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1.1 bertrand 1: SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
2: $ WORK, LWORK, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER SIDE, TRANS
11: INTEGER INFO, K, LDA, LDC, LWORK, M, N
12: * ..
13: * .. Array Arguments ..
14: COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZUNMQR overwrites the general complex M-by-N matrix C with
21: *
22: * SIDE = 'L' SIDE = 'R'
23: * TRANS = 'N': Q * C C * Q
24: * TRANS = 'C': Q**H * C C * Q**H
25: *
26: * where Q is a complex unitary matrix defined as the product of k
27: * elementary reflectors
28: *
29: * Q = H(1) H(2) . . . H(k)
30: *
31: * as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N
32: * if SIDE = 'R'.
33: *
34: * Arguments
35: * =========
36: *
37: * SIDE (input) CHARACTER*1
38: * = 'L': apply Q or Q**H from the Left;
39: * = 'R': apply Q or Q**H from the Right.
40: *
41: * TRANS (input) CHARACTER*1
42: * = 'N': No transpose, apply Q;
43: * = 'C': Conjugate transpose, apply Q**H.
44: *
45: * M (input) INTEGER
46: * The number of rows of the matrix C. M >= 0.
47: *
48: * N (input) INTEGER
49: * The number of columns of the matrix C. N >= 0.
50: *
51: * K (input) INTEGER
52: * The number of elementary reflectors whose product defines
53: * the matrix Q.
54: * If SIDE = 'L', M >= K >= 0;
55: * if SIDE = 'R', N >= K >= 0.
56: *
57: * A (input) COMPLEX*16 array, dimension (LDA,K)
58: * The i-th column must contain the vector which defines the
59: * elementary reflector H(i), for i = 1,2,...,k, as returned by
60: * ZGEQRF in the first k columns of its array argument A.
61: * A is modified by the routine but restored on exit.
62: *
63: * LDA (input) INTEGER
64: * The leading dimension of the array A.
65: * If SIDE = 'L', LDA >= max(1,M);
66: * if SIDE = 'R', LDA >= max(1,N).
67: *
68: * TAU (input) COMPLEX*16 array, dimension (K)
69: * TAU(i) must contain the scalar factor of the elementary
70: * reflector H(i), as returned by ZGEQRF.
71: *
72: * C (input/output) COMPLEX*16 array, dimension (LDC,N)
73: * On entry, the M-by-N matrix C.
74: * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
75: *
76: * LDC (input) INTEGER
77: * The leading dimension of the array C. LDC >= max(1,M).
78: *
79: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
80: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
81: *
82: * LWORK (input) INTEGER
83: * The dimension of the array WORK.
84: * If SIDE = 'L', LWORK >= max(1,N);
85: * if SIDE = 'R', LWORK >= max(1,M).
86: * For optimum performance LWORK >= N*NB if SIDE = 'L', and
87: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
88: * blocksize.
89: *
90: * If LWORK = -1, then a workspace query is assumed; the routine
91: * only calculates the optimal size of the WORK array, returns
92: * this value as the first entry of the WORK array, and no error
93: * message related to LWORK is issued by XERBLA.
94: *
95: * INFO (output) INTEGER
96: * = 0: successful exit
97: * < 0: if INFO = -i, the i-th argument had an illegal value
98: *
99: * =====================================================================
100: *
101: * .. Parameters ..
102: INTEGER NBMAX, LDT
103: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
104: * ..
105: * .. Local Scalars ..
106: LOGICAL LEFT, LQUERY, NOTRAN
107: INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
108: $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
109: * ..
110: * .. Local Arrays ..
111: COMPLEX*16 T( LDT, NBMAX )
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: INTEGER ILAENV
116: EXTERNAL LSAME, ILAENV
117: * ..
118: * .. External Subroutines ..
119: EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2R
120: * ..
121: * .. Intrinsic Functions ..
122: INTRINSIC MAX, MIN
123: * ..
124: * .. Executable Statements ..
125: *
126: * Test the input arguments
127: *
128: INFO = 0
129: LEFT = LSAME( SIDE, 'L' )
130: NOTRAN = LSAME( TRANS, 'N' )
131: LQUERY = ( LWORK.EQ.-1 )
132: *
133: * NQ is the order of Q and NW is the minimum dimension of WORK
134: *
135: IF( LEFT ) THEN
136: NQ = M
137: NW = N
138: ELSE
139: NQ = N
140: NW = M
141: END IF
142: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
143: INFO = -1
144: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
145: INFO = -2
146: ELSE IF( M.LT.0 ) THEN
147: INFO = -3
148: ELSE IF( N.LT.0 ) THEN
149: INFO = -4
150: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
151: INFO = -5
152: ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
153: INFO = -7
154: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
155: INFO = -10
156: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
157: INFO = -12
158: END IF
159: *
160: IF( INFO.EQ.0 ) THEN
161: *
162: * Determine the block size. NB may be at most NBMAX, where NBMAX
163: * is used to define the local array T.
164: *
165: NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N, K,
166: $ -1 ) )
167: LWKOPT = MAX( 1, NW )*NB
168: WORK( 1 ) = LWKOPT
169: END IF
170: *
171: IF( INFO.NE.0 ) THEN
172: CALL XERBLA( 'ZUNMQR', -INFO )
173: RETURN
174: ELSE IF( LQUERY ) THEN
175: RETURN
176: END IF
177: *
178: * Quick return if possible
179: *
180: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
181: WORK( 1 ) = 1
182: RETURN
183: END IF
184: *
185: NBMIN = 2
186: LDWORK = NW
187: IF( NB.GT.1 .AND. NB.LT.K ) THEN
188: IWS = NW*NB
189: IF( LWORK.LT.IWS ) THEN
190: NB = LWORK / LDWORK
191: NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQR', SIDE // TRANS, M, N, K,
192: $ -1 ) )
193: END IF
194: ELSE
195: IWS = NW
196: END IF
197: *
198: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
199: *
200: * Use unblocked code
201: *
202: CALL ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
203: $ IINFO )
204: ELSE
205: *
206: * Use blocked code
207: *
208: IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
209: $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
210: I1 = 1
211: I2 = K
212: I3 = NB
213: ELSE
214: I1 = ( ( K-1 ) / NB )*NB + 1
215: I2 = 1
216: I3 = -NB
217: END IF
218: *
219: IF( LEFT ) THEN
220: NI = N
221: JC = 1
222: ELSE
223: MI = M
224: IC = 1
225: END IF
226: *
227: DO 10 I = I1, I2, I3
228: IB = MIN( NB, K-I+1 )
229: *
230: * Form the triangular factor of the block reflector
231: * H = H(i) H(i+1) . . . H(i+ib-1)
232: *
233: CALL ZLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
234: $ LDA, TAU( I ), T, LDT )
235: IF( LEFT ) THEN
236: *
237: * H or H' is applied to C(i:m,1:n)
238: *
239: MI = M - I + 1
240: IC = I
241: ELSE
242: *
243: * H or H' is applied to C(1:m,i:n)
244: *
245: NI = N - I + 1
246: JC = I
247: END IF
248: *
249: * Apply H or H'
250: *
251: CALL ZLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
252: $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
253: $ WORK, LDWORK )
254: 10 CONTINUE
255: END IF
256: WORK( 1 ) = LWKOPT
257: RETURN
258: *
259: * End of ZUNMQR
260: *
261: END