/* stgsen.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c__2 = 2;
static real c_b28 = 1.f;
/* Subroutine */ int stgsen_(integer *ijob, logical *wantq, logical *wantz,
logical *select, integer *n, real *a, integer *lda, real *b, integer *
ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq,
real *z__, integer *ldz, integer *m, real *pl, real *pr, real *dif,
real *work, integer *lwork, integer *iwork, integer *liwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
z_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal), r_sign(real *, real *);
/* Local variables */
integer i__, k, n1, n2, kk, ks, mn2, ijb;
real eps;
integer kase;
logical pair;
integer ierr;
real dsum;
logical swap;
extern /* Subroutine */ int slag2_(real *, integer *, real *, integer *,
real *, real *, real *, real *, real *, real *);
integer isave[3];
logical wantd;
integer lwmin;
logical wantp;
extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *,
real *, integer *, integer *);
logical wantd1, wantd2;
real dscale, rdscal;
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_(
char *, integer *, integer *, real *, integer *, real *, integer *
), stgexc_(logical *, logical *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, integer *
, integer *, integer *, real *, integer *, integer *);
integer liwmin;
extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *,
real *);
real smlnum;
logical lquery;
extern /* Subroutine */ int stgsyl_(char *, integer *, integer *, integer
*, real *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* January 2007 */
/* Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STGSEN reorders the generalized real Schur decomposition of a real */
/* matrix pair (A, B) (in terms of an orthonormal equivalence trans- */
/* formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues */
/* appears in the leading diagonal blocks of the upper quasi-triangular */
/* matrix A and the upper triangular B. The leading columns of Q and */
/* Z form orthonormal bases of the corresponding left and right eigen- */
/* spaces (deflating subspaces). (A, B) must be in generalized real */
/* Schur canonical form (as returned by SGGES), i.e. A is block upper */
/* triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper */
/* triangular. */
/* STGSEN also computes the generalized eigenvalues */
/* w(j) = (ALPHAR(j) + i*ALPHAI(j))/BETA(j) */
/* of the reordered matrix pair (A, B). */
/* Optionally, STGSEN computes the estimates of reciprocal condition */
/* numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11), */
/* (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) */
/* between the matrix pairs (A11, B11) and (A22,B22) that correspond to */
/* the selected cluster and the eigenvalues outside the cluster, resp., */
/* and norms of "projections" onto left and right eigenspaces w.r.t. */
/* the selected cluster in the (1,1)-block. */
/* Arguments */
/* ========= */
/* IJOB (input) INTEGER */
/* Specifies whether condition numbers are required for the */
/* cluster of eigenvalues (PL and PR) or the deflating subspaces */
/* (Difu and Difl): */
/* =0: Only reorder w.r.t. SELECT. No extras. */
/* =1: Reciprocal of norms of "projections" onto left and right */
/* eigenspaces w.r.t. the selected cluster (PL and PR). */
/* =2: Upper bounds on Difu and Difl. F-norm-based estimate */
/* (DIF(1:2)). */
/* =3: Estimate of Difu and Difl. 1-norm-based estimate */
/* (DIF(1:2)). */
/* About 5 times as expensive as IJOB = 2. */
/* =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic */
/* version to get it all. */
/* =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above) */
/* WANTQ (input) LOGICAL */
/* .TRUE. : update the left transformation matrix Q; */
/* .FALSE.: do not update Q. */
/* WANTZ (input) LOGICAL */
/* .TRUE. : update the right transformation matrix Z; */
/* .FALSE.: do not update Z. */
/* 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 matrices A and B. N >= 0. */
/* A (input/output) REAL array, dimension(LDA,N) */
/* On entry, the upper quasi-triangular matrix A, with (A, B) in */
/* generalized real Schur canonical form. */
/* On exit, A is overwritten by the reordered matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension(LDB,N) */
/* On entry, the upper triangular matrix B, with (A, B) in */
/* generalized real Schur canonical form. */
/* On exit, B is overwritten by the reordered matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* ALPHAR (output) REAL array, dimension (N) */
/* ALPHAI (output) REAL array, dimension (N) */
/* BETA (output) REAL array, dimension (N) */
/* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i */
/* and BETA(j),j=1,...,N are the diagonals of the complex Schur */
/* form (S,T) that would result if the 2-by-2 diagonal blocks of */
/* the real generalized Schur form of (A,B) were further reduced */
/* to triangular form using complex unitary transformations. */
/* If ALPHAI(j) is zero, then the j-th eigenvalue is real; if */
/* positive, then the j-th and (j+1)-st eigenvalues are a */
