1: SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, 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, LWORK, M, N
10: * ..
11: * .. Array Arguments ..
12: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * ZUNGRQ generates an M-by-N complex 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 ZGERQF.
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) COMPLEX*16 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 ZGERQF 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) COMPLEX*16 array, dimension (K)
50: * TAU(i) must contain the scalar factor of the elementary
51: * reflector H(i), as returned by ZGERQF.
52: *
53: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
54: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
55: *
56: * LWORK (input) INTEGER
57: * The dimension of the array WORK. LWORK >= max(1,M).
58: * For optimum performance LWORK >= M*NB, where NB is the
59: * optimal blocksize.
60: *
61: * If LWORK = -1, then a workspace query is assumed; the routine
62: * only calculates the optimal size of the WORK array, returns
63: * this value as the first entry of the WORK array, and no error
64: * message related to LWORK is issued by XERBLA.
65: *
66: * INFO (output) INTEGER
67: * = 0: successful exit
68: * < 0: if INFO = -i, the i-th argument has an illegal value
69: *
70: * =====================================================================
71: *
72: * .. Parameters ..
73: COMPLEX*16 ZERO
74: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
75: * ..
76: * .. Local Scalars ..
77: LOGICAL LQUERY
78: INTEGER I, IB, II, IINFO, IWS, J, KK, L, LDWORK,
79: $ LWKOPT, NB, NBMIN, NX
80: * ..
81: * .. External Subroutines ..
82: EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGR2
83: * ..
84: * .. Intrinsic Functions ..
85: INTRINSIC MAX, MIN
86: * ..
87: * .. External Functions ..
88: INTEGER ILAENV
89: EXTERNAL ILAENV
90: * ..
91: * .. Executable Statements ..
92: *
93: * Test the input arguments
94: *
95: INFO = 0
96: LQUERY = ( LWORK.EQ.-1 )
97: IF( M.LT.0 ) THEN
98: INFO = -1
99: ELSE IF( N.LT.M ) THEN
100: INFO = -2
101: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
102: INFO = -3
103: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
104: INFO = -5
105: END IF
106: *
107: IF( INFO.EQ.0 ) THEN
108: IF( M.LE.0 ) THEN
109: LWKOPT = 1
110: ELSE
111: NB = ILAENV( 1, 'ZUNGRQ', ' ', M, N, K, -1 )
112: LWKOPT = M*NB
113: END IF
114: WORK( 1 ) = LWKOPT
115: *
116: IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
117: INFO = -8
118: END IF
119: END IF
120: *
121: IF( INFO.NE.0 ) THEN
122: CALL XERBLA( 'ZUNGRQ', -INFO )
123: RETURN
124: ELSE IF( LQUERY ) THEN
125: RETURN
126: END IF
127: *
128: * Quick return if possible
129: *
130: IF( M.LE.0 ) THEN
131: RETURN
132: END IF
133: *
134: NBMIN = 2
135: NX = 0
136: IWS = M
137: IF( NB.GT.1 .AND. NB.LT.K ) THEN
138: *
139: * Determine when to cross over from blocked to unblocked code.
140: *
141: NX = MAX( 0, ILAENV( 3, 'ZUNGRQ', ' ', M, N, K, -1 ) )
142: IF( NX.LT.K ) THEN
143: *
144: * Determine if workspace is large enough for blocked code.
145: *
146: LDWORK = M
147: IWS = LDWORK*NB
148: IF( LWORK.LT.IWS ) THEN
149: *
150: * Not enough workspace to use optimal NB: reduce NB and
151: * determine the minimum value of NB.
152: *
153: NB = LWORK / LDWORK
154: NBMIN = MAX( 2, ILAENV( 2, 'ZUNGRQ', ' ', M, N, K, -1 ) )
155: END IF
156: END IF
157: END IF
158: *
159: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
160: *
161: * Use blocked code after the first block.
162: * The last kk rows are handled by the block method.
163: *
164: KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
165: *
166: * Set A(1:m-kk,n-kk+1:n) to zero.
167: *
168: DO 20 J = N - KK + 1, N
169: DO 10 I = 1, M - KK
170: A( I, J ) = ZERO
171: 10 CONTINUE
172: 20 CONTINUE
173: ELSE
174: KK = 0
175: END IF
176: *
177: * Use unblocked code for the first or only block.
178: *
179: CALL ZUNGR2( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
180: *
181: IF( KK.GT.0 ) THEN
182: *
183: * Use blocked code
184: *
185: DO 50 I = K - KK + 1, K, NB
186: IB = MIN( NB, K-I+1 )
187: II = M - K + I
188: IF( II.GT.1 ) THEN
189: *
190: * Form the triangular factor of the block reflector
191: * H = H(i+ib-1) . . . H(i+1) H(i)
192: *
193: CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
194: $ A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
195: *
196: * Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
197: *
198: CALL ZLARFB( 'Right', 'Conjugate transpose', 'Backward',
199: $ 'Rowwise', II-1, N-K+I+IB-1, IB, A( II, 1 ),
200: $ LDA, WORK, LDWORK, A, LDA, WORK( IB+1 ),
201: $ LDWORK )
202: END IF
203: *
204: * Apply H' to columns 1:n-k+i+ib-1 of current block
205: *
206: CALL ZUNGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
207: $ WORK, IINFO )
208: *
209: * Set columns n-k+i+ib:n of current block to zero
210: *
211: DO 40 L = N - K + I + IB, N
212: DO 30 J = II, II + IB - 1
213: A( J, L ) = ZERO
214: 30 CONTINUE
215: 40 CONTINUE
216: 50 CONTINUE
217: END IF
218: *
219: WORK( 1 ) = IWS
220: RETURN
221: *
222: * End of ZUNGRQ
223: *
224: END
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