (output) INTEGER */
/* The dimension of the specified invariant subspace. */
/* 0 < = M <= N. */
/* S (output) REAL */
/* If JOB = 'E' or 'B', S is a lower bound on the reciprocal */
/* condition number for the selected cluster of eigenvalues. */
/* S cannot underestimate the true reciprocal condition number */
/* by more than a factor of sqrt(N). If M = 0 or N, S = 1. */
/* If JOB = 'N' or 'V', S is not referenced. */
/* SEP (output) REAL */
/* If JOB = 'V' or 'B', SEP is the estimated reciprocal */
/* condition number of the specified invariant subspace. If */
/* M = 0 or N, SEP = norm(T). */
/* If JOB = 'N' or 'E', SEP is not referenced. */
/* WORK (workspace/output) REAL array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If JOB = 'N', LWORK >= max(1,N); */
/* if JOB = 'E', LWORK >= M*(N-M); */
/* if JOB = 'V' or 'B', LWORK >= 2*M*(N-M). */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* IWORK (workspace) INTEGER array, dimension (LIWORK) */
/* IF JOB = 'N' or 'E', IWORK is not referenced. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If JOB = 'N' or 'E', LIWORK >= 1; */
/* if JOB = 'V' or 'B', LIWORK >= M*(N-M). */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal size of the IWORK array, */
/* returns this value as the first entry of the IWORK array, and */
/* no error message related to LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* = 1: reordering of T failed because some eigenvalues are too */
/* close to separate (the problem is very ill-conditioned); */
/* T may have been partially reordered, and WR and WI */
/* contain the eigenvalues in the same order as in T; S and */
/* SEP (if requested) are set to zero. */
/* Further Details */
/* =============== */
/* STRSEN first collects the selected eigenvalues by computing an */
/* orthogonal transformation Z to move them to the top left corner of T. */
/* In other words, the selected eigenvalues are the eigenvalues of T11 */
/* in: */
/* Z'*T*Z = ( T11 T12 ) n1 */
/* ( 0 T22 ) n2 */
/* n1 n2 */
/* where N = n1+n2 and Z' means the transpose of Z. The first n1 columns */
/* of Z span the specified invariant subspace of T. */
/* If T has been obtained from the real Schur factorization of a matrix */
/* A = Q*T*Q', then the reordered real Schur factorization of A is given */
/* by A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span */
/* the corresponding invariant subspace of A. */
/* The reciprocal condition number of the average of the eigenvalues of */
/* T11 may be returned in S. S lies between 0 (very badly conditioned) */
/* and 1 (very well conditioned). It is computed as follows. First we */
/* compute R so that */
/* P = ( I R ) n1 */
/* ( 0 0 ) n2 */
/* n1 n2 */
/* is the projector on the invariant subspace associated with T11. */
/* R is the solution of the Sylvester equation: */
/* T11*R - R*T22 = T12. */
/* Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote */
/* the two-norm of M. Then S is computed as the lower bound */
/* (1 + F-norm(R)**2)**(-1/2) */
/* on the reciprocal of 2-norm(P), the true reciprocal condition number. */
/* S cannot underestimate 1 / 2-norm(P) by more than a factor of */
/* sqrt(N). */
/* An approximate error bound for the computed average of the */
/* eigenvalues of T11 is */
/* EPS * norm(T) / S */
/* where EPS is the machine precision. */
/* The reciprocal condition number of the right invariant subspace */
/* spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP. */
/* SEP is defined as the separation of T11 and T22: */
/* sep( T11, T22 ) = sigma-min( C ) */
/* where sigma-min(C) is the smallest singular value of the */
/* n1*n2-by-n1*n2 matrix */
/* C = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) ) */
/* I(m) is an m by m identity matrix, and kprod denotes the Kronecker */
/* product. We estimate sigma-min(C) by the reciprocal of an estimate of */
/* the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C) */
/* cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2). */
/* When SEP is small, small changes in T can cause large changes in */
/* the invariant subspace. An approximate bound on the maximum angular */
/* error in the computed right invariant subspace is */
/* EPS * norm(T) / SEP */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test the input parameters */
/* Parameter adjustments */
--select;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--wr;
--wi;
--work;
--iwork;
/* Function Body */
wantbh = lsame_(job, "B", (ftnlen)1, (ftnlen)1);
wants = lsame_(job, "E", (ftnlen)1, (ftnlen)1) || wantbh;
wantsp = lsame_(job, "V", (ftnlen)1, (ftnlen)1) || wantbh;
wantq = lsame_(compq, "V", (ftnlen)1, (ftnlen)1);
*info = 0;
lquery = *lwork == -1;
if (! lsame_(job, "N", (ftnlen)1, (ftnlen)1) && ! wants && ! wantsp) {
*info = -1;
} else if (! lsame_(compq, "N", (ftnlen)1, (ftnlen)1) && ! wantq) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*ldt < max(1,*n)) {
*info = -6;
} else if (*ldq < 1 || wantq && *ldq < *n) {
*info = -8;
} else {
/* Set M to the dimension of the specified invariant subspace, */
/* and test LWORK and LIWORK. */
*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);
}
}
}
/* L10: */
}
n1 = *m;
n2 = *n - *m;
nn = n1 * n2;
if (wantsp) {
/* Computing MAX */
i__1 = 1, i__2 = nn << 1;
lwmin = max(i__1,i__2);
liwmin = max(1,nn);
} else if (lsame_(job, "N", (ftnlen)1, (ftnlen)1)) {
lwmin = max(1,*n);
liwmin = 1;
} else if (lsame_(job, "E", (ftnlen)1, (ftnlen)1)) {
lwmin = max(1,nn);
liwmin = 1;
}
if (*lwork < lwmin && ! lquery) {
*info = -15;
} else if (*liwork < liwmin && ! lquery) {
*info = -17;
}
}
if (*info == 0) {
work[1] = (real) lwmin;
iwork[1] = liwmin;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STRSEN", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible. */
if (*m == *n || *m == 0) {
if (wants) {
*s = 1.f;
}
if (wantsp) {
*sep = slange_("1", n, n, &t[t_offset], ldt, &work[1], (ftnlen)1);
}
goto L40;
}
/* Collect the selected blocks at the top-left corner of T. */
ks = 0;
pair = FALSE_;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
swap = select[k];
if (k < *n) {
if (t[k + 1 + k * t_dim1] != 0.f) {
pair = TRUE_;
swap = swap || select[k + 1];
}
}
if (swap) {
++ks;
/* Swap the K-th block to position KS. */
ierr = 0;
kk = k;
if (k != ks) {
strexc_(compq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