/* complex conjugate pair, with ALPHAI(j+1) negative. */
/* Q (input/output) REAL array, dimension (LDQ,N) */
/* On entry, if WANTQ = .TRUE., Q is an N-by-N matrix. */
/* On exit, Q has been postmultiplied by the left orthogonal */
/* transformation matrix which reorder (A, B); The leading M */
/* columns of Q form orthonormal bases for the specified pair of */
/* left eigenspaces (deflating subspaces). */
/* If WANTQ = .FALSE., Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= 1; */
/* and if WANTQ = .TRUE., LDQ >= N. */
/* Z (input/output) REAL array, dimension (LDZ,N) */
/* On entry, if WANTZ = .TRUE., Z is an N-by-N matrix. */
/* On exit, Z has been postmultiplied by the left orthogonal */
/* transformation matrix which reorder (A, B); The leading M */
/* columns of Z form orthonormal bases for the specified pair of */
/* left eigenspaces (deflating subspaces). */
/* If WANTZ = .FALSE., Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1; */
/* If WANTZ = .TRUE., LDZ >= N. */
/* M (output) INTEGER */
/* The dimension of the specified pair of left and right eigen- */
/* spaces (deflating subspaces). 0 <= M <= N. */
/* PL (output) REAL */
/* PR (output) REAL */
/* If IJOB = 1, 4 or 5, PL, PR are lower bounds on the */
/* reciprocal of the norm of "projections" onto left and right */
/* eigenspaces with respect to the selected cluster. */
/* 0 < PL, PR <= 1. */
/* If M = 0 or M = N, PL = PR = 1. */
/* If IJOB = 0, 2 or 3, PL and PR are not referenced. */
/* DIF (output) REAL array, dimension (2). */
/* If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl. */
/* If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on */
/* Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based */
/* estimates of Difu and Difl. */
/* If M = 0 or N, DIF(1:2) = F-norm([A, B]). */
/* If IJOB = 0 or 1, DIF is not referenced. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 4*N+16. */
/* If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)). */
/* If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*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/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* IF IJOB = 0, IWORK is not referenced. Otherwise, */
/* on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. LIWORK >= 1. */
/* If IJOB = 1, 2 or 4, LIWORK >= N+6. */
/* If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6). */
/* 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 (A, B) failed because the transformed */
/* matrix pair (A, B) would be too far from generalized */
/* Schur form; the problem is very ill-conditioned. */
/* (A, B) may have been partially reordered. */
/* If requested, 0 is returned in DIF(*), PL and PR. */
/* Further Details */
/* =============== */
/* STGSEN first collects the selected eigenvalues by computing */
/* orthogonal U and W that move them to the top left corner of (A, B). */
/* In other words, the selected eigenvalues are the eigenvalues of */
/* (A11, B11) in: */
/* U'*(A, B)*W = (A11 A12) (B11 B12) n1 */
/* ( 0 A22),( 0 B22) n2 */
/* n1 n2 n1 n2 */
/* where N = n1+n2 and U' means the transpose of U. The first n1 columns */
/* of U and W span the specified pair of left and right eigenspaces */
/* (deflating subspaces) of (A, B). */
/* If (A, B) has been obtained from the generalized real Schur */
/* decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the */
/* reordered generalized real Schur form of (C, D) is given by */
/* (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)', */
/* and the first n1 columns of Q*U and Z*W span the corresponding */
/* deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.). */
/* Note that if the selected eigenvalue is sufficiently ill-conditioned, */
/* then its value may differ significantly from its value before */
/* reordering. */
/* The reciprocal condition numbers of the left and right eigenspaces */
/* spanned by the first n1 columns of U and W (or Q*U and Z*W) may */
/* be returned in DIF(1:2), corresponding to Difu and Difl, resp. */
/* The Difu and Difl are defined as: */
/* Difu[(A11, B11), (A22, B22)] = sigma-min( Zu ) */
/* and */
/* Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)], */
/* where sigma-min(Zu) is the smallest singular value of the */
/* (2*n1*n2)-by-(2*n1*n2) matrix */
/* Zu = [ kron(In2, A11) -kron(A22', In1) ] */
/* [ kron(In2, B11) -kron(B22', In1) ]. */
/* Here, Inx is the identity matrix of size nx and A22' is the */
/* transpose of A22. kron(X, Y) is the Kronecker product between */
/* the matrices X and Y. */
/* When DIF(2) is small, small changes in (A, B) can cause large changes */
/* in the deflating subspace. An approximate (asymptotic) bound on the */
/* maximum angular error in the computed deflating subspaces is */
/* EPS * norm((A, B)) / DIF(2), */
/* where EPS is the machine precision. */
/* The reciprocal norm of the projectors on the left and right */
/* eigenspaces associated with (A11, B11) may be returned in PL and PR. */
/* They are computed as follows. First we compute L and R so that */
