forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
cstt21.f
245 lines (245 loc) · 6.62 KB
/
cstt21.f
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
*> \brief \b CSTT21
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
* RESULT )
*
* .. Scalar Arguments ..
* INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
* REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
* $ SD( * ), SE( * )
* COMPLEX U( LDU, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CSTT21 checks a decomposition of the form
*>
*> A = U S U**H
*>
*> where **H means conjugate transpose, A is real symmetric tridiagonal,
*> U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
*> tridiagonal (if KBAND=1). Two tests are performed:
*>
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp )
*>
*> RESULT(2) = | I - U U**H | / ( n ulp )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, CSTT21 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] KBAND
*> \verbatim
*> KBAND is INTEGER
*> The bandwidth of the matrix S. It may only be zero or one.
*> If zero, then S is diagonal, and SE is not referenced. If
*> one, then S is symmetric tri-diagonal.
*> \endverbatim
*>
*> \param[in] AD
*> \verbatim
*> AD is REAL array, dimension (N)
*> The diagonal of the original (unfactored) matrix A. A is
*> assumed to be real symmetric tridiagonal.
*> \endverbatim
*>
*> \param[in] AE
*> \verbatim
*> AE is REAL array, dimension (N-1)
*> The off-diagonal of the original (unfactored) matrix A. A
*> is assumed to be symmetric tridiagonal. AE(1) is the (1,2)
*> and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
*> \endverbatim
*>
*> \param[in] SD
*> \verbatim
*> SD is REAL array, dimension (N)
*> The diagonal of the real (symmetric tri-) diagonal matrix S.
*> \endverbatim
*>
*> \param[in] SE
*> \verbatim
*> SE is REAL array, dimension (N-1)
*> The off-diagonal of the (symmetric tri-) diagonal matrix S.
*> Not referenced if KBSND=0. If KBAND=1, then AE(1) is the
*> (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
*> element, etc.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*> U is COMPLEX array, dimension (LDU, N)
*> The unitary matrix in the decomposition.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U. LDU must be at least N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (N**2)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (2)
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> RESULT(1) is always modified.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_eig
*
* =====================================================================
SUBROUTINE CSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
$ RESULT )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
$ SD( * ), SE( * )
COMPLEX U( LDU, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER J
REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
* ..
* .. External Functions ..
REAL CLANGE, CLANHE, SLAMCH
EXTERNAL CLANGE, CLANHE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CHER, CHER2, CLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CMPLX, MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
* 1) Constants
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
UNFL = SLAMCH( 'Safe minimum' )
ULP = SLAMCH( 'Precision' )
*
* Do Test 1
*
* Copy A & Compute its 1-Norm:
*
CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
*
ANORM = ZERO
TEMP1 = ZERO
*
DO 10 J = 1, N - 1
WORK( ( N+1 )*( J-1 )+1 ) = AD( J )
WORK( ( N+1 )*( J-1 )+2 ) = AE( J )
TEMP2 = ABS( AE( J ) )
ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 )
TEMP1 = TEMP2
10 CONTINUE
*
WORK( N**2 ) = AD( N )
ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
*
* Norm of A - U S U**H
*
DO 20 J = 1, N
CALL CHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
20 CONTINUE
*
IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
DO 30 J = 1, N - 1
CALL CHER2( 'L', N, -CMPLX( SE( J ) ), U( 1, J ), 1,
$ U( 1, J+1 ), 1, WORK, N )
30 CONTINUE
END IF
*
WNORM = CLANHE( '1', 'L', N, WORK, N, RWORK )
*
IF( ANORM.GT.WNORM ) THEN
RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
ELSE
RESULT( 1 ) = MIN( WNORM / ANORM, REAL( N ) ) / ( N*ULP )
END IF
END IF
*
* Do Test 2
*
* Compute U U**H - I
*
CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
$ N )
*
DO 40 J = 1, N
WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
40 CONTINUE
*
RESULT( 2 ) = MIN( REAL( N ), CLANGE( '1', N, N, WORK, N,
$ RWORK ) ) / ( N*ULP )
*
RETURN
*
* End of CSTT21
*
END