コード例 #1
0
ファイル: slals0.c プロジェクト: MichaelH13/sdkpub
/* Subroutine */ int slals0_(integer *icompq, integer *nl, integer *nr, 
	integer *sqre, integer *nrhs, real *b, integer *ldb, real *bx, 
	integer *ldbx, integer *perm, integer *givptr, integer *givcol, 
	integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
	difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
	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   
       December 1, 1999   


    Purpose   
    =======   

    SLALS0 applies back the multiplying factors of either the left or the   
    right singular vector matrix of a diagonal matrix appended by a row   
    to the right hand side matrix B in solving the least squares problem   
    using the divide-and-conquer SVD approach.   

    For the left singular vector matrix, three types of orthogonal   
    matrices are involved:   

    (1L) Givens rotations: the number of such rotations is GIVPTR; the   
         pairs of columns/rows they were applied to are stored in GIVCOL;   
         and the C- and S-values of these rotations are stored in GIVNUM.   

    (2L) Permutation. The (NL+1)-st row of B is to be moved to the first   
         row, and for J=2:N, PERM(J)-th row of B is to be moved to the   
         J-th row.   

    (3L) The left singular vector matrix of the remaining matrix.   

    For the right singular vector matrix, four types of orthogonal   
    matrices are involved:   

    (1R) The right singular vector matrix of the remaining matrix.   

    (2R) If SQRE = 1, one extra Givens rotation to generate the right   
         null space.   

    (3R) The inverse transformation of (2L).   

    (4R) The inverse transformation of (1L).   

    Arguments   
    =========   

    ICOMPQ (input) INTEGER   
           Specifies whether singular vectors are to be computed in   
           factored form:   
           = 0: Left singular vector matrix.   
           = 1: Right singular vector matrix.   

    NL     (input) INTEGER   
           The row dimension of the upper block. NL >= 1.   

    NR     (input) INTEGER   
           The row dimension of the lower block. NR >= 1.   

    SQRE   (input) INTEGER   
           = 0: the lower block is an NR-by-NR square matrix.   
           = 1: the lower block is an NR-by-(NR+1) rectangular matrix.   

           The bidiagonal matrix has row dimension N = NL + NR + 1,   
           and column dimension M = N + SQRE.   

    NRHS   (input) INTEGER   
           The number of columns of B and BX. NRHS must be at least 1.   

    B      (input/output) REAL array, dimension ( LDB, NRHS )   
           On input, B contains the right hand sides of the least   
           squares problem in rows 1 through M. On output, B contains   
           the solution X in rows 1 through N.   

    LDB    (input) INTEGER   
           The leading dimension of B. LDB must be at least   
           max(1,MAX( M, N ) ).   

    BX     (workspace) REAL array, dimension ( LDBX, NRHS )   

    LDBX   (input) INTEGER   
           The leading dimension of BX.   

    PERM   (input) INTEGER array, dimension ( N )   
           The permutations (from deflation and sorting) applied   
           to the two blocks.   

    GIVPTR (input) INTEGER   
           The number of Givens rotations which took place in this   
           subproblem.   

    GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 )   
           Each pair of numbers indicates a pair of rows/columns   
           involved in a Givens rotation.   

    LDGCOL (input) INTEGER   
           The leading dimension of GIVCOL, must be at least N.   

    GIVNUM (input) REAL array, dimension ( LDGNUM, 2 )   
           Each number indicates the C or S value used in the   
           corresponding Givens rotation.   

    LDGNUM (input) INTEGER   
           The leading dimension of arrays DIFR, POLES and   
           GIVNUM, must be at least K.   

    POLES  (input) REAL array, dimension ( LDGNUM, 2 )   
           On entry, POLES(1:K, 1) contains the new singular   
           values obtained from solving the secular equation, and   
           POLES(1:K, 2) is an array containing the poles in the secular   
           equation.   

    DIFL   (input) REAL array, dimension ( K ).   
           On entry, DIFL(I) is the distance between I-th updated   
           (undeflated) singular value and the I-th (undeflated) old   
           singular value.   

    DIFR   (input) REAL array, dimension ( LDGNUM, 2 ).   
           On entry, DIFR(I, 1) contains the distances between I-th   
           updated (undeflated) singular value and the I+1-th   
           (undeflated) old singular value. And DIFR(I, 2) is the   
           normalizing factor for the I-th right singular vector.   

    Z      (input) REAL array, dimension ( K )   
           Contain the components of the deflation-adjusted updating row   
           vector.   

    K      (input) INTEGER   
           Contains the dimension of the non-deflated matrix,   
           This is the order of the related secular equation. 1 <= K <=N.   

    C      (input) REAL   
           C contains garbage if SQRE =0 and the C-value of a Givens   
           rotation related to the right null space if SQRE = 1.   

    S      (input) REAL   
           S contains garbage if SQRE =0 and the S-value of a Givens   
           rotation related to the right null space if SQRE = 1.   

