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ElmerCSC
GitHub Repository: ElmerCSC/elmerfem
 Path: blob/devel/mathlibs/src/lapack/cgelq2.f
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      SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )

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*

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*  -- LAPACK routine (version 3.0) --

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*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

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*     Courant Institute, Argonne National Lab, and Rice University

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*     September 30, 1994

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*

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*     .. Scalar Arguments ..

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      INTEGER            INFO, LDA, M, N

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*     ..

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*     .. Array Arguments ..

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      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )

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*     ..

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*

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*  Purpose

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*  =======

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*

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*  CGELQ2 computes an LQ factorization of a complex m by n matrix A:

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*  A = L * Q.

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*

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*  Arguments

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*  =========

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*

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*  M       (input) INTEGER

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*          The number of rows of the matrix A.  M >= 0.

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*

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*  N       (input) INTEGER

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*          The number of columns of the matrix A.  N >= 0.

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*

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*  A       (input/output) COMPLEX array, dimension (LDA,N)

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*          On entry, the m by n matrix A.

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*          On exit, the elements on and below the diagonal of the array

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*          contain the m by min(m,n) lower trapezoidal matrix L (L is

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*          lower triangular if m <= n); the elements above the diagonal,

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*          with the array TAU, represent the unitary matrix Q as a

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*          product of elementary reflectors (see Further Details).

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*

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*  LDA     (input) INTEGER

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*          The leading dimension of the array A.  LDA >= max(1,M).

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*

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*  TAU     (output) COMPLEX array, dimension (min(M,N))

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*          The scalar factors of the elementary reflectors (see Further

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*          Details).

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*

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*  WORK    (workspace) COMPLEX array, dimension (M)

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*

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*  INFO    (output) INTEGER

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*          = 0: successful exit

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*          < 0: if INFO = -i, the i-th argument had an illegal value

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*

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*  Further Details

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*  ===============

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*

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*  The matrix Q is represented as a product of elementary reflectors

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*

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*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).

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*

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*  Each H(i) has the form

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*

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*     H(i) = I - tau * v * v'

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*

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*  where tau is a complex scalar, and v is a complex vector with

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*  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in

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*  A(i,i+1:n), and tau in TAU(i).

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*

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*  =====================================================================

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*

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*     .. Parameters ..

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      COMPLEX            ONE

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      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )

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*     ..

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*     .. Local Scalars ..

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      INTEGER            I, K

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      COMPLEX            ALPHA

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*     ..

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*     .. External Subroutines ..

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      EXTERNAL           CLACGV, CLARF, CLARFG, XERBLA

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*     ..

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*     .. Intrinsic Functions ..

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      INTRINSIC          MAX, MIN

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*     ..

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*     .. Executable Statements ..

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*

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*     Test the input arguments

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*

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      INFO = 0

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      IF( M.LT.0 ) THEN

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         INFO = -1

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      ELSE IF( N.LT.0 ) THEN

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         INFO = -2

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      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN

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         INFO = -4

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      END IF

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      IF( INFO.NE.0 ) THEN

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         CALL XERBLA( 'CGELQ2', -INFO )

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         RETURN

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      END IF

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*

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      K = MIN( M, N )

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*

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      DO 10 I = 1, K

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*

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*        Generate elementary reflector H(i) to annihilate A(i,i+1:n)

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*

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         CALL CLACGV( N-I+1, A( I, I ), LDA )

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         ALPHA = A( I, I )

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         CALL CLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA,

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     $                TAU( I ) )

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         IF( I.LT.M ) THEN

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*

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*           Apply H(i) to A(i+1:m,i:n) from the right

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*

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            A( I, I ) = ONE

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            CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),

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     $                  A( I+1, I ), LDA, WORK )

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         END IF

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         A( I, I ) = ALPHA

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         CALL CLACGV( N-I+1, A( I, I ), LDA )

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   10 CONTINUE

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      RETURN

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*

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*     End of CGELQ2

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*

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      END

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