dtgsy2.c

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/* lapack/double/dtgsy2.f -- translated by f2c (version 20050501).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"

/* Table of constant values */

static integer c__8 = 8;
static integer c__1 = 1;
static doublereal c_b27 = -1.;
static doublereal c_b42 = 1.;
static integer c__64 = 64;
static doublereal c_b54 = 0.;
static integer c__0 = 0;

/*<    >*/
/* Subroutine */ int dtgsy2_(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 *rdsum, doublereal *rdscal, integer *iwork, integer 
        *pq, 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;

    /* Local variables */
    integer i__, j, k, p, q;
    doublereal z__[64]  /* was [8][8] */;
    integer ie, je, mb, nb, ii, jj, is, js;
    doublereal rhs[8];
    integer isp1, jsp1;
    extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *);
    integer ierr, zdim, ipiv[8], jpiv[8];
    doublereal alpha;
    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);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, 
            doublereal *, integer *, doublereal *, integer *), daxpy_(integer 
            *, doublereal *, doublereal *, integer *, doublereal *, integer *)
            , dgesc2_(integer *, doublereal *, integer *, doublereal *, 
            integer *, integer *, doublereal *), dgetc2_(integer *, 
            doublereal *, integer *, integer *, integer *, integer *), 
            dlatdf_(integer *, integer *, doublereal *, integer *, doublereal 
            *, doublereal *, doublereal *, integer *, integer *);
    doublereal scaloc;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    logical notran;
    (void)trans_len;

/*  -- LAPACK auxiliary 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   RDSCAL, RDSUM, SCALE >*/
/*     .. */
/*     .. Array Arguments .. */
/*<       INTEGER            IWORK( * ) >*/
/*<    >*/
/*     .. */

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

/*  DTGSY2 solves the generalized Sylvester equation: */

/*              A * R - L * B = scale * C                (1) */
/*              D * R - L * E = scale * F, */

/*  using Level 1 and 2 BLAS. 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 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 solving equation (1) corresponds to solve */
/*  Z*x = scale*b, where Z is defined as */

/*         Z = [ kron(In, A)  -kron(B', Im) ]             (2) */
/*             [ kron(In, D)  -kron(E', Im) ], */

/*  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. */
/*  In the process of solving (1), we solve a number of such systems */
/*  where Dim(In), Dim(In) = 1 or 2. */

/*  If TRANS = 'T', solve the transposed system Z'*y = scale*b for y, */
/*  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 is used to compute an estimate of Dif[(A, D), (B, E)] = */
/*  sigma_min(Z) using reverse communicaton with DLACON. */

/*  DTGSY2 also (IJOB >= 1) contributes to the computation in STGSYL */
/*  of an upper bound on the separation between to matrix pairs. Then */
/*  the input (A, D), (B, E) are sub-pencils of the matrix pair in */
/*  DTGSYL. See STGSYL for details. */

/*  Arguments */
/*  ========= */

/*  TRANS   (input) CHARACTER */
/*          = '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: A contribution from this subsystem to a Frobenius */
/*               norm-based estimate of the separation between two matrix */
/*               pairs is computed. (look ahead strategy is used). */
/*          = 2: A contribution from this subsystem to a Frobenius */
/*               norm-based estimate of the separation between two matrix */
/*               pairs is computed. (DGECON on sub-systems is used.) */
/*          Not referenced if TRANS = 'T'. */

/*  M       (input) INTEGER */
/*          On entry, M specifies the order of A and D, and the row */
/*          dimension of C, F, R and L. */

/*  N       (input) INTEGER */
/*          On entry, N specifies the order of B and E, and the column */
/*          dimension of C, F, R and L. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA, M) */
/*          On entry, A contains an upper quasi triangular matrix. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the matrix A. LDA >= max(1, M). */

/*  B       (input) DOUBLE PRECISION array, dimension (LDB, N) */
/*          On entry, B contains an upper quasi triangular matrix. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the matrix 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). */
/*          On exit, if IJOB = 0, C has been overwritten by the */
/*          solution R. */

