LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cstt22.f
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1 *> \brief \b CSTT22
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE CSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
12 * LDWORK, RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER KBAND, LDU, LDWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
19 * $ SD( * ), SE( * )
20 * COMPLEX U( LDU, * ), WORK( LDWORK, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CSTT22 checks a set of M eigenvalues and eigenvectors,
30 *>
31 *> A U = U S
32 *>
33 *> where A is Hermitian tridiagonal, the columns of U are unitary,
34 *> and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
35 *> Two tests are performed:
36 *>
37 *> RESULT(1) = | U* A U - S | / ( |A| m ulp )
38 *>
39 *> RESULT(2) = | I - U*U | / ( m ulp )
40 *> \endverbatim
41 *
42 * Arguments:
43 * ==========
44 *
45 *> \param[in] N
46 *> \verbatim
47 *> N is INTEGER
48 *> The size of the matrix. If it is zero, CSTT22 does nothing.
49 *> It must be at least zero.
50 *> \endverbatim
51 *>
52 *> \param[in] M
53 *> \verbatim
54 *> M is INTEGER
55 *> The number of eigenpairs to check. If it is zero, CSTT22
56 *> does nothing. It must be at least zero.
57 *> \endverbatim
58 *>
59 *> \param[in] KBAND
60 *> \verbatim
61 *> KBAND is INTEGER
62 *> The bandwidth of the matrix S. It may only be zero or one.
63 *> If zero, then S is diagonal, and SE is not referenced. If
64 *> one, then S is Hermitian tri-diagonal.
65 *> \endverbatim
66 *>
67 *> \param[in] AD
68 *> \verbatim
69 *> AD is REAL array, dimension (N)
70 *> The diagonal of the original (unfactored) matrix A. A is
71 *> assumed to be Hermitian tridiagonal.
72 *> \endverbatim
73 *>
74 *> \param[in] AE
75 *> \verbatim
76 *> AE is REAL array, dimension (N)
77 *> The off-diagonal of the original (unfactored) matrix A. A
78 *> is assumed to be Hermitian tridiagonal. AE(1) is ignored,
79 *> AE(2) is the (1,2) and (2,1) element, etc.
80 *> \endverbatim
81 *>
82 *> \param[in] SD
83 *> \verbatim
84 *> SD is REAL array, dimension (N)
85 *> The diagonal of the (Hermitian tri-) diagonal matrix S.
86 *> \endverbatim
87 *>
88 *> \param[in] SE
89 *> \verbatim
90 *> SE is REAL array, dimension (N)
91 *> The off-diagonal of the (Hermitian tri-) diagonal matrix S.
92 *> Not referenced if KBSND=0. If KBAND=1, then AE(1) is
93 *> ignored, SE(2) is the (1,2) and (2,1) element, etc.
94 *> \endverbatim
95 *>
96 *> \param[in] U
97 *> \verbatim
98 *> U is REAL array, dimension (LDU, N)
99 *> The unitary matrix in the decomposition.
100 *> \endverbatim
101 *>
102 *> \param[in] LDU
103 *> \verbatim
104 *> LDU is INTEGER
105 *> The leading dimension of U. LDU must be at least N.
106 *> \endverbatim
107 *>
108 *> \param[out] WORK
109 *> \verbatim
110 *> WORK is COMPLEX array, dimension (LDWORK, M+1)
111 *> \endverbatim
112 *>
113 *> \param[in] LDWORK
114 *> \verbatim
115 *> LDWORK is INTEGER
116 *> The leading dimension of WORK. LDWORK must be at least
117 *> max(1,M).
118 *> \endverbatim
119 *>
120 *> \param[out] RWORK
121 *> \verbatim
122 *> RWORK is REAL array, dimension (N)
123 *> \endverbatim
124 *>
125 *> \param[out] RESULT
126 *> \verbatim
127 *> RESULT is REAL array, dimension (2)
128 *> The values computed by the two tests described above. The
129 *> values are currently limited to 1/ulp, to avoid overflow.
130 *> \endverbatim
131 *
132 * Authors:
133 * ========
134 *
135 *> \author Univ. of Tennessee
136 *> \author Univ. of California Berkeley
137 *> \author Univ. of Colorado Denver
138 *> \author NAG Ltd.
