/*< >*/
/* Subroutine */ int dtgsyl_(char *trans, integer *ijob, integer *m, integer *
n, doublereal *a, integer *lda, doublereal *b, integer *ldb,
doublereal *c__, integer *ldc, doublereal *d__, integer *ldd,
doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal *
scale, doublereal *dif, doublereal *work, integer *lwork, integer *
iwork, integer *info, ftnlen trans_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
i__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, p, q, ie, je, mb, nb, is, js, pq;
doublereal dsum;
integer ppqq;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemm_(char *, char *, integer *, integer *, integer *
, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, ftnlen, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
integer ifunc, linfo;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer lwmin;
doublereal scale2=0;
extern /* Subroutine */ int dtgsy2_(char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *, ftnlen);
doublereal dscale, scaloc;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen),
xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer iround;
logical notran;
integer isolve;
logical lquery;
(void)trans_len;
/* -- 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 .. */
/*< CHARACTER TRANS >*/
/*< >*/
/*< DOUBLE PRECISION DIF, SCALE >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IWORK( * ) >*/
/*< >*/
/* .. */
/* Purpose */
/* ======= */
/* DTGSYL solves the generalized Sylvester equation: */
/* A * R - L * B = scale * C (1) */
/* D * R - L * E = scale * F */
/* where R and L are unknown m-by-n matrices, (A, D), (B, E) and */
/* (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */
/* respectively, with real entries. (A, D) and (B, E) must be in */
/* generalized (real) Schur canonical form, i.e. A, B are upper quasi */
/* triangular and D, E are upper triangular. */
/* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
/* scaling factor chosen to avoid overflow. */
/* In matrix notation (1) is equivalent to solve Zx = scale b, where */
/* Z is defined as */
/* Z = [ kron(In, A) -kron(B', Im) ] (2) */
/* [ kron(In, D) -kron(E', Im) ]. */
/* Here Ik is the identity matrix of size k and X' is the transpose of */
/* X. kron(X, Y) is the Kronecker product between the matrices X and Y. */
/* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b, */
/* which is equivalent to solve for R and L in */
/* A' * R + D' * L = scale * C (3) */
/* R * B' + L * E' = scale * (-F) */
/* This case (TRANS = 'T') is used to compute an one-norm-based estimate */
/* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
/* and (B,E), using DLACON. */
/* If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate */
/* of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
/* reciprocal of the smallest singular value of Z. See [1-2] for more */
/* information. */
/* This is a level 3 BLAS algorithm. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* = 'N', solve the generalized Sylvester equation (1). */
/* = 'T', solve the 'transposed' system (3). */
/* IJOB (input) INTEGER */
/* Specifies what kind of functionality to be performed. */
/* =0: solve (1) only. */
/* =1: The functionality of 0 and 3. */
/* =2: The functionality of 0 and 4. */
/* =3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* (look ahead strategy IJOB = 1 is used). */
/* =4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* ( DGECON on sub-systems is used ). */
/* Not referenced if TRANS = 'T'. */
/* M (input) INTEGER */
/* The order of the matrices A and D, and the row dimension of */
/* the matrices C, F, R and L. */
/* N (input) INTEGER */
/* The order of the matrices B and E, and the column dimension */
/* of the matrices C, F, R and L. */
/* A (input) DOUBLE PRECISION array, dimension (LDA, M) */
/* The upper quasi triangular matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1, M). */
/* B (input) DOUBLE PRECISION array, dimension (LDB, N) */
/* The upper quasi triangular matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1, N). */
/* C (input/output) DOUBLE PRECISION array, dimension (LDC, N) */
/* On entry, C contains the right-hand-side of the first matrix */
/* equation in (1) or (3). */
/* On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
/* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
/* the solution achieved during the computation of the */
/* Dif-estimate. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1, M). */
/* D (input) DOUBLE PRECISION array, dimension (LDD, M) */
