LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sget54.f
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1*> \brief \b SGET54
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 SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
12* LDV, WORK, RESULT )
13*
14* .. Scalar Arguments ..
15* INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
16* REAL RESULT
17* ..
18* .. Array Arguments ..
19* REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
20* \$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
21* \$ WORK( * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> SGET54 checks a generalized decomposition of the form
31*>
32*> A = U*S*V' and B = U*T* V'
33*>
34*> where ' means transpose and U and V are orthogonal.
35*>
36*> Specifically,
37*>
38*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
39*> \endverbatim
40*
41* Arguments:
42* ==========
43*
44*> \param[in] N
45*> \verbatim
46*> N is INTEGER
47*> The size of the matrix. If it is zero, SGET54 does nothing.
48*> It must be at least zero.
49*> \endverbatim
50*>
51*> \param[in] A
52*> \verbatim
53*> A is REAL array, dimension (LDA, N)
54*> The original (unfactored) matrix A.
55*> \endverbatim
56*>
57*> \param[in] LDA
58*> \verbatim
59*> LDA is INTEGER
60*> The leading dimension of A. It must be at least 1
61*> and at least N.
62*> \endverbatim
63*>
64*> \param[in] B
65*> \verbatim
66*> B is REAL array, dimension (LDB, N)
67*> The original (unfactored) matrix B.
68*> \endverbatim
69*>
70*> \param[in] LDB
71*> \verbatim
72*> LDB is INTEGER
73*> The leading dimension of B. It must be at least 1
74*> and at least N.
75*> \endverbatim
76*>
77*> \param[in] S
78*> \verbatim
79*> S is REAL array, dimension (LDS, N)
80*> The factored matrix S.
81*> \endverbatim
82*>
83*> \param[in] LDS
84*> \verbatim
85*> LDS is INTEGER
86*> The leading dimension of S. It must be at least 1
87*> and at least N.
88*> \endverbatim
89*>
90*> \param[in] T
91*> \verbatim
92*> T is REAL array, dimension (LDT, N)
93*> The factored matrix T.
94*> \endverbatim
95*>
96*> \param[in] LDT
97*> \verbatim
98*> LDT is INTEGER
99*> The leading dimension of T. It must be at least 1
100*> and at least N.
101*> \endverbatim
102*>
103*> \param[in] U
104*> \verbatim
105*> U is REAL array, dimension (LDU, N)
106*> The orthogonal matrix on the left-hand side in the
107*> decomposition.
108*> \endverbatim
109*>
110*> \param[in] LDU
111*> \verbatim
112*> LDU is INTEGER
113*> The leading dimension of U. LDU must be at least N and
114*> at least 1.
115*> \endverbatim
116*>
117*> \param[in] V
118*> \verbatim
119*> V is REAL array, dimension (LDV, N)
120*> The orthogonal matrix on the left-hand side in the
121*> decomposition.
122*> \endverbatim
123*>
124*> \param[in] LDV
125*> \verbatim
126*> LDV is INTEGER
127*> The leading dimension of V. LDV must be at least N and
128*> at least 1.
129*> \endverbatim
130*>
131*> \param[out] WORK
132*> \verbatim
133*> WORK is REAL array, dimension (3*N**2)
134*> \endverbatim
135*>
136*> \param[out] RESULT
137*> \verbatim
138*> RESULT is REAL
139*> The value RESULT, It is currently limited to 1/ulp, to
140*> avoid overflow. Errors are flagged by RESULT=10/ulp.
141*> \endverbatim
142*
143* Authors:
144* ========
145*
146*> \author Univ. of Tennessee
147*> \author Univ. of California Berkeley
148*> \author Univ. of Colorado Denver
149*> \author NAG Ltd.
150*
151*> \ingroup single_eig
152*
153* =====================================================================
154 SUBROUTINE sget54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
155 \$ LDV, WORK, RESULT )
156*
157* -- LAPACK test routine --
158* -- LAPACK is a software package provided by Univ. of Tennessee, --
159* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160*
161* .. Scalar Arguments ..
162 INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
163 REAL RESULT
164* ..
165* .. Array Arguments ..
166 REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
167 \$ t( ldt, * ), u( ldu, * ), v( ldv, * ),
168 \$ work( * )
169* ..
170*
171* =====================================================================
172*
173* .. Parameters ..
174 REAL ZERO, ONE
175 parameter( zero = 0.0e+0, one = 1.0e+0 )
176* ..
177* .. Local Scalars ..
178 REAL ABNORM, ULP, UNFL, WNORM
179* ..
180* .. Local Arrays ..
181 REAL DUM( 1 )
182* ..
183* .. External Functions ..
184 REAL SLAMCH, SLANGE
185 EXTERNAL slamch, slange
186* ..
187* .. External Subroutines ..
188 EXTERNAL sgemm, slacpy
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max, min, real
192* ..
193* .. Executable Statements ..
194*
195 result = zero
196 IF( n.LE.0 )
197 \$ RETURN
198*
199* Constants
200*
201 unfl = slamch( 'Safe minimum' )
202 ulp = slamch( 'Epsilon' )*slamch( 'Base' )
203*
204* compute the norm of (A,B)
205*
206 CALL slacpy( 'Full', n, n, a, lda, work, n )
207 CALL slacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
208 abnorm = max( slange( '1', n, 2*n, work, n, dum ), unfl )
209*
210* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
211*
212 CALL slacpy( ' ', n, n, a, lda, work, n )
213 CALL sgemm( 'N', 'N', n, n, n, one, u, ldu, s, lds, zero,
214 \$ work( n*n+1 ), n )
215*
216 CALL sgemm( 'N', 'C', n, n, n, -one, work( n*n+1 ), n, v, ldv,
217 \$ one, work, n )
218*
219* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
220*
221 CALL slacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
222 CALL sgemm( 'N', 'N', n, n, n, one, u, ldu, t, ldt, zero,
223 \$ work( 2*n*n+1 ), n )
224*
225 CALL sgemm( 'N', 'C', n, n, n, -one, work( 2*n*n+1 ), n, v, ldv,
226 \$ one, work( n*n+1 ), n )
227*
228* Compute norm(W)/ ( ulp*norm((A,B)) )
229*
230 wnorm = slange( '1', n, 2*n, work, n, dum )
231*
232 IF( abnorm.GT.wnorm ) THEN
233 result = ( wnorm / abnorm ) / ( 2*n*ulp )
234 ELSE
235 IF( abnorm.LT.one ) THEN
236 result = ( min( wnorm, 2*n*abnorm ) / abnorm ) / ( 2*n*ulp )
237 ELSE
238 result = min( wnorm / abnorm, real( 2*n ) ) / ( 2*n*ulp )
239 END IF
240 END IF
241*
242 RETURN
243*
244* End of SGET54
245*
246 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 sget54(N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V, LDV, WORK, RESULT)
SGET54
Definition: sget54.f:156