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Annotation of rpl/lapack/lapack/dgeql2.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DGEQL2( 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:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        !            13: *     ..
        !            14: *
        !            15: *  Purpose
        !            16: *  =======
        !            17: *
        !            18: *  DGEQL2 computes a QL factorization of a real m by n matrix A:
        !            19: *  A = Q * L.
        !            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) DOUBLE PRECISION array, dimension (LDA,N)
        !            31: *          On entry, the m by n matrix A.
        !            32: *          On exit, if m >= n, the lower triangle of the subarray
        !            33: *          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
        !            34: *          if m <= n, the elements on and below the (n-m)-th
        !            35: *          superdiagonal contain the m by n lower trapezoidal matrix L;
        !            36: *          the remaining elements, with the array TAU, represent the
        !            37: *          orthogonal matrix Q as a product of elementary reflectors
        !            38: *          (see Further Details).
        !            39: *
        !            40: *  LDA     (input) INTEGER
        !            41: *          The leading dimension of the array A.  LDA >= max(1,M).
        !            42: *
        !            43: *  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
        !            44: *          The scalar factors of the elementary reflectors (see Further
        !            45: *          Details).
        !            46: *
        !            47: *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
        !            48: *
        !            49: *  INFO    (output) INTEGER
        !            50: *          = 0: successful exit
        !            51: *          < 0: if INFO = -i, the i-th argument had an illegal value
        !            52: *
        !            53: *  Further Details
        !            54: *  ===============
        !            55: *
        !            56: *  The matrix Q is represented as a product of elementary reflectors
        !            57: *
        !            58: *     Q = H(k) . . . H(2) H(1), where k = min(m,n).
        !            59: *
        !            60: *  Each H(i) has the form
        !            61: *
        !            62: *     H(i) = I - tau * v * v'
        !            63: *
        !            64: *  where tau is a real scalar, and v is a real vector with
        !            65: *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
        !            66: *  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
        !            67: *
        !            68: *  =====================================================================
        !            69: *
        !            70: *     .. Parameters ..
        !            71:       DOUBLE PRECISION   ONE
        !            72:       PARAMETER          ( ONE = 1.0D+0 )
        !            73: *     ..
        !            74: *     .. Local Scalars ..
        !            75:       INTEGER            I, K
        !            76:       DOUBLE PRECISION   AII
        !            77: *     ..
        !            78: *     .. External Subroutines ..
        !            79:       EXTERNAL           DLARF, DLARFP, XERBLA
        !            80: *     ..
        !            81: *     .. Intrinsic Functions ..
        !            82:       INTRINSIC          MAX, MIN
        !            83: *     ..
        !            84: *     .. Executable Statements ..
        !            85: *
        !            86: *     Test the input arguments
        !            87: *
        !            88:       INFO = 0
        !            89:       IF( M.LT.0 ) THEN
        !            90:          INFO = -1
        !            91:       ELSE IF( N.LT.0 ) THEN
        !            92:          INFO = -2
        !            93:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
        !            94:          INFO = -4
        !            95:       END IF
        !            96:       IF( INFO.NE.0 ) THEN
        !            97:          CALL XERBLA( 'DGEQL2', -INFO )
        !            98:          RETURN
        !            99:       END IF
        !           100: *
        !           101:       K = MIN( M, N )
        !           102: *
        !           103:       DO 10 I = K, 1, -1
        !           104: *
        !           105: *        Generate elementary reflector H(i) to annihilate
        !           106: *        A(1:m-k+i-1,n-k+i)
        !           107: *
        !           108:          CALL DLARFP( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
        !           109:      $                TAU( I ) )
        !           110: *
        !           111: *        Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
        !           112: *
        !           113:          AII = A( M-K+I, N-K+I )
        !           114:          A( M-K+I, N-K+I ) = ONE
        !           115:          CALL DLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
        !           116:      $               A, LDA, WORK )
        !           117:          A( M-K+I, N-K+I ) = AII
        !           118:    10 CONTINUE
        !           119:       RETURN
        !           120: *
        !           121: *     End of DGEQL2
        !           122: *
        !           123:       END