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Annotation of rpl/lapack/lapack/zgelq2.f, revision 1.4

1.1       bertrand    1:       SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )
                      2: *
                      3: *  -- LAPACK routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       INTEGER            INFO, LDA, M, N
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
                     13: *     ..
                     14: *
                     15: *  Purpose
                     16: *  =======
                     17: *
                     18: *  ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
                     19: *  A = L * Q.
                     20: *
                     21: *  Arguments
                     22: *  =========
                     23: *
                     24: *  M       (input) INTEGER
                     25: *          The number of rows of the matrix A.  M >= 0.
                     26: *
                     27: *  N       (input) INTEGER
                     28: *          The number of columns of the matrix A.  N >= 0.
                     29: *
                     30: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                     31: *          On entry, the m by n matrix A.
                     32: *          On exit, the elements on and below the diagonal of the array
                     33: *          contain the m by min(m,n) lower trapezoidal matrix L (L is
                     34: *          lower triangular if m <= n); the elements above the diagonal,
                     35: *          with the array TAU, represent the unitary matrix Q as a
                     36: *          product of elementary reflectors (see Further Details).
                     37: *
                     38: *  LDA     (input) INTEGER
                     39: *          The leading dimension of the array A.  LDA >= max(1,M).
                     40: *
                     41: *  TAU     (output) COMPLEX*16 array, dimension (min(M,N))
                     42: *          The scalar factors of the elementary reflectors (see Further
                     43: *          Details).
                     44: *
                     45: *  WORK    (workspace) COMPLEX*16 array, dimension (M)
                     46: *
                     47: *  INFO    (output) INTEGER
                     48: *          = 0: successful exit
                     49: *          < 0: if INFO = -i, the i-th argument had an illegal value
                     50: *
                     51: *  Further Details
                     52: *  ===============
                     53: *
                     54: *  The matrix Q is represented as a product of elementary reflectors
                     55: *
                     56: *     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
                     57: *
                     58: *  Each H(i) has the form
                     59: *
                     60: *     H(i) = I - tau * v * v'
                     61: *
                     62: *  where tau is a complex scalar, and v is a complex vector with
                     63: *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
                     64: *  A(i,i+1:n), and tau in TAU(i).
                     65: *
                     66: *  =====================================================================
                     67: *
                     68: *     .. Parameters ..
                     69:       COMPLEX*16         ONE
                     70:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
                     71: *     ..
                     72: *     .. Local Scalars ..
                     73:       INTEGER            I, K
                     74:       COMPLEX*16         ALPHA
                     75: *     ..
                     76: *     .. External Subroutines ..
                     77:       EXTERNAL           XERBLA, ZLACGV, ZLARF, ZLARFP
                     78: *     ..
                     79: *     .. Intrinsic Functions ..
                     80:       INTRINSIC          MAX, MIN
                     81: *     ..
                     82: *     .. Executable Statements ..
                     83: *
                     84: *     Test the input arguments
                     85: *
                     86:       INFO = 0
                     87:       IF( M.LT.0 ) THEN
                     88:          INFO = -1
                     89:       ELSE IF( N.LT.0 ) THEN
                     90:          INFO = -2
                     91:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                     92:          INFO = -4
                     93:       END IF
                     94:       IF( INFO.NE.0 ) THEN
                     95:          CALL XERBLA( 'ZGELQ2', -INFO )
                     96:          RETURN
                     97:       END IF
                     98: *
                     99:       K = MIN( M, N )
                    100: *
                    101:       DO 10 I = 1, K
                    102: *
                    103: *        Generate elementary reflector H(i) to annihilate A(i,i+1:n)
                    104: *
                    105:          CALL ZLACGV( N-I+1, A( I, I ), LDA )
                    106:          ALPHA = A( I, I )
                    107:          CALL ZLARFP( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA,
                    108:      $                TAU( I ) )
                    109:          IF( I.LT.M ) THEN
                    110: *
                    111: *           Apply H(i) to A(i+1:m,i:n) from the right
                    112: *
                    113:             A( I, I ) = ONE
                    114:             CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),
                    115:      $                  A( I+1, I ), LDA, WORK )
                    116:          END IF
                    117:          A( I, I ) = ALPHA
                    118:          CALL ZLACGV( N-I+1, A( I, I ), LDA )
                    119:    10 CONTINUE
                    120:       RETURN
                    121: *
                    122: *     End of ZGELQ2
                    123: *
                    124:       END