stgsyl.c

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/* stgsyl.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__2 = 2;
static integer c_n1 = -1;
static integer c__5 = 5;
static real c_b14 = 0.f;
static integer c__1 = 1;
static real c_b51 = -1.f;
static real c_b52 = 1.f;

/* Subroutine */ int stgsyl_(char *trans, integer *ijob, integer *m, integer *
        n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
        ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer 
        *ldf, real *scale, real *dif, real *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;
    real dsum;
    integer ppqq;
    extern logical lsame_(char *, char *);
    integer ifunc;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    integer linfo;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
            integer *, real *, real *, integer *, real *, integer *, real *, 
            real *, integer *);
    integer lwmin;
    real scale2, dscale;
    extern /* Subroutine */ int stgsy2_(char *, integer *, integer *, integer 
            *, real *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *, real *, 
             real *, integer *, integer *, integer *);
    real scaloc;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *), slaset_(char *, integer *, 
            integer *, real *, real *, real *, integer *);
    integer iround;
    logical notran;
    integer isolve;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  STGSYL 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', STGSYL 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 SLACON. */

/*  If IJOB >= 1, STGSYL 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. */
/*               ( SGECON 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL */
/*          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) REAL */
/*          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) 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 > = 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 SCOPY by calls to SLASET. */
/*  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] = (real) lwmin;

        if (*lwork < lwmin && ! lquery) {
            *info = -20;
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("STGSYL", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
        *scale = 1.f;
        if (notran) {
            if (*ijob != 0) {
                *dif = 0.f;
            }
        }
        return 0;
    }

/*     Determine optimal block sizes MB and NB */

    mb = ilaenv_(&c__2, "STGSYL", trans, m, n, &c_n1, &c_n1);
    nb = ilaenv_(&c__5, "STGSYL", trans, m, n, &c_n1, &c_n1);

    isolve = 1;
    ifunc = 0;
    if (notran) {
        if (*ijob >= 3) {
            ifunc = *ijob - 2;
            slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc)
                    ;
            slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
        } else if (*ijob >= 1 && notran) {
            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.f;
            dsum = 1.f;
            pq = 0;
            stgsy2_(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.f) {
                if (*ijob == 1 || *ijob == 3) {
                    *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
                            dsum));
                } else {
                    *dif = sqrt((real) pq) / (dscale * sqrt(dsum));
                }
            }

            if (isolve == 2 && iround == 1) {
                if (notran) {
                    ifunc = *ijob;
                }
                scale2 = *scale;
                slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
                slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
                slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
                slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
            } else if (isolve == 2 && iround == 2) {
                slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
                slacpy_("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.f) {
        ++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.f) {
        ++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.f;
            dsum = 1.f;
            pq = 0;
            *scale = 1.f;
            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;
                    stgsy2_(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.f) {
                        i__3 = js - 1;
                        for (k = 1; k <= i__3; ++k) {
                            sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
                            sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L80: */
                        }
                        i__3 = je;
                        for (k = js; k <= i__3; ++k) {
                            i__4 = is - 1;
                            sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &
                                    c__1);
                            i__4 = is - 1;
                            sscal_(&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;
                            sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], 
                                    &c__1);
                            i__4 = *m - ie;
                            sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &
                                    c__1);
/* L100: */
                        }
                        i__3 = *n;
                        for (k = je + 1; k <= i__3; ++k) {
                            sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
                            sscal_(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;
                        sgemm_("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;
                        sgemm_("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;
                        sgemm_("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;
                        sgemm_("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.f) {
                if (*ijob == 1 || *ijob == 3) {
                    *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
                            dsum));
                } else {
                    *dif = sqrt((real) pq) / (dscale * sqrt(dsum));
                }
            }
            if (isolve == 2 && iround == 1) {
                if (notran) {
                    ifunc = *ijob;
                }
                scale2 = *scale;
                slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
                slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
                slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
                slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
            } else if (isolve == 2 && iround == 2) {
                slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
                slacpy_("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.f;
        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;
                stgsy2_(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.f) {
                    i__3 = js - 1;
                    for (k = 1; k <= i__3; ++k) {
                        sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
                        sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L160: */
                    }
                    i__3 = je;
                    for (k = js; k <= i__3; ++k) {
                        i__4 = is - 1;
                        sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &c__1);
                        i__4 = is - 1;
                        sscal_(&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;
                        sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], &
                                c__1);
                        i__4 = *m - ie;
                        sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &c__1)
                                ;
/* L180: */
                    }
                    i__3 = *n;
                    for (k = je + 1; k <= i__3; ++k) {
                        sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
                        sscal_(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;
                    sgemm_("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;
                    sgemm_("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;
                    sgemm_("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;
                    sgemm_("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] = (real) lwmin;

    return 0;

/*     End of STGSYL */

} /* stgsyl_ */