/* P*(A, B)*Q is block diagonal, where */
/* P = ( I -L ) n1 Q = ( I R ) n1 */
/* ( 0 I ) n2 and ( 0 I ) n2 */
/* n1 n2 n1 n2 */
/* and (L, R) is the solution to the generalized Sylvester equation */
/* A11*R - L*A22 = -A12 */
/* B11*R - L*B22 = -B12 */
/* Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2). */
/* An approximate (asymptotic) bound on the average absolute error of */
/* the selected eigenvalues is */
/* EPS * norm((A, B)) / PL. */
/* There are also global error bounds which valid for perturbations up */
/* to a certain restriction: A lower bound (x) on the smallest */
/* F-norm(E,F) for which an eigenvalue of (A11, B11) may move and */
/* coalesce with an eigenvalue of (A22, B22) under perturbation (E,F), */
/* (i.e. (A + E, B + F), is */
/* x = min(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*max(1/PL,1/PR)). */
/* An approximate bound on x can be computed from DIF(1:2), PL and PR. */
/* If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed */
/* (L', R') and unperturbed (L, R) left and right deflating subspaces */
/* associated with the selected cluster in the (1,1)-blocks can be */
/* bounded as */
/* max-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2)) */
/* max-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2)) */
/* See LAPACK User's Guide section 4.11 or the following references */
/* for more information. */
/* Note that if the default method for computing the Frobenius-norm- */
/* based estimate DIF is not wanted (see SLATDF), then the parameter */
/* IDIFJB (see below) should be changed from 3 to 4 (routine SLATDF */
/* (IJOB = 2 will be used)). See STGSYL for more details. */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* References */
/* ========== */
/* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/* M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
/* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/* Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/* Estimation: Theory, Algorithms and Software, */
/* Report UMINF - 94.04, Department of Computing Science, Umea */
/* University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
/* Note 87. To appear in Numerical Algorithms, 1996. */
/* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/* for Solving the Generalized Sylvester Equation and Estimating the */
/* Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/* Department of Computing Science, Umea University, S-901 87 Umea, */
/* Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, */
/* 1996. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test the input parameters */
/* Parameter adjustments */
--select;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--dif;
--work;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1 || *liwork == -1;
if (*ijob < 0 || *ijob > 5) {
*info = -1;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldq < 1 || *wantq && *ldq < *n) {
*info = -14;
} else if (*ldz < 1 || *wantz && *ldz < *n) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STGSEN", &i__1);
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S") / eps;
ierr = 0;
wantp = *ijob == 1 || *ijob >= 4;
wantd1 = *ijob == 2 || *ijob == 4;
wantd2 = *ijob == 3 || *ijob == 5;
wantd = wantd1 || wantd2;
/* Set M to the dimension of the specified pair of deflating */
/* subspaces. */
*m = 0;
pair = FALSE_;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
if (k < *n) {
if (a[k + 1 + k * a_dim1] == 0.f) {
if (select[k]) {
++(*m);
}
} else {
pair = TRUE_;
if (select[k] || select[k + 1]) {
*m += 2;
}
}
} else {
if (select[*n]) {
++(*m);
}
}
}
/* L10: */
}
if (*ijob == 1 || *ijob == 2 || *ijob == 4) {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16, i__1 = max(i__1,i__2), i__2 = (*m <<
1) * (*n - *m);
lwmin = max(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n + 6;
liwmin = max(i__1,i__2);
} else if (*ijob == 3 || *ijob == 5) {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16, i__1 = max(i__1,i__2), i__2 = (*m <<
2) * (*n - *m);
lwmin = max(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = max(i__1,i__2), i__2 =
*n + 6;
liwmin = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16;
lwmin = max(i__1,i__2);
liwmin = 1;
}
work[1] = (real) lwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -22;
} else if (*liwork < liwmin && ! lquery) {
*info = -24;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STGSEN", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible. */
if (*m == *n || *m == 0) {
if (wantp) {
*pl = 1.f;
*pr = 1.f;
}
if (wantd) {
dscale = 0.f;
dsum = 1.f;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
slassq_(n, &a[i__ * a_dim1 + 1], &c__1, &dscale, &dsum);
slassq_(n, &b[i__ * b_dim1 + 1], &c__1, &dscale, &dsum);
/* L20: */
}
dif[1] = dscale * sqrt(dsum);
dif[2] = dif[1];
}
goto L60;
}
/* Collect the selected blocks at the top-left corner of (A, B). */
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 (a[k + 1 + k * a_dim1] != 0.f) {
pair = TRUE_;
swap = swap || select[k + 1];
}
}
if (swap) {
++ks;
