dgbbrd.c

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/* dgbbrd.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 doublereal c_b8 = 0.;
static doublereal c_b9 = 1.;
static integer c__1 = 1;

/* Subroutine */ int dgbbrd_(char *vect, integer *m, integer *n, integer *ncc, 
         integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal *
        d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt, 
        integer *ldpt, doublereal *c__, integer *ldc, doublereal *work, 
        integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1, 
            q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;

    /* Local variables */
    integer i__, j, l, j1, j2, kb;
    doublereal ra, rb, rc;
    integer kk, ml, mn, nr, mu;
    doublereal rs;
    integer kb1, ml0, mu0, klm, kun, nrt, klu1, inca;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *);
    extern logical lsame_(char *, char *);
    logical wantb, wantc;
    integer minmn;
    logical wantq;
    extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *), 
            dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *), xerbla_(char *, integer *), dlargv_(
            integer *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, integer *), dlartv_(integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *);
    logical wantpt;


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

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

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

/*  DGBBRD reduces a real general m-by-n band matrix A to upper */
/*  bidiagonal form B by an orthogonal transformation: Q' * A * P = B. */

/*  The routine computes B, and optionally forms Q or P', or computes */
/*  Q'*C for a given matrix C. */

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

/*  VECT    (input) CHARACTER*1 */
/*          Specifies whether or not the matrices Q and P' are to be */
/*          formed. */
/*          = 'N': do not form Q or P'; */
/*          = 'Q': form Q only; */
/*          = 'P': form P' only; */
/*          = 'B': form both. */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A.  M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix A.  N >= 0. */

/*  NCC     (input) INTEGER */
/*          The number of columns of the matrix C.  NCC >= 0. */

/*  KL      (input) INTEGER */
/*          The number of subdiagonals of the matrix A. KL >= 0. */

/*  KU      (input) INTEGER */
/*          The number of superdiagonals of the matrix A. KU >= 0. */

/*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          On entry, the m-by-n band matrix A, stored in rows 1 to */
/*          KL+KU+1. The j-th column of A is stored in the j-th column of */
/*          the array AB as follows: */
/*          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). */
/*          On exit, A is overwritten by values generated during the */
/*          reduction. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array A. LDAB >= KL+KU+1. */

/*  D       (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/*          The diagonal elements of the bidiagonal matrix B. */

/*  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
/*          The superdiagonal elements of the bidiagonal matrix B. */

/*  Q       (output) DOUBLE PRECISION array, dimension (LDQ,M) */
/*          If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. */
/*          If VECT = 'N' or 'P', the array Q is not referenced. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q. */
/*          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */

/*  PT      (output) DOUBLE PRECISION array, dimension (LDPT,N) */
/*          If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. */
/*          If VECT = 'N' or 'Q', the array PT is not referenced. */

/*  LDPT    (input) INTEGER */
/*          The leading dimension of the array PT. */
/*          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */

/*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,NCC) */
/*          On entry, an m-by-ncc matrix C. */
/*          On exit, C is overwritten by Q'*C. */
/*          C is not referenced if NCC = 0. */

/*  LDC     (input) INTEGER */
/*          The leading dimension of the array C. */
/*          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*max(M,N)) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --d__;
    --e;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    pt_dim1 = *ldpt;
    pt_offset = 1 + pt_dim1;
    pt -= pt_offset;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;
    --work;

    /* Function Body */
    wantb = lsame_(vect, "B");
    wantq = lsame_(vect, "Q") || wantb;
    wantpt = lsame_(vect, "P") || wantb;
    wantc = *ncc > 0;
    klu1 = *kl + *ku + 1;
    *info = 0;
    if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
        *info = -1;
    } else if (*m < 0) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*ncc < 0) {
        *info = -4;
    } else if (*kl < 0) {
        *info = -5;
    } else if (*ku < 0) {
        *info = -6;
    } else if (*ldab < klu1) {
        *info = -8;
    } else if (*ldq < 1 || wantq && *ldq < max(1,*m)) {
        *info = -12;
    } else if (*ldpt < 1 || wantpt && *ldpt < max(1,*n)) {
        *info = -14;
    } else if (*ldc < 1 || wantc && *ldc < max(1,*m)) {
        *info = -16;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGBBRD", &i__1);
        return 0;
    }

/*     Initialize Q and P' to the unit matrix, if needed */

    if (wantq) {
        dlaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq);
    }
    if (wantpt) {
        dlaset_("Full", n, n, &c_b8, &c_b9, &pt[pt_offset], ldpt);
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0) {
        return 0;
    }

    minmn = min(*m,*n);

    if (*kl + *ku > 1) {

/*        Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
/*        first to lower bidiagonal form and then transform to upper */
/*        bidiagonal */

        if (*ku > 0) {
            ml0 = 1;
            mu0 = 2;
        } else {
            ml0 = 2;
            mu0 = 1;
        }

