Annotation of rpl/lapack/lapack/dormbr.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DORMBR( 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: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
21: * with
22: * SIDE = 'L' SIDE = 'R'
23: * TRANS = 'N': Q * C C * Q
24: * TRANS = 'T': Q**T * C C * Q**T
25: *
26: * If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
27: * with
28: * SIDE = 'L' SIDE = 'R'
29: * TRANS = 'N': P * C C * P
30: * TRANS = 'T': P**T * C C * P**T
31: *
32: * Here Q and P**T are the orthogonal matrices determined by DGEBRD when
33: * reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
34: * P**T are defined as products of elementary reflectors H(i) and G(i)
35: * respectively.
36: *
37: * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
38: * order of the orthogonal matrix Q or P**T 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**T;
53: * = 'P': apply P or P**T.
54: *
55: * SIDE (input) CHARACTER*1
56: * = 'L': apply Q, Q**T, P or P**T from the Left;
57: * = 'R': apply Q, Q**T, P or P**T from the Right.
58: *
59: * TRANS (input) CHARACTER*1
60: * = 'N': No transpose, apply Q or P;
61: * = 'T': Transpose, apply Q**T or P**T.
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 DGEBRD.
72: * If VECT = 'P', the number of rows in the original
73: * matrix reduced by DGEBRD.
74: * K >= 0.
75: *
76: * A (input) DOUBLE PRECISION 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 DGEBRD.
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) DOUBLE PRECISION 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 DGEBRD in the array argument TAUQ or TAUP.
92: *
93: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
94: * On entry, the M-by-N matrix C.
95: * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
96: * or P*C or P**T*C or C*P or C*P**T.
97: *
98: * LDC (input) INTEGER
99: * The leading dimension of the array C. LDC >= max(1,M).
100: *
101: * WORK (workspace/output) DOUBLE PRECISION 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: * For optimum performance LWORK >= N*NB if SIDE = 'L', and
109: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
110: * blocksize.
111: *
112: * If LWORK = -1, then a workspace query is assumed; the routine
113: * only calculates the optimal size of the WORK array, returns
114: * this value as the first entry of the WORK array, and no error
115: * message related to LWORK is issued by XERBLA.
116: *
117: * INFO (output) INTEGER
118: * = 0: successful exit
119: * < 0: if INFO = -i, the i-th argument had an illegal value
120: *
121: * =====================================================================
122: *
123: * .. Local Scalars ..
124: LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
125: CHARACTER TRANST
126: INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
127: * ..
128: * .. External Functions ..
129: LOGICAL LSAME
130: INTEGER ILAENV
131: EXTERNAL LSAME, ILAENV
132: * ..
133: * .. External Subroutines ..
134: EXTERNAL DORMLQ, DORMQR, XERBLA
135: * ..
136: * .. Intrinsic Functions ..
137: INTRINSIC MAX, MIN
138: * ..
139: * .. Executable Statements ..
140: *
141: * Test the input arguments
142: *
143: INFO = 0
144: APPLYQ = LSAME( VECT, 'Q' )
145: LEFT = LSAME( SIDE, 'L' )
146: NOTRAN = LSAME( TRANS, 'N' )
147: LQUERY = ( LWORK.EQ.-1 )
148: *
149: * NQ is the order of Q or P and NW is the minimum dimension of WORK
150: *
151: IF( LEFT ) THEN
152: NQ = M
153: NW = N
154: ELSE
155: NQ = N
156: NW = M
157: END IF
158: IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
159: INFO = -1
160: ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
161: INFO = -2
162: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
163: INFO = -3
164: ELSE IF( M.LT.0 ) THEN
165: INFO = -4
166: ELSE IF( N.LT.0 ) THEN
167: INFO = -5
168: ELSE IF( K.LT.0 ) THEN
169: INFO = -6
170: ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
171: $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
172: $ THEN
173: INFO = -8
174: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
175: INFO = -11
176: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
177: INFO = -13
178: END IF
179: *
180: IF( INFO.EQ.0 ) THEN
181: IF( APPLYQ ) THEN
182: IF( LEFT ) THEN
183: NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
184: $ -1 )
185: ELSE
186: NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
187: $ -1 )
188: END IF
189: ELSE
190: IF( LEFT ) THEN
191: NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,
192: $ -1 )
193: ELSE
194: NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,
195: $ -1 )
196: END IF
197: END IF
198: LWKOPT = MAX( 1, NW )*NB
199: WORK( 1 ) = LWKOPT
200: END IF
201: *
202: IF( INFO.NE.0 ) THEN
203: CALL XERBLA( 'DORMBR', -INFO )
204: RETURN
205: ELSE IF( LQUERY ) THEN
206: RETURN
207: END IF
208: *
209: * Quick return if possible
210: *
211: WORK( 1 ) = 1
212: IF( M.EQ.0 .OR. N.EQ.0 )
213: $ RETURN
214: *
215: IF( APPLYQ ) THEN
216: *
217: * Apply Q
218: *
219: IF( NQ.GE.K ) THEN
220: *
221: * Q was determined by a call to DGEBRD with nq >= k
222: *
223: CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
224: $ WORK, LWORK, IINFO )
225: ELSE IF( NQ.GT.1 ) THEN
226: *
227: * Q was determined by a call to DGEBRD with nq < k
228: *
229: IF( LEFT ) THEN
230: MI = M - 1
231: NI = N
232: I1 = 2
233: I2 = 1
234: ELSE
235: MI = M
236: NI = N - 1
237: I1 = 1
238: I2 = 2
239: END IF
240: CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
241: $ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
242: END IF
243: ELSE
244: *
245: * Apply P
246: *
247: IF( NOTRAN ) THEN
248: TRANST = 'T'
249: ELSE
250: TRANST = 'N'
251: END IF
252: IF( NQ.GT.K ) THEN
253: *
254: * P was determined by a call to DGEBRD with nq > k
255: *
256: CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
257: $ WORK, LWORK, IINFO )
258: ELSE IF( NQ.GT.1 ) THEN
259: *
260: * P was determined by a call to DGEBRD with nq <= k
261: *
262: IF( LEFT ) THEN
263: MI = M - 1
264: NI = N
265: I1 = 2
266: I2 = 1
267: ELSE
268: MI = M
269: NI = N - 1
270: I1 = 1
271: I2 = 2
272: END IF
273: CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
274: $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
275: END IF
276: END IF
277: WORK( 1 ) = LWKOPT
278: RETURN
279: *
280: * End of DORMBR
281: *
282: END
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