コード例 #1
0
ファイル: sggsvp.c プロジェクト: dacap/loseface
/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
	integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, 
	real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu, 
	 real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
	tau, real *work, integer *info)
{
    /* 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;
    real r__1;

    /* Local variables */
    integer i__, j;
    extern logical lsame_(char *, char *);
    logical wantq, wantu, wantv;
    extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *), sgerq2_(integer *, integer *, real 
	    *, integer *, real *, real *, integer *), sorg2r_(integer *, 
	    integer *, integer *, real *, integer *, real *, real *, integer *
), sorm2r_(char *, char *, integer *, integer *, integer *, real *
, integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *, 
	     real *, integer *, real *, real *, integer *, real *, integer *), xerbla_(char *, integer *), sgeqpf_(
	    integer *, integer *, real *, integer *, integer *, real *, real *
, integer *), slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), slaset_(char *, integer *, 
	    integer *, real *, real *, real *, integer *), slapmt_(
	    logical *, integer *, integer *, real *, integer *, integer *);
    logical forwrd;


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SGGSVP computes orthogonal 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 */
/*  transpose of Z. */

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

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

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

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

/*  JOBQ    (input) CHARACTER*1 */
/*          = 'Q':  Orthogonal 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) REAL 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) REAL 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) REAL */
/*  TOLB    (input) REAL */
/*          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)*MACHEPS, */
/*             TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/*          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. */
/*          K + L = effective numerical rank of (A',B')'. */

/*  U       (output) REAL array, dimension (LDU,M) */
/*          If JOBU = 'U', U contains the orthogonal 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) REAL array, dimension (LDV,M) */
/*          If JOBV = 'V', V contains the orthogonal 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) REAL array, dimension (LDQ,N) */
/*          If JOBQ = 'Q', Q contains the orthogonal 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) */

/*  TAU     (workspace) REAL array, dimension (N) */

/*  WORK    (workspace) REAL 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 SGEQPF 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. */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --iwork;
    --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_("SGGSVP", &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: */
    }
    sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);

/*     Update A := A*P */

    slapmt_(&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__) {
	if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) > *tolb) {
	    ++(*l);
	}
/* L20: */
    }

    if (wantv) {

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

	slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv);
	if (*p > 1) {
	    i__1 = *p - 1;
	    slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2], 
		    ldv);
	}
	i__1 = min(*p,*n);
	sorg2r_(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__) {
	    b[i__ + j * b_dim1] = 0.f;
/* L30: */
	}
/* L40: */
    }
    if (*p > *l) {
	i__1 = *p - *l;
	slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb);
    }

    if (wantq) {

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

	slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq);
	slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
    }

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

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

	sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);

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

	sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
		a_offset], lda, &work[1], info);

	if (wantq) {

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

	    sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1], 
		     &q[q_offset], ldq, &work[1], info);
	}

/*        Clean up B */

	i__1 = *n - *l;
	slaset_("Full", l, &i__1, &c_b12, &c_b12, &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__) {
		b[i__ + j * b_dim1] = 0.f;
/* 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;
    sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[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__) {
	if ((r__1 = a[i__ + i__ * a_dim1], dabs(r__1)) > *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);
    sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
	    *n - *l + 1) * a_dim1 + 1], lda, &work[1], info);

    if (wantu) {

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

	slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu);
	if (*m > 1) {
	    i__1 = *m - 1;
	    i__2 = *n - *l;
	    slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
, ldu);
	}
/* Computing MIN */
	i__2 = *m, i__3 = *n - *l;
	i__1 = min(i__2,i__3);
	sorg2r_(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;
	slapmt_(&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__) {
	    a[i__ + j * a_dim1] = 0.f;
/* L90: */
	}
/* L100: */
    }
    if (*m > *k) {
	i__1 = *m - *k;
	i__2 = *n - *l;
	slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1], 
		lda);
    }

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

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

	i__1 = *n - *l;
	sgerq2_(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;
	    sormr2_("Right", "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;
	slaset_("Full", k, &i__1, &c_b12, &c_b12, &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__) {
		a[i__ + j * a_dim1] = 0.f;
/* L110: */
	    }
/* L120: */
	}

    }

    if (*m > *k) {

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

	i__1 = *m - *k;
	sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], 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);
	    sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n 
		    - *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 + 
		    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__) {
		a[i__ + j * a_dim1] = 0.f;
/* L130: */
	    }
/* L140: */
	}

    }

    return 0;

/*     End of SGGSVP */

} /* sggsvp_ */
コード例 #2
0
ファイル: sggsvp.c プロジェクト: axel971/itk
/*<    >*/
/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
        integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, 
        real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
         real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
        tau, real *work, integer *info, ftnlen jobu_len, ftnlen jobv_len, 
        ftnlen jobq_len)
{
    /* 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;
    real r__1;

    /* Local variables */
    integer i__, j;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    logical wantq, wantu, wantv;
    extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer 
            *, real *, real *, integer *), sgerq2_(integer *, integer *, real 
            *, integer *, real *, real *, integer *), sorg2r_(integer *, 
            integer *, integer *, real *, integer *, real *, real *, integer *
            ), sorm2r_(char *, char *, integer *, integer *, integer *, real *
            , integer *, real *, real *, integer *, real *, integer *, ftnlen,
             ftnlen), sormr2_(char *, char *, integer *, integer *, integer *,
             real *, integer *, real *, real *, integer *, real *, integer *, 
            ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen), sgeqpf_(
            integer *, integer *, real *, integer *, integer *, real *, real *
            , integer *), slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *, ftnlen), slaset_(char *, integer *, 
            integer *, real *, real *, real *, integer *, ftnlen), slapmt_(
            logical *, integer *, integer *, real *, integer *, integer *);
    logical forwrd;
    (void)jobu_len;
    (void)jobv_len;
    (void)jobq_len;

/*  -- 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 */

/*     .. Scalar Arguments .. */
/*<       CHARACTER          JOBQ, JOBU, JOBV >*/
/*<       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P >*/
/*<       REAL               TOLA, TOLB >*/
/*     .. */
/*     .. Array Arguments .. */
/*<       INTEGER            IWORK( * ) >*/
/*<    >*/
/*     .. */

