LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sget51.f
Go to the documentation of this file.
1 *> \brief \b SGET51
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 SGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
12 * RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER ITYPE, LDA, LDB, LDU, LDV, N
16 * REAL RESULT
17 * ..
18 * .. Array Arguments ..
19 * REAL A( LDA, * ), B( LDB, * ), U( LDU, * ),
20 * $ V( LDV, * ), WORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SGET51 generally checks a decomposition of the form
30 *>
31 *> A = U B V'
32 *>
33 *> where ' means transpose and U and V are orthogonal.
34 *>
35 *> Specifically, if ITYPE=1
36 *>
37 *> RESULT = | A - U B V' | / ( |A| n ulp )
38 *>
39 *> If ITYPE=2, then:
40 *>
41 *> RESULT = | A - B | / ( |A| n ulp )
42 *>
43 *> If ITYPE=3, then:
44 *>
45 *> RESULT = | I - UU' | / ( n ulp )
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] ITYPE
52 *> \verbatim
53 *> ITYPE is INTEGER
54 *> Specifies the type of tests to be performed.
55 *> =1: RESULT = | A - U B V' | / ( |A| n ulp )
56 *> =2: RESULT = | A - B | / ( |A| n ulp )
57 *> =3: RESULT = | I - UU' | / ( n ulp )
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The size of the matrix. If it is zero, SGET51 does nothing.
64 *> It must be at least zero.
65 *> \endverbatim
66 *>
67 *> \param[in] A
68 *> \verbatim
69 *> A is REAL array, dimension (LDA, N)
70 *> The original (unfactored) matrix.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of A. It must be at least 1
77 *> and at least N.
78 *> \endverbatim
79 *>
80 *> \param[in] B
81 *> \verbatim
82 *> B is REAL array, dimension (LDB, N)
83 *> The factored matrix.
84 *> \endverbatim
85 *>
86 *> \param[in] LDB
87 *> \verbatim
88 *> LDB is INTEGER
89 *> The leading dimension of B. It must be at least 1
90 *> and at least N.
91 *> \endverbatim
92 *>
93 *> \param[in] U
94 *> \verbatim
95 *> U is REAL array, dimension (LDU, N)
96 *> The orthogonal matrix on the left-hand side in the
97 *> decomposition.
98 *> Not referenced if ITYPE=2
99 *> \endverbatim
100 *>
101 *> \param[in] LDU
102 *> \verbatim
103 *> LDU is INTEGER
104 *> The leading dimension of U. LDU must be at least N and
105 *> at least 1.
106 *> \endverbatim
107 *>
108 *> \param[in] V
109 *> \verbatim
110 *> V is REAL array, dimension (LDV, N)
111 *> The orthogonal matrix on the left-hand side in the
112 *> decomposition.
113 *> Not referenced if ITYPE=2
114 *> \endverbatim
115 *>
116 *> \param[in] LDV
117 *> \verbatim
118 *> LDV is INTEGER
119 *> The leading dimension of V. LDV must be at least N and
120 *> at least 1.
121 *> \endverbatim
122 *>
123 *> \param[out] WORK
124 *> \verbatim
125 *> WORK is REAL array, dimension (2*N**2)
126 *> \endverbatim
127 *>
128 *> \param[out] RESULT
129 *> \verbatim
130 *> RESULT is REAL
131 *> The values computed by the test specified by ITYPE. The
132 *> value is currently limited to 1/ulp, to avoid overflow.
133 *> Errors are flagged by RESULT=10/ulp.
134 *> \endverbatim
135 *
136 * Authors:
137 * ========
138 *
139 *> \author Univ. of Tennessee
140 *> \author Univ. of California Berkeley
141 *> \author Univ. of Colorado Denver
142 *> \author NAG Ltd.
143 *
144 *> \ingroup single_eig
145 *
146 * =====================================================================
147  SUBROUTINE sget51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
148  $ RESULT )
149 *
150 * -- LAPACK test routine --
151 * -- LAPACK is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  INTEGER ITYPE, LDA, LDB, LDU, LDV, N
156  REAL RESULT
157 * ..
158 * .. Array Arguments ..
159  REAL A( LDA, * ), B( LDB, * ), U( LDU, * ),
160  $ v( ldv, * ), work( * )
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  REAL ZERO, ONE, TEN
167  parameter( zero = 0.0, one = 1.0e0, ten = 10.0e0 )
168 * ..
169 * .. Local Scalars ..
170  INTEGER JCOL, JDIAG, JROW
171  REAL ANORM, ULP, UNFL, WNORM
172 * ..
173 * .. External Functions ..
174  REAL SLAMCH, SLANGE
175  EXTERNAL slamch, slange
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL sgemm, slacpy
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max, min, real
182 * ..
183 * .. Executable Statements ..
184 *
185  result = zero
186  IF( n.LE.0 )
187  $ RETURN
188 *
189 * Constants
190 *
191  unfl = slamch( 'Safe minimum' )
192  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
193 *
194 * Some Error Checks
195 *
196  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
197  result = ten / ulp
198  RETURN
199  END IF
200 *
201  IF( itype.LE.2 ) THEN
202 *
203 * Tests scaled by the norm(A)
204 *
205  anorm = max( slange( '1', n, n, a, lda, work ), unfl )
206 *
207  IF( itype.EQ.1 ) THEN
208 *
209 * ITYPE=1: Compute W = A - UBV'
210 *
211  CALL slacpy( ' ', n, n, a, lda, work, n )
212  CALL sgemm( 'N', 'N', n, n, n, one, u, ldu, b, ldb, zero,
213  $ work( n**2+1 ), n )
214 *
215  CALL sgemm( 'N', 'C', n, n, n, -one, work( n**2+1 ), n, v,
216  $ ldv, one, work, n )
217 *
218  ELSE
219 *
220 * ITYPE=2: Compute W = A - B
221 *
222  CALL slacpy( ' ', n, n, b, ldb, work, n )
223 *
224  DO 20 jcol = 1, n
225  DO 10 jrow = 1, n
226  work( jrow+n*( jcol-1 ) ) = work( jrow+n*( jcol-1 ) )
227  $ - a( jrow, jcol )
228  10 CONTINUE
229  20 CONTINUE
230  END IF
231 *
232 * Compute norm(W)/ ( ulp*norm(A) )
233 *
234  wnorm = slange( '1', n, n, work, n, work( n**2+1 ) )
235 *
236  IF( anorm.GT.wnorm ) THEN
237  result = ( wnorm / anorm ) / ( n*ulp )
238  ELSE
239  IF( anorm.LT.one ) THEN
240  result = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
241  ELSE
242  result = min( wnorm / anorm, real( n ) ) / ( n*ulp )
243  END IF
244  END IF
245 *
246  ELSE
247 *
248 * Tests not scaled by norm(A)
249 *
250 * ITYPE=3: Compute UU' - I
251 *
252  CALL sgemm( 'N', 'C', n, n, n, one, u, ldu, u, ldu, zero, work,
253  $ n )
254 *
255  DO 30 jdiag = 1, n
256  work( ( n+1 )*( jdiag-1 )+1 ) = work( ( n+1 )*( jdiag-1 )+
257  $ 1 ) - one
258  30 CONTINUE
259 *
260  result = min( slange( '1', n, n, work, n, work( n**2+1 ) ),
261  $ real( n ) ) / ( n*ulp )
262  END IF
263 *
264  RETURN
265 *
266 * End of SGET51
267 *
268  END
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sget51(ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, RESULT)
SGET51
Definition: sget51.f:149