/*        Wherever possible, plane rotations are generated and applied in */
/*        vector operations of length NR over the index set J1:J2:KLU1. */

/*        The sines of the plane rotations are stored in WORK(1:max(m,n)) */
/*        and the cosines in WORK(max(m,n)+1:2*max(m,n)). */

        mn = max(*m,*n);
/* Computing MIN */
        i__1 = *m - 1;
        klm = min(i__1,*kl);
/* Computing MIN */
        i__1 = *n - 1;
        kun = min(i__1,*ku);
        kb = klm + kun;
        kb1 = kb + 1;
        inca = kb1 * *ldab;
        nr = 0;
        j1 = klm + 2;
        j2 = 1 - kun;

        i__1 = minmn;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Reduce i-th column and i-th row of matrix to bidiagonal form */

            ml = klm + 1;
            mu = kun + 1;
            i__2 = kb;
            for (kk = 1; kk <= i__2; ++kk) {
                j1 += kb;
                j2 += kb;

/*              generate plane rotations to annihilate nonzero elements */
/*              which have been created below the band */

                if (nr > 0) {
                    dlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca, 
                            &work[j1], &kb1, &work[mn + j1], &kb1);
                }

/*              apply plane rotations from the left */

                i__3 = kb;
                for (l = 1; l <= i__3; ++l) {
                    if (j2 - klm + l - 1 > *n) {
                        nrt = nr - 1;
                    } else {
                        nrt = nr;
                    }
                    if (nrt > 0) {
                        dlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) * 
                                ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm 
                                + l - 1) * ab_dim1], &inca, &work[mn + j1], &
                                work[j1], &kb1);
                    }
/* L10: */
                }

                if (ml > ml0) {
                    if (ml <= *m - i__ + 1) {

/*                    generate plane rotation to annihilate a(i+ml-1,i) */
/*                    within the band, and apply rotation from the left */

                        dlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku + 
                                ml + i__ * ab_dim1], &work[mn + i__ + ml - 1], 
                                 &work[i__ + ml - 1], &ra);
                        ab[*ku + ml - 1 + i__ * ab_dim1] = ra;
                        if (i__ < *n) {
/* Computing MIN */
                            i__4 = *ku + ml - 2, i__5 = *n - i__;
                            i__3 = min(i__4,i__5);
                            i__6 = *ldab - 1;
                            i__7 = *ldab - 1;
                            drot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) * 
                                    ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__ 
                                    + 1) * ab_dim1], &i__7, &work[mn + i__ + 
                                    ml - 1], &work[i__ + ml - 1]);
                        }
                    }
                    ++nr;
                    j1 -= kb1;
                }

                if (wantq) {

/*                 accumulate product of plane rotations in Q */

                    i__3 = j2;
                    i__4 = kb1;
                    for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) 
                            {
                        drot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j * 
                                q_dim1 + 1], &c__1, &work[mn + j], &work[j]);
/* L20: */
                    }
                }

                if (wantc) {

/*                 apply plane rotations to C */

                    i__4 = j2;
                    i__3 = kb1;
                    for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) 
                            {
                        drot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
, ldc, &work[mn + j], &work[j]);
/* L30: */
                    }
                }

                if (j2 + kun > *n) {

/*                 adjust J2 to keep within the bounds of the matrix */

                    --nr;
                    j2 -= kb1;
                }

                i__3 = j2;
                i__4 = kb1;
                for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {

/*                 create nonzero element a(j-1,j+ku) above the band */
/*                 and store it in WORK(n+1:2*n) */

                    work[j + kun] = work[j] * ab[(j + kun) * ab_dim1 + 1];
                    ab[(j + kun) * ab_dim1 + 1] = work[mn + j] * ab[(j + kun) 
                            * ab_dim1 + 1];
/* L40: */
                }

/*              generate plane rotations to annihilate nonzero elements */
/*              which have been generated above the band */

                if (nr > 0) {
                    dlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
                            work[j1 + kun], &kb1, &work[mn + j1 + kun], &kb1);
                }

/*              apply plane rotations from the right */

                i__4 = kb;
                for (l = 1; l <= i__4; ++l) {
                    if (j2 + l - 1 > *m) {
                        nrt = nr - 1;
                    } else {
                        nrt = nr;
                    }
                    if (nrt > 0) {
                        dlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
                                inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
                                work[mn + j1 + kun], &work[j1 + kun], &kb1);
                    }
/* L50: */
                }

                if (ml == ml0 && mu > mu0) {
                    if (mu <= *n - i__ + 1) {

/*                    generate plane rotation to annihilate a(i,i+mu-1) */
/*                    within the band, and apply rotation from the right */