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

/*  SGGSVP computes orthogonal 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 */
/*  transpose of Z. */

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

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

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

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

/*  JOBQ    (input) CHARACTER*1 */
/*          = 'Q':  Orthogonal 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) REAL 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) REAL 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) REAL */
/*  TOLB    (input) REAL */
/*          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)*MACHEPS, */
/*             TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/*          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. */
/*          K + L = effective numerical rank of (A',B')'. */

/*  U       (output) REAL array, dimension (LDU,M) */
/*          If JOBU = 'U', U contains the orthogonal 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) REAL array, dimension (LDV,M) */
/*          If JOBV = 'V', V contains the orthogonal 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) REAL array, dimension (LDQ,N) */
/*          If JOBQ = 'Q', Q contains the orthogonal 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) */

/*  TAU     (workspace) REAL array, dimension (N) */

/*  WORK    (workspace) REAL 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 SGEQPF 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. */

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

/*     .. Parameters .. */
/*<       REAL               ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<       LOGICAL            FORWRD, WANTQ, WANTU, WANTV >*/
/*<       INTEGER            I, J >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       EXTERNAL           LSAME >*/
/*     .. */
/*     .. External Subroutines .. */
/*<    >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          ABS, MAX, MIN >*/
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

/*<       WANTU = LSAME( JOBU, 'U' ) >*/
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --iwork;
    --tau;
    --work;

    /* Function Body */
    wantu = lsame_(jobu, "U", (ftnlen)1, (ftnlen)1);
/*<       WANTV = LSAME( JOBV, 'V' ) >*/
    wantv = lsame_(jobv, "V", (ftnlen)1, (ftnlen)1);
/*<       WANTQ = LSAME( JOBQ, 'Q' ) >*/
    wantq = lsame_(jobq, "Q", (ftnlen)1, (ftnlen)1);
/*<       FORWRD = .TRUE. >*/
    forwrd = TRUE_;

/*<       INFO = 0 >*/
    *info = 0;
/*<       IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN >*/
    if (! (wantu || lsame_(jobu, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -1 >*/
        *info = -1;
/*<       ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN >*/
    } else if (! (wantv || lsame_(jobv, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -2 >*/
        *info = -2;
/*<       ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN >*/
    } else if (! (wantq || lsame_(jobq, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -3 >*/
        *info = -3;
/*<       ELSE IF( M.LT.0 ) THEN >*/
    } else if (*m < 0) {
/*<          INFO = -4 >*/
        *info = -4;
/*<       ELSE IF( P.LT.0 ) THEN >*/
    } else if (*p < 0) {
/*<          INFO = -5 >*/
        *info = -5;
/*<       ELSE IF( N.LT.0 ) THEN >*/
    } else if (*n < 0) {
/*<          INFO = -6 >*/
        *info = -6;
/*<       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
    } else if (*lda < max(1,*m)) {
/*<          INFO = -8 >*/
        *info = -8;
/*<       ELSE IF( LDB.LT.MAX( 1, P ) ) THEN >*/
    } else if (*ldb < max(1,*p)) {
/*<          INFO = -10 >*/
        *info = -10;
/*<       ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN >*/
    } else if (*ldu < 1 || (wantu && *ldu < *m)) {
/*<          INFO = -16 >*/
        *info = -16;
/*<       ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN >*/
    } else if (*ldv < 1 || (wantv && *ldv < *p)) {
/*<          INFO = -18 >*/
        *info = -18;
/*<       ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN >*/
    } else if (*ldq < 1 || (wantq && *ldq < *n)) {
/*<          INFO = -20 >*/
        *info = -20;
/*<       END IF >*/
    }
/*<       IF( INFO.NE.0 ) THEN >*/
    if (*info != 0) {
/*<          CALL XERBLA( 'SGGSVP', -INFO ) >*/
        i__1 = -(*info);
        xerbla_("SGGSVP", &i__1, (ftnlen)6);
/*<          RETURN >*/
        return 0;
/*<       END IF >*/
    }

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

/*<       DO 10 I = 1, N >*/
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
/*<          IWORK( I ) = 0 >*/
        iwork[i__] = 0;
/*<    10 CONTINUE >*/
/* L10: */
    }
/*<       CALL SGEQPF( P, N, B, LDB, IWORK, TAU, WORK, INFO ) >*/
    sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);

/*     Update A := A*P */

/*<       CALL SLAPMT( FORWRD, M, N, A, LDA, IWORK ) >*/
    slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);

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

/*<       L = 0 >*/
    *l = 0;
/*<       DO 20 I = 1, MIN( P, N ) >*/
    i__1 = min(*p,*n);
    for (i__ = 1; i__ <= i__1; ++i__) {
/*<    >*/
        if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) > *tolb) {
            ++(*l);
        }
/*<    20 CONTINUE >*/
/* L20: */
    }

/*<       IF( WANTV ) THEN >*/
    if (wantv) {

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

/*<          CALL SLASET( 'Full', P, P, ZERO, ZERO, V, LDV ) >*/
        slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv, (ftnlen)4);
/*<    >*/
        if (*p > 1) {
            i__1 = *p - 1;
            slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2], 
                    ldv, (ftnlen)5);
        }
/*<          CALL SORG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO ) >*/
        i__1 = min(*p,*n);
        sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
/*<       END IF >*/
    }

/*     Clean up B */

/*<       DO 40 J = 1, L - 1 >*/
    i__1 = *l - 1;
    for (j = 1; j <= i__1; ++j) {
/*<          DO 30 I = J + 1, L >*/
        i__2 = *l;
        for (i__ = j + 1; i__ <= i__2; ++i__) {
/*<             B( I, J ) = ZERO >*/
            b[i__ + j * b_dim1] = (float)0.;
/*<    30    CONTINUE >*/
/* L30: */
        }
/*<    40 CONTINUE >*/
/* L40: */
    }
/*<    >*/
    if (*p > *l) {
        i__1 = *p - *l;
        slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb, (
                ftnlen)4);
    }

