Annotation of rpl/lapack/lapack/dorghr.f, revision 1.3
1.1 bertrand 1: SUBROUTINE DORGHR( N, ILO, IHI, 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: INTEGER IHI, ILO, INFO, LDA, LWORK, N
10: * ..
11: * .. Array Arguments ..
12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * DORGHR generates a real orthogonal matrix Q which is defined as the
19: * product of IHI-ILO elementary reflectors of order N, as returned by
20: * DGEHRD:
21: *
22: * Q = H(ilo) H(ilo+1) . . . H(ihi-1).
23: *
24: * Arguments
25: * =========
26: *
27: * N (input) INTEGER
28: * The order of the matrix Q. N >= 0.
29: *
30: * ILO (input) INTEGER
31: * IHI (input) INTEGER
32: * ILO and IHI must have the same values as in the previous call
33: * of DGEHRD. Q is equal to the unit matrix except in the
34: * submatrix Q(ilo+1:ihi,ilo+1:ihi).
35: * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
36: *
37: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
38: * On entry, the vectors which define the elementary reflectors,
39: * as returned by DGEHRD.
40: * On exit, the N-by-N orthogonal matrix Q.
41: *
42: * LDA (input) INTEGER
43: * The leading dimension of the array A. LDA >= max(1,N).
44: *
45: * TAU (input) DOUBLE PRECISION array, dimension (N-1)
46: * TAU(i) must contain the scalar factor of the elementary
47: * reflector H(i), as returned by DGEHRD.
48: *
49: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
50: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
51: *
52: * LWORK (input) INTEGER
53: * The dimension of the array WORK. LWORK >= IHI-ILO.
54: * For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
55: * the optimal blocksize.
56: *
57: * If LWORK = -1, then a workspace query is assumed; the routine
58: * only calculates the optimal size of the WORK array, returns
59: * this value as the first entry of the WORK array, and no error
60: * message related to LWORK is issued by XERBLA.
61: *
62: * INFO (output) INTEGER
63: * = 0: successful exit
64: * < 0: if INFO = -i, the i-th argument had an illegal value
65: *
66: * =====================================================================
67: *
68: * .. Parameters ..
69: DOUBLE PRECISION ZERO, ONE
70: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
71: * ..
72: * .. Local Scalars ..
73: LOGICAL LQUERY
74: INTEGER I, IINFO, J, LWKOPT, NB, NH
75: * ..
76: * .. External Subroutines ..
77: EXTERNAL DORGQR, XERBLA
78: * ..
79: * .. External Functions ..
80: INTEGER ILAENV
81: EXTERNAL ILAENV
82: * ..
83: * .. Intrinsic Functions ..
84: INTRINSIC MAX, MIN
85: * ..
86: * .. Executable Statements ..
87: *
88: * Test the input arguments
89: *
90: INFO = 0
91: NH = IHI - ILO
92: LQUERY = ( LWORK.EQ.-1 )
93: IF( N.LT.0 ) THEN
94: INFO = -1
95: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
96: INFO = -2
97: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
98: INFO = -3
99: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
100: INFO = -5
101: ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
102: INFO = -8
103: END IF
104: *
105: IF( INFO.EQ.0 ) THEN
106: NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )
107: LWKOPT = MAX( 1, NH )*NB
108: WORK( 1 ) = LWKOPT
109: END IF
110: *
111: IF( INFO.NE.0 ) THEN
112: CALL XERBLA( 'DORGHR', -INFO )
113: RETURN
114: ELSE IF( LQUERY ) THEN
115: RETURN
116: END IF
117: *
118: * Quick return if possible
119: *
120: IF( N.EQ.0 ) THEN
121: WORK( 1 ) = 1
122: RETURN
123: END IF
124: *
125: * Shift the vectors which define the elementary reflectors one
126: * column to the right, and set the first ilo and the last n-ihi
127: * rows and columns to those of the unit matrix
128: *
129: DO 40 J = IHI, ILO + 1, -1
130: DO 10 I = 1, J - 1
131: A( I, J ) = ZERO
132: 10 CONTINUE
133: DO 20 I = J + 1, IHI
134: A( I, J ) = A( I, J-1 )
135: 20 CONTINUE
136: DO 30 I = IHI + 1, N
137: A( I, J ) = ZERO
138: 30 CONTINUE
139: 40 CONTINUE
140: DO 60 J = 1, ILO
141: DO 50 I = 1, N
142: A( I, J ) = ZERO
143: 50 CONTINUE
144: A( J, J ) = ONE
145: 60 CONTINUE
146: DO 80 J = IHI + 1, N
147: DO 70 I = 1, N
148: A( I, J ) = ZERO
149: 70 CONTINUE
150: A( J, J ) = ONE
151: 80 CONTINUE
152: *
153: IF( NH.GT.0 ) THEN
154: *
155: * Generate Q(ilo+1:ihi,ilo+1:ihi)
156: *
157: CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
158: $ WORK, LWORK, IINFO )
159: END IF
160: WORK( 1 ) = LWKOPT
161: RETURN
162: *
163: * End of DORGHR
164: *
165: END
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