Пример #1
0
/* Subroutine */ int zgerqf_(integer *m, integer *n, doublecomplex *a,
                             integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
                             integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;

    /* Local variables */
    integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
    extern /* Subroutine */ int zgerq2_(integer *, integer *, doublecomplex *,
                                        integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
                                            char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
                           integer *, integer *);
    extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
                                        integer *, integer *, integer *, doublecomplex *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, integer *,
                                        doublecomplex *, integer *);
    integer ldwork;
    extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, doublecomplex *,
                                        integer *);
    integer lwkopt;
    logical lquery;


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

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

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

    /*  ZGERQF computes an RQ factorization of a complex M-by-N matrix A: */
    /*  A = R * Q. */

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

    /*  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. */

    /*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
    /*          On entry, the M-by-N matrix A. */
    /*          On exit, */
    /*          if m <= n, the upper triangle of the subarray */
    /*          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; */
    /*          if m >= n, the elements on and above the (m-n)-th subdiagonal */
    /*          contain the M-by-N upper trapezoidal matrix R; */
    /*          the remaining elements, with the array TAU, represent the */
    /*          unitary matrix Q as a product of min(m,n) elementary */
    /*          reflectors (see Further Details). */

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

    /*  TAU     (output) COMPLEX*16 array, dimension (min(M,N)) */
    /*          The scalar factors of the elementary reflectors (see Further */
    /*          Details). */

    /*  WORK    (workspace/output) COMPLEX*16 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 >= max(1,M). */
    /*          For optimum performance LWORK >= M*NB, where NB is */
    /*          the optimal blocksize. */

    /*          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 */

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

    /*  The matrix Q is represented as a product of elementary reflectors */

    /*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n). */

    /*  Each H(i) has the form */

    /*     H(i) = I - tau * v * v' */

    /*  where tau is a complex scalar, and v is a complex vector with */
    /*  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on */
    /*  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). */

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

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

    /*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*m)) {
        *info = -4;
    }

    if (*info == 0) {
        k = min(*m,*n);
        if (k == 0) {
            lwkopt = 1;
        } else {
            nb = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1);
            lwkopt = *m * nb;
        }
        work[1].r = (doublereal) lwkopt, work[1].i = 0.;

        if (*lwork < max(1,*m) && ! lquery) {
            *info = -7;
        }
    }

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

    /*     Quick return if possible */

    if (k == 0) {
        return 0;
    }

    nbmin = 2;
    nx = 1;
    iws = *m;
    if (nb > 1 && nb < k) {

        /*        Determine when to cross over from blocked to unblocked code. */

        /* Computing MAX */
        i__1 = 0, i__2 = ilaenv_(&c__3, "ZGERQF", " ", m, n, &c_n1, &c_n1);
        nx = max(i__1,i__2);
        if (nx < k) {

            /*           Determine if workspace is large enough for blocked code. */

            ldwork = *m;
            iws = ldwork * nb;
            if (*lwork < iws) {

                /*              Not enough workspace to use optimal NB:  reduce NB and */
                /*              determine the minimum value of NB. */

                nb = *lwork / ldwork;
                /* Computing MAX */
                i__1 = 2, i__2 = ilaenv_(&c__2, "ZGERQF", " ", m, n, &c_n1, &
                                         c_n1);
                nbmin = max(i__1,i__2);
            }
        }
    }

    if (nb >= nbmin && nb < k && nx < k) {

        /*        Use blocked code initially. */
        /*        The last kk rows are handled by the block method. */

        ki = (k - nx - 1) / nb * nb;
        /* Computing MIN */
        i__1 = k, i__2 = ki + nb;
        kk = min(i__1,i__2);

        i__1 = k - kk + 1;
        i__2 = -nb;
        for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
                += i__2) {
            /* Computing MIN */
            i__3 = k - i__ + 1;
            ib = min(i__3,nb);

            /*           Compute the RQ factorization of the current block */
            /*           A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) */

            i__3 = *n - k + i__ + ib - 1;
            zgerq2_(&ib, &i__3, &a[*m - k + i__ + a_dim1], lda, &tau[i__], &
                    work[1], &iinfo);
            if (*m - k + i__ > 1) {

                /*              Form the triangular factor of the block reflector */
                /*              H = H(i+ib-1) . . . H(i+1) H(i) */

                i__3 = *n - k + i__ + ib - 1;
                zlarft_("Backward", "Rowwise", &i__3, &ib, &a[*m - k + i__ +
                        a_dim1], lda, &tau[i__], &work[1], &ldwork);

                /*              Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */

                i__3 = *m - k + i__ - 1;
                i__4 = *n - k + i__ + ib - 1;
                zlarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3,
                        &i__4, &ib, &a[*m - k + i__ + a_dim1], lda, &work[1],
                        &ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
            }
            /* L10: */
        }
        mu = *m - k + i__ + nb - 1;
        nu = *n - k + i__ + nb - 1;
    } else {
        mu = *m;
        nu = *n;
    }