    WORK   (workspace) REAL array, dimension ( K )   

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

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

    Based on contributions by   
       Ming Gu and Ren-Cang Li, Computer Science Division, University of   
         California at Berkeley, USA   
       Osni Marques, LBNL/NERSC, USA   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static real c_b5 = -1.f;
    static integer c__1 = 1;
    static real c_b11 = 1.f;
    static real c_b13 = 0.f;
    static integer c__0 = 0;
    
    /* System generated locals */
    integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, 
	    difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, 
	    poles_offset, i__1, i__2;
    real r__1;
    /* Local variables */
    static real temp;
    extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, 
	    integer *, real *, real *);
    extern doublereal snrm2_(integer *, real *, integer *);
    static integer i__, j, m, n;
    static real diflj, difrj, dsigj;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), 
	    sgemv_(char *, integer *, integer *, real *, real *, integer *, 
	    real *, integer *, real *, real *, integer *), scopy_(
	    integer *, real *, integer *, real *, integer *);
    extern doublereal slamc3_(real *, real *);
    static real dj;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real dsigjp;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, 
	    real *, integer *);
    static integer nlp1;
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define bx_ref(a_1,a_2) bx[(a_2)*bx_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_dim1 + a_1]


    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    bx_dim1 = *ldbx;
    bx_offset = 1 + bx_dim1 * 1;
    bx -= bx_offset;
    --perm;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1 * 1;
    givcol -= givcol_offset;
    difr_dim1 = *ldgnum;
    difr_offset = 1 + difr_dim1 * 1;
    difr -= difr_offset;
    poles_dim1 = *ldgnum;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    givnum_dim1 = *ldgnum;
    givnum_offset = 1 + givnum_dim1 * 1;
    givnum -= givnum_offset;
    --difl;
    --z__;
    --work;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*nl < 1) {
	*info = -2;
    } else if (*nr < 1) {
	*info = -3;
    } else if (*sqre < 0 || *sqre > 1) {
	*info = -4;
    }

    n = *nl + *nr + 1;

    if (*nrhs < 1) {
	*info = -5;
    } else if (*ldb < n) {
	*info = -7;
    } else if (*ldbx < n) {
	*info = -9;
    } else if (*givptr < 0) {
	*info = -11;
    } else if (*ldgcol < n) {
	*info = -13;
    } else if (*ldgnum < n) {
	*info = -15;
    } else if (*k < 1) {
	*info = -20;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLALS0", &i__1);
	return 0;
    }

    m = n + *sqre;
    nlp1 = *nl + 1;

    if (*icompq == 0) {

/*        Apply back orthogonal transformations from the left.   

          Step (1L): apply back the Givens rotations performed. */

	i__1 = *givptr;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    srot_(nrhs, &b_ref(givcol_ref(i__, 2), 1), ldb, &b_ref(givcol_ref(
		    i__, 1), 1), ldb, &givnum_ref(i__, 2), &givnum_ref(i__, 1)
		    );
/* L10: */
	}

/*        Step (2L): permute rows of B. */

	scopy_(nrhs, &b_ref(nlp1, 1), ldb, &bx_ref(1, 1), ldbx);
	i__1 = n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    scopy_(nrhs, &b_ref(perm[i__], 1), ldb, &bx_ref(i__, 1), ldbx);
/* L20: */
	}

/*        Step (3L): apply the inverse of the left singular vector   
          matrix to BX. */

	if (*k == 1) {
	    scopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
	    if (z__[1] < 0.f) {
		sscal_(nrhs, &c_b5, &b[b_offset], ldb);
	    }
	} else {
	    i__1 = *k;
	    for (j = 1; j <= i__1; ++j) {
		diflj = difl[j];
		dj = poles_ref(j, 1);
		dsigj = -poles_ref(j, 2);
		if (j < *k) {
		    difrj = -difr_ref(j, 1);
		    dsigjp = -poles_ref(j + 1, 2);
		}
		if (z__[j] == 0.f || poles_ref(j, 2) == 0.f) {
		    work[j] = 0.f;
		} else {
		    work[j] = -poles_ref(j, 2) * z__[j] / diflj / (poles_ref(
			    j, 2) + dj);
		}
		i__2 = j - 1;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    if (z__[i__] == 0.f || poles_ref(i__, 2) == 0.f) {
			work[i__] = 0.f;
		    } else {
			work[i__] = poles_ref(i__, 2) * z__[i__] / (slamc3_(&
				poles_ref(i__, 2), &dsigj) - diflj) / (
				poles_ref(i__, 2) + dj);
		    }
/* L30: */
		}
		i__2 = *k;
		for (i__ = j + 1; i__ <= i__2; ++i__) {
		    if (z__[i__] == 0.f || poles_ref(i__, 2) == 0.f) {
			work[i__] = 0.f;
		    } else {
			work[i__] = poles_ref(i__, 2) * z__[i__] / (slamc3_(&
				poles_ref(i__, 2), &dsigjp) + difrj) / (
				poles_ref(i__, 2) + dj);
		    }
/* L40: */
		}
		work[1] = -1.f;
		temp = snrm2_(k, &work[1], &c__1);
		sgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
			c__1, &c_b13, &b_ref(j, 1), ldb);
		slascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b_ref(
			j, 1), ldb, info);
/* L50: */
	    }
	}

/*        Move the deflated rows of BX to B also. */

	if (*k < max(m,n)) {
	    i__1 = n - *k;
	    slacpy_("A", &i__1, nrhs, &bx_ref(*k + 1, 1), ldbx, &b_ref(*k + 1,
		     1), ldb);
	}
    } else {

/*        Apply back the right orthogonal transformations.   

