text: /* lapack/double/dorgqr.f -- translated by f2c (version 20050501).
     You must link the resulting object file with libf2c:
          on Microsoft Windows system, link with libf2c.lib;
          on Linux or Unix systems, link with .../path/to/libf2c.a -lm
          or, if you install libf2c.a in a standard place, with -lf2c -lm
          -- in that order, at the end of the command line, as in
                  cc *.o -lf2c -lm
          Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
  
                  http://www.netlib.org/f2c/libf2c.zip
  */
  
  #ifdef __cplusplus
  extern "C" {
  #endif
  #include "v3p_netlib.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  static integer c__3 = 3;
  static integer c__2 = 2;
  
  /*<       SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) >*/
  /* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal *
          a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
          integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3;
  
      /* Local variables */
      integer i__, j, l, ib, nb, ki=0, kk, nx, iws, nbmin, iinfo;
      extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *,
              doublereal *, integer *, doublereal *, doublereal *, integer *),
              dlarfb_(char *, char *, char *, char *, integer *, integer *,
              integer *, doublereal *, integer *, doublereal *, integer *,
              doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen,
              ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *,
              doublereal *, integer *, doublereal *, doublereal *, integer *,
              ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
              integer *, integer *, ftnlen, ftnlen);
      integer ldwork, lwkopt;
      logical lquery;
  
  
  /*  -- 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 */
  
  /*     .. Scalar Arguments .. */
  /*<       INTEGER            INFO, K, LDA, LWORK, M, N >*/
  /*     .. */
  /*     .. Array Arguments .. */
  /*<       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * ) >*/
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DORGQR generates an M-by-N real matrix Q with orthonormal columns, */
  /*  which is defined as the first N columns of a product of K elementary */
  /*  reflectors of order M */
  
  /*        Q  =  H(1) H(2) . . . H(k) */
  
  /*  as returned by DGEQRF. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  M       (input) INTEGER */
  /*          The number of rows of the matrix Q. M >= 0. */
  
  /*  N       (input) INTEGER */
  /*          The number of columns of the matrix Q. M >= N >= 0. */
  
  /*  K       (input) INTEGER */
  /*          The number of elementary reflectors whose product defines the */
  /*          matrix Q. N >= K >= 0. */
  
  /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
  /*          On entry, the i-th column must contain the vector which */
  /*          defines the elementary reflector H(i), for i = 1,2,...,k, as */
  /*          returned by DGEQRF in the first k columns of its array */
  /*          argument A. */
  /*          On exit, the M-by-N matrix Q. */
  
  /*  LDA     (input) INTEGER */
  /*          The first dimension of the array A. LDA >= max(1,M). */
  
  /*  TAU     (input) DOUBLE PRECISION array, dimension (K) */
  /*          TAU(i) must contain the scalar factor of the elementary */
  /*          reflector H(i), as returned by DGEQRF. */
  
  /*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The dimension of the array WORK. LWORK >= max(1,N). */
  /*          For optimum performance LWORK >= N*NB, where NB is the */
  /*          optimal blocksize. */
  
  /*          If LWORK = -1, then a workspace query is assumed; the routine */
  /*          only calculates the optimal size of the WORK array, returns */
  /*          this value as the first entry of the WORK array, and no error */
  /*          message related to LWORK is issued by XERBLA. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument has an illegal value */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*<       DOUBLE PRECISION   ZERO >*/
  /*<       PARAMETER          ( ZERO = 0.0D+0 ) >*/
  /*     .. */
  /*     .. Local Scalars .. */
  /*<       LOGICAL            LQUERY >*/
  /*<    >*/
  /*     .. */
  /*     .. External Subroutines .. */
  /*<       EXTERNAL           DLARFB, DLARFT, DORG2R, XERBLA >*/
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*<       INTRINSIC          MAX, MIN >*/
  /*     .. */
  /*     .. External Functions .. */
  /*<       INTEGER            ILAENV >*/
  /*<       EXTERNAL           ILAENV >*/
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input arguments */
  
