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1.1 bertrand 1: SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, 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, LDQ, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DOPGTR generates a real orthogonal matrix Q which is defined as the
20: * product of n-1 elementary reflectors H(i) of order n, as returned by
21: * DSPTRD using packed storage:
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 triangular packed storage used in previous
32: * call to DSPTRD;
33: * = 'L': Lower triangular packed storage used in previous
34: * call to DSPTRD.
35: *
36: * N (input) INTEGER
37: * The order of the matrix Q. N >= 0.
38: *
39: * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
40: * The vectors which define the elementary reflectors, as
41: * returned by DSPTRD.
42: *
43: * TAU (input) DOUBLE PRECISION array, dimension (N-1)
44: * TAU(i) must contain the scalar factor of the elementary
45: * reflector H(i), as returned by DSPTRD.
46: *
47: * Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
48: * The N-by-N orthogonal matrix Q.
49: *
50: * LDQ (input) INTEGER
51: * The leading dimension of the array Q. LDQ >= max(1,N).
52: *
53: * WORK (workspace) DOUBLE PRECISION array, dimension (N-1)
54: *
55: * INFO (output) INTEGER
56: * = 0: successful exit
57: * < 0: if INFO = -i, the i-th argument had an illegal value
58: *
59: * =====================================================================
60: *
61: * .. Parameters ..
62: DOUBLE PRECISION ZERO, ONE
63: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
64: * ..
65: * .. Local Scalars ..
66: LOGICAL UPPER
67: INTEGER I, IINFO, IJ, J
68: * ..
69: * .. External Functions ..
70: LOGICAL LSAME
71: EXTERNAL LSAME
72: * ..
73: * .. External Subroutines ..
74: EXTERNAL DORG2L, DORG2R, XERBLA
75: * ..
76: * .. Intrinsic Functions ..
77: INTRINSIC MAX
78: * ..
79: * .. Executable Statements ..
80: *
81: * Test the input arguments
82: *
83: INFO = 0
84: UPPER = LSAME( UPLO, 'U' )
85: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
86: INFO = -1
87: ELSE IF( N.LT.0 ) THEN
88: INFO = -2
89: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
90: INFO = -6
91: END IF
92: IF( INFO.NE.0 ) THEN
93: CALL XERBLA( 'DOPGTR', -INFO )
94: RETURN
95: END IF
96: *
97: * Quick return if possible
98: *
99: IF( N.EQ.0 )
100: $ RETURN
101: *
102: IF( UPPER ) THEN
103: *
104: * Q was determined by a call to DSPTRD with UPLO = 'U'
105: *
106: * Unpack the vectors which define the elementary reflectors and
107: * set the last row and column of Q equal to those of the unit
108: * matrix
109: *
110: IJ = 2
111: DO 20 J = 1, N - 1
112: DO 10 I = 1, J - 1
113: Q( I, J ) = AP( IJ )
114: IJ = IJ + 1
115: 10 CONTINUE
116: IJ = IJ + 2
117: Q( N, J ) = ZERO
118: 20 CONTINUE
119: DO 30 I = 1, N - 1
120: Q( I, N ) = ZERO
121: 30 CONTINUE
122: Q( N, N ) = ONE
123: *
124: * Generate Q(1:n-1,1:n-1)
125: *
126: CALL DORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
127: *
128: ELSE
129: *
130: * Q was determined by a call to DSPTRD with UPLO = 'L'.
131: *
132: * Unpack the vectors which define the elementary reflectors and
133: * set the first row and column of Q equal to those of the unit
134: * matrix
135: *
136: Q( 1, 1 ) = ONE
137: DO 40 I = 2, N
138: Q( I, 1 ) = ZERO
139: 40 CONTINUE
140: IJ = 3
141: DO 60 J = 2, N
142: Q( 1, J ) = ZERO
143: DO 50 I = J + 1, N
144: Q( I, J ) = AP( IJ )
145: IJ = IJ + 1
146: 50 CONTINUE
147: IJ = IJ + 2
148: 60 CONTINUE
149: IF( N.GT.1 ) THEN
150: *
151: * Generate Q(2:n,2:n)
152: *
153: CALL DORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
154: $ IINFO )
155: END IF
156: END IF
157: RETURN
158: *
159: * End of DOPGTR
160: *
161: END