LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 UC>
where * 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* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( 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.```
Date
December 2016

Definition at line 152 of file chbt21.f.

152 *
153 * -- LAPACK test routine (version 3.7.0) --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 * December 2016
157 *
158 * .. Scalar Arguments ..
159  CHARACTER uplo
160  INTEGER ka, ks, lda, ldu, n
161 * ..
162 * .. Array Arguments ..
163  REAL d( * ), e( * ), result( 2 ), rwork( * )
164  COMPLEX a( lda, * ), u( ldu, * ), work( * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  COMPLEX czero, cone
171  parameter( czero = ( 0.0e+0, 0.0e+0 ),
172  \$ cone = ( 1.0e+0, 0.0e+0 ) )
173  REAL zero, one
174  parameter( zero = 0.0e+0, one = 1.0e+0 )
175 * ..
176 * .. Local Scalars ..
177  LOGICAL lower
178  CHARACTER cuplo
179  INTEGER ika, j, jc, jr
180  REAL anorm, ulp, unfl, wnorm
181 * ..
182 * .. External Functions ..
183  LOGICAL lsame
184  REAL clange, clanhb, clanhp, slamch
185  EXTERNAL lsame, clange, clanhb, clanhp, slamch
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL cgemm, chpr, chpr2
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC cmplx, max, min, real
192 * ..
193 * .. Executable Statements ..
194 *
195 * Constants
196 *
197  result( 1 ) = zero
198  result( 2 ) = zero
199  IF( n.LE.0 )
200  \$ RETURN
201 *
202  ika = max( 0, min( n-1, ka ) )
203 *
204  IF( lsame( uplo, 'U' ) ) THEN
205  lower = .false.
206  cuplo = 'U'
207  ELSE
208  lower = .true.
209  cuplo = 'L'
210  END IF
211 *
212  unfl = slamch( 'Safe minimum' )
213  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
214 *
215 * Some Error Checks
216 *
217 * Do Test 1
218 *
219 * Norm of A:
220 *
221  anorm = max( clanhb( '1', cuplo, n, ika, a, lda, rwork ), unfl )
222 *
223 * Compute error matrix: Error = A - U S U*
224 *
225 * Copy A from SB to SP storage format.
226 *
227  j = 0
228  DO 50 jc = 1, n
229  IF( lower ) THEN
230  DO 10 jr = 1, min( ika+1, n+1-jc )
231  j = j + 1
232  work( j ) = a( jr, jc )
233  10 CONTINUE
234  DO 20 jr = ika + 2, n + 1 - jc
235  j = j + 1
236  work( j ) = zero
237  20 CONTINUE
238  ELSE
239  DO 30 jr = ika + 2, jc
240  j = j + 1
241  work( j ) = zero
242  30 CONTINUE
243  DO 40 jr = min( ika, jc-1 ), 0, -1
244  j = j + 1
245  work( j ) = a( ika+1-jr, jc )
246  40 CONTINUE
247  END IF
248  50 CONTINUE
249 *
250  DO 60 j = 1, n
251  CALL chpr( cuplo, n, -d( j ), u( 1, j ), 1, work )
252  60 CONTINUE
253 *
254  IF( n.GT.1 .AND. ks.EQ.1 ) THEN
255  DO 70 j = 1, n - 1
256  CALL chpr2( cuplo, n, -cmplx( e( j ) ), u( 1, j ), 1,
257  \$ u( 1, j+1 ), 1, work )
258  70 CONTINUE
259  END IF
260  wnorm = clanhp( '1', cuplo, n, work, rwork )
261 *
262  IF( anorm.GT.wnorm ) THEN
263  result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
264  ELSE
265  IF( anorm.LT.one ) THEN
266  result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
267  ELSE
268  result( 1 ) = min( wnorm / anorm, REAL( N ) ) / ( n*ulp )
269  END IF
270  END IF
271 *
272 * Do Test 2
273 *
274 * Compute UU* - I
275 *
276  CALL cgemm( 'N', 'C', n, n, n, cone, u, ldu, u, ldu, czero, work,
277  \$ n )
278 *
279  DO 80 j = 1, n
280  work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - cone
281  80 CONTINUE
282 *
283  result( 2 ) = min( clange( '1', n, n, work, n, rwork ),
284  \$ REAL( N ) ) / ( n*ulp )
285 *
286  RETURN
287 *
288 * End of CHBT21
289 *
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, or the element of largest absolute value of a Hermitian band matrix.
Definition: clanhb.f:134
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
subroutine chpr(UPLO, N, ALPHA, X, INCX, AP)
CHPR
Definition: chpr.f:132
subroutine chpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2
Definition: chpr2.f:147
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
real function clanhp(NORM, UPLO, N, AP, WORK)
CLANHP 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 Hermitian matrix supplied in packed form.
Definition: clanhp.f:119
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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