/* The upper triangular matrix D. */
/* LDD (input) INTEGER */
/* The leading dimension of the array D. LDD >= max(1, M). */
/* E (input) DOUBLE PRECISION array, dimension (LDE, N) */
/* The upper triangular matrix E. */
/* LDE (input) INTEGER */
/* The leading dimension of the array E. LDE >= max(1, N). */
/* F (input/output) DOUBLE PRECISION array, dimension (LDF, N) */
/* On entry, F contains the right-hand-side of the second matrix */
/* equation in (1) or (3). */
/* On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
/* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
/* the solution achieved during the computation of the */
/* Dif-estimate. */
/* LDF (input) INTEGER */
/* The leading dimension of the array F. LDF >= max(1, M). */
/* DIF (output) DOUBLE PRECISION */
/* On exit DIF is the reciprocal of a lower bound of the */
/* reciprocal of the Dif-function, i.e. DIF is an upper bound of */
/* Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2). */
/* IF IJOB = 0 or TRANS = 'T', DIF is not touched. */
/* SCALE (output) DOUBLE PRECISION */
/* On exit SCALE is the scaling factor in (1) or (3). */
/* If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
/* to a slightly perturbed system but the input matrices A, B, D */
/* and E have not been changed. If SCALE = 0, C and F hold the */
/* solutions R and L, respectively, to the homogeneous system */
/* with C = F = 0. Normally, SCALE = 1. */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) */
/* If IJOB = 0, WORK is not referenced. Otherwise, */
/* on exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK > = 1. */
/* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= 2*M*N. */
/* 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 (M+N+6) */
/* INFO (output) INTEGER */
/* =0: successful exit */
/* <0: If INFO = -i, the i-th argument had an illegal value. */
/* >0: (A, D) and (B, E) have common or close eigenvalues. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* [1] 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. */
/* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
/* Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
/* Appl., 15(4):1045-1060, 1994 */
/* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
/* Condition Estimators for Solving the Generalized Sylvester */
/* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
/* July 1989, pp 745-751. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY, NOTRAN >*/
/*< >*/
/*< DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC >*/
/* .. */
/* .. External Functions .. */
/*< LOGICAL LSAME >*/
/*< INTEGER ILAENV >*/
/*< EXTERNAL LSAME, ILAENV >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DCOPY, DGEMM, DLACPY, DSCAL, DTGSY2, XERBLA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC DBLE, MAX, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/* Decode and test input parameters */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
d_dim1 = *ldd;
d_offset = 1 + d_dim1;
d__ -= d_offset;
e_dim1 = *lde;
e_offset = 1 + e_dim1;
e -= e_offset;
f_dim1 = *ldf;
f_offset = 1 + f_dim1;
f -= f_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
/*< NOTRAN = LSAME( TRANS, 'N' ) >*/
notran = lsame_(trans, "N", (ftnlen)1, (ftnlen)1);
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( ( IJOB.EQ.1 .OR. IJOB.EQ.2 ) .AND. NOTRAN ) THEN >*/
if ((*ijob == 1 || *ijob == 2) && notran) {
/*< LWMIN = MAX( 1, 2*M*N ) >*/
/* Computing MAX */
i__1 = 1, i__2 = (*m << 1) * *n;
lwmin = max(i__1,i__2);
/*< ELSE >*/
} else {
/*< LWMIN = 1 >*/
lwmin = 1;
/*< END IF >*/
}
/*< IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN >*/
if (! notran && ! lsame_(trans, "T", (ftnlen)1, (ftnlen)1)) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN >*/
} else if (*ijob < 0 || *ijob > 4) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( M.LE.0 ) THEN >*/
} else if (*m <= 0) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( N.LE.0 ) THEN >*/
} else if (*n <= 0) {
/*< INFO = -4 >*/
*info = -4;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -6 >*/
*info = -6;
/*< ELSE IF( LDB.LT.MAX( 1, N ) ) THEN >*/
} else if (*ldb < max(1,*n)) {
/*< INFO = -8 >*/
*info = -8;
/*< ELSE IF( LDC.LT.MAX( 1, M ) ) THEN >*/
} else if (*ldc < max(1,*m)) {
/*< INFO = -10 >*/
*info = -10;
/*< ELSE IF( LDD.LT.MAX( 1, M ) ) THEN >*/
} else if (*ldd < max(1,*m)) {
/*< INFO = -12 >*/
*info = -12;
/*< ELSE IF( LDE.LT.MAX( 1, N ) ) THEN >*/
} else if (*lde < max(1,*n)) {
/*< INFO = -14 >*/
*info = -14;
/*< ELSE IF( LDF.LT.MAX( 1, M ) ) THEN >*/