139 *
140 *> \ingroup complex_eig
141 *
142 * =====================================================================
143  SUBROUTINE cstt22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
144  $ LDWORK, RWORK, RESULT )
145 *
146 * -- LAPACK test routine --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 *
150 * .. Scalar Arguments ..
151  INTEGER KBAND, LDU, LDWORK, M, N
152 * ..
153 * .. Array Arguments ..
154  REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
155  $ sd( * ), se( * )
156  COMPLEX U( LDU, * ), WORK( LDWORK, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ZERO, ONE
163  parameter( zero = 0.0e0, one = 1.0e0 )
164  COMPLEX CZERO, CONE
165  parameter( czero = ( 0.0e+0, 0.0e+0 ),
166  $ cone = ( 1.0e+0, 0.0e+0 ) )
167 * ..
168 * .. Local Scalars ..
169  INTEGER I, J, K
170  REAL ANORM, ULP, UNFL, WNORM
171  COMPLEX AUKJ
172 * ..
173 * .. External Functions ..
174  REAL CLANGE, CLANSY, SLAMCH
175  EXTERNAL clange, clansy, slamch
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL cgemm
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, max, min, real
182 * ..
183 * .. Executable Statements ..
184 *
185  result( 1 ) = zero
186  result( 2 ) = zero
187  IF( n.LE.0 .OR. m.LE.0 )
188  $ RETURN
189 *
190  unfl = slamch( 'Safe minimum' )
191  ulp = slamch( 'Epsilon' )
192 *
193 * Do Test 1
194 *
195 * Compute the 1-norm of A.
196 *
197  IF( n.GT.1 ) THEN
198  anorm = abs( ad( 1 ) ) + abs( ae( 1 ) )
199  DO 10 j = 2, n - 1
200  anorm = max( anorm, abs( ad( j ) )+abs( ae( j ) )+
201  $ abs( ae( j-1 ) ) )
202  10 CONTINUE
203  anorm = max( anorm, abs( ad( n ) )+abs( ae( n-1 ) ) )
204  ELSE
205  anorm = abs( ad( 1 ) )
206  END IF
207  anorm = max( anorm, unfl )
208 *
209 * Norm of U*AU - S
210 *
211  DO 40 i = 1, m
212  DO 30 j = 1, m
213  work( i, j ) = czero
214  DO 20 k = 1, n
215  aukj = ad( k )*u( k, j )
216  IF( k.NE.n )
217  $ aukj = aukj + ae( k )*u( k+1, j )
218  IF( k.NE.1 )
219  $ aukj = aukj + ae( k-1 )*u( k-1, j )
220  work( i, j ) = work( i, j ) + u( k, i )*aukj
221  20 CONTINUE
222  30 CONTINUE
223  work( i, i ) = work( i, i ) - sd( i )
224  IF( kband.EQ.1 ) THEN
225  IF( i.NE.1 )
226  $ work( i, i-1 ) = work( i, i-1 ) - se( i-1 )
227  IF( i.NE.n )
228  $ work( i, i+1 ) = work( i, i+1 ) - se( i )
229  END IF
230  40 CONTINUE
231 *
232  wnorm = clansy( '1', 'L', m, work, m, rwork )
233 *
234  IF( anorm.GT.wnorm ) THEN
235  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
236  ELSE
237  IF( anorm.LT.one ) THEN
238  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
239  ELSE
240  result( 1 ) = min( wnorm / anorm, real( m ) ) / ( m*ulp )
241  END IF
242  END IF
243 *
244 * Do Test 2
245 *
246 * Compute U*U - I
247 *
248  CALL cgemm( 'T', 'N', m, m, n, cone, u, ldu, u, ldu, czero, work,
249  $ m )
250 *
251  DO 50 j = 1, m
252  work( j, j ) = work( j, j ) - one
253  50 CONTINUE
254 *
255  result( 2 ) = min( real( m ), clange( '1', m, m, work, m,
256  $ rwork ) ) / ( m*ulp )
257 *
258  RETURN
259 *
260 * End of CSTT22
261 *
262  END
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cstt22(N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK, LDWORK, RWORK, RESULT)
CSTT22
Definition: cstt22.f:145