          Step (1R): apply back the new right singular vector matrix   
          to B. */

	if (*k == 1) {
	    scopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
	} else {
	    i__1 = *k;
	    for (j = 1; j <= i__1; ++j) {
		dsigj = poles_ref(j, 2);
		if (z__[j] == 0.f) {
		    work[j] = 0.f;
		} else {
		    work[j] = -z__[j] / difl[j] / (dsigj + poles_ref(j, 1)) / 
			    difr_ref(j, 2);
		}
		i__2 = j - 1;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    if (z__[j] == 0.f) {
			work[i__] = 0.f;
		    } else {
			r__1 = -poles_ref(i__ + 1, 2);
			work[i__] = z__[j] / (slamc3_(&dsigj, &r__1) - 
				difr_ref(i__, 1)) / (dsigj + poles_ref(i__, 1)
				) / difr_ref(i__, 2);
		    }
/* L60: */
		}
		i__2 = *k;
		for (i__ = j + 1; i__ <= i__2; ++i__) {
		    if (z__[j] == 0.f) {
			work[i__] = 0.f;
		    } else {
			r__1 = -poles_ref(i__, 2);
			work[i__] = z__[j] / (slamc3_(&dsigj, &r__1) - difl[
				i__]) / (dsigj + poles_ref(i__, 1)) / 
				difr_ref(i__, 2);
		    }
/* L70: */
		}
		sgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
			c__1, &c_b13, &bx_ref(j, 1), ldbx);
/* L80: */
	    }
	}

/*        Step (2R): if SQRE = 1, apply back the rotation that is   
          related to the right null space of the subproblem. */

	if (*sqre == 1) {
	    scopy_(nrhs, &b_ref(m, 1), ldb, &bx_ref(m, 1), ldbx);
	    srot_(nrhs, &bx_ref(1, 1), ldbx, &bx_ref(m, 1), ldbx, c__, s);
	}
	if (*k < max(m,n)) {
	    i__1 = n - *k;
	    slacpy_("A", &i__1, nrhs, &b_ref(*k + 1, 1), ldb, &bx_ref(*k + 1, 
		    1), ldbx);
	}

/*        Step (3R): permute rows of B. */

	scopy_(nrhs, &bx_ref(1, 1), ldbx, &b_ref(nlp1, 1), ldb);
	if (*sqre == 1) {
	    scopy_(nrhs, &bx_ref(m, 1), ldbx, &b_ref(m, 1), ldb);
	}
	i__1 = n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    scopy_(nrhs, &bx_ref(i__, 1), ldbx, &b_ref(perm[i__], 1), ldb);
/* L90: */
	}

/*        Step (4R): apply back the Givens rotations performed. */

	for (i__ = *givptr; i__ >= 1; --i__) {
	    r__1 = -givnum_ref(i__, 1);
	    srot_(nrhs, &b_ref(givcol_ref(i__, 2), 1), ldb, &b_ref(givcol_ref(
		    i__, 1), 1), ldb, &givnum_ref(i__, 2), &r__1);
/* L100: */
	}
    }

    return 0;

/*     End of SLALS0 */

} /* slals0_ */
コード例 #2
0
ファイル: clalsa.c プロジェクト: MichaelH13/sdkpub
/* Subroutine */ int clalsa_(integer *icompq, integer *smlsiz, integer *n, 
	integer *nrhs, complex *b, integer *ldb, complex *bx, integer *ldbx, 
	real *u, integer *ldu, real *vt, integer *k, real *difl, real *difr, 
	real *z__, real *poles, integer *givptr, integer *givcol, integer *
	ldgcol, integer *perm, real *givnum, real *c__, real *s, real *rwork, 
	integer *iwork, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    CLALSA is an itermediate step in solving the least squares problem   
    by computing the SVD of the coefficient matrix in compact form (The   
    singular vectors are computed as products of simple orthorgonal   
    matrices.).   

    If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector   
    matrix of an upper bidiagonal matrix to the right hand side; and if   
    ICOMPQ = 1, CLALSA applies the right singular vector matrix to the   
    right hand side. The singular vector matrices were generated in   
    compact form by CLALSA.   

    Arguments   
    =========   

    ICOMPQ (input) INTEGER   
           Specifies whether the left or the right singular vector   
           matrix is involved.   
           = 0: Left singular vector matrix   
           = 1: Right singular vector matrix   

    SMLSIZ (input) INTEGER   
           The maximum size of the subproblems at the bottom of the   
           computation tree.   

    N      (input) INTEGER   
           The row and column dimensions of the upper bidiagonal matrix.   

    NRHS   (input) INTEGER   
           The number of columns of B and BX. NRHS must be at least 1.   

    B      (input) COMPLEX array, dimension ( LDB, NRHS )   
           On input, B contains the right hand sides of the least   
           squares problem in rows 1 through M. On output, B contains   
           the solution X in rows 1 through N.   

    LDB    (input) INTEGER   
           The leading dimension of B in the calling subprogram.   
           LDB must be at least max(1,MAX( M, N ) ).   

    BX     (output) COMPLEX array, dimension ( LDBX, NRHS )   
           On exit, the result of applying the left or right singular   
           vector matrix to B.   

    LDBX   (input) INTEGER   
           The leading dimension of BX.   