    /*     Use unblocked code to factor the last or only block */

    if (mu > 0 && nu > 0) {
        zgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
    }

    work[1].r = (doublereal) iws, work[1].i = 0.;
    return 0;

    /*     End of ZGERQF */

} /* zgerqf_ */
Пример #2
0
/* Subroutine */ int zggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
	integer *p, integer *n, doublecomplex *a, integer *lda, doublecomplex 
	*b, integer *ldb, doublereal *tola, doublereal *tolb, integer *k, 
	integer *l, doublecomplex *u, integer *ldu, doublecomplex *v, integer 
	*ldv, doublecomplex *q, integer *ldq, integer *iwork, doublereal *
	rwork, doublecomplex *tau, doublecomplex *work, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    ZGGSVP computes unitary matrices U, V and Q such that   

                     N-K-L  K    L   
     U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;   
                  L ( 0     0   A23 )   
              M-K-L ( 0     0    0  )   

                     N-K-L  K    L   
            =     K ( 0    A12  A13 )  if M-K-L < 0;   
                M-K ( 0     0   A23 )   

                   N-K-L  K    L   
     V'*B*Q =   L ( 0     0   B13 )   
              P-L ( 0     0    0  )   

    where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular   
    upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,   
    otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective   
    numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the   
    conjugate transpose of Z.   

    This decomposition is the preprocessing step for computing the   
    Generalized Singular Value Decomposition (GSVD), see subroutine   
    ZGGSVD.   

    Arguments   
    =========   

    JOBU    (input) CHARACTER*1   
            = 'U':  Unitary matrix U is computed;   
            = 'N':  U is not computed.   

    JOBV    (input) CHARACTER*1   
            = 'V':  Unitary matrix V is computed;   
            = 'N':  V is not computed.   

    JOBQ    (input) CHARACTER*1   
            = 'Q':  Unitary matrix Q is computed;   
            = 'N':  Q is not computed.   

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

    P       (input) INTEGER   
            The number of rows of the matrix B.  P >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrices A and B.  N >= 0.   

    A       (input/output) COMPLEX*16 array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, A contains the triangular (or trapezoidal) matrix   
            described in the Purpose section.   

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

    B       (input/output) COMPLEX*16 array, dimension (LDB,N)   
            On entry, the P-by-N matrix B.   
            On exit, B contains the triangular matrix described in   
            the Purpose section.   

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

    TOLA    (input) DOUBLE PRECISION   
    TOLB    (input) DOUBLE PRECISION   
            TOLA and TOLB are the thresholds to determine the effective   
            numerical rank of matrix B and a subblock of A. Generally,   
            they are set to   
               TOLA = MAX(M,N)*norm(A)*MAZHEPS,   
               TOLB = MAX(P,N)*norm(B)*MAZHEPS.   
            The size of TOLA and TOLB may affect the size of backward   
            errors of the decomposition.   

    K       (output) INTEGER   
    L       (output) INTEGER   
            On exit, K and L specify the dimension of the subblocks   
            described in Purpose section.   
            K + L = effective numerical rank of (A',B')'.   

    U       (output) COMPLEX*16 array, dimension (LDU,M)   
            If JOBU = 'U', U contains the unitary matrix U.   
            If JOBU = 'N', U is not referenced.   

    LDU     (input) INTEGER   
            The leading dimension of the array U. LDU >= max(1,M) if   
            JOBU = 'U'; LDU >= 1 otherwise.   

    V       (output) COMPLEX*16 array, dimension (LDV,M)   
            If JOBV = 'V', V contains the unitary matrix V.   
            If JOBV = 'N', V is not referenced.   

    LDV     (input) INTEGER   
            The leading dimension of the array V. LDV >= max(1,P) if   
            JOBV = 'V'; LDV >= 1 otherwise.   

    Q       (output) COMPLEX*16 array, dimension (LDQ,N)   
            If JOBQ = 'Q', Q contains the unitary matrix Q.   
            If JOBQ = 'N', Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q. LDQ >= max(1,N) if   
            JOBQ = 'Q'; LDQ >= 1 otherwise.   

    IWORK   (workspace) INTEGER array, dimension (N)   

    RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)   

    TAU     (workspace) COMPLEX*16 array, dimension (N)   

    WORK    (workspace) COMPLEX*16 array, dimension (max(3*N,M,P))   

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

    Further Details   
    ===============   

    The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization   
    with column pivoting to detect the effective numerical rank of the   
    a matrix. It may be replaced by a better rank determination strategy.   

