1: *> \brief \b DORGHR
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGHR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorghr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorghr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorghr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER IHI, ILO, INFO, LDA, LWORK, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DORGHR generates a real orthogonal matrix Q which is defined as the
37: *> product of IHI-ILO elementary reflectors of order N, as returned by
38: *> DGEHRD:
39: *>
40: *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] N
47: *> \verbatim
48: *> N is INTEGER
49: *> The order of the matrix Q. N >= 0.
50: *> \endverbatim
51: *>
52: *> \param[in] ILO
53: *> \verbatim
54: *> ILO is INTEGER
55: *> \endverbatim
56: *>
57: *> \param[in] IHI
58: *> \verbatim
59: *> IHI is INTEGER
60: *>
61: *> ILO and IHI must have the same values as in the previous call
62: *> of DGEHRD. Q is equal to the unit matrix except in the
63: *> submatrix Q(ilo+1:ihi,ilo+1:ihi).
64: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is DOUBLE PRECISION array, dimension (LDA,N)
70: *> On entry, the vectors which define the elementary reflectors,
71: *> as returned by DGEHRD.
72: *> On exit, the N-by-N orthogonal matrix Q.
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(1,N).
79: *> \endverbatim
80: *>
81: *> \param[in] TAU
82: *> \verbatim
83: *> TAU is DOUBLE PRECISION array, dimension (N-1)
84: *> TAU(i) must contain the scalar factor of the elementary
85: *> reflector H(i), as returned by DGEHRD.
86: *> \endverbatim
87: *>
88: *> \param[out] WORK
89: *> \verbatim
90: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
91: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
92: *> \endverbatim
93: *>
94: *> \param[in] LWORK
95: *> \verbatim
96: *> LWORK is INTEGER
97: *> The dimension of the array WORK. LWORK >= IHI-ILO.
98: *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
99: *> the optimal blocksize.
100: *>
101: *> If LWORK = -1, then a workspace query is assumed; the routine
102: *> only calculates the optimal size of the WORK array, returns
103: *> this value as the first entry of the WORK array, and no error
104: *> message related to LWORK is issued by XERBLA.
105: *> \endverbatim
106: *>
107: *> \param[out] INFO
108: *> \verbatim
109: *> INFO is INTEGER
110: *> = 0: successful exit
111: *> < 0: if INFO = -i, the i-th argument had an illegal value
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
121: *
122: *> \ingroup doubleOTHERcomputational
123: *
124: * =====================================================================
125: SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
126: *
127: * -- LAPACK computational routine --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: *
131: * .. Scalar Arguments ..
132: INTEGER IHI, ILO, INFO, LDA, LWORK, N
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ZERO, ONE
142: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: LOGICAL LQUERY
146: INTEGER I, IINFO, J, LWKOPT, NB, NH
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DORGQR, XERBLA
150: * ..
151: * .. External Functions ..
152: INTEGER ILAENV
153: EXTERNAL ILAENV
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC MAX, MIN
157: * ..
158: * .. Executable Statements ..
159: *
160: * Test the input arguments
161: *
162: INFO = 0
163: NH = IHI - ILO
164: LQUERY = ( LWORK.EQ.-1 )
165: IF( N.LT.0 ) THEN
166: INFO = -1
167: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
168: INFO = -2
169: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
170: INFO = -3
171: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
172: INFO = -5
173: ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
174: INFO = -8
175: END IF
176: *
177: IF( INFO.EQ.0 ) THEN
178: NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )
179: LWKOPT = MAX( 1, NH )*NB
180: WORK( 1 ) = LWKOPT
181: END IF
182: *
183: IF( INFO.NE.0 ) THEN
184: CALL XERBLA( 'DORGHR', -INFO )
185: RETURN
186: ELSE IF( LQUERY ) THEN
187: RETURN
188: END IF
189: *
190: * Quick return if possible
191: *
192: IF( N.EQ.0 ) THEN
193: WORK( 1 ) = 1
194: RETURN
195: END IF
196: *
197: * Shift the vectors which define the elementary reflectors one
198: * column to the right, and set the first ilo and the last n-ihi
199: * rows and columns to those of the unit matrix
200: *
201: DO 40 J = IHI, ILO + 1, -1
202: DO 10 I = 1, J - 1
203: A( I, J ) = ZERO
204: 10 CONTINUE
205: DO 20 I = J + 1, IHI
206: A( I, J ) = A( I, J-1 )
207: 20 CONTINUE
208: DO 30 I = IHI + 1, N
209: A( I, J ) = ZERO
210: 30 CONTINUE
211: 40 CONTINUE
212: DO 60 J = 1, ILO
213: DO 50 I = 1, N
214: A( I, J ) = ZERO
215: 50 CONTINUE
216: A( J, J ) = ONE
217: 60 CONTINUE
218: DO 80 J = IHI + 1, N
219: DO 70 I = 1, N
220: A( I, J ) = ZERO
221: 70 CONTINUE
222: A( J, J ) = ONE
223: 80 CONTINUE
224: *
225: IF( NH.GT.0 ) THEN
226: *
227: * Generate Q(ilo+1:ihi,ilo+1:ihi)
228: *
229: CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
230: $ WORK, LWORK, IINFO )
231: END IF
232: WORK( 1 ) = LWKOPT
233: RETURN
234: *
235: * End of DORGHR
236: *
237: END
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