    U      (input) REAL array, dimension ( LDU, SMLSIZ ).   
           On entry, U contains the left singular vector matrices of all   
           subproblems at the bottom level.   

    LDU    (input) INTEGER, LDU = > N.   
           The leading dimension of arrays U, VT, DIFL, DIFR,   
           POLES, GIVNUM, and Z.   

    VT     (input) REAL array, dimension ( LDU, SMLSIZ+1 ).   
           On entry, VT' contains the right singular vector matrices of   
           all subproblems at the bottom level.   

    K      (input) INTEGER array, dimension ( N ).   

    DIFL   (input) REAL array, dimension ( LDU, NLVL ).   
           where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.   

    DIFR   (input) REAL array, dimension ( LDU, 2 * NLVL ).   
           On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record   
           distances between singular values on the I-th level and   
           singular values on the (I -1)-th level, and DIFR(*, 2 * I)   
           record the normalizing factors of the right singular vectors   
           matrices of subproblems on I-th level.   

    Z      (input) REAL array, dimension ( LDU, NLVL ).   
           On entry, Z(1, I) contains the components of the deflation-   
           adjusted updating row vector for subproblems on the I-th   
           level.   

    POLES  (input) REAL array, dimension ( LDU, 2 * NLVL ).   
           On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old   
           singular values involved in the secular equations on the I-th   
           level.   

    GIVPTR (input) INTEGER array, dimension ( N ).   
           On entry, GIVPTR( I ) records the number of Givens   
           rotations performed on the I-th problem on the computation   
           tree.   

    GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).   
           On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the   
           locations of Givens rotations performed on the I-th level on   
           the computation tree.   

    LDGCOL (input) INTEGER, LDGCOL = > N.   
           The leading dimension of arrays GIVCOL and PERM.   

    PERM   (input) INTEGER array, dimension ( LDGCOL, NLVL ).   
           On entry, PERM(*, I) records permutations done on the I-th   
           level of the computation tree.   

    GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ).   
           On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-   
           values of Givens rotations performed on the I-th level on the   
           computation tree.   

    C      (input) REAL array, dimension ( N ).   
           On entry, if the I-th subproblem is not square,   
           C( I ) contains the C-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    S      (input) REAL array, dimension ( N ).   
           On entry, if the I-th subproblem is not square,   
           S( I ) contains the S-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    RWORK  (workspace) REAL array, dimension at least   
           max ( N, (SMLSZ+1)*NRHS*3 ).   

    IWORK  (workspace) INTEGER array.   
           The dimension must be at least 3 * N   

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

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

    Based on contributions by   
       Ming Gu and Ren-Cang Li, Computer Science Division, University of   
         California at Berkeley, USA   
       Osni Marques, LBNL/NERSC, USA   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static real c_b9 = 1.f;
    static real c_b10 = 0.f;
    static integer c__2 = 2;
    
    /* System generated locals */
    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, 
	    difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, 
	    poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, 
	    z_dim1, z_offset, b_dim1, b_offset, bx_dim1, bx_offset, i__1, 
	    i__2, i__3, i__4, i__5, i__6;
    complex q__1;
    /* Builtin functions */
    double r_imag(complex *);
    integer pow_ii(integer *, integer *);
    /* Local variables */
    static integer jcol, nlvl, sqre, jrow, i__, j, jimag, jreal, inode, ndiml;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    static integer ndimr;
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *);
    static integer i1;
    extern /* Subroutine */ int clals0_(integer *, integer *, integer *, 
	    integer *, integer *, complex *, integer *, complex *, integer *, 
	    integer *, integer *, integer *, integer *, real *, integer *, 
	    real *, real *, real *, real *, integer *, real *, real *, real *,
	     integer *);
    static integer ic, lf, nd, ll, nl, nr;
    extern /* Subroutine */ int xerbla_(char *, integer *), slasdt_(
	    integer *, integer *, integer *, integer *, integer *, integer *, 
	    integer *);
    static integer im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1;
#define difl_ref(a_1,a_2) difl[(a_2)*difl_dim1 + a_1]
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define perm_ref(a_1,a_2) perm[(a_2)*perm_dim1 + a_1]
#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_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define bx_subscr(a_1,a_2) (a_2)*bx_dim1 + a_1
#define bx_ref(a_1,a_2) bx[bx_subscr(a_1,a_2)]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_dim1 + a_1]


    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    bx_dim1 = *ldbx;
    bx_offset = 1 + bx_dim1 * 1;
    bx -= bx_offset;
    givnum_dim1 = *ldu;
    givnum_offset = 1 + givnum_dim1 * 1;
    givnum -= givnum_offset;
    poles_dim1 = *ldu;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    difr_dim1 = *ldu;
    difr_offset = 1 + difr_dim1 * 1;
    difr -= difr_offset;
    difl_dim1 = *ldu;
    difl_offset = 1 + difl_dim1 * 1;
    difl -= difl_offset;
    vt_dim1 = *ldu;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    --k;
    --givptr;
    perm_dim1 = *ldgcol;
    perm_offset = 1 + perm_dim1 * 1;
    perm -= perm_offset;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1 * 1;
    givcol -= givcol_offset;
    --c__;
    --s;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*smlsiz < 3) {
	*info = -2;
    } else if (*n < *smlsiz) {
	*info = -3;
    } else if (*nrhs < 1) {
	*info = -4;
    } else if (*ldb < *n) {
	*info = -6;
    } else if (*ldbx < *n) {
	*info = -8;
    } else if (*ldu < *n) {
	*info = -10;
    } else if (*ldgcol < *n) {
	*info = -19;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CLALSA", &i__1);
	return 0;
    }