kk, &ks, &work[1], &ierr, (ftnlen)1);
}
if (ierr == 1 || ierr == 2) {
/* Blocks too close to swap: exit. */
*info = 1;
if (wants) {
*s = 0.f;
}
if (wantsp) {
*sep = 0.f;
}
goto L40;
}
if (pair) {
++ks;
}
}
}
/* L20: */
}
if (wants) {
/* Solve Sylvester equation for R: */
/* T11*R - R*T22 = scale*T12 */
slacpy_("F", &n1, &n2, &t[(n1 + 1) * t_dim1 + 1], ldt, &work[1], &n1,
(ftnlen)1);
strsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 1 + (n1
+ 1) * t_dim1], ldt, &work[1], &n1, &scale, &ierr, (ftnlen)1,
(ftnlen)1);
/* Estimate the reciprocal of the condition number of the cluster */
/* of eigenvalues. */
rnorm = slange_("F", &n1, &n2, &work[1], &n1, &work[1], (ftnlen)1);
if (rnorm == 0.f) {
*s = 1.f;
} else {
*s = scale / (sqrt(scale * scale / rnorm + rnorm) * sqrt(rnorm));
}
}
if (wantsp) {
/* Estimate sep(T11,T22). */
est = 0.f;
kase = 0;
L30:
slacon_(&nn, &work[nn + 1], &work[1], &iwork[1], &est, &kase);
if (kase != 0) {
if (kase == 1) {
/* Solve T11*R - R*T22 = scale*X. */
strsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 +
1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, &
ierr, (ftnlen)1, (ftnlen)1);
} else {
/* Solve T11'*R - R*T22' = scale*X. */
strsyl_("T", "T", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 +
1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, &
ierr, (ftnlen)1, (ftnlen)1);
}
goto L30;
}
*sep = scale / est;
}
L40:
/* Store the output eigenvalues in WR and WI. */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
wr[k] = t[k + k * t_dim1];
wi[k] = 0.f;
/* L50: */
}
i__1 = *n - 1;
for (k = 1; k <= i__1; ++k) {
if (t[k + 1 + k * t_dim1] != 0.f) {
wi[k] = sqrt((r__1 = t[k + (k + 1) * t_dim1], dabs(r__1))) * sqrt(
(r__2 = t[k + 1 + k * t_dim1], dabs(r__2)));
wi[k + 1] = -wi[k];
}
/* L60: */
}
work[1] = (real) lwmin;
iwork[1] = liwmin;
return 0;
/* End of STRSEN */
} /* strsen_ */
/* Subroutine */ int serrec_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
"ts of the error ex\002,\002its ***\002)";
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
real a[16] /* was [4][4] */, b[16] /* was [4][4] */, c__[16] /*
was [4][4] */;
integer i__, j, m;
real s[4], wi[4];
integer nt;
real wr[4];
logical sel[4];
real sep[4];
integer info, ifst, ilst;
real work[4], scale;
integer iwork[4];
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), strexc_(char *, integer *, real *, integer
*, real *, integer *, integer *, integer *, real *, integer *), strsna_(char *, char *, logical *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, real *,
integer *, integer *, real *, integer *, integer *, integer *), strsen_(char *, char *, logical *, integer *,
real *, integer *, real *, integer *, real *, real *, integer *,
real *, real *, real *, integer *, integer *, integer *, integer *
), strsyl_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *);
/* Fortran I/O blocks */
static cilist io___19 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___20 = { 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 .. */
/* .. */
/* Purpose */
/* ======= */
/* SERREC tests the error exits for the routines for eigen- condition */
/* estimation for REAL matrices: */
/* STRSYL, STREXC, STRSNA and STRSEN. */
/* 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 Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
infoc_1.ok = TRUE_;
nt = 0;
/* Initialize A, B and SEL */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (j << 2) - 5] = 0.f;
b[i__ + (j << 2) - 5] = 0.f;
/* L10: */
}
/* L20: */
}
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (i__ << 2) - 5] = 1.f;
sel[i__ - 1] = TRUE_;
/* L30: */
}
/* Test STRSYL */
s_copy(srnamc_1.srnamt, "STRSYL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
strsyl_("X", "N", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsyl_("N", "X", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
strsyl_("N", "N", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsyl_("N", "N", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
strsyl_("N", "N", &c__1, &c__0, &c_n1, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
strsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__1, b, &c__1, c__, &c__2, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
strsyl_("N", "N", &c__1, &c__0, &c__2, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
strsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__2, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test STREXC */
s_copy(srnamc_1.srnamt, "STREXC", (ftnlen)32, (ftnlen)6);
ifst = 1;
ilst = 1;
infoc_1.infot = 1;
strexc_("X", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
strexc_("N", &c__0, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ilst = 2;
strexc_("N", &c__2, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strexc_("V", &c__2, a, &c__2, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 0;
ilst = 1;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 2;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ifst = 1;
ilst = 0;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ilst = 2;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test STRSNA */
s_copy(srnamc_1.srnamt, "STRSNA", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
strsna_("X", "A", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsna_("B", "X", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsna_("B", "A", sel, &c_n1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strsna_("V", "A", sel, &c__2, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__1, c__, &c__2, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
strsna_("B", "A", sel, &c__1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__0, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
strsna_("B", "S", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__1, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 16;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__2, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* Test STRSEN */
sel[0] = FALSE_;
s_copy(srnamc_1.srnamt, "STRSEN", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
strsen_("X", "N", sel, &c__0, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsen_("N", "X", sel, &c__0, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsen_("N", "N", sel, &c_n1, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strsen_("N", "N", sel, &c__2, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__2, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