} else if (*ldf < max(1,*m)) {
/*< INFO = -16 >*/
*info = -16;
/*< ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < lwmin && ! lquery) {
/*< INFO = -20 >*/
*info = -20;
/*< END IF >*/
}
/*< IF( INFO.EQ.0 ) THEN >*/
if (*info == 0) {
/*< WORK( 1 ) = LWMIN >*/
work[1] = (doublereal) lwmin;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'DTGSYL', -INFO ) >*/
i__1 = -(*info);
xerbla_("DTGSYL", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Determine optimal block sizes MB and NB */
/*< MB = ILAENV( 2, 'DTGSYL', TRANS, M, N, -1, -1 ) >*/
mb = ilaenv_(&c__2, "DTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
/*< NB = ILAENV( 5, 'DTGSYL', TRANS, M, N, -1, -1 ) >*/
nb = ilaenv_(&c__5, "DTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
/*< ISOLVE = 1 >*/
isolve = 1;
/*< IFUNC = 0 >*/
ifunc = 0;
/*< IF( IJOB.GE.3 .AND. NOTRAN ) THEN >*/
if (*ijob >= 3 && notran) {
/*< IFUNC = IJOB - 2 >*/
ifunc = *ijob - 2;
/*< DO 10 J = 1, N >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< CALL DCOPY( M, ZERO, 0, C( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &c__[j * c_dim1 + 1], &c__1);
/*< CALL DCOPY( M, ZERO, 0, F( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &f[j * f_dim1 + 1], &c__1);
/*< 10 CONTINUE >*/
/* L10: */
}
/*< ELSE IF( IJOB.GE.1 .AND. NOTRAN ) THEN >*/
} else if (*ijob >= 1 && notran) {
/*< ISOLVE = 2 >*/
isolve = 2;
/*< END IF >*/
}
/*< >*/
if ((mb <= 1 && nb <= 1) || (mb >= *m && nb >= *n)) {
/*< DO 30 IROUND = 1, ISOLVE >*/
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Use unblocked Level 2 solver */
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< PQ = 0 >*/
pq = 0;
/*< >*/
dtgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
&c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
lde, &f[f_offset], ldf, scale, &dsum, &dscale, &iwork[1],
&pq, info, (ftnlen)1);
/*< IF( DSCALE.NE.ZERO ) THEN >*/
if (dscale != 0.) {
/*< IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN >*/
if (*ijob == 1 || *ijob == 3) {
/*< DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) ) >*/
*dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
sqrt(dsum));
/*< ELSE >*/
} else {
/*< DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) ) >*/
*dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN >*/
if (isolve == 2 && iround == 1) {
/*< IFUNC = IJOB >*/
ifunc = *ijob;
/*< SCALE2 = SCALE >*/
scale2 = *scale;
/*< CALL DLACPY( 'F', M, N, C, LDC, WORK, M ) >*/
dlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m, (ftnlen)
1);
/*< CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M ) >*/
dlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m, (
ftnlen)1);
/*< DO 20 J = 1, N >*/
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/*< CALL DCOPY( M, ZERO, 0, C( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &c__[j * c_dim1 + 1], &c__1);
/*< CALL DCOPY( M, ZERO, 0, F( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &f[j * f_dim1 + 1], &c__1);
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN >*/
} else if (isolve == 2 && iround == 2) {
/*< CALL DLACPY( 'F', M, N, WORK, M, C, LDC ) >*/
dlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc, (ftnlen)
1);
/*< CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF ) >*/
dlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf, (
ftnlen)1);
/*< SCALE = SCALE2 >*/
*scale = scale2;
/*< END IF >*/
}
/*< 30 CONTINUE >*/
/* L30: */
}
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Determine block structure of A */
/*< P = 0 >*/
p = 0;
/*< I = 1 >*/
i__ = 1;
/*< 40 CONTINUE >*/
L40:
/*< >*/
if (i__ > *m) {
goto L50;
}
/*< P = P + 1 >*/
++p;
/*< IWORK( P ) = I >*/
iwork[p] = i__;
/*< I = I + MB >*/
i__ += mb;
/*< >*/
if (i__ >= *m) {
goto L50;
}
/*< >*/
if (a[i__ + (i__ - 1) * a_dim1] != 0.) {
++i__;
}
/*< GO TO 40 >*/
goto L40;
/*< 50 CONTINUE >*/
L50:
/*< IWORK( P+1 ) = M + 1 >*/
iwork[p + 1] = *m + 1;
/*< >*/
if (iwork[p] == iwork[p + 1]) {
--p;
}
/* Determine block structure of B */
/*< Q = P + 1 >*/
q = p + 1;
/*< J = 1 >*/
j = 1;
/*< 60 CONTINUE >*/
L60:
/*< >*/
if (j > *n) {
goto L70;
}
/*< Q = Q + 1 >*/
++q;
/*< IWORK( Q ) = J >*/
iwork[q] = j;
/*< J = J + NB >*/
j += nb;
/*< >*/
if (j >= *n) {
goto L70;
}
/*< >*/
if (b[j + (j - 1) * b_dim1] != 0.) {
++j;
}
/*< GO TO 60 >*/
goto L60;
/*< 70 CONTINUE >*/
L70:
/*< IWORK( Q+1 ) = N + 1 >*/
iwork[q + 1] = *n + 1;
/*< >*/
if (iwork[q] == iwork[q + 1]) {
--q;
}
/*< IF( NOTRAN ) THEN >*/
if (notran) {
/*< DO 150 IROUND = 1, ISOLVE >*/
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Solve (I, J)-subsystem */
/* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
/* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
/* for I = P, P - 1,..., 1; J = 1, 2,..., Q */
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< PQ = 0 >*/
pq = 0;
/*< SCALE = ONE >*/
*scale = 1.;
/*< DO 130 J = P + 2, Q >*/
i__2 = q;
for (j = p + 2; j <= i__2; ++j) {
/*< JS = IWORK( J ) >*/
js = iwork[j];
/*< JE = IWORK( J+1 ) - 1 >*/
je = iwork[j + 1] - 1;
/*< NB = JE - JS + 1 >*/
nb = je - js + 1;
/*< DO 120 I = P, 1, -1 >*/
for (i__ = p; i__ >= 1; --i__) {
/*< IS = IWORK( I ) >*/
is = iwork[i__];
/*< IE = IWORK( I+1 ) - 1 >*/
ie = iwork[i__ + 1] - 1;
/*< MB = IE - IS + 1 >*/
mb = ie - is + 1;
/*< PPQQ = 0 >*/
ppqq = 0;
/*< >*/
dtgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
lda, &b[js + js * b_dim1], ldb, &c__[is + js *
c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
+ js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
scaloc, &dsum, &dscale, &iwork[q + 2], &ppqq, &
linfo, (ftnlen)1);
/*< >*/
if (linfo > 0) {
*info = linfo;
}
/*< PQ = PQ + PPQQ >*/
pq += ppqq;
/*< IF( SCALOC.NE.ONE ) THEN >*/
if (scaloc != 1.) {
/*< DO 80 K = 1, JS - 1 >*/
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
/*< CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
/*< CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 80 CONTINUE >*/
/* L80: */
}
/*< DO 90 K = JS, JE >*/
i__3 = je;
for (k = js; k <= i__3; ++k) {
/*< CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 ) >*/
i__4 = is - 1;
dscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
/*< CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 ) >*/
i__4 = is - 1;
dscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 90 CONTINUE >*/
/* L90: */
}
/*< DO 100 K = JS, JE >*/
i__3 = je;
for (k = js; k <= i__3; ++k) {
/*< CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 ) >*/
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1],
&c__1);
/*< CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 ) >*/
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &
c__1);
/*< 100 CONTINUE >*/
/* L100: */
}
/*< DO 110 K = JE + 1, N >*/
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
/*< CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
/*< CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 110 CONTINUE >*/
/* L110: */
}
/*< SCALE = SCALE*SCALOC >*/
*scale *= scaloc;
/*< END IF >*/
}
/* Substitute R(I, J) and L(I, J) into remaining */
/* equation. */
/*< IF( I.GT.1 ) THEN >*/
if (i__ > 1) {
/*< >*/
i__3 = is - 1;
dgemm_("N", "N", &i__3, &nb, &mb, &c_b53, &a[is *
a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
&c_b54, &c__[js * c_dim1 + 1], ldc, (ftnlen)
1, (ftnlen)1);
/*< >*/
i__3 = is - 1;
dgemm_("N", "N", &i__3, &nb, &mb, &c_b53, &d__[is *
d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
&c_b54, &f[js * f_dim1 + 1], ldf, (ftnlen)1,
(ftnlen)1);
/*< END IF >*/
}
/*< IF( J.LT.Q ) THEN >*/
if (j < q) {
/*< >*/
i__3 = *n - je;
dgemm_("N", "N", &mb, &i__3, &nb, &c_b54, &f[is + js *
f_dim1], ldf, &b[js + (je + 1) * b_dim1],
ldb, &c_b54, &c__[is + (je + 1) * c_dim1],
ldc, (ftnlen)1, (ftnlen)1);
/*< >*/
i__3 = *n - je;
dgemm_("N", "N", &mb, &i__3, &nb, &c_b54, &f[is + js *
f_dim1], ldf, &e[js + (je + 1) * e_dim1],
lde, &c_b54, &f[is + (je + 1) * f_dim1], ldf,
(ftnlen)1, (ftnlen)1);
/*< END IF >*/
}
/*< 120 CONTINUE >*/
/* L120: */
}
/*< 130 CONTINUE >*/
/* L130: */
}
/*< IF( DSCALE.NE.ZERO ) THEN >*/
if (dscale != 0.) {
/*< IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN >*/
if (*ijob == 1 || *ijob == 3) {
/*< DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) ) >*/
*dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
sqrt(dsum));
/*< ELSE >*/
} else {
/*< DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) ) >*/
*dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN >*/
if (isolve == 2 && iround == 1) {
/*< IFUNC = IJOB >*/
ifunc = *ijob;
/*< SCALE2 = SCALE >*/
scale2 = *scale;
/*< CALL DLACPY( 'F', M, N, C, LDC, WORK, M ) >*/
dlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m, (ftnlen)
1);
/*< CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M ) >*/
dlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m, (
ftnlen)1);
/*< DO 140 J = 1, N >*/
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/*< CALL DCOPY( M, ZERO, 0, C( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &c__[j * c_dim1 + 1], &c__1);
/*< CALL DCOPY( M, ZERO, 0, F( 1, J ), 1 ) >*/
dcopy_(m, &c_b14, &c__0, &f[j * f_dim1 + 1], &c__1);
/*< 140 CONTINUE >*/
/* L140: */
}
/*< ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN >*/
