dtgexc.c

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/* dtgexc.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;

/* Subroutine */ int dtgexc_(logical *wantq, logical *wantz, integer *n, 
        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
        q, integer *ldq, doublereal *z__, integer *ldz, integer *ifst, 
        integer *ilst, doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, 
            z_offset, i__1;

    /* Local variables */
    integer nbf, nbl, here, lwmin;
    extern /* Subroutine */ int dtgex2_(logical *, logical *, integer *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, integer *, integer *, integer *, integer 
            *, doublereal *, integer *, integer *), xerbla_(char *, integer *);
    integer nbnext;
    logical lquery;


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

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

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

/*  DTGEXC reorders the generalized real Schur decomposition of a real */
/*  matrix pair (A,B) using an orthogonal equivalence transformation */

/*                 (A, B) = Q * (A, B) * Z', */

/*  so that the diagonal block of (A, B) with row index IFST is moved */
/*  to row ILST. */

/*  (A, B) must be in generalized real Schur canonical form (as returned */
/*  by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
/*  diagonal blocks. B is upper triangular. */

/*  Optionally, the matrices Q and Z of generalized Schur vectors are */
/*  updated. */

/*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' */
/*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' */


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

/*  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. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B. N >= 0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the matrix A in generalized real Schur canonical */
/*          form. */
/*          On exit, the updated matrix A, again in generalized */
/*          real Schur canonical form. */

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

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,N) */
/*          On entry, the matrix B in generalized real Schur canonical */
/*          form (A,B). */
/*          On exit, the updated matrix B, again in generalized */
/*          real Schur canonical form (A,B). */

/*  LDB     (input)  INTEGER */
/*          The leading dimension of the array B. LDB >= max(1,N). */

/*  Q       (input/output) DOUBLE PRECISION array, dimension (LDZ,N) */
/*          On entry, if WANTQ = .TRUE., the orthogonal matrix Q. */
/*          On exit, the updated matrix Q. */
/*          If WANTQ = .FALSE., Q is not referenced. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q. LDQ >= 1. */
/*          If WANTQ = .TRUE., LDQ >= N. */

/*  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ,N) */
/*          On entry, if WANTZ = .TRUE., the orthogonal matrix Z. */
/*          On exit, the updated matrix Z. */
/*          If WANTZ = .FALSE., Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z. LDZ >= 1. */
/*          If WANTZ = .TRUE., LDZ >= N. */

/*  IFST    (input/output) INTEGER */
/*  ILST    (input/output) INTEGER */
/*          Specify the reordering of the diagonal blocks of (A, B). */
/*          The block with row index IFST is moved to row ILST, by a */
/*          sequence of swapping between adjacent blocks. */
/*          On exit, if IFST pointed on entry to the second row of */
/*          a 2-by-2 block, it is changed to point to the first row; */
/*          ILST always points to the first row of the block in its */
/*          final position (which may differ from its input value by */
/*          +1 or -1). 1 <= IFST, ILST <= N. */

/*  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 when N <= 1, otherwise LWORK >= 4*N + 16. */

/*          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. */

/*  INFO    (output) INTEGER */
/*           =0:  successful exit. */
/*           <0:  if INFO = -i, the i-th argument had an illegal value. */
/*           =1:  The transformed matrix pair (A, B) would be too far */
/*                from generalized Schur form; the problem is ill- */
/*                conditioned. (A, B) may have been partially reordered, */
/*                and ILST points to the first row of the current */
/*                position of the block being moved. */

/*  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; 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. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and test input arguments. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    if (*n < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    } else if (*ldq < 1 || *wantq && *ldq < max(1,*n)) {
        *info = -9;
    } else if (*ldz < 1 || *wantz && *ldz < max(1,*n)) {
        *info = -11;
    } else if (*ifst < 1 || *ifst > *n) {
        *info = -12;
    } else if (*ilst < 1 || *ilst > *n) {
        *info = -13;
    }

    if (*info == 0) {
        if (*n <= 1) {
            lwmin = 1;
        } else {
            lwmin = (*n << 2) + 16;
        }
        work[1] = (doublereal) lwmin;

        if (*lwork < lwmin && ! lquery) {
            *info = -15;
        }
    }

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

/*     Quick return if possible */

    if (*n <= 1) {
        return 0;
    }

/*     Determine the first row of the specified block and find out */
/*     if it is 1-by-1 or 2-by-2. */

    if (*ifst > 1) {
        if (a[*ifst + (*ifst - 1) * a_dim1] != 0.) {
            --(*ifst);
        }
    }
    nbf = 1;
    if (*ifst < *n) {
        if (a[*ifst + 1 + *ifst * a_dim1] != 0.) {
            nbf = 2;
        }
    }

/*     Determine the first row of the final block */
/*     and find out if it is 1-by-1 or 2-by-2. */

    if (*ilst > 1) {
        if (a[*ilst + (*ilst - 1) * a_dim1] != 0.) {
            --(*ilst);
        }
    }
    nbl = 1;
    if (*ilst < *n) {
        if (a[*ilst + 1 + *ilst * a_dim1] != 0.) {
            nbl = 2;
        }
    }
    if (*ifst == *ilst) {
        return 0;
    }

    if (*ifst < *ilst) {

/*        Update ILST. */

        if (nbf == 2 && nbl == 1) {
            --(*ilst);
        }
        if (nbf == 1 && nbl == 2) {
            ++(*ilst);
        }

        here = *ifst;