strsen_("N", "V", sel, &c__2, a, &c__2, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("N", "V", sel, &c__2, a, &c__2, b, &c__2, wr, wi, &m, s, sep,
work, &c__0, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("E", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__3, iwork, &c__2, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 17;
strsen_("E", "V", sel, &c__2, a, &c__2, b, &c__2, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__0, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 17;
strsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__4, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 10;
/* Print a summary line. */
if (infoc_1.ok) {
io___19.ciunit = infoc_1.nout;
s_wsfe(&io___19);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___20.ciunit = infoc_1.nout;
s_wsfe(&io___20);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of SERREC */
} /* serrec_ */
/* Subroutine */
int slaqr2_(logical *wantt, logical *wantz, integer *n, integer *ktop, integer *kbot, integer *nw, real *h__, integer *ldh, integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *ns, integer *nd, real *sr, real *si, real *v, integer *ldv, integer *nh, real *t, integer *ldt, integer *nv, real *wv, integer *ldwv, real * work, integer *lwork)
{
/* System generated locals */
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1, wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
real s, aa, bb, cc, dd, cs, sn;
integer jw;
real evi, evk, foo;
integer kln;
real tau, ulp;
integer lwk1, lwk2;
real beta;
integer kend, kcol, info, ifst, ilst, ltop, krow;
logical bulge;
extern /* Subroutine */
int slarf_(char *, integer *, integer *, real *, integer *, real *, real *, integer *, real *), sgemm_( char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *);
integer infqr;
extern /* Subroutine */
int scopy_(integer *, real *, integer *, real *, integer *);
integer kwtop;
extern /* Subroutine */
int slanv2_(real *, real *, real *, real *, real * , real *, real *, real *, real *, real *), slabad_(real *, real *) ;
extern real slamch_(char *);
extern /* Subroutine */
int sgehrd_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
real safmin;
extern /* Subroutine */
int slarfg_(integer *, real *, real *, integer *, real *);
real safmax;
extern /* Subroutine */
int slahqr_(logical *, logical *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *);
logical sorted;
extern /* Subroutine */
int strexc_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, integer *), sormhr_(char *, char *, integer *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *);
real smlnum;
integer lwkopt;
/* -- LAPACK auxiliary routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ================================================================ */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* ==== Estimate optimal workspace. ==== */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--sr;
--si;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1;
wv -= wv_offset;
--work;
/* Function Body */
/* Computing MIN */
i__1 = *nw;
i__2 = *kbot - *ktop + 1; // , expr subst
jw = min(i__1,i__2);
if (jw <= 2)
{
lwkopt = 1;
}
else
{
/* ==== Workspace query call to SGEHRD ==== */
i__1 = jw - 1;
sgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], & c_n1, &info);
lwk1 = (integer) work[1];
/* ==== Workspace query call to SORMHR ==== */
i__1 = jw - 1;
sormhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[1], &c_n1, &info);
lwk2 = (integer) work[1];
/* ==== Optimal workspace ==== */
lwkopt = jw + max(lwk1,lwk2);
}
/* ==== Quick return in case of workspace query. ==== */
if (*lwork == -1)
{
work[1] = (real) lwkopt;
return 0;
}
/* ==== Nothing to do ... */
/* ... for an empty active block ... ==== */
*ns = 0;
*nd = 0;
work[1] = 1.f;
if (*ktop > *kbot)
{
return 0;
}
/* ... nor for an empty deflation window. ==== */
if (*nw < 1)
{
return 0;
}
/* ==== Machine constants ==== */
safmin = slamch_("SAFE MINIMUM");
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
ulp = slamch_("PRECISION");
smlnum = safmin * ((real) (*n) / ulp);
/* ==== Setup deflation window ==== */
/* Computing MIN */
i__1 = *nw;
i__2 = *kbot - *ktop + 1; // , expr subst
jw = min(i__1,i__2);
kwtop = *kbot - jw + 1;
if (kwtop == *ktop)
{
s = 0.f;
}
else
{
s = h__[kwtop + (kwtop - 1) * h_dim1];
}
if (*kbot == kwtop)
{
/* ==== 1-by-1 deflation window: not much to do ==== */
sr[kwtop] = h__[kwtop + kwtop * h_dim1];
si[kwtop] = 0.f;
*ns = 1;
*nd = 0;
/* Computing MAX */
r__2 = smlnum;
r__3 = ulp * (r__1 = h__[kwtop + kwtop * h_dim1], abs( r__1)); // , expr subst
if (abs(s) <= max(r__2,r__3))
{
*ns = 0;
*nd = 1;
if (kwtop > *ktop)
{
h__[kwtop + (kwtop - 1) * h_dim1] = 0.f;
}
}
work[1] = 1.f;
return 0;
}
/* ==== Convert to spike-triangular form. (In case of a */
/* . rare QR failure, this routine continues to do */
/* . aggressive early deflation using that part of */
/* . the deflation window that converged using INFQR */
/* . here and there to keep track.) ==== */
slacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset], ldt);
i__1 = jw - 1;
i__2 = *ldh + 1;
i__3 = *ldt + 1;
scopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], & i__3);
slaset_("A", &jw, &jw, &c_b12, &c_b13, &v[v_offset], ldv);
slahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop], &si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
/* ==== STREXC needs a clean margin near the diagonal ==== */
i__1 = jw - 3;
for (j = 1;
j <= i__1;
++j)
{
t[j + 2 + j * t_dim1] = 0.f;
t[j + 3 + j * t_dim1] = 0.f;
/* L10: */
}
if (jw > 2)
{
t[jw + (jw - 2) * t_dim1] = 0.f;
}
/* ==== Deflation detection loop ==== */
*ns = jw;
ilst = infqr + 1;
L20:
if (ilst <= *ns)
{
if (*ns == 1)
{
bulge = FALSE_;
}
else
{
bulge = t[*ns + (*ns - 1) * t_dim1] != 0.f;
}
/* ==== Small spike tip test for deflation ==== */
if (! bulge)
{
/* ==== Real eigenvalue ==== */
foo = (r__1 = t[*ns + *ns * t_dim1], abs(r__1));
if (foo == 0.f)
{
foo = abs(s);
}
/* Computing MAX */
r__2 = smlnum;
r__3 = ulp * foo; // , expr subst
if ((r__1 = s * v[*ns * v_dim1 + 1], abs(r__1)) <= max(r__2,r__3))
{
/* ==== Deflatable ==== */
--(*ns);
}
else
{
/* ==== Undeflatable. Move it up out of the way. */
/* . (STREXC can not fail in this case.) ==== */