/*     Book-keeping and  setting up the computation tree. */

    inode = 1;
    ndiml = inode + *n;
    ndimr = ndiml + *n;

    slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 
	    smlsiz);

/*     The following code applies back the left singular vector factors.   
       For applying back the right singular vector factors, go to 170. */

    if (*icompq == 1) {
	goto L170;
    }

/*     The nodes on the bottom level of the tree were solved   
       by SLASDQ. The corresponding left and right singular vector   
       matrices are in explicit form. First apply back the left   
       singular vector matrices. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node   
          NL : number of rows of left  subproblem   
          NR : number of rows of right subproblem   
          NLF: starting row of the left   subproblem   
          NRF: starting row of the right  subproblem */

	i1 = i__ - 1;
	ic = iwork[inode + i1];
	nl = iwork[ndiml + i1];
	nr = iwork[ndimr + i1];
	nlf = ic - nl;
	nrf = ic + 1;

/*        Since B and BX are complex, the following call to SGEMM   
          is performed in two steps (real and imaginary parts).   

          CALL SGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU,   
       $               B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */

	j = nl * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nl - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++j;
		i__4 = b_subscr(jrow, jcol);
		rwork[j] = b[i__4].r;
/* L10: */
	    }
/* L20: */
	}
	sgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u_ref(nlf, 1), ldu, &rwork[(
		nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[1], &nl);
	j = nl * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nl - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++j;
		rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L30: */
	    }
/* L40: */
	}
	sgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u_ref(nlf, 1), ldu, &rwork[(
		nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[nl * *nrhs + 1], &
		nl);
	jreal = 0;
	jimag = nl * *nrhs;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nl - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++jreal;
		++jimag;
		i__4 = bx_subscr(jrow, jcol);
		i__5 = jreal;
		i__6 = jimag;
		q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L50: */
	    }
/* L60: */
	}

/*        Since B and BX are complex, the following call to SGEMM   
          is performed in two steps (real and imaginary parts).   

          CALL SGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,   
      $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */

	j = nr * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nr - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++j;
		i__4 = b_subscr(jrow, jcol);
		rwork[j] = b[i__4].r;
/* L70: */
	    }
/* L80: */
	}
	sgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u_ref(nrf, 1), ldu, &rwork[(
		nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[1], &nr);
	j = nr * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nr - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++j;
		rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L90: */
	    }
/* L100: */
	}
	sgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u_ref(nrf, 1), ldu, &rwork[(
		nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[nr * *nrhs + 1], &
		nr);
	jreal = 0;
	jimag = nr * *nrhs;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nr - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++jreal;
		++jimag;
		i__4 = bx_subscr(jrow, jcol);
		i__5 = jreal;
		i__6 = jimag;
		q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L110: */
	    }
/* L120: */
	}

/* L130: */
    }

/*     Next copy the rows of B that correspond to unchanged rows   
       in the bidiagonal matrix to BX. */

    i__1 = nd;
    for (i__ = 1; i__ <= i__1; ++i__) {
	ic = iwork[inode + i__ - 1];
	ccopy_(nrhs, &b_ref(ic, 1), ldb, &bx_ref(ic, 1), ldbx);
/* L140: */
    }

/*     Finally go through the left singular vector matrices of all   
       the other subproblems bottom-up on the tree. */

    j = pow_ii(&c__2, &nlvl);
    sqre = 0;

    for (lvl = nlvl; lvl >= 1; --lvl) {
	lvl2 = (lvl << 1) - 1;

/*        find the first node LF and last node LL on   
          the current level LVL */

	if (lvl == 1) {
	    lf = 1;
	    ll = 1;
	} else {
	    i__1 = lvl - 1;
	    lf = pow_ii(&c__2, &i__1);
	    ll = (lf << 1) - 1;
	}
	i__1 = ll;
	for (i__ = lf; i__ <= i__1; ++i__) {
	    im1 = i__ - 1;
	    ic = iwork[inode + im1];
	    nl = iwork[ndiml + im1];
	    nr = iwork[ndimr + im1];
	    nlf = ic - nl;
	    nrf = ic + 1;
	    --j;
	    clals0_(icompq, &nl, &nr, &sqre, nrhs, &bx_ref(nlf, 1), ldbx, &
		    b_ref(nlf, 1), ldb, &perm_ref(nlf, lvl), &givptr[j], &
		    givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2), 
		    ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
		    difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
		    s[j], &rwork[1], info);
/* L150: */
	}
/* L160: */
    }
    goto L330;

/*     ICOMPQ = 1: applying back the right singular vector factors. */

L170:

/*     First now go through the right singular vector matrices of all   
       the tree nodes top-down. */

    j = 0;
    i__1 = nlvl;
    for (lvl = 1; lvl <= i__1; ++lvl) {
	lvl2 = (lvl << 1) - 1;