/* Swap the K-th block to position KS. */
/* Perform the reordering of diagonal blocks in (A, B) */
/* by orthogonal transformation matrices and update */
/* Q and Z accordingly (if requested): */
kk = k;
if (k != ks) {
stgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &kk,
&ks, &work[1], lwork, &ierr);
}
if (ierr > 0) {
/* Swap is rejected: exit. */
*info = 1;
if (wantp) {
*pl = 0.f;
*pr = 0.f;
}
if (wantd) {
dif[1] = 0.f;
dif[2] = 0.f;
}
goto L60;
}
if (pair) {
++ks;
}
}
}
/* L30: */
}
if (wantp) {
/* Solve generalized Sylvester equation for R and L */
/* and compute PL and PR. */
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 0;
slacpy_("Full", &n1, &n2, &a[i__ * a_dim1 + 1], lda, &work[1], &n1);
slacpy_("Full", &n1, &n2, &b[i__ * b_dim1 + 1], ldb, &work[n1 * n2 +
1], &n1);
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * a_dim1]
, lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + i__ *
b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], &
work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &ierr);
/* Estimate the reciprocal of norms of "projections" onto left */
/* and right eigenspaces. */
rdscal = 0.f;
dsum = 1.f;
i__1 = n1 * n2;
slassq_(&i__1, &work[1], &c__1, &rdscal, &dsum);
*pl = rdscal * sqrt(dsum);
if (*pl == 0.f) {
*pl = 1.f;
} else {
*pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl));
}
rdscal = 0.f;
dsum = 1.f;
i__1 = n1 * n2;
slassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum);
*pr = rdscal * sqrt(dsum);
if (*pr == 0.f) {
*pr = 1.f;
} else {
*pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr));
}
}
if (wantd) {
/* Compute estimates of Difu and Difl. */
if (wantd1) {
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 3;
/* Frobenius norm-based Difu-estimate. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ *
a_dim1], lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ +
i__ * b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &
dif[1], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
ierr);
/* Frobenius norm-based Difl-estimate. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, &a[
a_offset], lda, &work[1], &n2, &b[i__ + i__ * b_dim1],
ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &dscale,
&dif[2], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
ierr);
} else {
/* Compute 1-norm-based estimates of Difu and Difl using */
/* reversed communication with SLACN2. In each step a */
/* generalized Sylvester equation or a transposed variant */
/* is solved. */
kase = 0;
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 0;
mn2 = (n1 << 1) * n2;
/* 1-norm-based estimate of Difu. */
L40:
slacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[1], &kase,
isave);
if (kase != 0) {
if (kase == 1) {
/* Solve generalized Sylvester equation. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
} else {
/* Solve the transposed variant. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("T", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
}
goto L40;
}
dif[1] = dscale / dif[1];
/* 1-norm-based estimate of Difl. */
L50:
slacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[2], &kase,
isave);
if (kase != 0) {
if (kase == 1) {
/* Solve generalized Sylvester equation. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
&a[a_offset], lda, &work[1], &n2, &b[i__ + i__ *
b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 +
1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
} else {
/* Solve the transposed variant. */
i__1 = *lwork - (n1 << 1) * n2;
stgsyl_("T", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
&a[a_offset], lda, &work[1], &n2, &b[i__ + i__ *
b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 +
1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
}
goto L50;
}
dif[2] = dscale / dif[2];
}
}
L60:
/* Compute generalized eigenvalues of reordered pair (A, B) and */
/* normalize the generalized Schur form. */
pair = FALSE_;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
if (k < *n) {
if (a[k + 1 + k * a_dim1] != 0.f) {
pair = TRUE_;
}
}
if (pair) {
/* Compute the eigenvalue(s) at position K. */
work[1] = a[k + k * a_dim1];
work[2] = a[k + 1 + k * a_dim1];
work[3] = a[k + (k + 1) * a_dim1];
work[4] = a[k + 1 + (k + 1) * a_dim1];
work[5] = b[k + k * b_dim1];
work[6] = b[k + 1 + k * b_dim1];
work[7] = b[k + (k + 1) * b_dim1];
work[8] = b[k + 1 + (k + 1) * b_dim1];
r__1 = smlnum * eps;
slag2_(&work[1], &c__2, &work[5], &c__2, &r__1, &beta[k], &
beta[k + 1], &alphar[k], &alphar[k + 1], &alphai[k]);
alphai[k + 1] = -alphai[k];
} else {
if (r_sign(&c_b28, &b[k + k * b_dim1]) < 0.f) {
/* If B(K,K) is negative, make it positive */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
a[k + i__ * a_dim1] = -a[k + i__ * a_dim1];
b[k + i__ * b_dim1] = -b[k + i__ * b_dim1];
if (*wantq) {
q[i__ + k * q_dim1] = -q[i__ + k * q_dim1];
}
/* L80: */
}
}
alphar[k] = a[k + k * a_dim1];
alphai[k] = 0.f;
beta[k] = b[k + k * b_dim1];
}
}
/* L70: */
}
work[1] = (real) lwmin;
iwork[1] = liwmin;
return 0;
/* End of STGSEN */
} /* stgsen_ */