ifst = *ns;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &ilst, &work[1], &info);
++ilst;
}
}
else
{
/* ==== Complex conjugate pair ==== */
foo = (r__3 = t[*ns + *ns * t_dim1], abs(r__3)) + sqrt((r__1 = t[* ns + (*ns - 1) * t_dim1], abs(r__1))) * sqrt((r__2 = t[* ns - 1 + *ns * t_dim1], abs(r__2)));
if (foo == 0.f)
{
foo = abs(s);
}
/* Computing MAX */
r__3 = (r__1 = s * v[*ns * v_dim1 + 1], abs(r__1));
r__4 = (r__2 = s * v[(*ns - 1) * v_dim1 + 1], abs(r__2)); // , expr subst
/* Computing MAX */
r__5 = smlnum;
r__6 = ulp * foo; // , expr subst
if (max(r__3,r__4) <= max(r__5,r__6))
{
/* ==== Deflatable ==== */
*ns += -2;
}
else
{
/* ==== Undeflatable. Move them up out of the way. */
/* . Fortunately, STREXC does the right thing with */
/* . ILST in case of a rare exchange failure. ==== */
ifst = *ns;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &ilst, &work[1], &info);
ilst += 2;
}
}
/* ==== End deflation detection loop ==== */
goto L20;
}
/* ==== Return to Hessenberg form ==== */
if (*ns == 0)
{
s = 0.f;
}
if (*ns < jw)
{
/* ==== sorting diagonal blocks of T improves accuracy for */
/* . graded matrices. Bubble sort deals well with */
/* . exchange failures. ==== */
sorted = FALSE_;
i__ = *ns + 1;
L30:
if (sorted)
{
goto L50;
}
sorted = TRUE_;
kend = i__ - 1;
i__ = infqr + 1;
if (i__ == *ns)
{
k = i__ + 1;
}
else if (t[i__ + 1 + i__ * t_dim1] == 0.f)
{
k = i__ + 1;
}
else
{
k = i__ + 2;
}
L40:
if (k <= kend)
{
if (k == i__ + 1)
{
evi = (r__1 = t[i__ + i__ * t_dim1], abs(r__1));
}
else
{
evi = (r__3 = t[i__ + i__ * t_dim1], abs(r__3)) + sqrt((r__1 = t[i__ + 1 + i__ * t_dim1], abs(r__1))) * sqrt((r__2 = t[i__ + (i__ + 1) * t_dim1], abs(r__2)));
}
if (k == kend)
{
evk = (r__1 = t[k + k * t_dim1], abs(r__1));
}
else if (t[k + 1 + k * t_dim1] == 0.f)
{
evk = (r__1 = t[k + k * t_dim1], abs(r__1));
}
else
{
evk = (r__3 = t[k + k * t_dim1], abs(r__3)) + sqrt((r__1 = t[ k + 1 + k * t_dim1], abs(r__1))) * sqrt((r__2 = t[k + (k + 1) * t_dim1], abs(r__2)));
}
if (evi >= evk)
{
i__ = k;
}
else
{
sorted = FALSE_;
ifst = i__;
ilst = k;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &ilst, &work[1], &info);
if (info == 0)
{
i__ = ilst;
}
else
{
i__ = k;
}
}
if (i__ == kend)
{
k = i__ + 1;
}
else if (t[i__ + 1 + i__ * t_dim1] == 0.f)
{
k = i__ + 1;
}
else
{
k = i__ + 2;
}
goto L40;
}
goto L30;
L50:
;
}
/* ==== Restore shift/eigenvalue array from T ==== */
i__ = jw;
L60:
if (i__ >= infqr + 1)
{
if (i__ == infqr + 1)
{
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.f;
--i__;
}
else if (t[i__ + (i__ - 1) * t_dim1] == 0.f)
{
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.f;
--i__;
}
else
{
aa = t[i__ - 1 + (i__ - 1) * t_dim1];
cc = t[i__ + (i__ - 1) * t_dim1];
bb = t[i__ - 1 + i__ * t_dim1];
dd = t[i__ + i__ * t_dim1];
slanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__ - 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, & sn);
i__ += -2;
}
goto L60;
}
if (*ns < jw || s == 0.f)
{
if (*ns > 1 && s != 0.f)
{
/* ==== Reflect spike back into lower triangle ==== */
scopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
beta = work[1];
slarfg_(ns, &beta, &work[2], &c__1, &tau);
work[1] = 1.f;
i__1 = jw - 2;
i__2 = jw - 2;
slaset_("L", &i__1, &i__2, &c_b12, &c_b12, &t[t_dim1 + 3], ldt);
slarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, & work[jw + 1]);
slarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, & work[jw + 1]);
slarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, & work[jw + 1]);
i__1 = *lwork - jw;
sgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1] , &i__1, &info);
}
/* ==== Copy updated reduced window into place ==== */
if (kwtop > 1)
{
h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
}
slacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1] , ldh);
i__1 = jw - 1;
i__2 = *ldt + 1;
i__3 = *ldh + 1;
scopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1], &i__3);
/* ==== Accumulate orthogonal matrix in order update */
/* . H and Z, if requested. ==== */
if (*ns > 1 && s != 0.f)
{
i__1 = *lwork - jw;
sormhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[jw + 1], &i__1, &info);
}
/* ==== Update vertical slab in H ==== */
if (*wantt)
{
ltop = 1;
}
else
{
ltop = *ktop;
}
i__1 = kwtop - 1;
i__2 = *nv;
for (krow = ltop;
i__2 < 0 ? krow >= i__1 : krow <= i__1;
krow += i__2)
{
/* Computing MIN */
i__3 = *nv;
i__4 = kwtop - krow; // , expr subst
kln = min(i__3,i__4);
sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &h__[krow + kwtop * h_dim1], ldh, &v[v_offset], ldv, &c_b12, &wv[wv_offset], ldwv);
slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop * h_dim1], ldh);
/* L70: */
}
/* ==== Update horizontal slab in H ==== */
if (*wantt)
{
i__2 = *n;
i__1 = *nh;
for (kcol = *kbot + 1;
i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
kcol += i__1)
{
/* Computing MIN */
i__3 = *nh;
i__4 = *n - kcol + 1; // , expr subst
kln = min(i__3,i__4);
sgemm_("C", "N", &jw, &kln, &jw, &c_b13, &v[v_offset], ldv, & h__[kwtop + kcol * h_dim1], ldh, &c_b12, &t[t_offset], ldt);
slacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol * h_dim1], ldh);
/* L80: */
}
}
/* ==== Update vertical slab in Z ==== */
if (*wantz)
{
i__1 = *ihiz;
i__2 = *nv;
for (krow = *iloz;
i__2 < 0 ? krow >= i__1 : krow <= i__1;
krow += i__2)
{
/* Computing MIN */
i__3 = *nv;
i__4 = *ihiz - krow + 1; // , expr subst
kln = min(i__3,i__4);
sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &z__[krow + kwtop * z_dim1], ldz, &v[v_offset], ldv, &c_b12, &wv[ wv_offset], ldwv);
slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow + kwtop * z_dim1], ldz);
/* L90: */
}
}
}
/* ==== Return the number of deflations ... ==== */
*nd = jw - *ns;
/* ==== ... and the number of shifts. (Subtracting */
/* . INFQR from the spike length takes care */
/* . of the case of a rare QR failure while */
/* . calculating eigenvalues of the deflation */
/* . window.) ==== */
*ns -= infqr;
/* ==== Return optimal workspace. ==== */
work[1] = (real) lwkopt;
/* ==== End of SLAQR2 ==== */
return 0;
}
/* Subroutine */ int slaqr2_(logical *wantt, logical *wantz, integer *n,
integer *ktop, integer *kbot, integer *nw, real *h__, integer *ldh,
integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *ns,
integer *nd, real *sr, real *si, real *v, integer *ldv, integer *nh,
real *t, integer *ldt, integer *nv, real *wv, integer *ldwv, real *
work, integer *lwork)