/*        Find the first node LF and last node LL on   
          the current level LVL. */

	if (lvl == 1) {
	    lf = 1;
	    ll = 1;
	} else {
	    i__2 = lvl - 1;
	    lf = pow_ii(&c__2, &i__2);
	    ll = (lf << 1) - 1;
	}
	i__2 = lf;
	for (i__ = ll; i__ >= i__2; --i__) {
	    im1 = i__ - 1;
	    ic = iwork[inode + im1];
	    nl = iwork[ndiml + im1];
	    nr = iwork[ndimr + im1];
	    nlf = ic - nl;
	    nrf = ic + 1;
	    if (i__ == ll) {
		sqre = 0;
	    } else {
		sqre = 1;
	    }
	    ++j;
	    clals0_(icompq, &nl, &nr, &sqre, nrhs, &b_ref(nlf, 1), ldb, &
		    bx_ref(nlf, 1), ldbx, &perm_ref(nlf, lvl), &givptr[j], &
		    givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2), 
		    ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
		    difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
		    s[j], &rwork[1], info);
/* L180: */
	}
/* L190: */
    }

/*     The nodes on the bottom level of the tree were solved   
       by SLASDQ. The corresponding right singular vector   
       matrices are in explicit form. Apply them back. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {
	i1 = i__ - 1;
	ic = iwork[inode + i1];
	nl = iwork[ndiml + i1];
	nr = iwork[ndimr + i1];
	nlp1 = nl + 1;
	if (i__ == nd) {
	    nrp1 = nr;
	} else {
	    nrp1 = nr + 1;
	}
	nlf = ic - nl;
	nrf = ic + 1;

/*        Since B and BX are complex, the following call to SGEMM is   
          performed in two steps (real and imaginary parts).   

          CALL SGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,   
      $               B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */

	j = nlp1 * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nlp1 - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++j;
		i__4 = b_subscr(jrow, jcol);
		rwork[j] = b[i__4].r;
/* L200: */
	    }
/* L210: */
	}
	sgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt_ref(nlf, 1), ldu, &
		rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[1], &
		nlp1);
	j = nlp1 * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nlp1 - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++j;
		rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L220: */
	    }
/* L230: */
	}
	sgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt_ref(nlf, 1), ldu, &
		rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[nlp1 * *
		nrhs + 1], &nlp1);
	jreal = 0;
	jimag = nlp1 * *nrhs;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nlf + nlp1 - 1;
	    for (jrow = nlf; jrow <= i__3; ++jrow) {
		++jreal;
		++jimag;
		i__4 = bx_subscr(jrow, jcol);
		i__5 = jreal;
		i__6 = jimag;
		q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L240: */
	    }
/* L250: */
	}

/*        Since B and BX are complex, the following call to SGEMM is   
          performed in two steps (real and imaginary parts).   

          CALL SGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,   
      $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */

	j = nrp1 * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nrp1 - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++j;
		i__4 = b_subscr(jrow, jcol);
		rwork[j] = b[i__4].r;
/* L260: */
	    }
/* L270: */
	}
	sgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt_ref(nrf, 1), ldu, &
		rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[1], &
		nrp1);
	j = nrp1 * *nrhs << 1;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nrp1 - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++j;
		rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L280: */
	    }
/* L290: */
	}
	sgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt_ref(nrf, 1), ldu, &
		rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[nrp1 * *
		nrhs + 1], &nrp1);
	jreal = 0;
	jimag = nrp1 * *nrhs;
	i__2 = *nrhs;
	for (jcol = 1; jcol <= i__2; ++jcol) {
	    i__3 = nrf + nrp1 - 1;
	    for (jrow = nrf; jrow <= i__3; ++jrow) {
		++jreal;
		++jimag;
		i__4 = bx_subscr(jrow, jcol);
		i__5 = jreal;
		i__6 = jimag;
		q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L300: */
	    }
/* L310: */
	}

/* L320: */
    }

L330:

    return 0;

/*     End of CLALSA */

} /* clalsa_ */
コード例 #3
0
ファイル: dlalsa.c プロジェクト: zangel/uquad
/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, 
	integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *
	ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, 
	doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
	poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
	perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
	work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, 
	    b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, 
	    difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset,
	     u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, 
	    i__2;

    /* Builtin functions */
    integer pow_ii(integer *, integer *);

    /* Local variables */
    static integer nlvl, sqre, i__, j;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static integer inode, ndiml, ndimr;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer i1;
    extern /* Subroutine */ int dlals0_(integer *, integer *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, integer *, integer *, integer *, integer *, doublereal 
	    *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     integer *);
    extern doublereal dopbl3_(char *, integer *, integer *, integer *)
	    ;
    static integer ic, lf, nd, ll, nl, nr;
    extern /* Subroutine */ int dlasdt_(integer *, integer *, integer *, 
	    integer *, integer *, integer *, integer *), xerbla_(char *, 
	    integer *);
    static integer im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1;


#define difl_ref(a_1,a_2) difl[(a_2)*difl_dim1 + a_1]
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define perm_ref(a_1,a_2) perm[(a_2)*perm_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define bx_ref(a_1,a_2) bx[(a_2)*bx_dim1 + a_1]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_dim1 + a_1]


/*  -- LAPACK routine (instrumented to count ops, version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    DLALSA is an itermediate step in solving the least squares problem   
    by computing the SVD of the coefficient matrix in compact form (The   
    singular vectors are computed as products of simple orthorgonal   
    matrices.).   