/*<       IF( WANTQ ) THEN >*/
    if (wantq) {

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

/*<          CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDQ ) >*/
        slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq, (ftnlen)4);
/*<          CALL SLAPMT( FORWRD, N, N, Q, LDQ, IWORK ) >*/
        slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
/*<       END IF >*/
    }

/*<       IF( P.GE.L .AND. N.NE.L ) THEN >*/
    if (*p >= *l && *n != *l) {

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

/*<          CALL SGERQ2( L, N, B, LDB, TAU, WORK, INFO ) >*/
        sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);

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

/*<    >*/
        sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
                a_offset], lda, &work[1], info, (ftnlen)5, (ftnlen)9);

/*<          IF( WANTQ ) THEN >*/
        if (wantq) {

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

/*<    >*/
            sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1],
                     &q[q_offset], ldq, &work[1], info, (ftnlen)5, (ftnlen)9);
/*<          END IF >*/
        }

/*        Clean up B */

/*<          CALL SLASET( 'Full', L, N-L, ZERO, ZERO, B, LDB ) >*/
        i__1 = *n - *l;
        slaset_("Full", l, &i__1, &c_b12, &c_b12, &b[b_offset], ldb, (ftnlen)
                4);
/*<          DO 60 J = N - L + 1, N >*/
        i__1 = *n;
        for (j = *n - *l + 1; j <= i__1; ++j) {
/*<             DO 50 I = J - N + L + 1, L >*/
            i__2 = *l;
            for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
/*<                B( I, J ) = ZERO >*/
                b[i__ + j * b_dim1] = (float)0.;
/*<    50       CONTINUE >*/
/* L50: */
            }
/*<    60    CONTINUE >*/
/* L60: */
        }

/*<       END IF >*/
    }

/*     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  ) */

/*<       DO 70 I = 1, N - L >*/
    i__1 = *n - *l;
    for (i__ = 1; i__ <= i__1; ++i__) {
/*<          IWORK( I ) = 0 >*/
        iwork[i__] = 0;
/*<    70 CONTINUE >*/
/* L70: */
    }
/*<       CALL SGEQPF( M, N-L, A, LDA, IWORK, TAU, WORK, INFO ) >*/
    i__1 = *n - *l;
    sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);

/*     Determine the effective rank of A11 */

/*<       K = 0 >*/
    *k = 0;
/*<       DO 80 I = 1, MIN( M, N-L ) >*/
/* Computing MIN */
    i__2 = *m, i__3 = *n - *l;
    i__1 = min(i__2,i__3);
    for (i__ = 1; i__ <= i__1; ++i__) {
/*<    >*/
        if ((r__1 = a[i__ + i__ * a_dim1], dabs(r__1)) > *tola) {
            ++(*k);
        }
/*<    80 CONTINUE >*/
/* 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);
    sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
            *n - *l + 1) * a_dim1 + 1], lda, &work[1], info, (ftnlen)4, (
            ftnlen)9);

/*<       IF( WANTU ) THEN >*/
    if (wantu) {

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

/*<          CALL SLASET( 'Full', M, M, ZERO, ZERO, U, LDU ) >*/
        slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu, (ftnlen)4);
/*<    >*/
        if (*m > 1) {
            i__1 = *m - 1;
            i__2 = *n - *l;
            slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
                    , ldu, (ftnlen)5);
        }
/*<          CALL SORG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO ) >*/
/* Computing MIN */
        i__2 = *m, i__3 = *n - *l;
        i__1 = min(i__2,i__3);
        sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
/*<       END IF >*/
    }

/*<       IF( WANTQ ) THEN >*/
    if (wantq) {

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

/*<          CALL SLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK ) >*/
        i__1 = *n - *l;
        slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
/*<       END IF >*/
    }

/*     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. */

/*<       DO 100 J = 1, K - 1 >*/
    i__1 = *k - 1;
    for (j = 1; j <= i__1; ++j) {
/*<          DO 90 I = J + 1, K >*/
        i__2 = *k;
        for (i__ = j + 1; i__ <= i__2; ++i__) {
/*<             A( I, J ) = ZERO >*/
            a[i__ + j * a_dim1] = (float)0.;
/*<    90    CONTINUE >*/
/* L90: */
        }
/*<   100 CONTINUE >*/
/* L100: */
    }
/*<    >*/
    if (*m > *k) {
        i__1 = *m - *k;
        i__2 = *n - *l;
        slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1], 
                lda, (ftnlen)4);
    }

/*<       IF( N-L.GT.K ) THEN >*/
    if (*n - *l > *k) {

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

/*<          CALL SGERQ2( K, N-L, A, LDA, TAU, WORK, INFO ) >*/
        i__1 = *n - *l;
        sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);

/*<          IF( WANTQ ) THEN >*/
        if (wantq) {

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

/*<    >*/
            i__1 = *n - *l;
            sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, &
                    tau[1], &q[q_offset], ldq, &work[1], info, (ftnlen)5, (
                    ftnlen)9);
/*<          END IF >*/
        }

/*        Clean up A */

/*<          CALL SLASET( 'Full', K, N-L-K, ZERO, ZERO, A, LDA ) >*/
        i__1 = *n - *l - *k;
        slaset_("Full", k, &i__1, &c_b12, &c_b12, &a[a_offset], lda, (ftnlen)
                4);
/*<          DO 120 J = N - L - K + 1, N - L >*/
        i__1 = *n - *l;
        for (j = *n - *l - *k + 1; j <= i__1; ++j) {
/*<             DO 110 I = J - N + L + K + 1, K >*/
            i__2 = *k;
            for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
/*<                A( I, J ) = ZERO >*/
                a[i__ + j * a_dim1] = (float)0.;
/*<   110       CONTINUE >*/
/* L110: */
            }
/*<   120    CONTINUE >*/
/* L120: */
        }

/*<       END IF >*/
    }

/*<       IF( M.GT.K ) THEN >*/
    if (*m > *k) {

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

/*<          CALL SGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO ) >*/
        i__1 = *m - *k;
        sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
                work[1], info);