/*  LDC     (input) INTEGER */
/*          The leading dimension of the matrix C. LDC >= max(1, M). */

/*  D       (input) DOUBLE PRECISION array, dimension (LDD, M) */
/*          On entry, D contains an upper triangular matrix. */

/*  LDD     (input) INTEGER */
/*          The leading dimension of the matrix D. LDD >= max(1, M). */

/*  E       (input) DOUBLE PRECISION array, dimension (LDE, N) */
/*          On entry, E contains an upper triangular matrix. */

/*  LDE     (input) INTEGER */
/*          The leading dimension of the matrix 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). */
/*          On exit, if IJOB = 0, F has been overwritten by the */
/*          solution L. */

/*  LDF     (input) INTEGER */
/*          The leading dimension of the matrix F. LDF >= max(1, M). */

/*  SCALE   (output) DOUBLE PRECISION */
/*          On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */
/*          R and L (C and F on entry) will hold the solutions to a */
/*          slightly perturbed system but the input matrices A, B, D and */
/*          E have not been changed. If SCALE = 0, R and L will hold the */
/*          solutions to the homogeneous system with C = F = 0. Normally, */
/*          SCALE = 1. */

/*  RDSUM   (input/output) DOUBLE PRECISION */
/*          On entry, the sum of squares of computed contributions to */
/*          the Dif-estimate under computation by DTGSYL, where the */
/*          scaling factor RDSCAL (see below) has been factored out. */
/*          On exit, the corresponding sum of squares updated with the */
/*          contributions from the current sub-system. */
/*          If TRANS = 'T' RDSUM is not touched. */
/*          NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL. */

/*  RDSCAL  (input/output) DOUBLE PRECISION */
/*          On entry, scaling factor used to prevent overflow in RDSUM. */
/*          On exit, RDSCAL is updated w.r.t. the current contributions */
/*          in RDSUM. */
/*          If TRANS = 'T', RDSCAL is not touched. */
/*          NOTE: RDSCAL only makes sense when DTGSY2 is called by */
/*                DTGSYL. */

/*  IWORK   (workspace) INTEGER array, dimension (M+N+2) */

/*  PQ      (output) INTEGER */
/*          On exit, the number of subsystems (of size 2-by-2, 4-by-4 and */
/*          8-by-8) solved by this routine. */

/*  INFO    (output) INTEGER */
/*          On exit, if INFO is set to */
/*            =0: Successful exit */
/*            <0: If INFO = -i, the i-th argument had an illegal value. */
/*            >0: The matrix pairs (A, D) and (B, E) have common or very */
/*                close eigenvalues. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*<       INTEGER            LDZ >*/
/*<       PARAMETER          ( LDZ = 8 ) >*/
/*<       DOUBLE PRECISION   ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<       LOGICAL            NOTRAN >*/
/*<    >*/
/*<       DOUBLE PRECISION   ALPHA, SCALOC >*/
/*     .. */
/*     .. Local Arrays .. */
/*<       INTEGER            IPIV( LDZ ), JPIV( LDZ ) >*/
/*<       DOUBLE PRECISION   RHS( LDZ ), Z( LDZ, LDZ ) >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       EXTERNAL           LSAME >*/
/*     .. */
/*     .. External Subroutines .. */
/*<    >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          MAX >*/
/*     .. */
/*     .. 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;
    --iwork;

    /* Function Body */
    *info = 0;
/*<       IERR = 0 >*/
    ierr = 0;
/*<       NOTRAN = LSAME( TRANS, 'N' ) >*/
    notran = lsame_(trans, "N", (ftnlen)1, (ftnlen)1);
/*<       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.2 ) ) THEN >*/
    } else if (*ijob < 0 || *ijob > 2) {
/*<          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 = -5 >*/
        *info = -5;
/*<       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)) {