zgeqrs.f

Go to the documentation of this file.

      SUBROUTINE zgeqrs( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
     $                   info )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            info, lda, ldb, lwork, m, n, nrhs
*     ..
*     .. Array Arguments ..
      COMPLEX*16         a( lda, * ), b( ldb, * ), tau( * ),
     $                   work( lwork )
*     ..
*
*  Purpose
*  =======
*
*  Solve the least squares problem
*      min || A*X - B ||
*  using the QR factorization
*      A = Q*R
*  computed by ZGEQRF.
*
*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  M >= N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of columns of B.  NRHS >= 0.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          Details of the QR factorization of the original matrix A as
*          returned by ZGEQRF.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= M.
*
*  TAU     (input) COMPLEX*16 array, dimension (N)
*          Details of the orthogonal matrix Q.
*
*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
*          On entry, the m-by-nrhs right hand side matrix B.
*          On exit, the n-by-nrhs solution matrix X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B. LDB >= M.
*
*  WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
*
*  LWORK   (input) INTEGER
*          The length of the array WORK.  LWORK must be at least NRHS,
*          and should be at least NRHS*NB, where NB is the block size
*          for this environment.
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         one
      parameter( one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, ztrsm, zunmqr
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments.
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
         info = -2
      ELSE IF( nrhs.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      ELSE IF( ldb.LT.max( 1, m ) ) THEN
         info = -8
      ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
     $          THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZGEQRS', -info )
         return
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
     $   return
*
*     B := Q' * B
*
      CALL zunmqr( 'Left', 'Conjugate transpose', m, nrhs, n, a, lda,
     $             tau, b, ldb, work, lwork, info )
*
*     Solve R*X = B(1:n,:)
*
      CALL ztrsm( 'Left', 'Upper', 'No transpose', 'Non-unit', n, nrhs,
     $            one, a, lda, b, ldb )
*
      return
*
*     End of ZGEQRS
*
      END