/*<          IF( WANTU ) THEN >*/
        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);
            sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n 
                    - *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 + 
                    1], ldu, &work[1], info, (ftnlen)5, (ftnlen)12);
/*<          END IF >*/
        }

/*        Clean up */

/*<          DO 140 J = N - L + 1, N >*/
        i__1 = *n;
        for (j = *n - *l + 1; j <= i__1; ++j) {
/*<             DO 130 I = J - N + K + L + 1, M >*/
            i__2 = *m;
            for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
/*<                A( I, J ) = ZERO >*/
                a[i__ + j * a_dim1] = (float)0.;
/*<   130       CONTINUE >*/
/* L130: */
            }
/*<   140    CONTINUE >*/
/* L140: */
        }

/*<       END IF >*/
    }

/*<       RETURN >*/
    return 0;

/*     End of SGGSVP */

/*<       END >*/
} /* sggsvp_ */
コード例 #3
0
ファイル: sorcsd2by1.c プロジェクト: flame/libflame
/* Subroutine */
int sorcsd2by1_(char *jobu1, char *jobu2, char *jobv1t, integer *m, integer *p, integer *q, real *x11, integer *ldx11, real * x21, integer *ldx21, real *theta, real *u1, integer *ldu1, real *u2, integer *ldu2, real *v1t, integer *ldv1t, real *work, integer *lwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset, x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9;
    /* Local variables */
    integer lworkmin, lworkopt, i__, j, r__, childinfo, lorglqmin, lorgqrmin, lorglqopt, lorgqropt, ib11d, ib11e, ib12d, ib12e, ib21d, ib21e, ib22d, ib22e, iphi;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int scopy_(integer *, real *, integer *, real *, integer *);
    integer itaup1, itaup2, itauq1;
    logical wantu1, wantu2;
    integer ibbcsd, lbbcsd;
    extern /* Subroutine */
    int sbbcsd_();
    integer iorbdb, lorbdb;
    extern /* Subroutine */
    int xerbla_(char *, integer *), slacpy_( char *, integer *, integer *, real *, integer *, real *, integer * );
    integer iorglq;
    extern /* Subroutine */
    int slapmr_(logical *, integer *, integer *, real *, integer *, integer *);
    integer lorglq;
    extern /* Subroutine */
    int slapmt_(logical *, integer *, integer *, real *, integer *, integer *);
    integer iorgqr, lorgqr;
    extern int /* Subroutine */
      sorglq_fla(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *),
      sorgqr_fla(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
    logical lquery;
    extern /* Subroutine */
    int sorbdb1_(), sorbdb2_(), sorbdb3_(), sorbdb4_() ;
    logical wantv1t;
    /* -- LAPACK computational routine (version 3.5.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* July 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. Intrinsic Function .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test input arguments */
    /* Parameter adjustments */
    x11_dim1 = *ldx11;
    x11_offset = 1 + x11_dim1;
    x11 -= x11_offset;
    x21_dim1 = *ldx21;
    x21_offset = 1 + x21_dim1;
    x21 -= x21_offset;
    --theta;
    u1_dim1 = *ldu1;
    u1_offset = 1 + u1_dim1;
    u1 -= u1_offset;
    u2_dim1 = *ldu2;
    u2_offset = 1 + u2_dim1;
    u2 -= u2_offset;
    v1t_dim1 = *ldv1t;
    v1t_offset = 1 + v1t_dim1;
    v1t -= v1t_offset;
    --work;
    --iwork;
    /* Function Body */
    *info = 0;
    wantu1 = lsame_(jobu1, "Y");
    wantu2 = lsame_(jobu2, "Y");
    wantv1t = lsame_(jobv1t, "Y");
    lquery = *lwork == -1;
    if (*m < 0)
    {
        *info = -4;
    }
    else if (*p < 0 || *p > *m)
    {
        *info = -5;
    }
    else if (*q < 0 || *q > *m)
    {
        *info = -6;
    }
    else if (*ldx11 < max(1,*p))
    {
        *info = -8;
    }
    else /* if(complicated condition) */
    {
        /* Computing MAX */
        i__1 = 1;
        i__2 = *m - *p; // , expr subst
        if (*ldx21 < max(i__1,i__2))
        {
            *info = -10;
        }
        else if (wantu1 && *ldu1 < *p)
        {
            *info = -13;
        }
        else if (wantu2 && *ldu2 < *m - *p)
        {
            *info = -15;
        }
        else if (wantv1t && *ldv1t < *q)
        {
            *info = -17;
        }
    }
    /* Computing MIN */
    i__1 = *p, i__2 = *m - *p, i__1 = min(i__1,i__2);
    i__1 = min(i__1,*q);
    i__2 = *m - *q; // ; expr subst
    r__ = min(i__1,i__2);
    /* Compute workspace */
    /* WORK layout: */
    /* |-------------------------------------------------------| */
    /* | LWORKOPT (1) | */
    /* |-------------------------------------------------------| */
    /* | PHI (MAX(1,R-1)) | */
    /* |-------------------------------------------------------| */
    /* | TAUP1 (MAX(1,P)) | B11D (R) | */
    /* | TAUP2 (MAX(1,M-P)) | B11E (R-1) | */
    /* | TAUQ1 (MAX(1,Q)) | B12D (R) | */
    /* |-----------------------------------------| B12E (R-1) | */
    /* | SORBDB WORK | SORGQR WORK | SORGLQ WORK | B21D (R) | */
    /* | | | | B21E (R-1) | */
    /* | | | | B22D (R) | */
    /* | | | | B22E (R-1) | */
    /* | | | | SBBCSD WORK | */
    /* |-------------------------------------------------------| */
    if (*info == 0)
    {
        iphi = 2;
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        ib11d = iphi + max(i__1,i__2);
        ib11e = ib11d + max(1,r__);
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        ib12d = ib11e + max(i__1,i__2);
        ib12e = ib12d + max(1,r__);
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        ib21d = ib12e + max(i__1,i__2);
        ib21e = ib21d + max(1,r__);
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        ib22d = ib21e + max(i__1,i__2);
        ib22e = ib22d + max(1,r__);
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        ibbcsd = ib22e + max(i__1,i__2);
        /* Computing MAX */
        i__1 = 1;
        i__2 = r__ - 1; // , expr subst
        itaup1 = iphi + max(i__1,i__2);
        itaup2 = itaup1 + max(1,*p);
        /* Computing MAX */
        i__1 = 1;
        i__2 = *m - *p; // , expr subst
        itauq1 = itaup2 + max(i__1,i__2);
        iorbdb = itauq1 + max(1,*q);
        iorgqr = itauq1 + max(1,*q);
        iorglq = itauq1 + max(1,*q);
        if (r__ == *q)