{
/* System generated locals */
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Local variables */
integer i__, j, k;
real s, aa, bb, cc, dd, cs, sn;
integer jw;
real evi, evk, foo;
integer kln;
real tau, ulp;
integer lwk1, lwk2;
real beta;
integer kend, kcol, info, ifst, ilst, ltop, krow;
logical bulge;
integer infqr;
integer kwtop;
real safmin;
real safmax;
logical sorted;
real smlnum;
integer lwkopt;
/* -- LAPACK auxiliary routine (version 3.2.1) -- */
/* -- April 2009 -- */
/* This subroutine is identical to SLAQR3 except that it avoids */
/* recursion by calling SLAHQR instead of SLAQR4. */
/* ****************************************************************** */
/* Aggressive early deflation: */
/* This subroutine accepts as input an upper Hessenberg matrix */
/* H and performs an orthogonal similarity transformation */
/* designed to detect and deflate fully converged eigenvalues from */
/* a trailing principal submatrix. On output H has been over- */
/* written by a new Hessenberg matrix that is a perturbation of */
/* an orthogonal similarity transformation of H. It is to be */
/* hoped that the final version of H has many zero subdiagonal */
/* entries. */
/* ****************************************************************** */
/* WANTT (input) LOGICAL */
/* If .TRUE., then the Hessenberg matrix H is fully updated */
/* so that the quasi-triangular Schur factor may be */
/* computed (in cooperation with the calling subroutine). */
/* If .FALSE., then only enough of H is updated to preserve */
/* the eigenvalues. */
/* WANTZ (input) LOGICAL */
/* If .TRUE., then the orthogonal matrix Z is updated so */
/* so that the orthogonal Schur factor may be computed */
/* (in cooperation with the calling subroutine). */
/* If .FALSE., then Z is not referenced. */
/* N (input) INTEGER */
/* The order of the matrix H and (if WANTZ is .TRUE.) the */
/* order of the orthogonal matrix Z. */
/* KTOP (input) INTEGER */
/* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
/* KBOT and KTOP together determine an isolated block */
/* along the diagonal of the Hessenberg matrix. */
/* KBOT (input) INTEGER */
/* It is assumed without a check that either */
/* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */
/* determine an isolated block along the diagonal of the */
/* Hessenberg matrix. */
/* NW (input) INTEGER */
/* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1). */
/* H (input/output) REAL array, dimension (LDH,N) */
/* On input the initial N-by-N section of H stores the */
/* Hessenberg matrix undergoing aggressive early deflation. */
/* On output H has been transformed by an orthogonal */
/* similarity transformation, perturbed, and the returned */
/* to Hessenberg form that (it is to be hoped) has some */
/* zero subdiagonal entries. */
/* LDH (input) integer */
/* Leading dimension of H just as declared in the calling */
/* subroutine. N .LE. LDH */
/* ILOZ (input) INTEGER */
/* IHIZ (input) INTEGER */
/* Specify the rows of Z to which transformations must be */
/* Z (input/output) REAL array, dimension (LDZ,N) */
/* IF WANTZ is .TRUE., then on output, the orthogonal */
/* similarity transformation mentioned above has been */
/* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. */
/* If WANTZ is .FALSE., then Z is unreferenced. */
/* LDZ (input) integer */
/* The leading dimension of Z just as declared in the */
/* calling subroutine. 1 .LE. LDZ. */
/* NS (output) integer */
/* The number of unconverged (ie approximate) eigenvalues */
/* returned in SR and SI that may be used as shifts by the */
/* calling subroutine. */
/* ND (output) integer */
/* The number of converged eigenvalues uncovered by this */
/* subroutine. */
/* SR (output) REAL array, dimension KBOT */
/* SI (output) REAL array, dimension KBOT */
/* On output, the real and imaginary parts of approximate */
/* eigenvalues that may be used for shifts are stored in */
/* SR(KBOT-ND-NS+1) through SR(KBOT-ND) and */
/* SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively. */
/* The real and imaginary parts of converged eigenvalues */
/* are stored in SR(KBOT-ND+1) through SR(KBOT) and */
/* SI(KBOT-ND+1) through SI(KBOT), respectively. */
/* V (workspace) REAL array, dimension (LDV,NW) */
/* An NW-by-NW work array. */
/* LDV (input) integer scalar */
/* The leading dimension of V just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* NH (input) integer scalar */
/* The number of columns of T. NH.GE.NW. */
/* T (workspace) REAL array, dimension (LDT,NW) */
/* LDT (input) integer */
/* The leading dimension of T just as declared in the */
/* calling subroutine. NW .LE. LDT */
/* NV (input) integer */
/* The number of rows of work array WV available for */
/* workspace. NV.GE.NW. */
/* WV (workspace) REAL array, dimension (LDWV,NW) */
/* LDWV (input) integer */
/* The leading dimension of W just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* WORK (workspace) REAL array, dimension LWORK. */
/* On exit, WORK(1) is set to an estimate of the optimal value */
/* of LWORK for the given values of N, NW, KTOP and KBOT. */
/* LWORK (input) integer */
/* The dimension of the work array WORK. LWORK = 2*NW */
/* suffices, but greater efficiency may result from larger */
/* values of LWORK. */
/* If LWORK = -1, then a workspace query is assumed; SLAQR2 */
/* only estimates the optimal workspace size for the given */
/* values of N, NW, KTOP and KBOT. The estimate is returned */
/* in WORK(1). No error message related to LWORK is issued */
/* by XERBLA. Neither H nor Z are accessed. */
/* ================================================================ */
/* Based on contributions by */
/* Karen Braman and Ralph Byers, Department of Mathematics, */
/* University of Kansas, USA */
/* ================================================================ */
/* ==== Estimate optimal workspace. ==== */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--sr;
--si;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1;
wv -= wv_offset;
--work;
/* Function Body */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
if (jw <= 2) {
lwkopt = 1;
} else {
/* ==== Workspace query call to SGEHRD ==== */
i__1 = jw - 1;
sgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
c_n1, &info);
lwk1 = (integer) work[1];
/* ==== Workspace query call to SORMHR ==== */
