Annotation of rpl/lapack/lapack/zunmbr.f, revision 1.5
1.1 bertrand 1: SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
2: $ LDC, 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, VECT
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: * If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
21: * with
22: * SIDE = 'L' SIDE = 'R'
23: * TRANS = 'N': Q * C C * Q
24: * TRANS = 'C': Q**H * C C * Q**H
25: *
26: * If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
27: * with
28: * SIDE = 'L' SIDE = 'R'
29: * TRANS = 'N': P * C C * P
30: * TRANS = 'C': P**H * C C * P**H
31: *
32: * Here Q and P**H are the unitary matrices determined by ZGEBRD when
33: * reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
34: * and P**H are defined as products of elementary reflectors H(i) and
35: * G(i) respectively.
36: *
37: * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
38: * order of the unitary matrix Q or P**H that is applied.
39: *
40: * If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
41: * if nq >= k, Q = H(1) H(2) . . . H(k);
42: * if nq < k, Q = H(1) H(2) . . . H(nq-1).
43: *
44: * If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
45: * if k < nq, P = G(1) G(2) . . . G(k);
46: * if k >= nq, P = G(1) G(2) . . . G(nq-1).
47: *
48: * Arguments
49: * =========
50: *
51: * VECT (input) CHARACTER*1
52: * = 'Q': apply Q or Q**H;
53: * = 'P': apply P or P**H.
54: *
55: * SIDE (input) CHARACTER*1
56: * = 'L': apply Q, Q**H, P or P**H from the Left;
57: * = 'R': apply Q, Q**H, P or P**H from the Right.
58: *
59: * TRANS (input) CHARACTER*1
60: * = 'N': No transpose, apply Q or P;
61: * = 'C': Conjugate transpose, apply Q**H or P**H.
62: *
63: * M (input) INTEGER
64: * The number of rows of the matrix C. M >= 0.
65: *
66: * N (input) INTEGER
67: * The number of columns of the matrix C. N >= 0.
68: *
69: * K (input) INTEGER
70: * If VECT = 'Q', the number of columns in the original
71: * matrix reduced by ZGEBRD.
72: * If VECT = 'P', the number of rows in the original
73: * matrix reduced by ZGEBRD.
74: * K >= 0.
75: *
76: * A (input) COMPLEX*16 array, dimension
77: * (LDA,min(nq,K)) if VECT = 'Q'
78: * (LDA,nq) if VECT = 'P'
79: * The vectors which define the elementary reflectors H(i) and
80: * G(i), whose products determine the matrices Q and P, as
81: * returned by ZGEBRD.
82: *
83: * LDA (input) INTEGER
84: * The leading dimension of the array A.
85: * If VECT = 'Q', LDA >= max(1,nq);
86: * if VECT = 'P', LDA >= max(1,min(nq,K)).
87: *
88: * TAU (input) COMPLEX*16 array, dimension (min(nq,K))
89: * TAU(i) must contain the scalar factor of the elementary
90: * reflector H(i) or G(i) which determines Q or P, as returned
91: * by ZGEBRD in the array argument TAUQ or TAUP.
92: *
93: * C (input/output) COMPLEX*16 array, dimension (LDC,N)
94: * On entry, the M-by-N matrix C.
95: * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
96: * or P*C or P**H*C or C*P or C*P**H.
97: *
98: * LDC (input) INTEGER
99: * The leading dimension of the array C. LDC >= max(1,M).
100: *
101: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
102: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
103: *
104: * LWORK (input) INTEGER
105: * The dimension of the array WORK.
106: * If SIDE = 'L', LWORK >= max(1,N);
107: * if SIDE = 'R', LWORK >= max(1,M);
108: * if N = 0 or M = 0, LWORK >= 1.
109: * For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
110: * and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
111: * optimal blocksize. (NB = 0 if M = 0 or N = 0.)
112: *
113: * If LWORK = -1, then a workspace query is assumed; the routine
114: * only calculates the optimal size of the WORK array, returns
115: * this value as the first entry of the WORK array, and no error
116: * message related to LWORK is issued by XERBLA.
117: *
118: * INFO (output) INTEGER
119: * = 0: successful exit
120: * < 0: if INFO = -i, the i-th argument had an illegal value
121: *
122: * =====================================================================
123: *
124: * .. Local Scalars ..
