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ElmerCSC
GitHub Repository: ElmerCSC/elmerfem
 Path: blob/devel/mathlibs/src/lapack/cgeqr2.f
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      SUBROUTINE CGEQR2( 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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*  CGEQR2 computes a QR factorization of a complex m by n matrix A:

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*  A = Q * R.

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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 above the diagonal of the array

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*          contain the min(m,n) by n upper trapezoidal matrix R (R is

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*          upper triangular if m >= n); the elements below 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 (N)

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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(1) H(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i),

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*  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           CLARF, CLARFG, XERBLA

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*     ..

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*     .. Intrinsic Functions ..

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      INTRINSIC          CONJG, 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( 'CGEQR2', -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+1:m,i)

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*

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         CALL CLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,

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     $                TAU( I ) )

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         IF( I.LT.N ) THEN

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*

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

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*

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            ALPHA = A( I, I )

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            A( I, I ) = ONE

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            CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,

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

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            A( I, I ) = ALPHA

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         END IF

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   10 CONTINUE

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      RETURN

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*

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*     End of CGEQR2

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*

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      END

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