i__1 = jw - 1;
sormhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[1], &c_n1, &info);
lwk2 = (integer) work[1];
/* ==== Optimal workspace ==== */
lwkopt = jw + max(lwk1,lwk2);
}
/* ==== Quick return in case of workspace query. ==== */
if (*lwork == -1) {
work[1] = (real) lwkopt;
return 0;
}
*ns = 0;
*nd = 0;
work[1] = 1.f;
if (*ktop > *kbot) {
return 0;
}
if (*nw < 1) {
return 0;
}
/* ==== Machine constants ==== */
safmin = slamch_("SAFE MINIMUM");
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
ulp = slamch_("PRECISION");
smlnum = safmin * ((real) (*n) / ulp);
/* ==== Setup deflation window ==== */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
kwtop = *kbot - jw + 1;
if (kwtop == *ktop) {
s = 0.f;
} else {
s = h__[kwtop + (kwtop - 1) * h_dim1];
}
if (*kbot == kwtop) {
/* ==== 1-by-1 deflation window: not much to do ==== */
sr[kwtop] = h__[kwtop + kwtop * h_dim1];
si[kwtop] = 0.f;
*ns = 1;
*nd = 0;
/* Computing MAX */
r__2 = smlnum, r__3 = ulp * (r__1 = h__[kwtop + kwtop * h_dim1], dabs(
r__1));
if (dabs(s) <= dmax(r__2,r__3)) {
*ns = 0;
*nd = 1;
if (kwtop > *ktop) {
h__[kwtop + (kwtop - 1) * h_dim1] = 0.f;
}
}
work[1] = 1.f;
return 0;
}
/* ==== Convert to spike-triangular form. (In case of a */
/* . rare QR failure, this routine continues to do */
/* . aggressive early deflation using that part of */
/* . the deflation window that converged using INFQR */
/* . here and there to keep track.) ==== */
slacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
ldt);
i__1 = jw - 1;
i__2 = *ldh + 1;
i__3 = *ldt + 1;
scopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
i__3);
slaset_("A", &jw, &jw, &c_b12, &c_b13, &v[v_offset], ldv);
slahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop],
&si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
/* ==== STREXC needs a clean margin near the diagonal ==== */
i__1 = jw - 3;
for (j = 1; j <= i__1; ++j) {
t[j + 2 + j * t_dim1] = 0.f;
t[j + 3 + j * t_dim1] = 0.f;
}
if (jw > 2) {
t[jw + (jw - 2) * t_dim1] = 0.f;
}
/* ==== Deflation detection loop ==== */
*ns = jw;
ilst = infqr + 1;
L20:
if (ilst <= *ns) {
if (*ns == 1) {
bulge = FALSE_;
} else {
bulge = t[*ns + (*ns - 1) * t_dim1] != 0.f;
}
/* ==== Small spike tip test for deflation ==== */
if (! bulge) {
/* ==== Real eigenvalue ==== */
foo = (r__1 = t[*ns + *ns * t_dim1], dabs(r__1));
if (foo == 0.f) {
foo = dabs(s);
}
/* Computing MAX */
r__2 = smlnum, r__3 = ulp * foo;
if ((r__1 = s * v[*ns * v_dim1 + 1], dabs(r__1)) <= dmax(r__2,
r__3)) {
/* ==== Deflatable ==== */
--(*ns);
} else {
/* ==== Undeflatable. Move it up out of the way. */
/* . (STREXC can not fail in this case.) ==== */
ifst = *ns;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
++ilst;
}
} else {
/* ==== Complex conjugate pair ==== */
foo = (r__3 = t[*ns + *ns * t_dim1], dabs(r__3)) + sqrt((r__1 = t[
*ns + (*ns - 1) * t_dim1], dabs(r__1))) * sqrt((r__2 = t[*
ns - 1 + *ns * t_dim1], dabs(r__2)));
if (foo == 0.f) {
foo = dabs(s);
}
/* Computing MAX */
r__3 = (r__1 = s * v[*ns * v_dim1 + 1], dabs(r__1)), r__4 = (r__2
= s * v[(*ns - 1) * v_dim1 + 1], dabs(r__2));
/* Computing MAX */
r__5 = smlnum, r__6 = ulp * foo;
if (dmax(r__3,r__4) <= dmax(r__5,r__6)) {
/* ==== Deflatable ==== */
*ns += -2;
} else {
/* ==== Undeflatable. Move them up out of the way. */
/* . Fortunately, STREXC does the right thing with */
/* . ILST in case of a rare exchange failure. ==== */
ifst = *ns;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
ilst += 2;
}
}
/* ==== End deflation detection loop ==== */
goto L20;
}
/* ==== Return to Hessenberg form ==== */
if (*ns == 0) {
s = 0.f;
}
if (*ns < jw) {
/* ==== sorting diagonal blocks of T improves accuracy for */
/* . graded matrices. Bubble sort deals well with */
/* . exchange failures. ==== */
sorted = FALSE_;
i__ = *ns + 1;
L30:
if (sorted) {
goto L50;
}
sorted = TRUE_;
kend = i__ - 1;
i__ = infqr + 1;
if (i__ == *ns) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.f) {
k = i__ + 1;
} else {
k = i__ + 2;
}
L40:
if (k <= kend) {
if (k == i__ + 1) {
evi = (r__1 = t[i__ + i__ * t_dim1], dabs(r__1));
} else {
evi = (r__3 = t[i__ + i__ * t_dim1], dabs(r__3)) + sqrt((r__1
= t[i__ + 1 + i__ * t_dim1], dabs(r__1))) * sqrt((
r__2 = t[i__ + (i__ + 1) * t_dim1], dabs(r__2)));
}
if (k == kend) {
evk = (r__1 = t[k + k * t_dim1], dabs(r__1));
} else if (t[k + 1 + k * t_dim1] == 0.f) {
evk = (r__1 = t[k + k * t_dim1], dabs(r__1));
} else {
evk = (r__3 = t[k + k * t_dim1], dabs(r__3)) + sqrt((r__1 = t[
k + 1 + k * t_dim1], dabs(r__1))) * sqrt((r__2 = t[k
+ (k + 1) * t_dim1], dabs(r__2)));
}
if (evi >= evk) {
i__ = k;
} else {
sorted = FALSE_;
ifst = i__;
ilst = k;
strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
if (info == 0) {
i__ = ilst;
} else {
i__ = k;
}
}
if (i__ == kend) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.f) {
k = i__ + 1;
} else {
k = i__ + 2;
}
goto L40;
}
goto L30;
L50:
;
}
/* ==== Restore shift/eigenvalue array from T ==== */
i__ = jw;
L60:
if (i__ >= infqr + 1) {
if (i__ == infqr + 1) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.f;
--i__;
} else if (t[i__ + (i__ - 1) * t_dim1] == 0.f) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.f;
--i__;
} else {
aa = t[i__ - 1 + (i__ - 1) * t_dim1];
cc = t[i__ + (i__ - 1) * t_dim1];
bb = t[i__ - 1 + i__ * t_dim1];
dd = t[i__ + i__ * t_dim1];
slanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__
- 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, &
sn);
i__ += -2;
}
goto L60;
}
if (*ns < jw || s == 0.f) {
if (*ns > 1 && s != 0.f) {
/* ==== Reflect spike back into lower triangle ==== */
scopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
beta = work[1];
slarfg_(ns, &beta, &work[2], &c__1, &tau);
work[1] = 1.f;
i__1 = jw - 2;
i__2 = jw - 2;
slaset_("L", &i__1, &i__2, &c_b12, &c_b12, &t[t_dim1 + 3], ldt);
slarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
slarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
slarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
work[jw + 1]);
i__1 = *lwork - jw;
sgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
}
/* ==== Copy updated reduced window into place ==== */
if (kwtop > 1) {
h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
}
slacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
i__1 = jw - 1;
i__2 = *ldt + 1;
i__3 = *ldh + 1;
scopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
