LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 *
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
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
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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