L10:

/*        Swap with next one below. */

        if (nbf == 1 || nbf == 2) {

/*           Current block either 1-by-1 or 2-by-2. */

            nbnext = 1;
            if (here + nbf + 1 <= *n) {
                if (a[here + nbf + 1 + (here + nbf) * a_dim1] != 0.) {
                    nbnext = 2;
                }
            }
            dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
                    q_offset], ldq, &z__[z_offset], ldz, &here, &nbf, &nbnext, 
                     &work[1], lwork, info);
            if (*info != 0) {
                *ilst = here;
                return 0;
            }
            here += nbnext;

/*           Test if 2-by-2 block breaks into two 1-by-1 blocks. */

            if (nbf == 2) {
                if (a[here + 1 + here * a_dim1] == 0.) {
                    nbf = 3;
                }
            }

        } else {

/*           Current block consists of two 1-by-1 blocks, each of which */
/*           must be swapped individually. */

            nbnext = 1;
            if (here + 3 <= *n) {
                if (a[here + 3 + (here + 2) * a_dim1] != 0.) {
                    nbnext = 2;
                }
            }
            i__1 = here + 1;
            dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
                    q_offset], ldq, &z__[z_offset], ldz, &i__1, &c__1, &
                    nbnext, &work[1], lwork, info);
            if (*info != 0) {
                *ilst = here;
                return 0;
            }
            if (nbnext == 1) {

/*              Swap two 1-by-1 blocks. */

                dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, 
                         &q[q_offset], ldq, &z__[z_offset], ldz, &here, &c__1, 
                         &c__1, &work[1], lwork, info);
                if (*info != 0) {
                    *ilst = here;
                    return 0;
                }
                ++here;

            } else {

/*              Recompute NBNEXT in case of 2-by-2 split. */

                if (a[here + 2 + (here + 1) * a_dim1] == 0.) {
                    nbnext = 1;
                }
                if (nbnext == 2) {

/*                 2-by-2 block did not split. */

                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            here, &c__1, &nbnext, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    here += 2;
                } else {

/*                 2-by-2 block did split. */

                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            here, &c__1, &c__1, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    ++here;
                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            here, &c__1, &c__1, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    ++here;
                }

            }
        }
        if (here < *ilst) {
            goto L10;
        }
    } else {
        here = *ifst;

L20:

/*        Swap with next one below. */

        if (nbf == 1 || nbf == 2) {

/*           Current block either 1-by-1 or 2-by-2. */

            nbnext = 1;
            if (here >= 3) {
                if (a[here - 1 + (here - 2) * a_dim1] != 0.) {
                    nbnext = 2;
                }
            }
            i__1 = here - nbnext;
            dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
                    q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, &nbf, 
                     &work[1], lwork, info);
            if (*info != 0) {
                *ilst = here;
                return 0;
            }
            here -= nbnext;

/*           Test if 2-by-2 block breaks into two 1-by-1 blocks. */

            if (nbf == 2) {
                if (a[here + 1 + here * a_dim1] == 0.) {
                    nbf = 3;
                }
            }

        } else {

/*           Current block consists of two 1-by-1 blocks, each of which */
/*           must be swapped individually. */

            nbnext = 1;
            if (here >= 3) {
                if (a[here - 1 + (here - 2) * a_dim1] != 0.) {
                    nbnext = 2;
                }
            }
            i__1 = here - nbnext;
            dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
                    q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, &
                    c__1, &work[1], lwork, info);
            if (*info != 0) {
                *ilst = here;
                return 0;
            }
            if (nbnext == 1) {

/*              Swap two 1-by-1 blocks. */

                dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, 
                         &q[q_offset], ldq, &z__[z_offset], ldz, &here, &
                        nbnext, &c__1, &work[1], lwork, info);
                if (*info != 0) {
                    *ilst = here;
                    return 0;
                }
                --here;
            } else {

/*             Recompute NBNEXT in case of 2-by-2 split. */

                if (a[here + (here - 1) * a_dim1] == 0.) {
                    nbnext = 1;
                }
                if (nbnext == 2) {

/*                 2-by-2 block did not split. */

                    i__1 = here - 1;
                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            i__1, &c__2, &c__1, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    here += -2;
                } else {

/*                 2-by-2 block did split. */

                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            here, &c__1, &c__1, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    --here;
                    dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
                            ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
                            here, &c__1, &c__1, &work[1], lwork, info);
                    if (*info != 0) {
                        *ilst = here;
                        return 0;
                    }
                    --here;
                }
            }
        }
        if (here > *ilst) {
            goto L20;
        }
    }
    *ilst = here;
    work[1] = (doublereal) lwmin;
    return 0;

/*     End of DTGEXC */

} /* dtgexc_ */