LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zhbt21()

subroutine zhbt21 ( character  UPLO,
integer  N,
integer  KA,
integer  KS,
complex*16, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
complex*16, dimension( ldu, * )  U,
integer  LDU,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
double precision, dimension( 2 )  RESULT 
)

ZHBT21

Purpose:
 ZHBT21  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, ZHBT21 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*16 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 DOUBLE PRECISION array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix S.
[in]E
          E is DOUBLE PRECISION 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*16 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*16 array, dimension (N**2)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESULT
          RESULT is DOUBLE PRECISION 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 152 of file zhbt21.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  DOUBLE PRECISION d( * ), e( * ), result( 2 ), rwork( * )
164  COMPLEX*16 a( lda, * ), u( ldu, * ), work( * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  COMPLEX*16 czero, cone
171  parameter( czero = ( 0.0d+0, 0.0d+0 ),
172  $ cone = ( 1.0d+0, 0.0d+0 ) )
173  DOUBLE PRECISION zero, one
174  parameter( zero = 0.0d+0, one = 1.0d+0 )
175 * ..
176 * .. Local Scalars ..
177  LOGICAL lower
178  CHARACTER cuplo
179  INTEGER ika, j, jc, jr
180  DOUBLE PRECISION anorm, ulp, unfl, wnorm
181 * ..
182 * .. External Functions ..
183  LOGICAL lsame
184  DOUBLE PRECISION dlamch, zlange, zlanhb, zlanhp
185  EXTERNAL lsame, dlamch, zlange, zlanhb, zlanhp
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL zgemm, zhpr, zhpr2
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC dble, dcmplx, max, min
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 = dlamch( 'Safe minimum' )
213  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
214 *
215 * Some Error Checks
216 *
217 * Do Test 1
218 *
219 * Norm of A:
220 *
221  anorm = max( zlanhb( '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 zhpr( 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 zhpr2( cuplo, n, -dcmplx( e( j ) ), u( 1, j ), 1,
257  $ u( 1, j+1 ), 1, work )
258  70 CONTINUE
259  END IF
260  wnorm = zlanhp( '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, dble( n ) ) / ( n*ulp )
269  END IF
270  END IF
271 *
272 * Do Test 2
273 *
274 * Compute UU* - I
275 *
276  CALL zgemm( '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( zlange( '1', n, n, work, n, rwork ),
284  $ dble( n ) ) / ( n*ulp )
285 *
286  RETURN
287 *
288 * End of ZHBT21
289 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zhpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
ZHPR2
Definition: zhpr2.f:147
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB 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: zlanhb.f:134
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:117
subroutine zhpr(UPLO, N, ALPHA, X, INCX, AP)
ZHPR
Definition: zhpr.f:132
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function zlanhp(NORM, UPLO, N, AP, WORK)
ZLANHP 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: zlanhp.f:119
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