text: #include "clapack.h"
  
  /* Table of constant values */
  
  static integer c__0 = 0;
  static real c_b7 = 1.f;
  static integer c__1 = 1;
  static integer c_n1 = -1;
  
  /* Subroutine */ int slasd6_(integer* icompq, integer* nl, integer* nr,
                               integer* sqre, real* d__, real* vf, real* vl, real* alpha, real* beta,
                               integer* idxq, 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* iwork, integer* info) {
      /* System generated locals */
      integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
              poles_dim1, poles_offset, i__1;
      real r__1, r__2;
  
      /* Local variables */
      integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
      extern /* Subroutine */ int scopy_(integer*, real*, integer*, real*,
                                         integer*), slasd7_(integer*, integer*, integer*, integer*,
                                                 integer*, real*, real*, real*, real*, real*, real*, real*,
                                                 real*, real*, real*, integer*, integer*, integer*, integer
                                                 *, integer*, integer*, integer*, real*, integer*, real*,
                                                 real*, integer*), slasd8_(integer*, integer*, real*, real*,
                                                         real*, real*, real*, real*, integer*, real*, real*,
                                                         integer*);
      integer isigma;
      extern /* Subroutine */ int xerbla_(char*, integer*), slascl_(
          char*, integer*, integer*, real*, real*, integer*, integer *
          , real*, integer*, integer*), slamrg_(integer*,
                  integer*, real*, integer*, integer*, integer*);
      real orgnrm;
  
  
      /*  -- LAPACK auxiliary routine (version 3.1) -- */
      /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
      /*     November 2006 */
  
      /*     .. Scalar Arguments .. */
      /*     .. */
      /*     .. Array Arguments .. */
      /*     .. */
  
      /*  Purpose */
      /*  ======= */
  
      /*  SLASD6 computes the SVD of an updated upper bidiagonal matrix B */
      /*  obtained by merging two smaller ones by appending a row. This */
      /*  routine is used only for the problem which requires all singular */
      /*  values and optionally singular vector matrices in factored form. */
      /*  B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
      /*  A related subroutine, SLASD1, handles the case in which all singular */
      /*  values and singular vectors of the bidiagonal matrix are desired. */
  
      /*  SLASD6 computes the SVD as follows: */
  
      /*                ( D1(in)  0    0     0 ) */
      /*    B = U(in) * (   Z1'   a   Z2'    b ) * VT(in) */
      /*                (   0     0   D2(in) 0 ) */
  
      /*      = U(out) * ( D(out) 0) * VT(out) */
  
      /*  where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */
      /*  with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
      /*  elsewhere; and the entry b is empty if SQRE = 0. */
  
      /*  The singular values of B can be computed using D1, D2, the first */
      /*  components of all the right singular vectors of the lower block, and */
      /*  the last components of all the right singular vectors of the upper */
      /*  block. These components are stored and updated in VF and VL, */
      /*  respectively, in SLASD6. Hence U and VT are not explicitly */
      /*  referenced. */
  
      /*  The singular values are stored in D. The algorithm consists of two */
      /*  stages: */
  
      /*        The first stage consists of deflating the size of the problem */
      /*        when there are multiple singular values or if there is a zero */
      /*        in the Z vector. For each such occurence the dimension of the */
      /*        secular equation problem is reduced by one. This stage is */
      /*        performed by the routine SLASD7. */
  
      /*        The second stage consists of calculating the updated */
      /*        singular values. This is done by finding the roots of the */
      /*        secular equation via the routine SLASD4 (as called by SLASD8). */
      /*        This routine also updates VF and VL and computes the distances */
      /*        between the updated singular values and the old singular */
      /*        values. */
  
      /*  SLASD6 is called from SLASDA. */
  
      /*  Arguments */
      /*  ========= */
  
      /*  ICOMPQ (input) INTEGER */
      /*         Specifies whether singular vectors are to be computed in */
      /*         factored form: */
      /*         = 0: Compute singular values only. */
      /*         = 1: Compute singular vectors in factored form as well. */
  
      /*  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. */
  
      /*  D      (input/output) REAL array, dimension (NL+NR+1). */
      /*         On entry D(1:NL,1:NL) contains the singular values of the */
      /*         upper block, and D(NL+2:N) contains the singular values */
      /*         of the lower block. On exit D(1:N) contains the singular */
      /*         values of the modified matrix. */
  
      /*  VF     (input/output) REAL array, dimension (M) */
      /*         On entry, VF(1:NL+1) contains the first components of all */
      /*         right singular vectors of the upper block; and VF(NL+2:M) */
      /*         contains the first components of all right singular vectors */
      /*         of the lower block. On exit, VF contains the first components */
      /*         of all right singular vectors of the bidiagonal matrix. */
  
      /*  VL     (input/output) REAL array, dimension (M) */
      /*         On entry, VL(1:NL+1) contains the  last components of all */
      /*         right singular vectors of the upper block; and VL(NL+2:M) */
      /*         contains the last components of all right singular vectors of */
      /*         the lower block. On exit, VL contains the last components of */
      /*         all right singular vectors of the bidiagonal matrix. */
  
      /*  ALPHA  (input/output) REAL */
      /*         Contains the diagonal element associated with the added row. */
  
      /*  BETA   (input/output) REAL */
      /*         Contains the off-diagonal element associated with the added */
      /*         row. */
  
      /*  IDXQ   (output) INTEGER array, dimension (N) */
      /*         This contains the permutation which will reintegrate the */
      /*         subproblem just solved back into sorted order, i.e. */
      /*         D( IDXQ( I = 1, N ) ) will be in ascending order. */
  
