 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cstt22()

 subroutine cstt22 ( integer N, integer M, integer KBAND, real, dimension( * ) AD, real, dimension( * ) AE, real, dimension( * ) SD, real, dimension( * ) SE, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real, dimension( 2 ) RESULT )

CSTT22

Purpose:
``` CSTT22  checks a set of M eigenvalues and eigenvectors,

A U = U S

where A is Hermitian tridiagonal, the columns of U are unitary,
and S is diagonal (if KBAND=0) or Hermitian 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, CSTT22 does nothing. It must be at least zero.``` [in] M ``` M is INTEGER The number of eigenpairs to check. If it is zero, CSTT22 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 Hermitian tri-diagonal.``` [in] AD ``` AD is REAL array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian tridiagonal.``` [in] AE ``` AE is REAL array, dimension (N) The off-diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian 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 (Hermitian tri-) diagonal matrix S.``` [in] SE ``` SE is REAL array, dimension (N) The off-diagonal of the (Hermitian 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 unitary matrix in the decomposition.``` [in] LDU ``` LDU is INTEGER The leading dimension of U. LDU must be at least N.``` [out] WORK ` WORK is COMPLEX array, dimension (LDWORK, M+1)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of WORK. LDWORK must be at least max(1,M).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [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.```

Definition at line 143 of file cstt22.f.

145 *
146 * -- LAPACK test routine --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 *
150 * .. Scalar Arguments ..
151  INTEGER KBAND, LDU, LDWORK, M, N
152 * ..
153 * .. Array Arguments ..
154  REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
155  \$ SD( * ), SE( * )
156  COMPLEX U( LDU, * ), WORK( LDWORK, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ZERO, ONE
163  parameter( zero = 0.0e0, one = 1.0e0 )
164  COMPLEX CZERO, CONE
165  parameter( czero = ( 0.0e+0, 0.0e+0 ),
166  \$ cone = ( 1.0e+0, 0.0e+0 ) )
167 * ..
168 * .. Local Scalars ..
169  INTEGER I, J, K
170  REAL ANORM, ULP, UNFL, WNORM
171  COMPLEX AUKJ
172 * ..
173 * .. External Functions ..
174  REAL CLANGE, CLANSY, SLAMCH
175  EXTERNAL clange, clansy, slamch
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL cgemm
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, max, min, real
182 * ..
183 * .. Executable Statements ..
184 *
185  result( 1 ) = zero
186  result( 2 ) = zero
187  IF( n.LE.0 .OR. m.LE.0 )
188  \$ RETURN
189 *
190  unfl = slamch( 'Safe minimum' )
191  ulp = slamch( 'Epsilon' )
192 *
193 * Do Test 1
194 *
195 * Compute the 1-norm of A.
196 *
197  IF( n.GT.1 ) THEN
198  anorm = abs( ad( 1 ) ) + abs( ae( 1 ) )
199  DO 10 j = 2, n - 1
200  anorm = max( anorm, abs( ad( j ) )+abs( ae( j ) )+
201  \$ abs( ae( j-1 ) ) )
202  10 CONTINUE
203  anorm = max( anorm, abs( ad( n ) )+abs( ae( n-1 ) ) )
204  ELSE
205  anorm = abs( ad( 1 ) )
206  END IF
207  anorm = max( anorm, unfl )
208 *
209 * Norm of U*AU - S
210 *
211  DO 40 i = 1, m
212  DO 30 j = 1, m
213  work( i, j ) = czero
214  DO 20 k = 1, n
215  aukj = ad( k )*u( k, j )
216  IF( k.NE.n )
217  \$ aukj = aukj + ae( k )*u( k+1, j )
218  IF( k.NE.1 )
219  \$ aukj = aukj + ae( k-1 )*u( k-1, j )
220  work( i, j ) = work( i, j ) + u( k, i )*aukj
221  20 CONTINUE
222  30 CONTINUE
223  work( i, i ) = work( i, i ) - sd( i )
224  IF( kband.EQ.1 ) THEN
225  IF( i.NE.1 )
226  \$ work( i, i-1 ) = work( i, i-1 ) - se( i-1 )
227  IF( i.NE.n )
228  \$ work( i, i+1 ) = work( i, i+1 ) - se( i )
229  END IF
230  40 CONTINUE
231 *
232  wnorm = clansy( '1', 'L', m, work, m, rwork )
233 *
234  IF( anorm.GT.wnorm ) THEN
235  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
236  ELSE
237  IF( anorm.LT.one ) THEN
238  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
239  ELSE
240  result( 1 ) = min( wnorm / anorm, real( m ) ) / ( m*ulp )
241  END IF
242  END IF
243 *
244 * Do Test 2
245 *
246 * Compute U*U - I
247 *
248  CALL cgemm( 'T', 'N', m, m, n, cone, u, ldu, u, ldu, czero, work,
249  \$ m )
250 *
251  DO 50 j = 1, m
252  work( j, j ) = work( j, j ) - one
253  50 CONTINUE
254 *
255  result( 2 ) = min( real( m ), clange( '1', m, m, work, m,
256  \$ rwork ) ) / ( m*ulp )
257 *
258  RETURN
259 *
260 * End of CSTT22
261 *
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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