  /*<       INFO = 0 >*/
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --tau;
      --work;
  
      /* Function Body */
      *info = 0;
  /*<       NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) >*/
      nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
  /*<       LWKOPT = MAX( 1, N )*NB >*/
      lwkopt = max(1,*n) * nb;
  /*<       WORK( 1 ) = LWKOPT >*/
      work[1] = (doublereal) lwkopt;
  /*<       LQUERY = ( LWORK.EQ.-1 ) >*/
      lquery = *lwork == -1;
  /*<       IF( M.LT.0 ) THEN >*/
      if (*m < 0) {
  /*<          INFO = -1 >*/
          *info = -1;
  /*<       ELSE IF( N.LT.0 .OR. N.GT.M ) THEN >*/
      } else if (*n < 0 || *n > *m) {
  /*<          INFO = -2 >*/
          *info = -2;
  /*<       ELSE IF( K.LT.0 .OR. K.GT.N ) THEN >*/
      } else if (*k < 0 || *k > *n) {
  /*<          INFO = -3 >*/
          *info = -3;
  /*<       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
      } else if (*lda < max(1,*m)) {
  /*<          INFO = -5 >*/
          *info = -5;
  /*<       ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
      } else if (*lwork < max(1,*n) && ! lquery) {
  /*<          INFO = -8 >*/
          *info = -8;
  /*<       END IF >*/
      }
  /*<       IF( INFO.NE.0 ) THEN >*/
      if (*info != 0) {
  /*<          CALL XERBLA( 'DORGQR', -INFO ) >*/
          i__1 = -(*info);
          xerbla_("DORGQR", &i__1, (ftnlen)6);
  /*<          RETURN >*/
          return 0;
  /*<       ELSE IF( LQUERY ) THEN >*/
      } else if (lquery) {
  /*<          RETURN >*/
          return 0;
  /*<       END IF >*/
      }
  
  /*     Quick return if possible */
  
  /*<       IF( N.LE.0 ) THEN >*/
      if (*n <= 0) {
  /*<          WORK( 1 ) = 1 >*/
          work[1] = 1.;
  /*<          RETURN >*/
          return 0;
  /*<       END IF >*/
      }
  
  /*<       NBMIN = 2 >*/
      nbmin = 2;
  /*<       NX = 0 >*/
      nx = 0;
  /*<       IWS = N >*/
      iws = *n;
  /*<       IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
      if (nb > 1 && nb < *k) {
  
  /*        Determine when to cross over from blocked to unblocked code. */
  
  /*<          NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
  /* Computing MAX */
          i__1 = 0, i__2 = ilaenv_(&c__3, "DORGQR", " ", m, n, k, &c_n1, (
                  ftnlen)6, (ftnlen)1);
          nx = max(i__1,i__2);
  /*<          IF( NX.LT.K ) THEN >*/
          if (nx < *k) {
  
  /*           Determine if workspace is large enough for blocked code. */
  
  /*<             LDWORK = N >*/
              ldwork = *n;
  /*<             IWS = LDWORK*NB >*/
              iws = ldwork * nb;
  /*<             IF( LWORK.LT.IWS ) THEN >*/
              if (*lwork < iws) {
  
  /*              Not enough workspace to use optimal NB:  reduce NB and */
  /*              determine the minimum value of NB. */
  
  /*<                NB = LWORK / LDWORK >*/
                  nb = *lwork / ldwork;
  /*<                NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
  /* Computing MAX */
                  i__1 = 2, i__2 = ilaenv_(&c__2, "DORGQR", " ", m, n, k, &c_n1,
                           (ftnlen)6, (ftnlen)1);
                  nbmin = max(i__1,i__2);
  /*<             END IF >*/
              }
  /*<          END IF >*/
          }
  /*<       END IF >*/
      }
  
  /*<       IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
      if (nb >= nbmin && nb < *k && nx < *k) {
  
