LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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sstt21.f
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1*> \brief \b SSTT21
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 SSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
12* RESULT )
13*
14* .. Scalar Arguments ..
15* INTEGER KBAND, LDU, N
16* ..
17* .. Array Arguments ..
18* REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
19* $ SE( * ), U( LDU, * ), WORK( * )
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> SSTT21 checks a decomposition of the form
29*>
30*> A = U S U'
31*>
32*> where ' means transpose, A is symmetric tridiagonal, U is orthogonal,
33*> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
34*> Two tests are performed:
35*>
36*> RESULT(1) = | A - U S U' | / ( |A| n ulp )
37*>
38*> RESULT(2) = | I - UU' | / ( 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, SSTT21 does nothing.
48*> It must be at least zero.
49*> \endverbatim
50*>
51*> \param[in] KBAND
52*> \verbatim
53*> KBAND is INTEGER
54*> The bandwidth of the matrix S. It may only be zero or one.
55*> If zero, then S is diagonal, and SE is not referenced. If
56*> one, then S is symmetric tri-diagonal.
57*> \endverbatim
58*>
59*> \param[in] AD
60*> \verbatim
61*> AD is REAL array, dimension (N)
62*> The diagonal of the original (unfactored) matrix A. A is
63*> assumed to be symmetric tridiagonal.
64*> \endverbatim
65*>
66*> \param[in] AE
67*> \verbatim
68*> AE is REAL array, dimension (N-1)
69*> The off-diagonal of the original (unfactored) matrix A. A
70*> is assumed to be symmetric tridiagonal. AE(1) is the (1,2)
71*> and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
72*> \endverbatim
73*>
74*> \param[in] SD
75*> \verbatim
76*> SD is REAL array, dimension (N)
77*> The diagonal of the (symmetric tri-) diagonal matrix S.
78*> \endverbatim
79*>
80*> \param[in] SE
81*> \verbatim
82*> SE is REAL array, dimension (N-1)
83*> The off-diagonal of the (symmetric tri-) diagonal matrix S.
84*> Not referenced if KBSND=0. If KBAND=1, then AE(1) is the
85*> (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
86*> element, etc.
87*> \endverbatim
88*>
89*> \param[in] U
90*> \verbatim
91*> U is REAL array, dimension (LDU, N)
92*> The orthogonal matrix in the decomposition.
93*> \endverbatim
94*>
95*> \param[in] LDU
96*> \verbatim
97*> LDU is INTEGER
98*> The leading dimension of U. LDU must be at least N.
99*> \endverbatim
100*>
101*> \param[out] WORK
102*> \verbatim
103*> WORK is REAL array, dimension (N*(N+1))
104*> \endverbatim
105*>
106*> \param[out] RESULT
107*> \verbatim
108*> RESULT is REAL array, dimension (2)
109*> The values computed by the two tests described above. The
110*> values are currently limited to 1/ulp, to avoid overflow.
111*> RESULT(1) is always modified.
112*> \endverbatim
113*
114* Authors:
115* ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \ingroup single_eig
123*
124* =====================================================================
125 SUBROUTINE sstt21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
126 $ RESULT )
127*
128* -- LAPACK test routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 INTEGER KBAND, LDU, N
134* ..
135* .. Array Arguments ..
136 REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
137 $ se( * ), u( ldu, * ), work( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e0, one = 1.0e0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
149* ..
150* .. External Functions ..
151 REAL SLAMCH, SLANGE, SLANSY
152 EXTERNAL slamch, slange, slansy
153* ..
154* .. External Subroutines ..
155 EXTERNAL sgemm, slaset, ssyr, ssyr2
156* ..
157* .. Intrinsic Functions ..
158 INTRINSIC abs, max, min, real
159* ..
160* .. Executable Statements ..
161*
162* 1) Constants
163*
164 result( 1 ) = zero
165 result( 2 ) = zero
166 IF( n.LE.0 )
167 $ RETURN
168*
169 unfl = slamch( 'Safe minimum' )
170 ulp = slamch( 'Precision' )
171*
172* Do Test 1
173*
174* Copy A & Compute its 1-Norm:
175*
176 CALL slaset( 'Full', n, n, zero, zero, work, n )
177*
178 anorm = zero
179 temp1 = zero
180*
181 DO 10 j = 1, n - 1
182 work( ( n+1 )*( j-1 )+1 ) = ad( j )
183 work( ( n+1 )*( j-1 )+2 ) = ae( j )
184 temp2 = abs( ae( j ) )
185 anorm = max( anorm, abs( ad( j ) )+temp1+temp2 )
186 temp1 = temp2
187 10 CONTINUE
188*
189 work( n**2 ) = ad( n )
190 anorm = max( anorm, abs( ad( n ) )+temp1, unfl )
191*
192* Norm of A - USU'
193*
194 DO 20 j = 1, n
195 CALL ssyr( 'L', n, -sd( j ), u( 1, j ), 1, work, n )
196 20 CONTINUE
197*
198 IF( n.GT.1 .AND. kband.EQ.1 ) THEN
199 DO 30 j = 1, n - 1
200 CALL ssyr2( 'L', n, -se( j ), u( 1, j ), 1, u( 1, j+1 ), 1,
201 $ work, n )
202 30 CONTINUE
203 END IF
204*
205 wnorm = slansy( '1', 'L', n, work, n, work( n**2+1 ) )
206*
207 IF( anorm.GT.wnorm ) THEN
208 result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
209 ELSE
210 IF( anorm.LT.one ) THEN
211 result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
212 ELSE
213 result( 1 ) = min( wnorm / anorm, real( n ) ) / ( n*ulp )
214 END IF
215 END IF
216*
217* Do Test 2
218*
219* Compute UU' - I
220*
221 CALL sgemm( 'N', 'C', n, n, n, one, u, ldu, u, ldu, zero, work,
222 $ n )
223*
224 DO 40 j = 1, n
225 work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - one
226 40 CONTINUE
227*
228 result( 2 ) = min( real( n ), slange( '1', n, n, work, n,
229 $ work( n**2+1 ) ) ) / ( n*ulp )
230*
231 RETURN
232*
233* End of SSTT21
234*
235 END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:132
subroutine ssyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SSYR2
Definition: ssyr2.f:147
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sstt21(N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RESULT)
SSTT21
Definition: sstt21.f:127