    If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector   
    matrix of an upper bidiagonal matrix to the right hand side; and if   
    ICOMPQ = 1, DLALSA applies the right singular vector matrix to the   
    right hand side. The singular vector matrices were generated in   
    compact form by DLALSA.   

    Arguments   
    =========   


    ICOMPQ (input) INTEGER   
           Specifies whether the left or the right singular vector   
           matrix is involved.   
           = 0: Left singular vector matrix   
           = 1: Right singular vector matrix   

    SMLSIZ (input) INTEGER   
           The maximum size of the subproblems at the bottom of the   
           computation tree.   

    N      (input) INTEGER   
           The row and column dimensions of the upper bidiagonal matrix.   

    NRHS   (input) INTEGER   
           The number of columns of B and BX. NRHS must be at least 1.   

    B      (input) DOUBLE PRECISION array, dimension ( LDB, NRHS )   
           On input, B contains the right hand sides of the least   
           squares problem in rows 1 through M. On output, B contains   
           the solution X in rows 1 through N.   

    LDB    (input) INTEGER   
           The leading dimension of B in the calling subprogram.   
           LDB must be at least max(1,MAX( M, N ) ).   

    BX     (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS )   
           On exit, the result of applying the left or right singular   
           vector matrix to B.   

    LDBX   (input) INTEGER   
           The leading dimension of BX.   

    U      (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).   
           On entry, U contains the left singular vector matrices of all   
           subproblems at the bottom level.   

    LDU    (input) INTEGER, LDU = > N.   
           The leading dimension of arrays U, VT, DIFL, DIFR,   
           POLES, GIVNUM, and Z.   

    VT     (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).   
           On entry, VT' contains the right singular vector matrices of   
           all subproblems at the bottom level.   

    K      (input) INTEGER array, dimension ( N ).   

    DIFL   (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).   
           where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.   

    DIFR   (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).   
           On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record   
           distances between singular values on the I-th level and   
           singular values on the (I -1)-th level, and DIFR(*, 2 * I)   
           record the normalizing factors of the right singular vectors   
           matrices of subproblems on I-th level.   

    Z      (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).   
           On entry, Z(1, I) contains the components of the deflation-   
           adjusted updating row vector for subproblems on the I-th   
           level.   

    POLES  (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).   
           On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old   
           singular values involved in the secular equations on the I-th   
           level.   

    GIVPTR (input) INTEGER array, dimension ( N ).   
           On entry, GIVPTR( I ) records the number of Givens   
           rotations performed on the I-th problem on the computation   
           tree.   

    GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).   
           On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the   
           locations of Givens rotations performed on the I-th level on   
           the computation tree.   

    LDGCOL (input) INTEGER, LDGCOL = > N.   
           The leading dimension of arrays GIVCOL and PERM.   

    PERM   (input) INTEGER array, dimension ( LDGCOL, NLVL ).   
           On entry, PERM(*, I) records permutations done on the I-th   
           level of the computation tree.   

    GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).   
           On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-   
           values of Givens rotations performed on the I-th level on the   
           computation tree.   

    C      (input) DOUBLE PRECISION array, dimension ( N ).   
           On entry, if the I-th subproblem is not square,   
           C( I ) contains the C-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    S      (input) DOUBLE PRECISION array, dimension ( N ).   
           On entry, if the I-th subproblem is not square,   
           S( I ) contains the S-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    WORK   (workspace) DOUBLE PRECISION array.   
           The dimension must be at least N.   

    IWORK  (workspace) INTEGER array.   
           The dimension must be at least 3 * N   

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

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


       Test the input parameters.   

       Parameter adjustments */
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    bx_dim1 = *ldbx;
    bx_offset = 1 + bx_dim1 * 1;
    bx -= bx_offset;
    givnum_dim1 = *ldu;
    givnum_offset = 1 + givnum_dim1 * 1;
    givnum -= givnum_offset;
    poles_dim1 = *ldu;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    difr_dim1 = *ldu;
    difr_offset = 1 + difr_dim1 * 1;
    difr -= difr_offset;
    difl_dim1 = *ldu;
    difl_offset = 1 + difl_dim1 * 1;
    difl -= difl_offset;
    vt_dim1 = *ldu;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    --k;
    --givptr;
    perm_dim1 = *ldgcol;
    perm_offset = 1 + perm_dim1 * 1;
    perm -= perm_offset;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1 * 1;
    givcol -= givcol_offset;
    --c__;
    --s;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*smlsiz < 3) {
	*info = -2;
    } else if (*n < *smlsiz) {
	*info = -3;
    } else if (*nrhs < 1) {
	*info = -4;
    } else if (*ldb < *n) {
	*info = -6;
    } else if (*ldbx < *n) {
	*info = -8;
    } else if (*ldu < *n) {
	*info = -10;
    } else if (*ldgcol < *n) {
	*info = -19;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DLALSA", &i__1);
	return 0;
    }

/*     Book-keeping and  setting up the computation tree. */

    inode = 1;
    ndiml = inode + *n;
    ndimr = ndiml + *n;

    dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 
	    smlsiz);