        {
            sorbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &theta[1], &c__0, &c__0, &c__0, &c__0, &work[1], & c_n1, &childinfo);
            lorbdb = (integer) work[1];
            if (*p >= *m - *p)
            {
                sorgqr_fla(p, p, q, &u1[u1_offset], ldu1, (real*)&c__0, &work[1], &c_n1, &childinfo);
                lorgqrmin = max(1,*p);
                lorgqropt = (integer) work[1];
            }
            else
            {
                i__1 = *m - *p;
                i__2 = *m - *p;
                sorgqr_fla(&i__1, &i__2, q, &u2[u2_offset], ldu2, (real*)&c__0, &work[1] , &c_n1, &childinfo);
                /* Computing MAX */
                i__1 = 1;
                i__2 = *m - *p; // , expr subst
                lorgqrmin = max(i__1,i__2);
                lorgqropt = (integer) work[1];
            }
            /* Computing MAX */
            i__2 = 0;
            i__3 = *q - 1; // , expr subst
            i__1 = max(i__2,i__3);
            /* Computing MAX */
            i__5 = 0;
            i__6 = *q - 1; // , expr subst
            i__4 = max(i__5,i__6);
            /* Computing MAX */
            i__8 = 0;
            i__9 = *q - 1; // , expr subst
            i__7 = max(i__8,i__9);
            sorglq_fla(&i__1, &i__4, &i__7, &v1t[v1t_offset], ldv1t, (real*)&c__0, & work[1], &c_n1, &childinfo);
            /* Computing MAX */
            i__1 = 1;
            i__2 = *q - 1; // , expr subst
            lorglqmin = max(i__1,i__2);
            lorglqopt = (integer) work[1];
            sbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], &c__0, &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[ v1t_offset], ldv1t, &c__0, &c__1, &c__0, &c__0, &c__0, & c__0, &c__0, &c__0, &c__0, &c__0, &work[1], &c_n1, & childinfo);
            lbbcsd = (integer) work[1];
        }
        else if (r__ == *p)
        {
            sorbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &theta[1], &c__0, &c__0, &c__0, &c__0, &work[1], & c_n1, &childinfo);
            lorbdb = (integer) work[1];
            if (*p - 1 >= *m - *p)
            {
                i__1 = *p - 1;
                i__2 = *p - 1;
                i__3 = *p - 1;
                sorgqr_fla(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1, (real*)&c__0, &work[1], &c_n1, &childinfo);
                /* Computing MAX */
                i__1 = 1;
                i__2 = *p - 1; // , expr subst
                lorgqrmin = max(i__1,i__2);
                lorgqropt = (integer) work[1];
            }
            else
            {
                i__1 = *m - *p;
                i__2 = *m - *p;
                sorgqr_fla(&i__1, &i__2, q, &u2[u2_offset], ldu2, (real*)&c__0, &work[1] , &c_n1, &childinfo);
                /* Computing MAX */
                i__1 = 1;
                i__2 = *m - *p; // , expr subst
                lorgqrmin = max(i__1,i__2);
                lorgqropt = (integer) work[1];
            }
            sorglq_fla(q, q, &r__, &v1t[v1t_offset], ldv1t, (real*)&c__0, &work[1], & c_n1, &childinfo);
            lorglqmin = max(1,*q);
            lorglqopt = (integer) work[1];
            sbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], &c__0, &v1t[v1t_offset], ldv1t, &c__0, &c__1, &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &c__0, &c__0, &c__0, &c__0, & c__0, &c__0, &c__0, &c__0, &work[1], &c_n1, &childinfo);
            lbbcsd = (integer) work[1];
        }
        else if (r__ == *m - *p)
        {
            sorbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &theta[1], &c__0, &c__0, &c__0, &c__0, &work[1], & c_n1, &childinfo);
            lorbdb = (integer) work[1];
            if (*p >= *m - *p - 1)
            {
                sorgqr_fla(p, p, q, &u1[u1_offset], ldu1, (real*)&c__0, &work[1], &c_n1, &childinfo);
                lorgqrmin = max(1,*p);
                lorgqropt = (integer) work[1];
            }
            else
            {
                i__1 = *m - *p - 1;
                i__2 = *m - *p - 1;
                i__3 = *m - *p - 1;
                sorgqr_fla(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2, (real*)&c__0, &work[1], &c_n1, &childinfo);
                /* Computing MAX */
                i__1 = 1;
                i__2 = *m - *p - 1; // , expr subst
                lorgqrmin = max(i__1,i__2);
                lorgqropt = (integer) work[1];
            }
            sorglq_fla(q, q, &r__, &v1t[v1t_offset], ldv1t, (real*)&c__0, &work[1], & c_n1, &childinfo);
            lorglqmin = max(1,*q);
            lorglqopt = (integer) work[1];
            i__1 = *m - *q;
            i__2 = *m - *p;
            sbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1] , &c__0, &c__0, &c__1, &v1t[v1t_offset], ldv1t, &u2[ u2_offset], ldu2, &u1[u1_offset], ldu1, &c__0, &c__0, & c__0, &c__0, &c__0, &c__0, &c__0, &c__0, &work[1], &c_n1, &childinfo);
            lbbcsd = (integer) work[1];
        }
        else
        {
            sorbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &theta[1], &c__0, &c__0, &c__0, &c__0, &c__0, & work[1], &c_n1, &childinfo);
            lorbdb = *m + (integer) work[1];
            if (*p >= *m - *p)
            {
                i__1 = *m - *q;
                sorgqr_fla(p, p, &i__1, &u1[u1_offset], ldu1, (real*)&c__0, &work[1], & c_n1, &childinfo);
                lorgqrmin = max(1,*p);
                lorgqropt = (integer) work[1];
            }
            else
            {
                i__1 = *m - *p;
                i__2 = *m - *p;
                i__3 = *m - *q;
                sorgqr_fla(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, (real*)&c__0, & work[1], &c_n1, &childinfo);
                /* Computing MAX */
                i__1 = 1;
                i__2 = *m - *p; // , expr subst
                lorgqrmin = max(i__1,i__2);
                lorgqropt = (integer) work[1];
            }
            sorglq_fla(q, q, q, &v1t[v1t_offset], ldv1t, (real*)&c__0, &work[1], &c_n1, &childinfo);
            lorglqmin = max(1,*q);
            lorglqopt = (integer) work[1];
            i__1 = *m - *p;
            i__2 = *m - *q;
            sbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1] , &c__0, &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, & c__0, &c__1, &v1t[v1t_offset], ldv1t, &c__0, &c__0, &c__0, &c__0, &c__0, &c__0, &c__0, &c__0, &work[1], &c_n1, & childinfo);
            lbbcsd = (integer) work[1];
        }
        /* Computing MAX */
        i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqrmin - 1, i__1 = max( i__1,i__2), i__2 = iorglq + lorglqmin - 1;
        i__1 = max(i__1, i__2);
        i__2 = ibbcsd + lbbcsd - 1; // ; expr subst
        lworkmin = max(i__1,i__2);
        /* Computing MAX */
        i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqropt - 1, i__1 = max( i__1,i__2), i__2 = iorglq + lorglqopt - 1;
        i__1 = max(i__1, i__2);
        i__2 = ibbcsd + lbbcsd - 1; // ; expr subst
        lworkopt = max(i__1,i__2);
        work[1] = (real) lworkopt;
        if (*lwork < lworkmin && ! lquery)
        {
            *info = -19;
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("SORCSD2BY1", &i__1);
        return 0;
    }
    else if (lquery)
    {
        return 0;
    }
    lorgqr = *lwork - iorgqr + 1;
    lorglq = *lwork - iorglq + 1;
    /* Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q, */
    /* in which R = MIN(P,M-P,Q,M-Q) */
    if (r__ == *q)
    {
        /* Case 1: R = Q */
        /* Simultaneously bidiagonalize X11 and X21 */
        sorbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, & theta[1], &work[iphi], &work[itaup1], &work[itaup2], &work[ itauq1], &work[iorbdb], &lorbdb, &childinfo);
        /* Accumulate Householder reflectors */
        if (wantu1 && *p > 0)
        {
            slacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
            sorgqr_fla(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[ iorgqr], &lorgqr, &childinfo);
        }
        if (wantu2 && *m - *p > 0)
        {
            i__1 = *m - *p;
            slacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset], ldu2);
            i__1 = *m - *p;
            i__2 = *m - *p;
            sorgqr_fla(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], & work[iorgqr], &lorgqr, &childinfo);
        }
        if (wantv1t && *q > 0)
        {
            v1t[v1t_dim1 + 1] = 1.f;
            i__1 = *q;
            for (j = 2;
                    j <= i__1;
                    ++j)
            {
                v1t[j * v1t_dim1 + 1] = 0.f;
                v1t[j + v1t_dim1] = 0.f;
            }
            i__1 = *q - 1;
            i__2 = *q - 1;
            slacpy_("U", &i__1, &i__2, &x21[(x21_dim1 << 1) + 1], ldx21, &v1t[ (v1t_dim1 << 1) + 2], ldv1t);
            i__1 = *q - 1;
            i__2 = *q - 1;
            i__3 = *q - 1;
            sorglq_fla(&i__1, &i__2, &i__3, &v1t[(v1t_dim1 << 1) + 2], ldv1t, & work[itauq1], &work[iorglq], &lorglq, &childinfo);
        }
        /* Simultaneously diagonalize X11 and X21. */
        sbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], &work[ iphi], &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[ v1t_offset], ldv1t, &c__0, &c__1, &work[ib11d], &work[ib11e], &work[ib12d], &work[ib12e], &work[ib21d], &work[ib21e], &work[ ib22d], &work[ib22e], &work[ibbcsd], &lbbcsd, &childinfo);
        /* Permute rows and columns to place zero submatrices in */
        /* preferred positions */
        if (*q > 0 && wantu2)
        {
            i__1 = *q;
            for (i__ = 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = *m - *p - *q + i__;
            }
            i__1 = *m - *p;
            for (i__ = *q + 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = i__ - *q;
            }
            i__1 = *m - *p;
            i__2 = *m - *p;
            slapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
        }
    }
    else if (r__ == *p)
    {
        /* Case 2: R = P */
        /* Simultaneously bidiagonalize X11 and X21 */
        sorbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, & theta[1], &work[iphi], &work[itaup1], &work[itaup2], &work[ itauq1], &work[iorbdb], &lorbdb, &childinfo);
        /* Accumulate Householder reflectors */
        if (wantu1 && *p > 0)
        {
            u1[u1_dim1 + 1] = 1.f;
            i__1 = *p;
            for (j = 2;
                    j <= i__1;
                    ++j)
            {
                u1[j * u1_dim1 + 1] = 0.f;
                u1[j + u1_dim1] = 0.f;
            }
            i__1 = *p - 1;
            i__2 = *p - 1;
            slacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[( u1_dim1 << 1) + 2], ldu1);
            i__1 = *p - 1;
            i__2 = *p - 1;
            i__3 = *p - 1;
            sorgqr_fla(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1, &work[ itaup1], &work[iorgqr], &lorgqr, &childinfo);
        }
        if (wantu2 && *m - *p > 0)
        {
            i__1 = *m - *p;
            slacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset], ldu2);
            i__1 = *m - *p;
            i__2 = *m - *p;
            sorgqr_fla(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], & work[iorgqr], &lorgqr, &childinfo);
        }
        if (wantv1t && *q > 0)
        {
            slacpy_("U", p, q, &x11[x11_offset], ldx11, &v1t[v1t_offset], ldv1t);
            sorglq_fla(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[ iorglq], &lorglq, &childinfo);
        }
        /* Simultaneously diagonalize X11 and X21. */
        sbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], &work[ iphi], &v1t[v1t_offset], ldv1t, &c__0, &c__1, &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &work[ib11d], &work[ib11e], &work[ ib12d], &work[ib12e], &work[ib21d], &work[ib21e], &work[ib22d] , &work[ib22e], &work[ibbcsd], &lbbcsd, &childinfo);
        /* Permute rows and columns to place identity submatrices in */
        /* preferred positions */
        if (*q > 0 && wantu2)
        {
            i__1 = *q;
            for (i__ = 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = *m - *p - *q + i__;
            }
            i__1 = *m - *p;
            for (i__ = *q + 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = i__ - *q;
            }