125: LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
126: CHARACTER TRANST
127: INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
128: * ..
129: * .. External Functions ..
130: LOGICAL LSAME
131: INTEGER ILAENV
132: EXTERNAL LSAME, ILAENV
133: * ..
134: * .. External Subroutines ..
135: EXTERNAL XERBLA, ZUNMLQ, ZUNMQR
136: * ..
137: * .. Intrinsic Functions ..
138: INTRINSIC MAX, MIN
139: * ..
140: * .. Executable Statements ..
141: *
142: * Test the input arguments
143: *
144: INFO = 0
145: APPLYQ = LSAME( VECT, 'Q' )
146: LEFT = LSAME( SIDE, 'L' )
147: NOTRAN = LSAME( TRANS, 'N' )
148: LQUERY = ( LWORK.EQ.-1 )
149: *
150: * NQ is the order of Q or P and NW is the minimum dimension of WORK
151: *
152: IF( LEFT ) THEN
153: NQ = M
154: NW = N
155: ELSE
156: NQ = N
157: NW = M
158: END IF
159: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
160: NW = 0
161: END IF
162: IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
163: INFO = -1
164: ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
165: INFO = -2
166: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
167: INFO = -3
168: ELSE IF( M.LT.0 ) THEN
169: INFO = -4
170: ELSE IF( N.LT.0 ) THEN
171: INFO = -5
172: ELSE IF( K.LT.0 ) THEN
173: INFO = -6
174: ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
175: $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
176: $ THEN
177: INFO = -8
178: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
179: INFO = -11
180: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
181: INFO = -13
182: END IF
183: *
184: IF( INFO.EQ.0 ) THEN
185: IF( NW.GT.0 ) THEN
186: IF( APPLYQ ) THEN
187: IF( LEFT ) THEN
188: NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1,
189: $ -1 )
190: ELSE
191: NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1,
192: $ -1 )
193: END IF
194: ELSE
195: IF( LEFT ) THEN
196: NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1,
197: $ -1 )
198: ELSE
199: NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1,
200: $ -1 )
201: END IF
202: END IF
203: LWKOPT = MAX( 1, NW*NB )
204: ELSE
205: LWKOPT = 1
206: END IF
207: WORK( 1 ) = LWKOPT
208: END IF
209: *
210: IF( INFO.NE.0 ) THEN
211: CALL XERBLA( 'ZUNMBR', -INFO )
212: RETURN
213: ELSE IF( LQUERY ) THEN
214: RETURN
215: END IF
216: *
217: * Quick return if possible
218: *
219: IF( M.EQ.0 .OR. N.EQ.0 )
220: $ RETURN
221: *
222: IF( APPLYQ ) THEN
223: *
224: * Apply Q
225: *
226: IF( NQ.GE.K ) THEN
227: *
228: * Q was determined by a call to ZGEBRD with nq >= k
229: *
230: CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
231: $ WORK, LWORK, IINFO )
232: ELSE IF( NQ.GT.1 ) THEN
233: *
234: * Q was determined by a call to ZGEBRD with nq < k
235: *
236: IF( LEFT ) THEN
237: MI = M - 1
238: NI = N
239: I1 = 2
240: I2 = 1
241: ELSE
242: MI = M
243: NI = N - 1
244: I1 = 1
245: I2 = 2
246: END IF
247: CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
248: $ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
249: END IF
250: ELSE
251: *
252: * Apply P
253: *
254: IF( NOTRAN ) THEN
255: TRANST = 'C'
256: ELSE
257: TRANST = 'N'
258: END IF
259: IF( NQ.GT.K ) THEN
260: *
261: * P was determined by a call to ZGEBRD with nq > k
262: *
263: CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
264: $ WORK, LWORK, IINFO )
265: ELSE IF( NQ.GT.1 ) THEN
266: *
267: * P was determined by a call to ZGEBRD with nq <= k
268: *
269: IF( LEFT ) THEN
270: MI = M - 1
271: NI = N
272: I1 = 2
273: I2 = 1
274: ELSE
275: MI = M
276: NI = N - 1
277: I1 = 1
278: I2 = 2
279: END IF
280: CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
281: $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
282: END IF
283: END IF
284: WORK( 1 ) = LWKOPT
285: RETURN
286: *
287: * End of ZUNMBR
288: *
289: END
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