                        dlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1], 
                                &ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1], 
                                &work[mn + i__ + mu - 1], &work[i__ + mu - 1], 
                                 &ra);
                        ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1] = ra;
/* Computing MIN */
                        i__3 = *kl + mu - 2, i__5 = *m - i__;
                        i__4 = min(i__3,i__5);
                        drot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) * 
                                ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu 
                                - 1) * ab_dim1], &c__1, &work[mn + i__ + mu - 
                                1], &work[i__ + mu - 1]);
                    }
                    ++nr;
                    j1 -= kb1;
                }

                if (wantpt) {

/*                 accumulate product of plane rotations in P' */

                    i__4 = j2;
                    i__3 = kb1;
                    for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) 
                            {
                        drot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j + 
                                kun + pt_dim1], ldpt, &work[mn + j + kun], &
                                work[j + kun]);
/* L60: */
                    }
                }

                if (j2 + kb > *m) {

/*                 adjust J2 to keep within the bounds of the matrix */

                    --nr;
                    j2 -= kb1;
                }

                i__3 = j2;
                i__4 = kb1;
                for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {

/*                 create nonzero element a(j+kl+ku,j+ku-1) below the */
/*                 band and store it in WORK(1:n) */

                    work[j + kb] = work[j + kun] * ab[klu1 + (j + kun) * 
                            ab_dim1];
                    ab[klu1 + (j + kun) * ab_dim1] = work[mn + j + kun] * ab[
                            klu1 + (j + kun) * ab_dim1];
/* L70: */
                }

                if (ml > ml0) {
                    --ml;
                } else {
                    --mu;
                }
/* L80: */
            }
/* L90: */
        }
    }

    if (*ku == 0 && *kl > 0) {

/*        A has been reduced to lower bidiagonal form */

/*        Transform lower bidiagonal form to upper bidiagonal by applying */
/*        plane rotations from the left, storing diagonal elements in D */
/*        and off-diagonal elements in E */

/* Computing MIN */
        i__2 = *m - 1;
        i__1 = min(i__2,*n);
        for (i__ = 1; i__ <= i__1; ++i__) {
            dlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs, 
                    &ra);
            d__[i__] = ra;
            if (i__ < *n) {
                e[i__] = rs * ab[(i__ + 1) * ab_dim1 + 1];
                ab[(i__ + 1) * ab_dim1 + 1] = rc * ab[(i__ + 1) * ab_dim1 + 1]
                        ;
            }
            if (wantq) {
                drot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 + 
                        1], &c__1, &rc, &rs);
            }
            if (wantc) {
                drot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1], 
                        ldc, &rc, &rs);
            }
/* L100: */
        }
        if (*m <= *n) {
            d__[*m] = ab[*m * ab_dim1 + 1];
        }
    } else if (*ku > 0) {

/*        A has been reduced to upper bidiagonal form */

        if (*m < *n) {

/*           Annihilate a(m,m+1) by applying plane rotations from the */
/*           right, storing diagonal elements in D and off-diagonal */
/*           elements in E */

            rb = ab[*ku + (*m + 1) * ab_dim1];
            for (i__ = *m; i__ >= 1; --i__) {
                dlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
                d__[i__] = ra;
                if (i__ > 1) {
                    rb = -rs * ab[*ku + i__ * ab_dim1];
                    e[i__ - 1] = rc * ab[*ku + i__ * ab_dim1];
                }
                if (wantpt) {
                    drot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1], 
                            ldpt, &rc, &rs);
                }
/* L110: */
            }
        } else {

/*           Copy off-diagonal elements to E and diagonal elements to D */

            i__1 = minmn - 1;
            for (i__ = 1; i__ <= i__1; ++i__) {
                e[i__] = ab[*ku + (i__ + 1) * ab_dim1];
/* L120: */
            }
            i__1 = minmn;
            for (i__ = 1; i__ <= i__1; ++i__) {
                d__[i__] = ab[*ku + 1 + i__ * ab_dim1];
/* L130: */
            }
        }
    } else {

/*        A is diagonal. Set elements of E to zero and copy diagonal */
/*        elements to D. */

        i__1 = minmn - 1;
        for (i__ = 1; i__ <= i__1; ++i__) {
            e[i__] = 0.;
/* L140: */
        }
        i__1 = minmn;
        for (i__ = 1; i__ <= i__1; ++i__) {
            d__[i__] = ab[i__ * ab_dim1 + 1];
/* L150: */
        }
    }
    return 0;

/*     End of DGBBRD */

} /* dgbbrd_ */