LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sstt22()

subroutine sstt22 ( integer  n,
integer  m,
integer  kband,
real, dimension( * )  ad,
real, dimension( * )  ae,
real, dimension( * )  sd,
real, dimension( * )  se,
real, dimension( ldu, * )  u,
integer  ldu,
real, dimension( ldwork, * )  work,
integer  ldwork,
real, dimension( 2 )  result 
)

SSTT22

Purpose:
 SSTT22  checks a set of M eigenvalues and eigenvectors,

     A U = U S

 where A is symmetric tridiagonal, the columns of U are orthogonal,
 and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
 Two tests are performed:

    RESULT(1) = | U' A U - S | / ( |A| m ulp )

    RESULT(2) = | I - U'U | / ( m ulp )
Parameters
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, SSTT22 does nothing.
          It must be at least zero.
[in]M
          M is INTEGER
          The number of eigenpairs to check.  If it is zero, SSTT22
          does nothing.  It must be at least zero.
[in]KBAND
          KBAND is INTEGER
          The bandwidth of the matrix S.  It may only be zero or one.
          If zero, then S is diagonal, and SE is not referenced.  If
          one, then S is symmetric tri-diagonal.
[in]AD
          AD is REAL array, dimension (N)
          The diagonal of the original (unfactored) matrix A.  A is
          assumed to be symmetric tridiagonal.
[in]AE
          AE is REAL array, dimension (N)
          The off-diagonal of the original (unfactored) matrix A.  A
          is assumed to be symmetric tridiagonal.  AE(1) is ignored,
          AE(2) is the (1,2) and (2,1) element, etc.
[in]SD
          SD is REAL array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix S.
[in]SE
          SE is REAL array, dimension (N)
          The off-diagonal of the (symmetric tri-) diagonal matrix S.
          Not referenced if KBSND=0.  If KBAND=1, then AE(1) is
          ignored, SE(2) is the (1,2) and (2,1) element, etc.
[in]U
          U is REAL array, dimension (LDU, N)
          The orthogonal matrix in the decomposition.
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N.
[out]WORK
          WORK is REAL array, dimension (LDWORK, M+1)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of WORK.  LDWORK must be at least
          max(1,M).
[out]RESULT
          RESULT is REAL array, dimension (2)
          The values computed by the two tests described above.  The
          values are currently limited to 1/ulp, to avoid overflow.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 137 of file sstt22.f.

139*
140* -- LAPACK test routine --
141* -- LAPACK is a software package provided by Univ. of Tennessee, --
142* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143*
144* .. Scalar Arguments ..
145 INTEGER KBAND, LDU, LDWORK, M, N
146* ..
147* .. Array Arguments ..
148 REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
149 $ SE( * ), U( LDU, * ), WORK( LDWORK, * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 REAL ZERO, ONE
156 parameter( zero = 0.0e0, one = 1.0e0 )
157* ..
158* .. Local Scalars ..
159 INTEGER I, J, K
160 REAL ANORM, AUKJ, ULP, UNFL, WNORM
161* ..
162* .. External Functions ..
163 REAL SLAMCH, SLANGE, SLANSY
164 EXTERNAL slamch, slange, slansy
165* ..
166* .. External Subroutines ..
167 EXTERNAL sgemm
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC abs, max, min, real
171* ..
172* .. Executable Statements ..
173*
174 result( 1 ) = zero
175 result( 2 ) = zero
176 IF( n.LE.0 .OR. m.LE.0 )
177 $ RETURN
178*
179 unfl = slamch( 'Safe minimum' )
180 ulp = slamch( 'Epsilon' )
181*
182* Do Test 1
183*
184* Compute the 1-norm of A.
185*
186 IF( n.GT.1 ) THEN
187 anorm = abs( ad( 1 ) ) + abs( ae( 1 ) )
188 DO 10 j = 2, n - 1
189 anorm = max( anorm, abs( ad( j ) )+abs( ae( j ) )+
190 $ abs( ae( j-1 ) ) )
191 10 CONTINUE
192 anorm = max( anorm, abs( ad( n ) )+abs( ae( n-1 ) ) )
193 ELSE
194 anorm = abs( ad( 1 ) )
195 END IF
196 anorm = max( anorm, unfl )
197*
198* Norm of U'AU - S
199*
200 DO 40 i = 1, m
201 DO 30 j = 1, m
202 work( i, j ) = zero
203 DO 20 k = 1, n
204 aukj = ad( k )*u( k, j )
205 IF( k.NE.n )
206 $ aukj = aukj + ae( k )*u( k+1, j )
207 IF( k.NE.1 )
208 $ aukj = aukj + ae( k-1 )*u( k-1, j )
209 work( i, j ) = work( i, j ) + u( k, i )*aukj
210 20 CONTINUE
211 30 CONTINUE
212 work( i, i ) = work( i, i ) - sd( i )
213 IF( kband.EQ.1 ) THEN
214 IF( i.NE.1 )
215 $ work( i, i-1 ) = work( i, i-1 ) - se( i-1 )
216 IF( i.NE.n )
217 $ work( i, i+1 ) = work( i, i+1 ) - se( i )
218 END IF
219 40 CONTINUE
220*
221 wnorm = slansy( '1', 'L', m, work, m, work( 1, m+1 ) )
222*
223 IF( anorm.GT.wnorm ) THEN
224 result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
225 ELSE
226 IF( anorm.LT.one ) THEN
227 result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
228 ELSE
229 result( 1 ) = min( wnorm / anorm, real( m ) ) / ( m*ulp )
230 END IF
231 END IF
232*
233* Do Test 2
234*
235* Compute U'U - I
236*
237 CALL sgemm( 'T', 'N', m, m, n, one, u, ldu, u, ldu, zero, work,
238 $ m )
239*
240 DO 50 j = 1, m
241 work( j, j ) = work( j, j ) - one
242 50 CONTINUE
243*
244 result( 2 ) = min( real( m ), slange( '1', m, m, work, m, work( 1,
245 $ m+1 ) ) ) / ( m*ulp )
246*
247 RETURN
248*
249* End of SSTT22
250*
sgemm
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
slange
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
slansy
real function slansy(norm, uplo, n, a, lda, work)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansy.f:122
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