1*> \brief \b ZGEQRFP
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INFO, LDA, LWORK, M, N
25*       ..
26*       .. Array Arguments ..
27*       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
28*       ..
29*
30*
31*> \par Purpose:
32*  =============
33*>
34*> \verbatim
35*>
36*> ZGEQR2P computes a QR factorization of a complex M-by-N matrix A:
37*>
38*>    A = Q * ( R ),
39*>            ( 0 )
40*>
41*> where:
42*>
43*>    Q is a M-by-M orthogonal matrix;
44*>    R is an upper-triangular N-by-N matrix with nonnegative diagonal
45*>    entries;
46*>    0 is a (M-N)-by-N zero matrix, if M > N.
47*>
48*> \endverbatim
49*
50*  Arguments:
51*  ==========
52*
53*> \param[in] M
54*> \verbatim
55*>          M is INTEGER
56*>          The number of rows of the matrix A.  M >= 0.
57*> \endverbatim
58*>
59*> \param[in] N
60*> \verbatim
61*>          N is INTEGER
62*>          The number of columns of the matrix A.  N >= 0.
63*> \endverbatim
64*>
65*> \param[in,out] A
66*> \verbatim
67*>          A is COMPLEX*16 array, dimension (LDA,N)
68*>          On entry, the M-by-N matrix A.
69*>          On exit, the elements on and above the diagonal of the array
70*>          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
71*>          upper triangular if m >= n). The diagonal entries of R
72*>          are real and nonnegative; The elements below the diagonal,
73*>          with the array TAU, represent the unitary matrix Q as a
74*>          product of min(m,n) elementary reflectors (see Further
75*>          Details).
76*> \endverbatim
77*>
78*> \param[in] LDA
79*> \verbatim
80*>          LDA is INTEGER
81*>          The leading dimension of the array A.  LDA >= max(1,M).
82*> \endverbatim
83*>
84*> \param[out] TAU
85*> \verbatim
86*>          TAU is COMPLEX*16 array, dimension (min(M,N))
87*>          The scalar factors of the elementary reflectors (see Further
88*>          Details).
89*> \endverbatim
90*>
91*> \param[out] WORK
92*> \verbatim
93*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
94*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
95*> \endverbatim
96*>
97*> \param[in] LWORK
98*> \verbatim
99*>          LWORK is INTEGER
100*>          The dimension of the array WORK.  LWORK >= max(1,N).
101*>          For optimum performance LWORK >= N*NB, where NB is
102*>          the optimal blocksize.
103*>
104*>          If LWORK = -1, then a workspace query is assumed; the routine
105*>          only calculates the optimal size of the WORK array, returns
106*>          this value as the first entry of the WORK array, and no error
107*>          message related to LWORK is issued by XERBLA.
108*> \endverbatim
109*>
110*> \param[out] INFO
111*> \verbatim
112*>          INFO is INTEGER
113*>          = 0:  successful exit
114*>          < 0:  if INFO = -i, the i-th argument had an illegal value
115*> \endverbatim
116*
117*  Authors:
118*  ========
119*
120*> \author Univ. of Tennessee
121*> \author Univ. of California Berkeley
122*> \author Univ. of Colorado Denver
123*> \author NAG Ltd.
124*
125*> \ingroup complex16GEcomputational
126*
127*> \par Further Details:
128*  =====================
129*>
130*> \verbatim
131*>
132*>  The matrix Q is represented as a product of elementary reflectors
133*>
134*>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
135*>
136*>  Each H(i) has the form
137*>
138*>     H(i) = I - tau * v * v**H
139*>
140*>  where tau is a complex scalar, and v is a complex vector with
141*>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
142*>  and tau in TAU(i).
143*>
144*> See Lapack Working Note 203 for details
145*> \endverbatim
146*>
147*  =====================================================================
148      SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
149*
150*  -- LAPACK computational routine --
151*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
152*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*
154*     .. Scalar Arguments ..
155      INTEGER            INFO, LDA, LWORK, M, N
156*     ..
157*     .. Array Arguments ..
158      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
159*     ..
160*
161*  =====================================================================
162*
163*     .. Local Scalars ..
164      LOGICAL            LQUERY
165      INTEGER            I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
166     $                   NBMIN, NX
167*     ..
168*     .. External Subroutines ..
169      EXTERNAL           XERBLA, ZGEQR2P, ZLARFB, ZLARFT
170*     ..
171*     .. Intrinsic Functions ..
172      INTRINSIC          MAX, MIN
173*     ..
174*     .. External Functions ..
175      INTEGER            ILAENV
176      EXTERNAL           ILAENV
177*     ..
178*     .. Executable Statements ..
179*
180*     Test the input arguments
181*
182      INFO = 0
183      NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
184      LWKOPT = N*NB
185      WORK( 1 ) = LWKOPT
186      LQUERY = ( LWORK.EQ.-1 )
187      IF( M.LT.0 ) THEN
188         INFO = -1
189      ELSE IF( N.LT.0 ) THEN
190         INFO = -2
191      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
192         INFO = -4
193      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
194         INFO = -7
195      END IF
196      IF( INFO.NE.0 ) THEN
197         CALL XERBLA( 'ZGEQRFP', -INFO )
198         RETURN
199      ELSE IF( LQUERY ) THEN
200         RETURN
201      END IF
202*
203*     Quick return if possible
204*
205      K = MIN( M, N )
206      IF( K.EQ.0 ) THEN
207         WORK( 1 ) = 1
208         RETURN
209      END IF
210*
211      NBMIN = 2
212      NX = 0
213      IWS = N
214      IF( NB.GT.1 .AND. NB.LT.K ) THEN
215*
216*        Determine when to cross over from blocked to unblocked code.
217*
218         NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) )
219         IF( NX.LT.K ) THEN
220*
221*           Determine if workspace is large enough for blocked code.
222*
223            LDWORK = N
224            IWS = LDWORK*NB
225            IF( LWORK.LT.IWS ) THEN
226*
227*              Not enough workspace to use optimal NB:  reduce NB and
228*              determine the minimum value of NB.
229*
230               NB = LWORK / LDWORK
231               NBMIN = MAX( 2, ILAENV( 2, 'ZGEQRF', ' ', M, N, -1,
232     $                 -1 ) )
233            END IF
234         END IF
235      END IF
236*
237      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
238*
239*        Use blocked code initially
240*
241         DO 10 I = 1, K - NX, NB
242            IB = MIN( K-I+1, NB )
243*
244*           Compute the QR factorization of the current block
245*           A(i:m,i:i+ib-1)
246*
247            CALL ZGEQR2P( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
248     $                   IINFO )
249            IF( I+IB.LE.N ) THEN
250*
251*              Form the triangular factor of the block reflector
252*              H = H(i) H(i+1) . . . H(i+ib-1)
253*
254               CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB,
255     $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
256*
257*              Apply H**H to A(i:m,i+ib:n) from the left
258*
259               CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',
260     $                      'Columnwise', M-I+1, N-I-IB+1, IB,
261     $                      A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
262     $                      LDA, WORK( IB+1 ), LDWORK )
263            END IF
264   10    CONTINUE
265      ELSE
266         I = 1
267      END IF
268*
269*     Use unblocked code to factor the last or only block.
270*
271      IF( I.LE.K )
272     $   CALL ZGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
273     $                IINFO )
274*
275      WORK( 1 ) = IWS
276      RETURN
277*
278*     End of ZGEQRFP
279*
280      END
281