LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ chbt21()

subroutine chbt21 ( character  UPLO,
integer  N,
integer  KA,
integer  KS,
complex, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  D,
real, dimension( * )  E,
complex, dimension( ldu, * )  U,
integer  LDU,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
real, dimension( 2 )  RESULT 
)

CHBT21

Purpose:
 CHBT21  generally checks a decomposition of the form

         A = U S U**H

 where **H means conjugate transpose, A is hermitian banded, U is
 unitary, and S is diagonal (if KS=0) or symmetric
 tridiagonal (if KS=1).

 Specifically:

         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
         RESULT(2) = | I - U U**H | / ( n ulp )
Parameters
[in]UPLO
          UPLO is CHARACTER
          If UPLO='U', the upper triangle of A and V will be used and
          the (strictly) lower triangle will not be referenced.
          If UPLO='L', the lower triangle of A and V will be used and
          the (strictly) upper triangle will not be referenced.
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, CHBT21 does nothing.
          It must be at least zero.
[in]KA
          KA is INTEGER
          The bandwidth of the matrix A.  It must be at least zero.  If
          it is larger than N-1, then max( 0, N-1 ) will be used.
[in]KS
          KS is INTEGER
          The bandwidth of the matrix S.  It may only be zero or one.
          If zero, then S is diagonal, and E is not referenced.  If
          one, then S is symmetric tri-diagonal.
[in]A
          A is COMPLEX array, dimension (LDA, N)
          The original (unfactored) matrix.  It is assumed to be
          hermitian, and only the upper (UPLO='U') or only the lower
          (UPLO='L') will be referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 1
          and at least min( KA, N-1 ).
[in]D
          D is REAL array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix S.
[in]E
          E is REAL array, dimension (N-1)
          The off-diagonal of the (symmetric tri-) diagonal matrix S.
          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
          (3,2) element, etc.
          Not referenced if KS=0.
[in]U
          U is COMPLEX array, dimension (LDU, N)
          The unitary matrix in the decomposition, expressed as a
          dense matrix (i.e., not as a product of Householder
          transformations, Givens transformations, etc.)
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N and
          at least 1.
[out]WORK
          WORK is COMPLEX array, dimension (N**2)
[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.

Definition at line 150 of file chbt21.f.

152*
153* -- LAPACK test routine --
154* -- LAPACK is a software package provided by Univ. of Tennessee, --
155* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157* .. Scalar Arguments ..
158 CHARACTER UPLO
159 INTEGER KA, KS, LDA, LDU, N
160* ..
161* .. Array Arguments ..
162 REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
163 COMPLEX A( LDA, * ), U( LDU, * ), WORK( * )
164* ..
165*
166* =====================================================================
167*
168* .. Parameters ..
169 COMPLEX CZERO, CONE
170 parameter( czero = ( 0.0e+0, 0.0e+0 ),
171 $ cone = ( 1.0e+0, 0.0e+0 ) )
172 REAL ZERO, ONE
173 parameter( zero = 0.0e+0, one = 1.0e+0 )
174* ..
175* .. Local Scalars ..
176 LOGICAL LOWER
177 CHARACTER CUPLO
178 INTEGER IKA, J, JC, JR
179 REAL ANORM, ULP, UNFL, WNORM
180* ..
181* .. External Functions ..
182 LOGICAL LSAME
183 REAL CLANGE, CLANHB, CLANHP, SLAMCH
184 EXTERNAL lsame, clange, clanhb, clanhp, slamch
185* ..
186* .. External Subroutines ..
187 EXTERNAL cgemm, chpr, chpr2
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC cmplx, max, min, real
191* ..
192* .. Executable Statements ..
193*
194* Constants
195*
196 result( 1 ) = zero
197 result( 2 ) = zero
198 IF( n.LE.0 )
199 $ RETURN
200*
201 ika = max( 0, min( n-1, ka ) )
202*
203 IF( lsame( uplo, 'U' ) ) THEN
204 lower = .false.
205 cuplo = 'U'
206 ELSE
207 lower = .true.
208 cuplo = 'L'
209 END IF
210*
211 unfl = slamch( 'Safe minimum' )
212 ulp = slamch( 'Epsilon' )*slamch( 'Base' )
213*
214* Some Error Checks
215*
216* Do Test 1
217*
218* Norm of A:
219*
220 anorm = max( clanhb( '1', cuplo, n, ika, a, lda, rwork ), unfl )
221*
222* Compute error matrix: Error = A - U S U**H
223*
224* Copy A from SB to SP storage format.
225*
226 j = 0
227 DO 50 jc = 1, n
228 IF( lower ) THEN
229 DO 10 jr = 1, min( ika+1, n+1-jc )
230 j = j + 1
231 work( j ) = a( jr, jc )
232 10 CONTINUE
233 DO 20 jr = ika + 2, n + 1 - jc
234 j = j + 1
235 work( j ) = zero
236 20 CONTINUE
237 ELSE
238 DO 30 jr = ika + 2, jc
239 j = j + 1
240 work( j ) = zero
241 30 CONTINUE
242 DO 40 jr = min( ika, jc-1 ), 0, -1
243 j = j + 1
244 work( j ) = a( ika+1-jr, jc )
245 40 CONTINUE
246 END IF
247 50 CONTINUE
248*
249 DO 60 j = 1, n
250 CALL chpr( cuplo, n, -d( j ), u( 1, j ), 1, work )
251 60 CONTINUE
252*
253 IF( n.GT.1 .AND. ks.EQ.1 ) THEN
254 DO 70 j = 1, n - 1
255 CALL chpr2( cuplo, n, -cmplx( e( j ) ), u( 1, j ), 1,
256 $ u( 1, j+1 ), 1, work )
257 70 CONTINUE
258 END IF
259 wnorm = clanhp( '1', cuplo, n, work, rwork )
260*
261 IF( anorm.GT.wnorm ) THEN
262 result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
263 ELSE
264 IF( anorm.LT.one ) THEN
265 result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
266 ELSE
267 result( 1 ) = min( wnorm / anorm, real( n ) ) / ( n*ulp )
268 END IF
269 END IF
270*
271* Do Test 2
272*
273* Compute U U**H - I
274*
275 CALL cgemm( 'N', 'C', n, n, n, cone, u, ldu, u, ldu, czero, work,
276 $ n )
277*
278 DO 80 j = 1, n
279 work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - cone
280 80 CONTINUE
281*
282 result( 2 ) = min( clange( '1', n, n, work, n, rwork ),
283 $ real( n ) ) / ( n*ulp )
284*
285 RETURN
286*
287* End of CHBT21
288*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2
Definition: chpr2.f:145
subroutine chpr(UPLO, N, ALPHA, X, INCX, AP)
CHPR
Definition: chpr.f:130
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 clanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhb.f:132
real function clanhp(NORM, UPLO, N, AP, WORK)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhp.f:117
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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