      /*  PERM   (output) INTEGER array, dimension ( N ) */
      /*         The permutations (from deflation and sorting) to be applied */
      /*         to each block. Not referenced if ICOMPQ = 0. */
  
      /*  GIVPTR (output) INTEGER */
      /*         The number of Givens rotations which took place in this */
      /*         subproblem. Not referenced if ICOMPQ = 0. */
  
      /*  GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) */
      /*         Each pair of numbers indicates a pair of columns to take place */
      /*         in a Givens rotation. Not referenced if ICOMPQ = 0. */
  
      /*  LDGCOL (input) INTEGER */
      /*         leading dimension of GIVCOL, must be at least N. */
  
      /*  GIVNUM (output) REAL array, dimension ( LDGNUM, 2 ) */
      /*         Each number indicates the C or S value to be used in the */
      /*         corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
  
      /*  LDGNUM (input) INTEGER */
      /*         The leading dimension of GIVNUM and POLES, must be at least N. */
  
      /*  POLES  (output) REAL array, dimension ( LDGNUM, 2 ) */
      /*         On exit, POLES(1,*) is an array containing the new singular */
      /*         values obtained from solving the secular equation, and */
      /*         POLES(2,*) is an array containing the poles in the secular */
      /*         equation. Not referenced if ICOMPQ = 0. */
  
      /*  DIFL   (output) REAL array, dimension ( N ) */
      /*         On exit, DIFL(I) is the distance between I-th updated */
      /*         (undeflated) singular value and the I-th (undeflated) old */
      /*         singular value. */
  
      /*  DIFR   (output) REAL array, */
      /*                  dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */
      /*                  dimension ( N ) if ICOMPQ = 0. */
      /*         On exit, DIFR(I, 1) is the distance between I-th updated */
      /*         (undeflated) singular value and the I+1-th (undeflated) old */
      /*         singular value. */
  
      /*         If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
      /*         normalizing factors for the right singular vector matrix. */
  
      /*         See SLASD8 for details on DIFL and DIFR. */
  
      /*  Z      (output) REAL array, dimension ( M ) */
      /*         The first elements of this array contain the components */
      /*         of the deflation-adjusted updating row vector. */
  
      /*  K      (output) INTEGER */
      /*         Contains the dimension of the non-deflated matrix, */
      /*         This is the order of the related secular equation. 1 <= K <=N. */
  
      /*  C      (output) 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      (output) 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 ( 4 * M ) */
  
      /*  IWORK  (workspace) INTEGER array, dimension ( 3 * N ) */
  
      /*  INFO   (output) INTEGER */
      /*          = 0:  successful exit. */
      /*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
      /*          > 0:  if INFO = 1, an singular value did not converge */
  
      /*  Further Details */
      /*  =============== */
  
      /*  Based on contributions by */
      /*     Ming Gu and Huan Ren, Computer Science Division, University of */
      /*     California at Berkeley, USA */
  
      /*  ===================================================================== */
  
      /*     .. Parameters .. */
      /*     .. */
      /*     .. Local Scalars .. */
      /*     .. */
      /*     .. External Subroutines .. */
      /*     .. */
      /*     .. Intrinsic Functions .. */
      /*     .. */
      /*     .. Executable Statements .. */
  
      /*     Test the input parameters. */
  
      /* Parameter adjustments */
      --d__;
      --vf;
      --vl;
      --idxq;
      --perm;
      givcol_dim1 = *ldgcol;
      givcol_offset = 1 + givcol_dim1;
      givcol -= givcol_offset;
      poles_dim1 = *ldgnum;
      poles_offset = 1 + poles_dim1;
      poles -= poles_offset;
      givnum_dim1 = *ldgnum;
      givnum_offset = 1 + givnum_dim1;
      givnum -= givnum_offset;
      --difl;
      --difr;
      --z__;
      --work;
      --iwork;
  
      /* Function Body */
      *info = 0;
      n = *nl + *nr + 1;
      m = n + *sqre;
  
      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;
      } else if (*ldgcol < n) {
          *info = -14;
      } else if (*ldgnum < n) {
          *info = -16;
      }
      if (*info != 0) {
          i__1 = -(*info);
          xerbla_("SLASD6", &i__1);
          return 0;
      }
  
      /*     The following values are for bookkeeping purposes only.  They are */
      /*     integer pointers which indicate the portion of the workspace */
      /*     used by a particular array in SLASD7 and SLASD8. */
  
      isigma = 1;
      iw = isigma + n;
      ivfw = iw + m;
      ivlw = ivfw + m;
  
      idx = 1;
      idxc = idx + n;
      idxp = idxc + n;
  
      /*     Scale. */
  
      /* Computing MAX */
      r__1 = dabs(*alpha), r__2 = dabs(*beta);
      orgnrm = dmax(r__1, r__2);
      d__[*nl + 1] = 0.f;
      i__1 = n;
      for (i__ = 1; i__ <= i__1; ++i__) {
          if ((r__1 = d__[i__], dabs(r__1)) > orgnrm) {
              orgnrm = (r__1 = d__[i__], dabs(r__1));
          }
          /* L10: */
      }
      slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
      *alpha /= orgnrm;
      *beta /= orgnrm;
  
      /*     Sort and Deflate singular values. */
  
      slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
              work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
              iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
                  givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
              info);
  
      /*     Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
  
      slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
              ldgnum, &work[isigma], &work[iw], info);
  
      /*     Save the poles if ICOMPQ = 1. */
  
      if (*icompq == 1) {
          scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
          scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
      }
  
      /*     Unscale. */
  
      slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
  
      /*     Prepare the IDXQ sorting permutation. */
  
      n1 = *k;
      n2 = n - *k;
      slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
  
      return 0;
  
      /*     End of SLASD6 */
  
  } /* slasd6_ */
  