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Annotation of rpl/lapack/lapack/dgeql2.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
                      2: *
1.5       bertrand    3: *  -- LAPACK routine (version 3.2.2) --
1.1       bertrand    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.5       bertrand    6: *     June 2010
1.1       bertrand    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 ..
1.5       bertrand   79:       EXTERNAL           DLARF, DLARFG, XERBLA
1.1       bertrand   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: *
1.5       bertrand  108:          CALL DLARFG( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
1.1       bertrand  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