dtgsyl.c

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#include "f2c.h"
#include "netlib.h"
extern double sqrt(double); /* #include <math.h> */

/* Table of constant values */
static integer c__2 = 2;
static integer c_n1 = -1;
static integer c__5 = 5;
static doublereal c_b14 = 0.;
static integer c__0 = 0;
static integer c__1 = 1;
static doublereal c_b53 = -1.;
static doublereal c_b54 = 1.;

/* Subroutine */ void dtgsyl_(trans, ijob, m, n, a, lda, b, ldb, c, ldc, d,
         ldd, e, lde, f, ldf, scale, dif, work, lwork, iwork, info)
char *trans;
integer *ijob, *m, *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, *dif, *work;
integer *lwork, *iwork, *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;

    /* Local variables */
    static doublereal dsum;
    static integer ppqq, i, j, k, p, q;
    static integer ifunc, linfo;
    static integer lwmin;
    static doublereal scale2;
    static integer ie, je, mb, nb;
    static doublereal dscale;
    static integer is, js, pq;
    static doublereal scaloc;
    static integer iround;
    static logical notran;
    static integer isolve;
    static logical lquery;


/*  -- 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 */

/*  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. */

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

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1 * 1;
    c -= c_offset;
    d_dim1 = *ldd;
    d_offset = 1 + d_dim1 * 1;
    d -= d_offset;
    e_dim1 = *lde;
    e_offset = 1 + e_dim1 * 1;
    e -= e_offset;
    f_dim1 = *ldf;
    f_offset = 1 + f_dim1 * 1;
    f -= f_offset;
    --work;
    --iwork;

/*     Decode and test input parameters */

    *info = 0;
    notran = lsame_(trans, "N");
    lquery = *lwork == -1;

    if ((*ijob == 1 || *ijob == 2) && notran) {
        lwmin = max(1, 2 * *m * *n);
    } else {
        lwmin = 1;
    }

    if (! notran && ! lsame_(trans, "T")) {
        *info = -1;
    } else if (*ijob < 0 || *ijob > 4) {
        *info = -2;
    } else 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;
    } else if (*lwork < lwmin && ! lquery) {
        *info = -20;
    }

    if (*info == 0) {