LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
dsgt01.f
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1 *> \brief \b DSGT01
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 DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
12 * WORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER ITYPE, LDA, LDB, LDZ, M, N
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ),
20 * \$ WORK( * ), Z( LDZ, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DDGT01 checks a decomposition of the form
30 *>
31 *> A Z = B Z D or
32 *> A B Z = Z D or
33 *> B A Z = Z D
34 *>
35 *> where A is a symmetric matrix, B is
36 *> symmetric positive definite, Z is orthogonal, and D is diagonal.
37 *>
38 *> One of the following test ratios is computed:
39 *>
40 *> ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )
41 *>
42 *> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
43 *>
44 *> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
45 *> \endverbatim
46 *
47 * Arguments:
48 * ==========
49 *
50 *> \param[in] ITYPE
51 *> \verbatim
52 *> ITYPE is INTEGER
53 *> The form of the symmetric generalized eigenproblem.
54 *> = 1: A*z = (lambda)*B*z
55 *> = 2: A*B*z = (lambda)*z
56 *> = 3: B*A*z = (lambda)*z
57 *> \endverbatim
58 *>
59 *> \param[in] UPLO
60 *> \verbatim
61 *> UPLO is CHARACTER*1
62 *> Specifies whether the upper or lower triangular part of the
63 *> symmetric matrices A and B is stored.
64 *> = 'U': Upper triangular
65 *> = 'L': Lower triangular
66 *> \endverbatim
67 *>
68 *> \param[in] N
69 *> \verbatim
70 *> N is INTEGER
71 *> The order of the matrix A. N >= 0.
72 *> \endverbatim
73 *>
74 *> \param[in] M
75 *> \verbatim
76 *> M is INTEGER
77 *> The number of eigenvalues found. 0 <= M <= N.
78 *> \endverbatim
79 *>
80 *> \param[in] A
81 *> \verbatim
82 *> A is DOUBLE PRECISION array, dimension (LDA, N)
83 *> The original symmetric matrix A.
84 *> \endverbatim
85 *>
86 *> \param[in] LDA
87 *> \verbatim
88 *> LDA is INTEGER
89 *> The leading dimension of the array A. LDA >= max(1,N).
90 *> \endverbatim
91 *>
92 *> \param[in] B
93 *> \verbatim
94 *> B is DOUBLE PRECISION array, dimension (LDB, N)
95 *> The original symmetric positive definite matrix B.
96 *> \endverbatim
97 *>
98 *> \param[in] LDB
99 *> \verbatim
100 *> LDB is INTEGER
101 *> The leading dimension of the array B. LDB >= max(1,N).
102 *> \endverbatim
103 *>
104 *> \param[in] Z
105 *> \verbatim
106 *> Z is DOUBLE PRECISION array, dimension (LDZ, M)
107 *> The computed eigenvectors of the generalized eigenproblem.
108 *> \endverbatim
109 *>
110 *> \param[in] LDZ
111 *> \verbatim
112 *> LDZ is INTEGER
113 *> The leading dimension of the array Z. LDZ >= max(1,N).
114 *> \endverbatim
115 *>
116 *> \param[in] D
117 *> \verbatim
118 *> D is DOUBLE PRECISION array, dimension (M)
119 *> The computed eigenvalues of the generalized eigenproblem.
120 *> \endverbatim
121 *>
122 *> \param[out] WORK
123 *> \verbatim
124 *> WORK is DOUBLE PRECISION array, dimension (N*N)
125 *> \endverbatim
126 *>
127 *> \param[out] RESULT
128 *> \verbatim
129 *> RESULT is DOUBLE PRECISION array, dimension (1)
130 *> The test ratio as described above.
131 *> \endverbatim
132 *
133 * Authors:
134 * ========
135 *
136 *> \author Univ. of Tennessee
137 *> \author Univ. of California Berkeley
138 *> \author Univ. of Colorado Denver
139 *> \author NAG Ltd.
140 *
141 *> \date December 2016
142 *
143 *> \ingroup double_eig
144 *
145 * =====================================================================
146  SUBROUTINE dsgt01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
147  \$ work, result )
148 *
149 * -- LAPACK test routine (version 3.7.0) --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 * December 2016
153 *
154 * .. Scalar Arguments ..
155  CHARACTER UPLO
156  INTEGER ITYPE, LDA, LDB, LDZ, M, N
157 * ..
158 * .. Array Arguments ..
159  DOUBLE PRECISION A( lda, * ), B( ldb, * ), D( * ), RESULT( * ),
160  \$ work( * ), z( ldz, * )
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  DOUBLE PRECISION ZERO, ONE
167  parameter ( zero = 0.0d0, one = 1.0d0 )
168 * ..
169 * .. Local Scalars ..
170  INTEGER I
171  DOUBLE PRECISION ANORM, ULP
172 * ..
173 * .. External Functions ..
174  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
175  EXTERNAL dlamch, dlange, dlansy
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL dscal, dsymm
179 * ..
180 * .. Executable Statements ..
181 *
182  result( 1 ) = zero
183  IF( n.LE.0 )
184  \$ RETURN
185 *
186  ulp = dlamch( 'Epsilon' )
187 *
188 * Compute product of 1-norms of A and Z.
189 *
190  anorm = dlansy( '1', uplo, n, a, lda, work )*
191  \$ dlange( '1', n, m, z, ldz, work )
192  IF( anorm.EQ.zero )
193  \$ anorm = one
194 *
195  IF( itype.EQ.1 ) THEN
196 *
197 * Norm of AZ - BZD
198 *
199  CALL dsymm( 'Left', uplo, n, m, one, a, lda, z, ldz, zero,
200  \$ work, n )
201  DO 10 i = 1, m
202  CALL dscal( n, d( i ), z( 1, i ), 1 )
203  10 CONTINUE
204  CALL dsymm( 'Left', uplo, n, m, one, b, ldb, z, ldz, -one,
205  \$ work, n )
206 *
207  result( 1 ) = ( dlange( '1', n, m, work, n, work ) / anorm ) /
208  \$ ( n*ulp )
209 *
210  ELSE IF( itype.EQ.2 ) THEN
211 *
212 * Norm of ABZ - ZD
213 *
214  CALL dsymm( 'Left', uplo, n, m, one, b, ldb, z, ldz, zero,
215  \$ work, n )
216  DO 20 i = 1, m
217  CALL dscal( n, d( i ), z( 1, i ), 1 )
218  20 CONTINUE
219  CALL dsymm( 'Left', uplo, n, m, one, a, lda, work, n, -one, z,
220  \$ ldz )
221 *
222  result( 1 ) = ( dlange( '1', n, m, z, ldz, work ) / anorm ) /
223  \$ ( n*ulp )
224 *
225  ELSE IF( itype.EQ.3 ) THEN
226 *
227 * Norm of BAZ - ZD
228 *
229  CALL dsymm( 'Left', uplo, n, m, one, a, lda, z, ldz, zero,
230  \$ work, n )
231  DO 30 i = 1, m
232  CALL dscal( n, d( i ), z( 1, i ), 1 )
233  30 CONTINUE
234  CALL dsymm( 'Left', uplo, n, m, one, b, ldb, work, n, -one, z,
235  \$ ldz )
236 *
237  result( 1 ) = ( dlange( '1', n, m, z, ldz, work ) / anorm ) /
238  \$ ( n*ulp )
239  END IF
240 *
241  RETURN
242 *
243 * End of DDGT01
244 *
245  END
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:191
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:55
subroutine dsgt01(ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D, WORK, RESULT)
DSGT01
Definition: dsgt01.f:148