            i__1 = *m - *p;
            i__2 = *m - *p;
            slapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
        }
    }
    else if (r__ == *m - *p)
    {
        /* Case 3: R = M-P */
        /* Simultaneously bidiagonalize X11 and X21 */
        sorbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, & theta[1], &work[iphi], &work[itaup1], &work[itaup2], &work[ itauq1], &work[iorbdb], &lorbdb, &childinfo);
        /* Accumulate Householder reflectors */
        if (wantu1 && *p > 0)
        {
            slacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
            sorgqr_fla(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[ iorgqr], &lorgqr, &childinfo);
        }
        if (wantu2 && *m - *p > 0)
        {
            u2[u2_dim1 + 1] = 1.f;
            i__1 = *m - *p;
            for (j = 2;
                    j <= i__1;
                    ++j)
            {
                u2[j * u2_dim1 + 1] = 0.f;
                u2[j + u2_dim1] = 0.f;
            }
            i__1 = *m - *p - 1;
            i__2 = *m - *p - 1;
            slacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[( u2_dim1 << 1) + 2], ldu2);
            i__1 = *m - *p - 1;
            i__2 = *m - *p - 1;
            i__3 = *m - *p - 1;
            sorgqr_fla(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2, &work[ itaup2], &work[iorgqr], &lorgqr, &childinfo);
        }
        if (wantv1t && *q > 0)
        {
            i__1 = *m - *p;
            slacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset], ldv1t);
            sorglq_fla(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[ iorglq], &lorglq, &childinfo);
        }
        /* Simultaneously diagonalize X11 and X21. */
        i__1 = *m - *q;
        i__2 = *m - *p;
        sbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1], & work[iphi], &c__0, &c__1, &v1t[v1t_offset], ldv1t, &u2[ u2_offset], ldu2, &u1[u1_offset], ldu1, &work[ib11d], &work[ ib11e], &work[ib12d], &work[ib12e], &work[ib21d], &work[ib21e] , &work[ib22d], &work[ib22e], &work[ibbcsd], &lbbcsd, & childinfo);
        /* Permute rows and columns to place identity submatrices in */
        /* preferred positions */
        if (*q > r__)
        {
            i__1 = r__;
            for (i__ = 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = *q - r__ + i__;
            }
            i__1 = *q;
            for (i__ = r__ + 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = i__ - r__;
            }
            if (wantu1)
            {
                slapmt_(&c_false, p, q, &u1[u1_offset], ldu1, &iwork[1]);
            }
            if (wantv1t)
            {
                slapmr_(&c_false, q, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
            }
        }
    }
    else
    {
        /* Case 4: R = M-Q */
        /* Simultaneously bidiagonalize X11 and X21 */
        i__1 = lorbdb - *m;
        sorbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, & theta[1], &work[iphi], &work[itaup1], &work[itaup2], &work[ itauq1], &work[iorbdb], &work[iorbdb + *m], &i__1, &childinfo) ;
        /* Accumulate Householder reflectors */
        if (wantu1 && *p > 0)
        {
            scopy_(p, &work[iorbdb], &c__1, &u1[u1_offset], &c__1);
            i__1 = *p;
            for (j = 2;
                    j <= i__1;
                    ++j)
            {
                u1[j * u1_dim1 + 1] = 0.f;
            }
            i__1 = *p - 1;
            i__2 = *m - *q - 1;
            slacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[( u1_dim1 << 1) + 2], ldu1);
            i__1 = *m - *q;
            sorgqr_fla(p, p, &i__1, &u1[u1_offset], ldu1, &work[itaup1], &work[ iorgqr], &lorgqr, &childinfo);
        }
        if (wantu2 && *m - *p > 0)
        {
            i__1 = *m - *p;
            scopy_(&i__1, &work[iorbdb + *p], &c__1, &u2[u2_offset], &c__1);
            i__1 = *m - *p;
            for (j = 2;
                    j <= i__1;
                    ++j)
            {
                u2[j * u2_dim1 + 1] = 0.f;
            }
            i__1 = *m - *p - 1;
            i__2 = *m - *q - 1;
            slacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[( u2_dim1 << 1) + 2], ldu2);
            i__1 = *m - *p;
            i__2 = *m - *p;
            i__3 = *m - *q;
            sorgqr_fla(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, &work[itaup2], &work[iorgqr], &lorgqr, &childinfo);
        }
        if (wantv1t && *q > 0)
        {
            i__1 = *m - *q;
            slacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset], ldv1t);
            i__1 = *p - (*m - *q);
            i__2 = *q - (*m - *q);
            slacpy_("U", &i__1, &i__2, &x11[*m - *q + 1 + (*m - *q + 1) * x11_dim1], ldx11, &v1t[*m - *q + 1 + (*m - *q + 1) * v1t_dim1], ldv1t);
            i__1 = -(*p) + *q;
            i__2 = *q - *p;
            slacpy_("U", &i__1, &i__2, &x21[*m - *q + 1 + (*p + 1) * x21_dim1] , ldx21, &v1t[*p + 1 + (*p + 1) * v1t_dim1], ldv1t);
            sorglq_fla(q, q, q, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[ iorglq], &lorglq, &childinfo);
        }
        /* Simultaneously diagonalize X11 and X21. */
        i__1 = *m - *p;
        i__2 = *m - *q;
        sbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1], & work[iphi], &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, &c__0, &c__1, &v1t[v1t_offset], ldv1t, &work[ib11d], &work[ib11e], & work[ib12d], &work[ib12e], &work[ib21d], &work[ib21e], &work[ ib22d], &work[ib22e], &work[ibbcsd], &lbbcsd, &childinfo);
        /* Permute rows and columns to place identity submatrices in */
        /* preferred positions */
        if (*p > r__)
        {
            i__1 = r__;
            for (i__ = 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = *p - r__ + i__;
            }
            i__1 = *p;
            for (i__ = r__ + 1;
                    i__ <= i__1;
                    ++i__)
            {
                iwork[i__] = i__ - r__;
            }
            if (wantu1)
            {
                slapmt_(&c_false, p, p, &u1[u1_offset], ldu1, &iwork[1]);
            }
            if (wantv1t)
            {