&i__3);
/* ==== Accumulate orthogonal matrix in order update */
/* . H and Z, if requested. ==== */
if (*ns > 1 && s != 0.f) {
i__1 = *lwork - jw;
sormhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[jw + 1], &i__1, &info);
}
/* ==== Update vertical slab in H ==== */
if (*wantt) {
ltop = 1;
} else {
ltop = *ktop;
}
i__1 = kwtop - 1;
i__2 = *nv;
for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = kwtop - krow;
kln = min(i__3,i__4);
sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &h__[krow + kwtop *
h_dim1], ldh, &v[v_offset], ldv, &c_b12, &wv[wv_offset],
ldwv);
slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
h_dim1], ldh);
}
/* ==== Update horizontal slab in H ==== */
if (*wantt) {
i__2 = *n;
i__1 = *nh;
for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
kcol += i__1) {
/* Computing MIN */
i__3 = *nh, i__4 = *n - kcol + 1;
kln = min(i__3,i__4);
sgemm_("C", "N", &jw, &kln, &jw, &c_b13, &v[v_offset], ldv, &
h__[kwtop + kcol * h_dim1], ldh, &c_b12, &t[t_offset],
ldt);
slacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
h_dim1], ldh);
}
}
/* ==== Update vertical slab in Z ==== */
if (*wantz) {
i__1 = *ihiz;
i__2 = *nv;
for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = *ihiz - krow + 1;
kln = min(i__3,i__4);
sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &z__[krow + kwtop *
z_dim1], ldz, &v[v_offset], ldv, &c_b12, &wv[
wv_offset], ldwv);
slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
kwtop * z_dim1], ldz);
}
}
}
*nd = jw - *ns;
/* . INFQR from the spike length takes care */
/* . of the case of a rare QR failure while */
/* . calculating eigenvalues of the deflation */
/* . window.) ==== */
*ns -= infqr;
/* ==== Return optimal workspace. ==== */
work[1] = (real) lwkopt;
/* ==== End of SLAQR2 ==== */
return 0;
} /* slaqr2_ */
/* 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 serrec_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
"ts of the error ex\002,\002its ***\002)";
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer info, ifst, ilst;
static real work[4], a[16] /* was [4][4] */, b[16] /* was [4][4] */, c__[
16] /* was [4][4] */;
static integer i__, j, m;
static real s[4], scale;
static integer iwork[4];
static real wi[4];
static integer nt;
static real wr[4];
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), strexc_(char *, integer *, real *, integer
*, real *, integer *, integer *, integer *, real *, integer *), strsna_(char *, char *, logical *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, real *,
integer *, integer *, real *, integer *, integer *, integer *), strsen_(char *, char *, logical *, integer *,
real *, integer *, real *, integer *, real *, real *, integer *,
real *, real *, real *, integer *, integer *, integer *, integer *
), strsyl_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *);
static logical sel[4];
static real sep[4];
/* Fortran I/O blocks */
static cilist io___19 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___20 = { 0, 0, 0, fmt_9998, 0 };
#define a_ref(a_1,a_2) a[(a_2)*4 + a_1 - 5]
#define b_ref(a_1,a_2) b[(a_2)*4 + a_1 - 5]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
SERREC tests the error exits for the routines for eigen- condition
estimation for REAL matrices:
STRSYL, STREXC, STRSNA and STRSEN.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
infoc_1.ok = TRUE_;
nt = 0;
/* Initialize A, B and SEL */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a_ref(i__, j) = 0.f;
b_ref(i__, j) = 0.f;
/* L10: */
}
/* L20: */
}
for (i__ = 1; i__ <= 4; ++i__) {
a_ref(i__, i__) = 1.f;
sel[i__ - 1] = TRUE_;
/* L30: */
}
/* Test STRSYL */
s_copy(srnamc_1.srnamt, "STRSYL", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
strsyl_("X", "N", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsyl_("N", "X", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
strsyl_("N", "N", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsyl_("N", "N", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
strsyl_("N", "N", &c__1, &c__0, &c_n1, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
strsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__1, b, &c__1, c__, &c__2, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
strsyl_("N", "N", &c__1, &c__0, &c__2, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
strsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__2, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("STRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test STREXC */
s_copy(srnamc_1.srnamt, "STREXC", (ftnlen)6, (ftnlen)6);
ifst = 1;
ilst = 1;
infoc_1.infot = 1;
strexc_("X", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
strexc_("N", &c__0, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ilst = 2;
strexc_("N", &c__2, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strexc_("V", &c__2, a, &c__2, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 0;
ilst = 1;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 2;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ifst = 1;
ilst = 0;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ilst = 2;
strexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, work, &info);
chkxer_("STREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test STRSNA */
s_copy(srnamc_1.srnamt, "STRSNA", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
strsna_("X", "A", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsna_("B", "X", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsna_("B", "A", sel, &c_n1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strsna_("V", "A", sel, &c__2, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__1, c__, &c__2, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
strsna_("B", "A", sel, &c__1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__0, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
strsna_("B", "S", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__1, &m, work, &c__2, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 16;
strsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__2, &m, work, &c__1, iwork, &info);
chkxer_("STRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* Test STRSEN */
sel[0] = FALSE_;
s_copy(srnamc_1.srnamt, "STRSEN", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
strsen_("X", "N", sel, &c__0, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