  /*        Use blocked code after the last block. */
  /*        The first kk columns are handled by the block method. */
  
  /*<          KI = ( ( K-NX-1 ) / NB )*NB >*/
          ki = (*k - nx - 1) / nb * nb;
  /*<          KK = MIN( K, KI+NB ) >*/
  /* Computing MIN */
          i__1 = *k, i__2 = ki + nb;
          kk = min(i__1,i__2);
  
  /*        Set A(1:kk,kk+1:n) to zero. */
  
  /*<          DO 20 J = KK + 1, N >*/
          i__1 = *n;
          for (j = kk + 1; j <= i__1; ++j) {
  /*<             DO 10 I = 1, KK >*/
              i__2 = kk;
              for (i__ = 1; i__ <= i__2; ++i__) {
  /*<                A( I, J ) = ZERO >*/
                  a[i__ + j * a_dim1] = 0.;
  /*<    10       CONTINUE >*/
  /* L10: */
              }
  /*<    20    CONTINUE >*/
  /* L20: */
          }
  /*<       ELSE >*/
      } else {
  /*<          KK = 0 >*/
          kk = 0;
  /*<       END IF >*/
      }
  
  /*     Use unblocked code for the last or only block. */
  
  /*<    >*/
      if (kk < *n) {
          i__1 = *m - kk;
          i__2 = *n - kk;
          i__3 = *k - kk;
          dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
                  tau[kk + 1], &work[1], &iinfo);
      }
  
  /*<       IF( KK.GT.0 ) THEN >*/
      if (kk > 0) {
  
  /*        Use blocked code */
  
  /*<          DO 50 I = KI + 1, 1, -NB >*/
          i__1 = -nb;
          for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
  /*<             IB = MIN( NB, K-I+1 ) >*/
  /* Computing MIN */
              i__2 = nb, i__3 = *k - i__ + 1;
              ib = min(i__2,i__3);
  /*<             IF( I+IB.LE.N ) THEN >*/
              if (i__ + ib <= *n) {
  
  /*              Form the triangular factor of the block reflector */
  /*              H = H(i) H(i+1) . . . H(i+ib-1) */
  
  /*<    >*/
                  i__2 = *m - i__ + 1;
                  dlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
                          a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
                           (ftnlen)10);
  
  /*              Apply H to A(i:m,i+ib:n) from the left */
  
  /*<    >*/
                  i__2 = *m - i__ + 1;
                  i__3 = *n - i__ - ib + 1;
                  dlarfb_("Left", "No transpose", "Forward", "Columnwise", &
                          i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
                          1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
                          work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)
                          7, (ftnlen)10);
  /*<             END IF >*/
              }
  
  /*           Apply H to rows i:m of current block */
  
  /*<    >*/
              i__2 = *m - i__ + 1;
              dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
                      work[1], &iinfo);
  
  /*           Set rows 1:i-1 of current block to zero */
  
  /*<             DO 40 J = I, I + IB - 1 >*/
              i__2 = i__ + ib - 1;
              for (j = i__; j <= i__2; ++j) {
  /*<                DO 30 L = 1, I - 1 >*/
                  i__3 = i__ - 1;
                  for (l = 1; l <= i__3; ++l) {
  /*<                   A( L, J ) = ZERO >*/
                      a[l + j * a_dim1] = 0.;
  /*<    30          CONTINUE >*/
  /* L30: */
                  }
  /*<    40       CONTINUE >*/
  /* L40: */
              }
  /*<    50    CONTINUE >*/
  /* L50: */
          }
  /*<       END IF >*/
      }
  
  /*<       WORK( 1 ) = IWS >*/
      work[1] = (doublereal) iws;
  /*<       RETURN >*/
      return 0;
  
  /*     End of DORGQR */
  
  /*<       END >*/
  } /* dorgqr_ */
  
  #ifdef __cplusplus
          }
  #endif
  