text: /* dggqrf.f -- translated by f2c (version 20061008).
     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
  */
  
  #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  
  /* Subroutine */ int dggqrf_(integer *n, integer *m, integer *p, doublereal *
  	a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, 
  	doublereal *taub, doublereal *work, integer *lwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
  
      /* Local variables */
      integer nb, nb1, nb2, nb3, lopt;
      extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, integer *, integer *), 
  	    dgerqf_(integer *, integer *, doublereal *, integer *, doublereal 
  	    *, doublereal *, integer *, integer *), xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
  	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
  	    integer *, doublereal *, integer *, integer *);
      integer lwkopt;
      logical lquery;
  
  
  /*  -- LAPACK routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DGGQRF computes a generalized QR factorization of an N-by-M matrix A */
  /*  and an N-by-P matrix B: */
  
  /*              A = Q*R,        B = Q*T*Z, */
  
  /*  where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
  /*  matrix, and R and T assume one of the forms: */
  
  /*  if N >= M,  R = ( R11 ) M  ,   or if N < M,  R = ( R11  R12 ) N, */
  /*                  (  0  ) N-M                         N   M-N */
  /*                     M */
  
  /*  where R11 is upper triangular, and */
  
  /*  if N <= P,  T = ( 0  T12 ) N,   or if N > P,  T = ( T11 ) N-P, */
  /*                   P-N  N                           ( T21 ) P */
  /*                                                       P */
  
  /*  where T12 or T21 is upper triangular. */
  
  /*  In particular, if B is square and nonsingular, the GQR factorization */
  /*  of A and B implicitly gives the QR factorization of inv(B)*A: */
  
  /*               inv(B)*A = Z'*(inv(T)*R) */
  
  /*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the */
  /*  transpose of the matrix Z. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  N       (input) INTEGER */
  /*          The number of rows of the matrices A and B. N >= 0. */
  
  /*  M       (input) INTEGER */
  /*          The number of columns of the matrix A.  M >= 0. */
  
  /*  P       (input) INTEGER */
  /*          The number of columns of the matrix B.  P >= 0. */
  
  /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,M) */
  /*          On entry, the N-by-M matrix A. */
  /*          On exit, the elements on and above the diagonal of the array */
  /*          contain the min(N,M)-by-M upper trapezoidal matrix R (R is */
  /*          upper triangular if N >= M); the elements below the diagonal, */
  /*          with the array TAUA, represent the orthogonal matrix Q as a */
  /*          product of min(N,M) elementary reflectors (see Further */
  /*          Details). */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A. LDA >= max(1,N). */
  
  /*  TAUA    (output) DOUBLE PRECISION array, dimension (min(N,M)) */
  /*          The scalar factors of the elementary reflectors which */
  /*          represent the orthogonal matrix Q (see Further Details). */
  
  /*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,P) */
  /*          On entry, the N-by-P matrix B. */
  /*          On exit, if N <= P, the upper triangle of the subarray */
  /*          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
  /*          if N > P, the elements on and above the (N-P)-th subdiagonal */
  /*          contain the N-by-P upper trapezoidal matrix T; the remaining */
  /*          elements, with the array TAUB, represent the orthogonal */
  /*          matrix Z as a product of elementary reflectors (see Further */
  /*          Details). */
  
  /*  LDB     (input) INTEGER */
  /*          The leading dimension of the array B. LDB >= max(1,N). */
  
  /*  TAUB    (output) DOUBLE PRECISION array, dimension (min(N,P)) */
  /*          The scalar factors of the elementary reflectors which */
  /*          represent the orthogonal matrix Z (see Further Details). */
  
  /*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The dimension of the array WORK. LWORK >= max(1,N,M,P). */
  /*          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */
  /*          where NB1 is the optimal blocksize for the QR factorization */
  /*          of an N-by-M matrix, NB2 is the optimal blocksize for the */
  /*          RQ factorization of an N-by-P matrix, and NB3 is the optimal */
  /*          blocksize for a call of DORMQR. */
  
  /*          If LWORK = -1, then a workspace query is assumed; the routine */
  /*          only calculates the optimal size of the WORK array, returns */
  /*          this value as the first entry of the WORK array, and no error */
  /*          message related to LWORK is issued by XERBLA. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  The matrix Q is represented as a product of elementary reflectors */
  
  /*     Q = H(1) H(2) . . . H(k), where k = min(n,m). */
  
  /*  Each H(i) has the form */
  
  /*     H(i) = I - taua * v * v' */
  
  /*  where taua is a real scalar, and v is a real vector with */
  /*  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
  /*  and taua in TAUA(i). */
  /*  To form Q explicitly, use LAPACK subroutine DORGQR. */
  /*  To use Q to update another matrix, use LAPACK subroutine DORMQR. */
  
  /*  The matrix Z is represented as a product of elementary reflectors */
  
  /*     Z = H(1) H(2) . . . H(k), where k = min(n,p). */
  
  /*  Each H(i) has the form */
  
  /*     H(i) = I - taub * v * v' */
  
  /*  where taub is a real scalar, and v is a real vector with */
  /*  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */
  /*  B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */
  /*  To form Z explicitly, use LAPACK subroutine DORGRQ. */
  /*  To use Z to update another matrix, use LAPACK subroutine DORMRQ. */
  
  /*  ===================================================================== */
  
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --taua;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1;
      b -= b_offset;
      --taub;
      --work;
  
      /* Function Body */
      *info = 0;
      nb1 = ilaenv_(&c__1, "DGEQRF", " ", n, m, &c_n1, &c_n1);
      nb2 = ilaenv_(&c__1, "DGERQF", " ", n, p, &c_n1, &c_n1);
      nb3 = ilaenv_(&c__1, "DORMQR", " ", n, m, p, &c_n1);
  /* Computing MAX */
      i__1 = max(nb1,nb2);
      nb = max(i__1,nb3);
  /* Computing MAX */
      i__1 = max(*n,*m);
      lwkopt = max(i__1,*p) * nb;
      work[1] = (doublereal) lwkopt;
      lquery = *lwork == -1;
      if (*n < 0) {
  	*info = -1;
      } else if (*m < 0) {
  	*info = -2;
      } else if (*p < 0) {
  	*info = -3;
      } else if (*lda < max(1,*n)) {
  	*info = -5;
      } else if (*ldb < max(1,*n)) {
  	*info = -8;
      } else /* if(complicated condition) */ {
  /* Computing MAX */
  	i__1 = max(1,*n), i__1 = max(i__1,*m);
  	if (*lwork < max(i__1,*p) && ! lquery) {
  	    *info = -11;
  	}
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DGGQRF", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     QR factorization of N-by-M matrix A: A = Q*R */
  
      dgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
      lopt = (integer) work[1];
  
  /*     Update B := Q'*B. */
  
      i__1 = min(*n,*m);
      dormqr_("Left", "Transpose", n, p, &i__1, &a[a_offset], lda, &taua[1], &b[
  	    b_offset], ldb, &work[1], lwork, info);
  /* Computing MAX */
      i__1 = lopt, i__2 = (integer) work[1];
      lopt = max(i__1,i__2);
  
  /*     RQ factorization of N-by-P matrix B: B = T*Z. */
  
      dgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
  /* Computing MAX */
      i__1 = lopt, i__2 = (integer) work[1];
      work[1] = (doublereal) max(i__1,i__2);
  
      return 0;
  
  /*     End of DGGQRF */
  
  } /* dggqrf_ */
  