} else if (isolve == 2 && iround == 2) {
/*< CALL DLACPY( 'F', M, N, WORK, M, C, LDC ) >*/
dlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc, (ftnlen)
1);
/*< CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF ) >*/
dlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf, (
ftnlen)1);
/*< SCALE = SCALE2 >*/
*scale = scale2;
/*< END IF >*/
}
/*< 150 CONTINUE >*/
/* L150: */
}
/*< ELSE >*/
} else {
/* Solve transposed (I, J)-subsystem */
/* A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J) */
/* R(I, J) * B(J, J)' + L(I, J) * E(J, J)' = -F(I, J) */
/* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
/*< SCALE = ONE >*/
*scale = 1.;
/*< DO 210 I = 1, P >*/
i__1 = p;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IS = IWORK( I ) >*/
is = iwork[i__];
/*< IE = IWORK( I+1 ) - 1 >*/
ie = iwork[i__ + 1] - 1;
/*< MB = IE - IS + 1 >*/
mb = ie - is + 1;
/*< DO 200 J = Q, P + 2, -1 >*/
i__2 = p + 2;
for (j = q; j >= i__2; --j) {
/*< JS = IWORK( J ) >*/
js = iwork[j];
/*< JE = IWORK( J+1 ) - 1 >*/
je = iwork[j + 1] - 1;
/*< NB = JE - JS + 1 >*/
nb = je - js + 1;
/*< >*/
dtgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
&d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
dscale, &iwork[q + 2], &ppqq, &linfo, (ftnlen)1);
/*< >*/
if (linfo > 0) {
*info = linfo;
}
/*< IF( SCALOC.NE.ONE ) THEN >*/
if (scaloc != 1.) {
/*< DO 160 K = 1, JS - 1 >*/
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
/*< CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
/*< CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 160 CONTINUE >*/
/* L160: */
}
/*< DO 170 K = JS, JE >*/
i__3 = je;
for (k = js; k <= i__3; ++k) {
/*< CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 ) >*/
i__4 = is - 1;
dscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &c__1);
/*< CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 ) >*/
i__4 = is - 1;
dscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 170 CONTINUE >*/
/* L170: */
}
/*< DO 180 K = JS, JE >*/
i__3 = je;
for (k = js; k <= i__3; ++k) {
/*< CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 ) >*/
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], &
c__1);
/*< CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 ) >*/
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &c__1)
;
/*< 180 CONTINUE >*/
/* L180: */
}
/*< DO 190 K = JE + 1, N >*/
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
/*< CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
/*< CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) >*/
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/*< 190 CONTINUE >*/
/* L190: */
}
/*< SCALE = SCALE*SCALOC >*/
*scale *= scaloc;
/*< END IF >*/
}
/* Substitute R(I, J) and L(I, J) into remaining equation. */
/*< IF( J.GT.P+2 ) THEN >*/
if (j > p + 2) {
/*< >*/
i__3 = js - 1;
dgemm_("N", "T", &mb, &i__3, &nb, &c_b54, &c__[is + js *
c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b54, &
f[is + f_dim1], ldf, (ftnlen)1, (ftnlen)1);
/*< >*/
i__3 = js - 1;
dgemm_("N", "T", &mb, &i__3, &nb, &c_b54, &f[is + js *
f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b54, &
f[is + f_dim1], ldf, (ftnlen)1, (ftnlen)1);
/*< END IF >*/
}
/*< IF( I.LT.P ) THEN >*/
if (i__ < p) {
/*< >*/
i__3 = *m - ie;
dgemm_("T", "N", &i__3, &nb, &mb, &c_b53, &a[is + (ie + 1)
* a_dim1], lda, &c__[is + js * c_dim1], ldc, &
c_b54, &c__[ie + 1 + js * c_dim1], ldc, (ftnlen)1,
(ftnlen)1);
/*< >*/
i__3 = *m - ie;
dgemm_("T", "N", &i__3, &nb, &mb, &c_b53, &d__[is + (ie +
1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
c_b54, &c__[ie + 1 + js * c_dim1], ldc, (ftnlen)1,
(ftnlen)1);
/*< END IF >*/
}
/*< 200 CONTINUE >*/
/* L200: */
}
/*< 210 CONTINUE >*/
/* L210: */
}
/*< END IF >*/
}
/*< WORK( 1 ) = LWMIN >*/
work[1] = (doublereal) lwmin;
/*< RETURN >*/
return 0;
/* End of DTGSYL */
/*< END >*/
} /* dtgsyl_ */
/* Subroutine */ int dtgsyl_(char *trans, integer *ijob, integer *m, integer *
n, doublereal *a, integer *lda, doublereal *b, integer *ldb,
doublereal *c__, integer *ldc, doublereal *d__, integer *ldd,
doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal *
scale, doublereal *dif, doublereal *work, integer *lwork, integer *
iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
i__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, p, q, ie, je, mb, nb, is, js, pq;
doublereal dsum;
integer ppqq;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemm_(char *, char *, integer *, integer *, integer *
, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