    =====================================================================   


       Test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b1 = {0.,0.};
    static doublecomplex c_b2 = {1.,0.};
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1, 
	    u_offset, v_dim1, v_offset, i__1, i__2, i__3;
    doublereal d__1, d__2;
    /* Builtin functions */
    double d_imag(doublecomplex *);
    /* Local variables */
    static integer i__, j;
    extern logical lsame_(char *, char *);
    static logical wantq, wantu, wantv;
    extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *), zgerq2_(
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     doublecomplex *, integer *), zung2r_(integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *), zunm2r_(char *, char *, integer *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     doublecomplex *, integer *, doublecomplex *, integer *), zunmr2_(char *, char *, integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *), xerbla_(
	    char *, integer *), zgeqpf_(integer *, integer *, 
	    doublecomplex *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublereal *, integer *), zlacpy_(char *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     integer *);
    static logical forwrd;
    extern /* Subroutine */ int zlaset_(char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlapmt_(logical *, integer *, integer *, doublecomplex *,
	     integer *, integer *);
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1
#define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)]
#define v_subscr(a_1,a_2) (a_2)*v_dim1 + a_1
#define v_ref(a_1,a_2) v[v_subscr(a_1,a_2)]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1 * 1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --iwork;
    --rwork;
    --tau;
    --work;

    /* Function Body */
    wantu = lsame_(jobu, "U");
    wantv = lsame_(jobv, "V");
    wantq = lsame_(jobq, "Q");
    forwrd = TRUE_;

    *info = 0;
    if (! (wantu || lsame_(jobu, "N"))) {
	*info = -1;
    } else if (! (wantv || lsame_(jobv, "N"))) {
	*info = -2;
    } else if (! (wantq || lsame_(jobq, "N"))) {
	*info = -3;
    } else if (*m < 0) {
	*info = -4;
    } else if (*p < 0) {
	*info = -5;
    } else if (*n < 0) {
	*info = -6;
    } else if (*lda < max(1,*m)) {
	*info = -8;
    } else if (*ldb < max(1,*p)) {
	*info = -10;
    } else if (*ldu < 1 || wantu && *ldu < *m) {
	*info = -16;
    } else if (*ldv < 1 || wantv && *ldv < *p) {
	*info = -18;
    } else if (*ldq < 1 || wantq && *ldq < *n) {
	*info = -20;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGGSVP", &i__1);
	return 0;
    }

/*     QR with column pivoting of B: B*P = V*( S11 S12 )   
                                             (  0   0  ) */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	iwork[i__] = 0;
/* L10: */
    }
    zgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], &rwork[1], 
	    info);

/*     Update A := A*P */

    zlapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);

/*     Determine the effective rank of matrix B. */

    *l = 0;
    i__1 = min(*p,*n);
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = b_subscr(i__, i__);
	if ((d__1 = b[i__2].r, abs(d__1)) + (d__2 = d_imag(&b_ref(i__, i__)), 
		abs(d__2)) > *tolb) {
	    ++(*l);
	}
/* L20: */
    }

    if (wantv) {

/*        Copy the details of V, and form V. */

	zlaset_("Full", p, p, &c_b1, &c_b1, &v[v_offset], ldv);
	if (*p > 1) {
	    i__1 = *p - 1;
	    zlacpy_("Lower", &i__1, n, &b_ref(2, 1), ldb, &v_ref(2, 1), ldv);
	}
	i__1 = min(*p,*n);
	zung2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
    }

/*     Clean up B */

    i__1 = *l - 1;
    for (j = 1; j <= i__1; ++j) {
	i__2 = *l;
	for (i__ = j + 1; i__ <= i__2; ++i__) {
	    i__3 = b_subscr(i__, j);
	    b[i__3].r = 0., b[i__3].i = 0.;
/* L30: */
	}
/* L40: */
    }
    if (*p > *l) {
	i__1 = *p - *l;
	zlaset_("Full", &i__1, n, &c_b1, &c_b1, &b_ref(*l + 1, 1), ldb);
    }

    if (wantq) {

/*        Set Q = I and Update Q := Q*P */

	zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
	zlapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
    }

    if (*p >= *l && *n != *l) {

/*        RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z */

	zgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);

/*        Update A := A*Z' */

	zunmr2_("Right", "Conjugate transpose", m, n, l, &b[b_offset], ldb, &
		tau[1], &a[a_offset], lda, &work[1], info);
	if (wantq) {

/*           Update Q := Q*Z' */

	    zunmr2_("Right", "Conjugate transpose", n, n, l, &b[b_offset], 
		    ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
	}

/*        Clean up B */

	i__1 = *n - *l;
	zlaset_("Full", l, &i__1, &c_b1, &c_b1, &b[b_offset], ldb);
	i__1 = *n;
	for (j = *n - *l + 1; j <= i__1; ++j) {
	    i__2 = *l;
	    for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
		i__3 = b_subscr(i__, j);
		b[i__3].r = 0., b[i__3].i = 0.;
/* L50: */
	    }
/* L60: */
	}

