Annotation of rpl/lapack/lapack/dorgtr.f, revision 1.1.1.1
1.1 bertrand 1: SUBROUTINE DORGTR( UPLO, N, 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 UPLO
10: INTEGER INFO, LDA, LWORK, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DORGTR generates a real orthogonal matrix Q which is defined as the
20: * product of n-1 elementary reflectors of order N, as returned by
21: * DSYTRD:
22: *
23: * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
24: *
25: * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
26: *
27: * Arguments
28: * =========
29: *
30: * UPLO (input) CHARACTER*1
31: * = 'U': Upper triangle of A contains elementary reflectors
32: * from DSYTRD;
33: * = 'L': Lower triangle of A contains elementary reflectors
34: * from DSYTRD.
35: *
36: * N (input) INTEGER
37: * The order of the matrix Q. N >= 0.
38: *
39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40: * On entry, the vectors which define the elementary reflectors,
41: * as returned by DSYTRD.
42: * On exit, the N-by-N orthogonal matrix Q.
43: *
44: * LDA (input) INTEGER
45: * The leading dimension of the array A. LDA >= max(1,N).
46: *
47: * TAU (input) DOUBLE PRECISION array, dimension (N-1)
48: * TAU(i) must contain the scalar factor of the elementary
49: * reflector H(i), as returned by DSYTRD.
50: *
51: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
52: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
53: *
54: * LWORK (input) INTEGER
55: * The dimension of the array WORK. LWORK >= max(1,N-1).
56: * For optimum performance LWORK >= (N-1)*NB, where NB is
57: * the optimal blocksize.
58: *
59: * If LWORK = -1, then a workspace query is assumed; the routine
60: * only calculates the optimal size of the WORK array, returns
61: * this value as the first entry of the WORK array, and no error
62: * message related to LWORK is issued by XERBLA.
63: *
64: * INFO (output) INTEGER
65: * = 0: successful exit
66: * < 0: if INFO = -i, the i-th argument had an illegal value
67: *
68: * =====================================================================
69: *
70: * .. Parameters ..
71: DOUBLE PRECISION ZERO, ONE
72: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
73: * ..
74: * .. Local Scalars ..
75: LOGICAL LQUERY, UPPER
76: INTEGER I, IINFO, J, LWKOPT, NB
77: * ..
78: * .. External Functions ..
79: LOGICAL LSAME
80: INTEGER ILAENV
81: EXTERNAL LSAME, ILAENV
82: * ..
83: * .. External Subroutines ..
84: EXTERNAL DORGQL, DORGQR, XERBLA
85: * ..
86: * .. Intrinsic Functions ..
87: INTRINSIC MAX
88: * ..
89: * .. Executable Statements ..
90: *
91: * Test the input arguments
92: *
93: INFO = 0
94: LQUERY = ( LWORK.EQ.-1 )
95: UPPER = LSAME( UPLO, 'U' )
96: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
97: INFO = -1
98: ELSE IF( N.LT.0 ) THEN
99: INFO = -2
100: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
101: INFO = -4
102: ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
103: INFO = -7
104: END IF
105: *
106: IF( INFO.EQ.0 ) THEN
107: IF( UPPER ) THEN
108: NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
109: ELSE
110: NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
111: END IF
112: LWKOPT = MAX( 1, N-1 )*NB
113: WORK( 1 ) = LWKOPT
114: END IF
115: *
116: IF( INFO.NE.0 ) THEN
117: CALL XERBLA( 'DORGTR', -INFO )
118: RETURN
119: ELSE IF( LQUERY ) THEN
120: RETURN
121: END IF
122: *
123: * Quick return if possible
124: *
125: IF( N.EQ.0 ) THEN
126: WORK( 1 ) = 1
127: RETURN
128: END IF
129: *
130: IF( UPPER ) THEN
131: *
132: * Q was determined by a call to DSYTRD with UPLO = 'U'
133: *
134: * Shift the vectors which define the elementary reflectors one
135: * column to the left, and set the last row and column of Q to
136: * those of the unit matrix
137: *
138: DO 20 J = 1, N - 1
139: DO 10 I = 1, J - 1
140: A( I, J ) = A( I, J+1 )
141: 10 CONTINUE
142: A( N, J ) = ZERO
143: 20 CONTINUE
144: DO 30 I = 1, N - 1
145: A( I, N ) = ZERO
146: 30 CONTINUE
147: A( N, N ) = ONE
148: *
149: * Generate Q(1:n-1,1:n-1)
150: *
151: CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
152: *
153: ELSE
154: *
155: * Q was determined by a call to DSYTRD with UPLO = 'L'.
156: *
157: * Shift the vectors which define the elementary reflectors one
158: * column to the right, and set the first row and column of Q to
159: * those of the unit matrix
160: *
161: DO 50 J = N, 2, -1
162: A( 1, J ) = ZERO
163: DO 40 I = J + 1, N
164: A( I, J ) = A( I, J-1 )
165: 40 CONTINUE
166: 50 CONTINUE
167: A( 1, 1 ) = ONE
168: DO 60 I = 2, N
169: A( I, 1 ) = ZERO
170: 60 CONTINUE
171: IF( N.GT.1 ) THEN
172: *
173: * Generate Q(2:n,2:n)
174: *
175: CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
176: $ LWORK, IINFO )
177: END IF
178: END IF
179: WORK( 1 ) = LWKOPT
180: RETURN
181: *
182: * End of DORGTR
183: *
184: END
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