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Annotation of rpl/lapack/lapack/dorgr2.f, revision 1.6

1.1       bertrand    1:       SUBROUTINE DORGR2( M, N, K, 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, K, LDA, M, N
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
                     13: *     ..
                     14: *
                     15: *  Purpose
                     16: *  =======
                     17: *
                     18: *  DORGR2 generates an m by n real matrix Q with orthonormal rows,
                     19: *  which is defined as the last m rows of a product of k elementary
                     20: *  reflectors of order n
                     21: *
                     22: *        Q  =  H(1) H(2) . . . H(k)
                     23: *
                     24: *  as returned by DGERQF.
                     25: *
                     26: *  Arguments
                     27: *  =========
                     28: *
                     29: *  M       (input) INTEGER
                     30: *          The number of rows of the matrix Q. M >= 0.
                     31: *
                     32: *  N       (input) INTEGER
                     33: *          The number of columns of the matrix Q. N >= M.
                     34: *
                     35: *  K       (input) INTEGER
                     36: *          The number of elementary reflectors whose product defines the
                     37: *          matrix Q. M >= K >= 0.
                     38: *
                     39: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
                     40: *          On entry, the (m-k+i)-th row must contain the vector which
                     41: *          defines the elementary reflector H(i), for i = 1,2,...,k, as
                     42: *          returned by DGERQF in the last k rows of its array argument
                     43: *          A.
                     44: *          On exit, the m by n matrix Q.
                     45: *
                     46: *  LDA     (input) INTEGER
                     47: *          The first dimension of the array A. LDA >= max(1,M).
                     48: *
                     49: *  TAU     (input) DOUBLE PRECISION array, dimension (K)
                     50: *          TAU(i) must contain the scalar factor of the elementary
                     51: *          reflector H(i), as returned by DGERQF.
                     52: *
                     53: *  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
                     54: *
                     55: *  INFO    (output) INTEGER
                     56: *          = 0: successful exit
                     57: *          < 0: if INFO = -i, the i-th argument has an illegal value
                     58: *
                     59: *  =====================================================================
                     60: *
                     61: *     .. Parameters ..
                     62:       DOUBLE PRECISION   ONE, ZERO
                     63:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
                     64: *     ..
                     65: *     .. Local Scalars ..
                     66:       INTEGER            I, II, J, L
                     67: *     ..
                     68: *     .. External Subroutines ..
                     69:       EXTERNAL           DLARF, DSCAL, XERBLA
                     70: *     ..
                     71: *     .. Intrinsic Functions ..
                     72:       INTRINSIC          MAX
                     73: *     ..
                     74: *     .. Executable Statements ..
                     75: *
                     76: *     Test the input arguments
                     77: *
                     78:       INFO = 0
                     79:       IF( M.LT.0 ) THEN
                     80:          INFO = -1
                     81:       ELSE IF( N.LT.M ) THEN
                     82:          INFO = -2
                     83:       ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
                     84:          INFO = -3
                     85:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                     86:          INFO = -5
                     87:       END IF
                     88:       IF( INFO.NE.0 ) THEN
                     89:          CALL XERBLA( 'DORGR2', -INFO )
                     90:          RETURN
                     91:       END IF
                     92: *
                     93: *     Quick return if possible
                     94: *
                     95:       IF( M.LE.0 )
                     96:      $   RETURN
                     97: *
                     98:       IF( K.LT.M ) THEN
                     99: *
                    100: *        Initialise rows 1:m-k to rows of the unit matrix
                    101: *
                    102:          DO 20 J = 1, N
                    103:             DO 10 L = 1, M - K
                    104:                A( L, J ) = ZERO
                    105:    10       CONTINUE
                    106:             IF( J.GT.N-M .AND. J.LE.N-K )
                    107:      $         A( M-N+J, J ) = ONE
                    108:    20    CONTINUE
                    109:       END IF
                    110: *
                    111:       DO 40 I = 1, K
                    112:          II = M - K + I
                    113: *
                    114: *        Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
                    115: *
                    116:          A( II, N-M+II ) = ONE
                    117:          CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
                    118:      $               A, LDA, WORK )
                    119:          CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
                    120:          A( II, N-M+II ) = ONE - TAU( I )
                    121: *
                    122: *        Set A(m-k+i,n-k+i+1:n) to zero
                    123: *
                    124:          DO 30 L = N - M + II + 1, N
                    125:             A( II, L ) = ZERO
                    126:    30    CONTINUE
                    127:    40 CONTINUE
                    128:       RETURN
                    129: *
                    130: *     End of DORGR2
                    131: *
                    132:       END