Annotation of rpl/lapack/lapack/zungbr.f, revision 1.8
1.1 bertrand 1: SUBROUTINE ZUNGBR( VECT, 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: CHARACTER VECT
10: INTEGER INFO, K, LDA, LWORK, M, N
11: * ..
12: * .. Array Arguments ..
13: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZUNGBR generates one of the complex unitary matrices Q or P**H
20: * determined by ZGEBRD when reducing a complex matrix A to bidiagonal
21: * form: A = Q * B * P**H. Q and P**H are defined as products of
22: * elementary reflectors H(i) or G(i) respectively.
23: *
24: * If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
25: * is of order M:
26: * if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
27: * columns of Q, where m >= n >= k;
28: * if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
29: * M-by-M matrix.
30: *
31: * If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
32: * is of order N:
33: * if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
34: * rows of P**H, where n >= m >= k;
35: * if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
36: * an N-by-N matrix.
37: *
38: * Arguments
39: * =========
40: *
41: * VECT (input) CHARACTER*1
42: * Specifies whether the matrix Q or the matrix P**H is
43: * required, as defined in the transformation applied by ZGEBRD:
44: * = 'Q': generate Q;
45: * = 'P': generate P**H.
46: *
47: * M (input) INTEGER
48: * The number of rows of the matrix Q or P**H to be returned.
49: * M >= 0.
50: *
51: * N (input) INTEGER
52: * The number of columns of the matrix Q or P**H to be returned.
53: * N >= 0.
54: * If VECT = 'Q', M >= N >= min(M,K);
55: * if VECT = 'P', N >= M >= min(N,K).
56: *
57: * K (input) INTEGER
58: * If VECT = 'Q', the number of columns in the original M-by-K
59: * matrix reduced by ZGEBRD.
60: * If VECT = 'P', the number of rows in the original K-by-N
61: * matrix reduced by ZGEBRD.
62: * K >= 0.
63: *
64: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
65: * On entry, the vectors which define the elementary reflectors,
66: * as returned by ZGEBRD.
67: * On exit, the M-by-N matrix Q or P**H.
68: *
69: * LDA (input) INTEGER
70: * The leading dimension of the array A. LDA >= M.
71: *
72: * TAU (input) COMPLEX*16 array, dimension
73: * (min(M,K)) if VECT = 'Q'
74: * (min(N,K)) if VECT = 'P'
75: * TAU(i) must contain the scalar factor of the elementary
76: * reflector H(i) or G(i), which determines Q or P**H, as
77: * returned by ZGEBRD in its array argument TAUQ or TAUP.
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. LWORK >= max(1,min(M,N)).
84: * For optimum performance LWORK >= min(M,N)*NB, where NB
85: * is the optimal blocksize.
86: *
87: * If LWORK = -1, then a workspace query is assumed; the routine
88: * only calculates the optimal size of the WORK array, returns
89: * this value as the first entry of the WORK array, and no error
90: * message related to LWORK is issued by XERBLA.
91: *
92: * INFO (output) INTEGER
93: * = 0: successful exit
94: * < 0: if INFO = -i, the i-th argument had an illegal value
95: *
96: * =====================================================================
97: *
98: * .. Parameters ..
99: COMPLEX*16 ZERO, ONE
100: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
101: $ ONE = ( 1.0D+0, 0.0D+0 ) )
102: * ..
103: * .. Local Scalars ..
104: LOGICAL LQUERY, WANTQ
105: INTEGER I, IINFO, J, LWKOPT, MN, NB
106: * ..
107: * .. External Functions ..
108: LOGICAL LSAME
109: INTEGER ILAENV
110: EXTERNAL LSAME, ILAENV
111: * ..
112: * .. External Subroutines ..
113: EXTERNAL XERBLA, ZUNGLQ, ZUNGQR
114: * ..
115: * .. Intrinsic Functions ..
116: INTRINSIC MAX, MIN
117: * ..
118: * .. Executable Statements ..
119: *
120: * Test the input arguments
121: *
122: INFO = 0
123: WANTQ = LSAME( VECT, 'Q' )
124: MN = MIN( M, N )
125: LQUERY = ( LWORK.EQ.-1 )
126: IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
127: INFO = -1
128: ELSE IF( M.LT.0 ) THEN
129: INFO = -2
130: ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
131: $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
132: $ MIN( N, K ) ) ) ) THEN
133: INFO = -3
134: ELSE IF( K.LT.0 ) THEN
135: INFO = -4
136: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
137: INFO = -6
138: ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
139: INFO = -9
140: END IF
141: *
142: IF( INFO.EQ.0 ) THEN
143: IF( WANTQ ) THEN
144: NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 )
145: ELSE
146: NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
147: END IF
148: LWKOPT = MAX( 1, MN )*NB
149: WORK( 1 ) = LWKOPT
150: END IF
151: *
152: IF( INFO.NE.0 ) THEN
153: CALL XERBLA( 'ZUNGBR', -INFO )
154: RETURN
155: ELSE IF( LQUERY ) THEN
156: RETURN
157: END IF
158: *
159: * Quick return if possible
160: *
161: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
162: WORK( 1 ) = 1
163: RETURN
164: END IF
165: *
166: IF( WANTQ ) THEN
167: *
168: * Form Q, determined by a call to ZGEBRD to reduce an m-by-k
169: * matrix
170: *
171: IF( M.GE.K ) THEN
172: *
173: * If m >= k, assume m >= n >= k
174: *
175: CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
176: *
177: ELSE
178: *
179: * If m < k, assume m = n
180: *
181: * Shift the vectors which define the elementary reflectors one
182: * column to the right, and set the first row and column of Q
183: * to those of the unit matrix
184: *
185: DO 20 J = M, 2, -1
186: A( 1, J ) = ZERO
187: DO 10 I = J + 1, M
188: A( I, J ) = A( I, J-1 )
189: 10 CONTINUE
190: 20 CONTINUE
191: A( 1, 1 ) = ONE
192: DO 30 I = 2, M
193: A( I, 1 ) = ZERO
194: 30 CONTINUE
195: IF( M.GT.1 ) THEN
196: *
197: * Form Q(2:m,2:m)
198: *
199: CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
200: $ LWORK, IINFO )
201: END IF
202: END IF
203: ELSE
204: *
1.8 ! bertrand 205: * Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
1.1 bertrand 206: * matrix
207: *
208: IF( K.LT.N ) THEN
209: *
210: * If k < n, assume k <= m <= n
211: *
212: CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
213: *
214: ELSE
215: *
216: * If k >= n, assume m = n
217: *
218: * Shift the vectors which define the elementary reflectors one
1.8 ! bertrand 219: * row downward, and set the first row and column of P**H to
1.1 bertrand 220: * those of the unit matrix
221: *
222: A( 1, 1 ) = ONE
223: DO 40 I = 2, N
224: A( I, 1 ) = ZERO
225: 40 CONTINUE
226: DO 60 J = 2, N
227: DO 50 I = J - 1, 2, -1
228: A( I, J ) = A( I-1, J )
229: 50 CONTINUE
230: A( 1, J ) = ZERO
231: 60 CONTINUE
232: IF( N.GT.1 ) THEN
233: *
1.8 ! bertrand 234: * Form P**H(2:n,2:n)
1.1 bertrand 235: *
236: CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
237: $ LWORK, IINFO )
238: END IF
239: END IF
240: END IF
241: WORK( 1 ) = LWKOPT
242: RETURN
243: *
244: * End of ZUNGBR
245: *
246: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zungbr.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack