1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
     164
     165
     166
     167
     168
     169
     170
     171
     172
     173
     174
     175
     176
     177
     178
     179
     180
     181
     182
     183
     184
     185
     186
     187
     188
     189
     190
     191
     192
     193
     194
     195
     196
     197
     198
     199
     200
     201
     202
     203
     204
     205
     206
     207
     208
     209
     210
     211
     212
     213
     214
     215
     216
     217
     218
     219
     220
     221
     222
     223
      SUBROUTINE CUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  CUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
*  which is defined as the last N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by CGEQLF.
*
*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the (n-k+i)-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGEQLF in the last k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQLF.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ZERO
      PARAMETER          ( ZERO = ( 0.0E+00.0E+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
     $                   NB, NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           CLARFB, CLARFT, CUNG2L, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAXMIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX1, M ) ) THEN
         INFO = -5
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( N.EQ.0 ) THEN
            LWKOPT = 1
         ELSE
            NB = ILAENV( 1'CUNGQL'' ', M, N, K, -1 )
            LWKOPT = N*NB
         END IF
         WORK( 1 ) = LWKOPT
*
         IF( LWORK.LT.MAX1, N ) .AND. .NOT.LQUERY ) THEN
            INFO = -8
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CUNGQL'-INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         RETURN
      END IF
*
      NBMIN = 2
      NX = 0
      IWS = N
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         NX = MAX0, ILAENV( 3'CUNGQL'' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = MAX2, ILAENV( 2'CUNGQL'' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT..AND. NX.LT.K ) THEN
*
*        Use blocked code after the first block.
*        The last kk columns are handled by the block method.
*
         KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
*
*        Set A(m-kk+1:m,1:n-kk) to zero.
*
         DO 20 J = 1, N - KK
            DO 10 I = M - KK + 1, M
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the first or only block.
*
      CALL CUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = K - KK + 1, K, NB
            IB = MIN( NB, K-I+1 )
            IF( N-K+I.GT.1 ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i+ib-1) . . . H(i+1) H(i)
*
               CALL CLARFT( 'Backward''Columnwise', M-K+I+IB-1, IB,
     $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
*
               CALL CLARFB( 'Left''No transpose''Backward',
     $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
     $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
     $                      WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H to rows 1:m-k+i+ib-1 of current block
*
            CALL CUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
     $                   TAU( I ), WORK, IINFO )
*
*           Set rows m-k+i+ib:m of current block to zero
*
            DO 40 J = N - K + I, N - K + I + IB - 1
               DO 30 L = M - K + I + IB, M
                  A( L, J ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of CUNGQL
*
      END