/*     The following code applies back the left singular vector factors.   
       For applying back the right singular vector factors, go to 50. */

    if (*icompq == 1) {
	goto L50;
    }

/*     The nodes on the bottom level of the tree were solved by DLASDQ.   
       The corresponding left and right singular vector matrices are in   
       explicit form. First apply back the left singular vector matrices. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node   
          NL : number of rows of left  subproblem   
          NR : number of rows of right subproblem   
          NLF: starting row of the left   subproblem   
          NRF: starting row of the right  subproblem */

	i1 = i__ - 1;
	ic = iwork[inode + i1];
	nl = iwork[ndiml + i1];
	nr = iwork[ndimr + i1];
	nlf = ic - nl;
	nrf = ic + 1;
	latime_1.ops += dopbl3_("DGEMM ", &nl, nrhs, &nl);
	latime_1.ops += dopbl3_("DGEMM ", &nr, nrhs, &nr);
	dgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u_ref(nlf, 1), ldu, &b_ref(
		nlf, 1), ldb, &c_b10, &bx_ref(nlf, 1), ldbx);
	dgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u_ref(nrf, 1), ldu, &b_ref(
		nrf, 1), ldb, &c_b10, &bx_ref(nrf, 1), ldbx);
/* L10: */
    }

/*     Next copy the rows of B that correspond to unchanged rows   
       in the bidiagonal matrix to BX. */

    i__1 = nd;
    for (i__ = 1; i__ <= i__1; ++i__) {
	ic = iwork[inode + i__ - 1];
	dcopy_(nrhs, &b_ref(ic, 1), ldb, &bx_ref(ic, 1), ldbx);
/* L20: */
    }

/*     Finally go through the left singular vector matrices of all   
       the other subproblems bottom-up on the tree. */

    j = pow_ii(&c__2, &nlvl);
    sqre = 0;

    for (lvl = nlvl; lvl >= 1; --lvl) {
	lvl2 = (lvl << 1) - 1;

/*        find the first node LF and last node LL on   
          the current level LVL */

	if (lvl == 1) {
	    lf = 1;
	    ll = 1;
	} else {
	    i__1 = lvl - 1;
	    lf = pow_ii(&c__2, &i__1);
	    ll = (lf << 1) - 1;
	}
	i__1 = ll;
	for (i__ = lf; i__ <= i__1; ++i__) {
	    im1 = i__ - 1;
	    ic = iwork[inode + im1];
	    nl = iwork[ndiml + im1];
	    nr = iwork[ndimr + im1];
	    nlf = ic - nl;
	    nrf = ic + 1;
	    --j;
	    dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx_ref(nlf, 1), ldbx, &
		    b_ref(nlf, 1), ldb, &perm_ref(nlf, lvl), &givptr[j], &
		    givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2), 
		    ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
		    difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
		    s[j], &work[1], info);
/* L30: */
	}
/* L40: */
    }
    goto L90;

/*     ICOMPQ = 1: applying back the right singular vector factors. */

L50:

/*     First now go through the right singular vector matrices of all   
       the tree nodes top-down. */

    j = 0;
    i__1 = nlvl;
    for (lvl = 1; lvl <= i__1; ++lvl) {
	lvl2 = (lvl << 1) - 1;

/*        Find the first node LF and last node LL on   
          the current level LVL. */

	if (lvl == 1) {
	    lf = 1;
	    ll = 1;
	} else {
	    i__2 = lvl - 1;
	    lf = pow_ii(&c__2, &i__2);
	    ll = (lf << 1) - 1;
	}
	i__2 = lf;
	for (i__ = ll; i__ >= i__2; --i__) {
	    im1 = i__ - 1;
	    ic = iwork[inode + im1];
	    nl = iwork[ndiml + im1];
	    nr = iwork[ndimr + im1];
	    nlf = ic - nl;
	    nrf = ic + 1;
	    if (i__ == ll) {
		sqre = 0;
	    } else {
		sqre = 1;
	    }
	    ++j;
	    dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b_ref(nlf, 1), ldb, &
		    bx_ref(nlf, 1), ldbx, &perm_ref(nlf, lvl), &givptr[j], &
		    givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2), 
		    ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
		    difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
		    s[j], &work[1], info);
/* L60: */
	}
/* L70: */
    }

/*     The nodes on the bottom level of the tree were solved by DLASDQ.   
       The corresponding right singular vector matrices are in explicit   
       form. Apply them back. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {
	i1 = i__ - 1;
	ic = iwork[inode + i1];
	nl = iwork[ndiml + i1];
	nr = iwork[ndimr + i1];
	nlp1 = nl + 1;
	if (i__ == nd) {
	    nrp1 = nr;
	} else {
	    nrp1 = nr + 1;
	}
	nlf = ic - nl;
	nrf = ic + 1;
	latime_1.ops += dopbl3_("DGEMM ", &nlp1, nrhs, &nlp1);
	latime_1.ops += dopbl3_("DGEMM ", &nrp1, nrhs, &nrp1);
	dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt_ref(nlf, 1), ldu, &
		b_ref(nlf, 1), ldb, &c_b10, &bx_ref(nlf, 1), ldbx);
	dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt_ref(nrf, 1), ldu, &
		b_ref(nrf, 1), ldb, &c_b10, &bx_ref(nrf, 1), ldbx);
/* L80: */
    }

L90:

    return 0;

/*     End of DLALSA */

} /* dlalsa_ */