LAPACK  3.8.0
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 147 of file cstt22.f.

147 *
148 * -- LAPACK test routine (version 3.7.0) --
149 * -- LAPACK is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 * December 2016
152 *
153 * .. Scalar Arguments ..
154  INTEGER kband, ldu, ldwork, m, n
155 * ..
156 * .. Array Arguments ..
157  REAL ad( * ), ae( * ), result( 2 ), rwork( * ),
158  $ sd( * ), se( * )
159  COMPLEX u( ldu, * ), work( ldwork, * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  REAL zero, one
166  parameter( zero = 0.0e0, one = 1.0e0 )
167  COMPLEX czero, cone
168  parameter( czero = ( 0.0e+0, 0.0e+0 ),
169  $ cone = ( 1.0e+0, 0.0e+0 ) )
170 * ..
171 * .. Local Scalars ..
172  INTEGER i, j, k
173  REAL anorm, ulp, unfl, wnorm
174  COMPLEX aukj
175 * ..
176 * .. External Functions ..
177  REAL clange, clansy, slamch
178  EXTERNAL clange, clansy, slamch
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL cgemm
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC abs, max, min, real
185 * ..
186 * .. Executable Statements ..
187 *
188  result( 1 ) = zero
189  result( 2 ) = zero
190  IF( n.LE.0 .OR. m.LE.0 )
191  $ RETURN
192 *
193  unfl = slamch( 'Safe minimum' )
194  ulp = slamch( 'Epsilon' )
195 *
196 * Do Test 1
197 *
198 * Compute the 1-norm of A.
199 *
200  IF( n.GT.1 ) THEN
201  anorm = abs( ad( 1 ) ) + abs( ae( 1 ) )
202  DO 10 j = 2, n - 1
203  anorm = max( anorm, abs( ad( j ) )+abs( ae( j ) )+
204  $ abs( ae( j-1 ) ) )
205  10 CONTINUE
206  anorm = max( anorm, abs( ad( n ) )+abs( ae( n-1 ) ) )
207  ELSE
208  anorm = abs( ad( 1 ) )
209  END IF
210  anorm = max( anorm, unfl )
211 *
212 * Norm of U*AU - S
213 *
214  DO 40 i = 1, m
215  DO 30 j = 1, m
216  work( i, j ) = czero
217  DO 20 k = 1, n
218  aukj = ad( k )*u( k, j )
219  IF( k.NE.n )
220  $ aukj = aukj + ae( k )*u( k+1, j )
221  IF( k.NE.1 )
222  $ aukj = aukj + ae( k-1 )*u( k-1, j )
223  work( i, j ) = work( i, j ) + u( k, i )*aukj
224  20 CONTINUE
225  30 CONTINUE
226  work( i, i ) = work( i, i ) - sd( i )
227  IF( kband.EQ.1 ) THEN
228  IF( i.NE.1 )
229  $ work( i, i-1 ) = work( i, i-1 ) - se( i-1 )
230  IF( i.NE.n )
231  $ work( i, i+1 ) = work( i, i+1 ) - se( i )
232  END IF
233  40 CONTINUE
234 *
235  wnorm = clansy( '1', 'L', m, work, m, rwork )
236 *
237  IF( anorm.GT.wnorm ) THEN
238  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
239  ELSE
240  IF( anorm.LT.one ) THEN
241  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
242  ELSE
243  result( 1 ) = min( wnorm / anorm, REAL( M ) ) / ( m*ulp )
244  END IF
245  END IF
246 *
247 * Do Test 2
248 *
249 * Compute U*U - I
250 *
251  CALL cgemm( 'T', 'N', m, m, n, cone, u, ldu, u, ldu, czero, work,
252  $ m )
253 *
254  DO 50 j = 1, m
255  work( j, j ) = work( j, j ) - one
256  50 CONTINUE
257 *
258  result( 2 ) = min( REAL( M ), clange( '1', m, m, work, m,
259  $ rwork ) ) / ( m*ulp )
260 *
261  RETURN
262 *
263 * End of CSTT22
264 *
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:117
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: clansy.f:125
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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