integer ifunc, linfo, lwmin;
doublereal scale2;
extern /* Subroutine */ int dtgsy2_(char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *);
doublereal dscale, scaloc;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
integer iround;
logical notran;
integer isolve;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTGSYL solves the generalized Sylvester equation: */
/* A * R - L * B = scale * C (1) */
/* D * R - L * E = scale * F */
/* where R and L are unknown m-by-n matrices, (A, D), (B, E) and */
/* (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */
/* respectively, with real entries. (A, D) and (B, E) must be in */
/* generalized (real) Schur canonical form, i.e. A, B are upper quasi */
/* triangular and D, E are upper triangular. */
/* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
/* scaling factor chosen to avoid overflow. */
/* In matrix notation (1) is equivalent to solve Zx = scale b, where */
/* Z is defined as */
/* Z = [ kron(In, A) -kron(B', Im) ] (2) */
/* [ kron(In, D) -kron(E', Im) ]. */
/* Here Ik is the identity matrix of size k and X' is the transpose of */
/* X. kron(X, Y) is the Kronecker product between the matrices X and Y. */
/* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b, */
/* which is equivalent to solve for R and L in */
/* A' * R + D' * L = scale * C (3) */
/* R * B' + L * E' = scale * (-F) */
/* This case (TRANS = 'T') is used to compute an one-norm-based estimate */
/* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
/* and (B,E), using DLACON. */
/* If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate */
/* of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
/* reciprocal of the smallest singular value of Z. See [1-2] for more */
/* information. */
/* This is a level 3 BLAS algorithm. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* = 'N', solve the generalized Sylvester equation (1). */
/* = 'T', solve the 'transposed' system (3). */
/* IJOB (input) INTEGER */
/* Specifies what kind of functionality to be performed. */
/* =0: solve (1) only. */
/* =1: The functionality of 0 and 3. */
/* =2: The functionality of 0 and 4. */
/* =3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* (look ahead strategy IJOB = 1 is used). */
/* =4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* ( DGECON on sub-systems is used ). */
/* Not referenced if TRANS = 'T'. */
/* M (input) INTEGER */
/* The order of the matrices A and D, and the row dimension of */
/* the matrices C, F, R and L. */
/* N (input) INTEGER */
/* The order of the matrices B and E, and the column dimension */
/* of the matrices C, F, R and L. */
/* A (input) DOUBLE PRECISION array, dimension (LDA, M) */
/* The upper quasi triangular matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1, M). */
/* B (input) DOUBLE PRECISION array, dimension (LDB, N) */
/* The upper quasi triangular matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1, N). */
/* C (input/output) DOUBLE PRECISION array, dimension (LDC, N) */
/* On entry, C contains the right-hand-side of the first matrix */
/* equation in (1) or (3). */
/* On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
/* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
/* the solution achieved during the computation of the */
/* Dif-estimate. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1, M). */
/* D (input) DOUBLE PRECISION array, dimension (LDD, M) */
/* The upper triangular matrix D. */
/* LDD (input) INTEGER */
/* The leading dimension of the array D. LDD >= max(1, M). */
/* E (input) DOUBLE PRECISION array, dimension (LDE, N) */
/* The upper triangular matrix E. */
/* LDE (input) INTEGER */
/* The leading dimension of the array E. LDE >= max(1, N). */
/* F (input/output) DOUBLE PRECISION array, dimension (LDF, N) */
/* On entry, F contains the right-hand-side of the second matrix */
/* equation in (1) or (3). */
/* On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
/* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
/* the solution achieved during the computation of the */
/* Dif-estimate. */
/* LDF (input) INTEGER */
/* The leading dimension of the array F. LDF >= max(1, M). */
/* DIF (output) DOUBLE PRECISION */
/* On exit DIF is the reciprocal of a lower bound of the */
/* reciprocal of the Dif-function, i.e. DIF is an upper bound of */
/* Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2). */
/* IF IJOB = 0 or TRANS = 'T', DIF is not touched. */
/* SCALE (output) DOUBLE PRECISION */
/* On exit SCALE is the scaling factor in (1) or (3). */