strsen_("N", "X", sel, &c__0, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
strsen_("N", "N", sel, &c_n1, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
strsen_("N", "N", sel, &c__2, a, &c__1, b, &c__1, wr, wi, &m, s, sep,
work, &c__2, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
strsen_("N", "V", sel, &c__2, a, &c__2, b, &c__1, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("N", "V", sel, &c__2, a, &c__2, b, &c__2, wr, wi, &m, s, sep,
work, &c__0, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("E", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
strsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__3, iwork, &c__2, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 17;
strsen_("E", "V", sel, &c__2, a, &c__2, b, &c__2, wr, wi, &m, s, sep,
work, &c__1, iwork, &c__0, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 17;
strsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, wr, wi, &m, s, sep,
work, &c__4, iwork, &c__1, &info);
chkxer_("STRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 10;
/* Print a summary line. */
if (infoc_1.ok) {
io___19.ciunit = infoc_1.nout;
s_wsfe(&io___19);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___20.ciunit = infoc_1.nout;
s_wsfe(&io___20);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of SERREC */
} /* serrec_ */
/* Subroutine */ int sget36_(real *rmax, integer *lmax, integer *ninfo,
integer *knt, integer *nin)
{
/* System generated locals */
integer i__1, i__2;
/* Builtin functions */
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
double r_sign(real *, real *);
/* Local variables */
integer i__, j, n;
real q[100] /* was [10][10] */, t1[100] /* was [10][10] */, t2[100]
/* was [10][10] */;
integer loc;
real eps, res, tmp[100] /* was [10][10] */;
integer ifst, ilst;
real work[200];
integer info1, info2, ifst1, ifst2, ilst1, ilst2;
extern /* Subroutine */ int shst01_(integer *, integer *, integer *, real
*, integer *, real *, integer *, real *, integer *, real *,
integer *, real *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), strexc_(
char *, integer *, real *, integer *, real *, integer *, integer *
, integer *, real *, integer *);
integer ifstsv;
real result[2];
integer ilstsv;
/* Fortran I/O blocks */
static cilist io___2 = { 0, 0, 0, 0, 0 };
static cilist io___7 = { 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 .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGET36 tests STREXC, a routine for moving blocks (either 1 by 1 or */
/* 2 by 2) on the diagonal of a matrix in real Schur form. Thus, SLAEXC */
/* computes an orthogonal matrix Q such that */
/* Q' * T1 * Q = T2 */
/* and where one of the diagonal blocks of T1 (the one at row IFST) has */
/* been moved to position ILST. */
/* The test code verifies that the residual Q'*T1*Q-T2 is small, that T2 */
/* is in Schur form, and that the final position of the IFST block is */
/* ILST (within +-1). */
/* The test matrices are read from a file with logical unit number NIN. */
/* Arguments */
/* ========== */
/* RMAX (output) REAL */
/* Value of the largest test ratio. */
/* LMAX (output) INTEGER */
/* Example number where largest test ratio achieved. */
/* NINFO (output) INTEGER array, dimension (3) */
/* NINFO(J) is the number of examples where INFO=J. */
/* KNT (output) INTEGER */
/* Total number of examples tested. */
/* NIN (input) INTEGER */
/* Input logical unit number. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ninfo;
/* Function Body */
eps = slamch_("P");
*rmax = 0.f;
*lmax = 0;
*knt = 0;
ninfo[1] = 0;
ninfo[2] = 0;
ninfo[3] = 0;
/* Read input data until N=0 */
L10:
io___2.ciunit = *nin;
s_rsle(&io___2);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ifst, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ilst, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
return 0;
}
++(*knt);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___7.ciunit = *nin;
s_rsle(&io___7);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__4, &c__1, (char *)&tmp[i__ + j * 10 - 11], (ftnlen)
sizeof(real));
}
e_rsle();
/* L20: */
}
slacpy_("F", &n, &n, tmp, &c__10, t1, &c__10);
slacpy_("F", &n, &n, tmp, &c__10, t2, &c__10);
ifstsv = ifst;
ilstsv = ilst;
ifst1 = ifst;
ilst1 = ilst;
ifst2 = ifst;
ilst2 = ilst;
res = 0.f;
/* Test without accumulating Q */
slaset_("Full", &n, &n, &c_b21, &c_b22, q, &c__10);
strexc_("N", &n, t1, &c__10, q, &c__10, &ifst1, &ilst1, work, &info1);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (i__ == j && q[i__ + j * 10 - 11] != 1.f) {
res += 1.f / eps;
}
if (i__ != j && q[i__ + j * 10 - 11] != 0.f) {
res += 1.f / eps;
}
/* L30: */
}
/* L40: */
}
/* Test with accumulating Q */
slaset_("Full", &n, &n, &c_b21, &c_b22, q, &c__10);
strexc_("V", &n, t2, &c__10, q, &c__10, &ifst2, &ilst2, work, &info2);
/* Compare T1 with T2 */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (t1[i__ + j * 10 - 11] != t2[i__ + j * 10 - 11]) {
res += 1.f / eps;
}
/* L50: */
}
/* L60: */
}
if (ifst1 != ifst2) {
res += 1.f / eps;
}
if (ilst1 != ilst2) {
res += 1.f / eps;
}
if (info1 != info2) {
res += 1.f / eps;
}
/* Test for successful reordering of T2 */
if (info2 != 0) {
++ninfo[info2];
} else {
if ((i__1 = ifst2 - ifstsv, abs(i__1)) > 1) {
res += 1.f / eps;
}
if ((i__1 = ilst2 - ilstsv, abs(i__1)) > 1) {
res += 1.f / eps;
}
}
/* Test for small residual, and orthogonality of Q */
shst01_(&n, &c__1, &n, tmp, &c__10, t2, &c__10, q, &c__10, work, &c__200,
result);
res = res + result[0] + result[1];
/* Test for T2 being in Schur form */
loc = 1;
L70:
if (t2[loc + 1 + loc * 10 - 11] != 0.f) {
/* 2 by 2 block */
if (t2[loc + (loc + 1) * 10 - 11] == 0.f || t2[loc + loc * 10 - 11] !=
t2[loc + 1 + (loc + 1) * 10 - 11] || r_sign(&c_b22, &t2[loc
+ (loc + 1) * 10 - 11]) == r_sign(&c_b22, &t2[loc + 1 + loc *
10 - 11])) {
res += 1.f / eps;
}
i__1 = n;
for (i__ = loc + 2; i__ <= i__1; ++i__) {
if (t2[i__ + loc * 10 - 11] != 0.f) {
res += 1.f / res;
}
if (t2[i__ + (loc + 1) * 10 - 11] != 0.f) {
res += 1.f / res;
}
/* L80: */
}
loc += 2;
} else {
/* 1 by 1 block */
i__1 = n;
for (i__ = loc + 1; i__ <= i__1; ++i__) {
if (t2[i__ + loc * 10 - 11] != 0.f) {
res += 1.f / res;
}
/* L90: */
}
++loc;
}
if (loc < n) {
goto L70;
}
if (res > *rmax) {
*rmax = res;
*lmax = *knt;
}
goto L10;
/* End of SGET36 */
} /* sget36_ */