LAPACK 3.12.0 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.```

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*
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
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
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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