/* If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
/* to a slightly perturbed system but the input matrices A, B, D */
/* and E have not been changed. If SCALE = 0, C and F hold the */
/* solutions R and L, respectively, to the homogeneous system */
/* with C = F = 0. Normally, SCALE = 1. */
/* WORK (workspace/output) DOUBLE PRECISION 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 > = 1. */
/* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). */
/* 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 (M+N+6) */
/* INFO (output) INTEGER */
/* =0: successful exit */
/* <0: If INFO = -i, the i-th argument had an illegal value. */
/* >0: (A, D) and (B, E) have common or close eigenvalues. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* [1] 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. */
/* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
/* Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
/* Appl., 15(4):1045-1060, 1994 */
/* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
/* Condition Estimators for Solving the Generalized Sylvester */
/* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
/* July 1989, pp 745-751. */
/* ===================================================================== */
/* Replaced various illegal calls to DCOPY by calls to DLASET. */
/* Sven Hammarling, 1/5/02. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
d_dim1 = *ldd;
d_offset = 1 + d_dim1;
d__ -= d_offset;
e_dim1 = *lde;
e_offset = 1 + e_dim1;
e -= e_offset;
f_dim1 = *ldf;
f_offset = 1 + f_dim1;
f -= f_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
lquery = *lwork == -1;
if (! notran && ! lsame_(trans, "T")) {
*info = -1;
} else if (notran) {
if (*ijob < 0 || *ijob > 4) {
*info = -2;
}
}
if (*info == 0) {
if (*m <= 0) {
*info = -3;
} else if (*n <= 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if (*ldd < max(1,*m)) {
*info = -12;
} else if (*lde < max(1,*n)) {
*info = -14;
} else if (*ldf < max(1,*m)) {
*info = -16;
}
}
if (*info == 0) {
if (notran) {
if (*ijob == 1 || *ijob == 2) {
/* Computing MAX */
i__1 = 1, i__2 = (*m << 1) * *n;
lwmin = max(i__1,i__2);
} else {
lwmin = 1;
}
} else {
lwmin = 1;
}
work[1] = (doublereal) lwmin;
if (*lwork < lwmin && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTGSYL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*scale = 1.;
if (notran) {
if (*ijob != 0) {
*dif = 0.;
}
}
return 0;
}
/* Determine optimal block sizes MB and NB */
mb = ilaenv_(&c__2, "DTGSYL", trans, m, n, &c_n1, &c_n1);
nb = ilaenv_(&c__5, "DTGSYL", trans, m, n, &c_n1, &c_n1);
isolve = 1;
ifunc = 0;
if (notran) {
if (*ijob >= 3) {
ifunc = *ijob - 2;
dlaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc)
;
dlaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (*ijob >= 1) {
isolve = 2;
}
}
if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) {
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Use unblocked Level 2 solver */
dscale = 0.;
dsum = 1.;
pq = 0;
dtgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
&c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
lde, &f[f_offset], ldf, scale, &dsum, &dscale, &iwork[1],
&pq, info);
if (dscale != 0.) {
if (*ijob == 1 || *ijob == 3) {
*dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
sqrt(dsum));
} else {
*dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
}
}
if (isolve == 2 && iround == 1) {
if (notran) {
ifunc = *ijob;
}
scale2 = *scale;
dlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
dlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
dlaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
dlaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (isolve == 2 && iround == 2) {
dlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
dlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
*scale = scale2;
}
/* L30: */
}
return 0;
}
/* Determine block structure of A */
p = 0;
i__ = 1;
L40:
if (i__ > *m) {
goto L50;
}
++p;
iwork[p] = i__;
i__ += mb;
if (i__ >= *m) {
goto L50;
}
if (a[i__ + (i__ - 1) * a_dim1] != 0.) {
++i__;
}
goto L40;
L50:
iwork[p + 1] = *m + 1;
if (iwork[p] == iwork[p + 1]) {
--p;
}
/* Determine block structure of B */
q = p + 1;
j = 1;
L60:
if (j > *n) {
goto L70;
}
++q;
iwork[q] = j;
j += nb;
if (j >= *n) {
goto L70;
}
if (b[j + (j - 1) * b_dim1] != 0.) {
++j;
}
goto L60;
L70:
iwork[q + 1] = *n + 1;
if (iwork[q] == iwork[q + 1]) {
--q;
}
if (notran) {
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Solve (I, J)-subsystem */
/* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
/* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
/* for I = P, P - 1,..., 1; J = 1, 2,..., Q */
dscale = 0.;
dsum = 1.;
pq = 0;
*scale = 1.;
i__2 = q;
for (j = p + 2; j <= i__2; ++j) {
js = iwork[j];
je = iwork[j + 1] - 1;
nb = je - js + 1;
for (i__ = p; i__ >= 1; --i__) {
is = iwork[i__];
ie = iwork[i__ + 1] - 1;
mb = ie - is + 1;
ppqq = 0;
dtgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
lda, &b[js + js * b_dim1], ldb, &c__[is + js *
c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
+ js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
scaloc, &dsum, &dscale, &iwork[q + 2], &ppqq, &
linfo);
if (linfo > 0) {
*info = linfo;
}
pq += ppqq;
if (scaloc != 1.) {
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L80: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = is - 1;
dscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
i__4 = is - 1;
dscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L90: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1],
&c__1);
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &
c__1);
/* L100: */
}
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L110: */
}
*scale *= scaloc;
}
/* Substitute R(I, J) and L(I, J) into remaining */
/* equation. */
if (i__ > 1) {
i__3 = is - 1;
dgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &a[is *
a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
&c_b52, &c__[js * c_dim1 + 1], ldc);
i__3 = is - 1;
dgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &d__[is *
d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
&c_b52, &f[js * f_dim1 + 1], ldf);
}
if (j < q) {
i__3 = *n - je;
dgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &b[js + (je + 1) * b_dim1],
ldb, &c_b52, &c__[is + (je + 1) * c_dim1],
ldc);
i__3 = *n - je;
dgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &e[js + (je + 1) * e_dim1],
lde, &c_b52, &f[is + (je + 1) * f_dim1], ldf);
}
/* L120: */
}
/* L130: */
}
if (dscale != 0.) {
if (*ijob == 1 || *ijob == 3) {
*dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
sqrt(dsum));
} else {
*dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
}
}
if (isolve == 2 && iround == 1) {
if (notran) {
ifunc = *ijob;
}
scale2 = *scale;
dlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
dlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
dlaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
dlaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (isolve == 2 && iround == 2) {
dlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
dlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
*scale = scale2;
}
/* L150: */
}
} else {
/* Solve transposed (I, J)-subsystem */
/* A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J) */
/* R(I, J) * B(J, J)' + L(I, J) * E(J, J)' = -F(I, J) */
/* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
*scale = 1.;
i__1 = p;
for (i__ = 1; i__ <= i__1; ++i__) {
is = iwork[i__];
ie = iwork[i__ + 1] - 1;
mb = ie - is + 1;
i__2 = p + 2;
for (j = q; j >= i__2; --j) {
js = iwork[j];
je = iwork[j + 1] - 1;
nb = je - js + 1;
dtgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
&d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
dscale, &iwork[q + 2], &ppqq, &linfo);
if (linfo > 0) {
*info = linfo;
}
if (scaloc != 1.) {
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L160: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = is - 1;
dscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &c__1);
i__4 = is - 1;
dscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L170: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], &
c__1);
i__4 = *m - ie;
dscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &c__1)
;
/* L180: */
}
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L190: */
}
*scale *= scaloc;
}
/* Substitute R(I, J) and L(I, J) into remaining equation. */
if (j > p + 2) {
i__3 = js - 1;
dgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &c__[is + js *
c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b52, &
f[is + f_dim1], ldf);
i__3 = js - 1;
dgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b52, &
f[is + f_dim1], ldf);
}
if (i__ < p) {
i__3 = *m - ie;
dgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &a[is + (ie + 1)
* a_dim1], lda, &c__[is + js * c_dim1], ldc, &
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
i__3 = *m - ie;
dgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &d__[is + (ie +
1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
}
/* L200: */
}
/* L210: */
}
}
work[1] = (doublereal) lwmin;
return 0;
/* End of DTGSYL */
} /* dtgsyl_ */