                slapmr_(&c_false, p, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
            }
        }
    }
    return 0;
    /* End of SORCSD2BY1 */
}
コード例 #4
0
ファイル: sggsvp.c プロジェクト: flame/libflame
/* Subroutine */
int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu, real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real * tau, real *work, integer *info)
{
    /* 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;
    real r__1;
    /* Local variables */
    integer i__, j;
    extern logical lsame_(char *, char *);
    logical wantq, wantu, wantv;
    extern /* Subroutine */
    int sgeqr2_(integer *, integer *, real *, integer *, real *, real *, integer *), sgerq2_(integer *, integer *, real *, integer *, real *, real *, integer *), sorg2r_(integer *, integer *, integer *, real *, integer *, real *, real *, integer * ), sorm2r_(char *, char *, integer *, integer *, integer *, real * , integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *), xerbla_(char *, integer *), sgeqpf_( integer *, integer *, real *, integer *, integer *, real *, real * , integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slapmt_( logical *, integer *, integer *, real *, integer *, integer *);
    logical forwrd;
    /* -- LAPACK computational routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test the input parameters */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --iwork;
    --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_("SGGSVP", &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: */
    }
    sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
    /* Update A := A*P */
    slapmt_(&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__)
    {
        if ((r__1 = b[i__ + i__ * b_dim1], f2c_abs(r__1)) > *tolb)
        {
            ++(*l);
        }
        /* L20: */
    }
    if (wantv)
    {
        /* Copy the details of V, and form V. */
        slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv);
        if (*p > 1)
        {
            i__1 = *p - 1;
            slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2], ldv);
        }
        i__1 = min(*p,*n);
        sorg2r_(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__)
        {
            b[i__ + j * b_dim1] = 0.f;
            /* L30: */
        }
        /* L40: */
    }
    if (*p > *l)
    {
        i__1 = *p - *l;
        slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb);
    }
    if (wantq)
    {
        /* Set Q = I and Update Q := Q*P */
        slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq);
        slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
    }
    if (*p >= *l && *n != *l)
    {
        /* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
        sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
        /* Update A := A*Z**T */
        sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[ a_offset], lda, &work[1], info);
        if (wantq)
        {
            /* Update Q := Q*Z**T */
            sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
        }
        /* Clean up B */
        i__1 = *n - *l;
        slaset_("Full", l, &i__1, &c_b12, &c_b12, &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__)
            {
                b[i__ + j * b_dim1] = 0.f;
                /* 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**T */
    /* ( 0 0 ) */
    i__1 = *n - *l;
    for (i__ = 1;
            i__ <= i__1;
            ++i__)
    {
        iwork[i__] = 0;
        /* L70: */
    }
    i__1 = *n - *l;
    sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);
    /* Determine the effective rank of A11 */
    *k = 0;
    /* Computing MIN */
    i__2 = *m;
    i__3 = *n - *l; // , expr subst
    i__1 = min(i__2,i__3);
    for (i__ = 1;
            i__ <= i__1;
            ++i__)
    {
        if ((r__1 = a[i__ + i__ * a_dim1], f2c_abs(r__1)) > *tola)
        {
            ++(*k);
        }
        /* L80: */
    }
    /* Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N ) */
    /* Computing MIN */
    i__2 = *m;
    i__3 = *n - *l; // , expr subst
    i__1 = min(i__2,i__3);
    sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[( *n - *l + 1) * a_dim1 + 1], lda, &work[1], info);
    if (wantu)
    {
        /* Copy the details of U, and form U */
        slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu);
        if (*m > 1)
        {
            i__1 = *m - 1;
            i__2 = *n - *l;
            slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2] , ldu);
        }
        /* Computing MIN */
        i__2 = *m;
        i__3 = *n - *l; // , expr subst
        i__1 = min(i__2,i__3);
        sorg2r_(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;
        slapmt_(&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__)
        {
            a[i__ + j * a_dim1] = 0.f;
            /* L90: */
        }
        /* L100: */
    }
    if (*m > *k)
    {
        i__1 = *m - *k;
        i__2 = *n - *l;
        slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1], lda);
    }
    if (*n - *l > *k)
    {
        /* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
        i__1 = *n - *l;
        sgerq2_(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**T */
            i__1 = *n - *l;
            sormr2_("Right", "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;
        slaset_("Full", k, &i__1, &c_b12, &c_b12, &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__)
            {
                a[i__ + j * a_dim1] = 0.f;
                /* L110: */
            }
            /* L120: */
        }
    }
    if (*m > *k)
    {
        /* QR factorization of A( K+1:M,N-L+1:N ) */
        i__1 = *m - *k;
        sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], 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);
            sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 + 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__)
            {
                a[i__ + j * a_dim1] = 0.f;
                /* L130: */
            }
            /* L140: */
        }
    }
    return 0;
    /* End of SGGSVP */
}