    }

/*     Let              N-L     L   
                  A = ( A11    A12 ) M,   

       then the following does the complete QR decomposition of A11:   

                A11 = U*(  0  T12 )*P1'   
                        (  0   0  ) */

    i__1 = *n - *l;
    for (i__ = 1; i__ <= i__1; ++i__) {
	iwork[i__] = 0;
/* L70: */
    }
    i__1 = *n - *l;
    zgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], &rwork[
	    1], info);

/*     Determine the effective rank of A11 */

    *k = 0;
/* Computing MIN */
    i__2 = *m, i__3 = *n - *l;
    i__1 = min(i__2,i__3);
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = a_subscr(i__, i__);
	if ((d__1 = a[i__2].r, abs(d__1)) + (d__2 = d_imag(&a_ref(i__, i__)), 
		abs(d__2)) > *tola) {
	    ++(*k);
	}
/* L80: */
    }

/*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )   

   Computing MIN */
    i__2 = *m, i__3 = *n - *l;
    i__1 = min(i__2,i__3);
    zunm2r_("Left", "Conjugate transpose", m, l, &i__1, &a[a_offset], lda, &
	    tau[1], &a_ref(1, *n - *l + 1), lda, &work[1], info);

    if (wantu) {

/*        Copy the details of U, and form U */

	zlaset_("Full", m, m, &c_b1, &c_b1, &u[u_offset], ldu);
	if (*m > 1) {
	    i__1 = *m - 1;
	    i__2 = *n - *l;
	    zlacpy_("Lower", &i__1, &i__2, &a_ref(2, 1), lda, &u_ref(2, 1), 
		    ldu);
	}
/* Computing MIN */
	i__2 = *m, i__3 = *n - *l;
	i__1 = min(i__2,i__3);
	zung2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
    }

    if (wantq) {

/*        Update Q( 1:N, 1:N-L )  = Q( 1:N, 1:N-L )*P1 */

	i__1 = *n - *l;
	zlapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
    }

/*     Clean up A: set the strictly lower triangular part of   
       A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */

    i__1 = *k - 1;
    for (j = 1; j <= i__1; ++j) {
	i__2 = *k;
	for (i__ = j + 1; i__ <= i__2; ++i__) {
	    i__3 = a_subscr(i__, j);
	    a[i__3].r = 0., a[i__3].i = 0.;
/* L90: */
	}
/* L100: */
    }
    if (*m > *k) {
	i__1 = *m - *k;
	i__2 = *n - *l;
	zlaset_("Full", &i__1, &i__2, &c_b1, &c_b1, &a_ref(*k + 1, 1), lda);
    }

    if (*n - *l > *k) {

/*        RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */

	i__1 = *n - *l;
	zgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);

	if (wantq) {

/*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */

	    i__1 = *n - *l;
	    zunmr2_("Right", "Conjugate transpose", n, &i__1, k, &a[a_offset],
		     lda, &tau[1], &q[q_offset], ldq, &work[1], info);
	}

/*        Clean up A */

	i__1 = *n - *l - *k;
	zlaset_("Full", k, &i__1, &c_b1, &c_b1, &a[a_offset], lda);
	i__1 = *n - *l;
	for (j = *n - *l - *k + 1; j <= i__1; ++j) {
	    i__2 = *k;
	    for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
		i__3 = a_subscr(i__, j);
		a[i__3].r = 0., a[i__3].i = 0.;
/* L110: */
	    }
/* L120: */
	}

    }

    if (*m > *k) {

/*        QR factorization of A( K+1:M,N-L+1:N ) */

	i__1 = *m - *k;
	zgeqr2_(&i__1, l, &a_ref(*k + 1, *n - *l + 1), lda, &tau[1], &work[1],
		 info);

	if (wantu) {

/*           Update U(:,K+1:M) := U(:,K+1:M)*U1 */

	    i__1 = *m - *k;
/* Computing MIN */
	    i__3 = *m - *k;
	    i__2 = min(i__3,*l);
	    zunm2r_("Right", "No transpose", m, &i__1, &i__2, &a_ref(*k + 1, *
		    n - *l + 1), lda, &tau[1], &u_ref(1, *k + 1), ldu, &work[
		    1], info);
	}

/*        Clean up */

	i__1 = *n;
	for (j = *n - *l + 1; j <= i__1; ++j) {
	    i__2 = *m;
	    for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
		i__3 = a_subscr(i__, j);
		a[i__3].r = 0., a[i__3].i = 0.;
/* L130: */
	    }
/* L140: */
	}

    }

    return 0;

/*     End of ZGGSVP */

} /* zggsvp_ */