LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zget51()

subroutine zget51 ( integer  ITYPE,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( ldu, * )  U,
integer  LDU,
complex*16, dimension( ldv, * )  V,
integer  LDV,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
double precision  RESULT 
)

ZGET51

Purpose:
      ZGET51  generally checks a decomposition of the form

              A = U B V**H

      where **H means conjugate transpose and U and V are unitary.

      Specifically, if ITYPE=1

              RESULT = | A - U B V**H | / ( |A| n ulp )

      If ITYPE=2, then:

              RESULT = | A - B | / ( |A| n ulp )

      If ITYPE=3, then:

              RESULT = | I - U U**H | / ( n ulp )
Parameters
[in]ITYPE
          ITYPE is INTEGER
          Specifies the type of tests to be performed.
          =1: RESULT = | A - U B V**H | / ( |A| n ulp )
          =2: RESULT = | A - B | / ( |A| n ulp )
          =3: RESULT = | I - U U**H | / ( n ulp )
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, ZGET51 does nothing.
          It must be at least zero.
[in]A
          A is COMPLEX*16 array, dimension (LDA, N)
          The original (unfactored) matrix.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 1
          and at least N.
[in]B
          B is COMPLEX*16 array, dimension (LDB, N)
          The factored matrix.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  It must be at least 1
          and at least N.
[in]U
          U is COMPLEX*16 array, dimension (LDU, N)
          The unitary matrix on the left-hand side in the
          decomposition.
          Not referenced if ITYPE=2
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N and
          at least 1.
[in]V
          V is COMPLEX*16 array, dimension (LDV, N)
          The unitary matrix on the left-hand side in the
          decomposition.
          Not referenced if ITYPE=2
[in]LDV
          LDV is INTEGER
          The leading dimension of V.  LDV must be at least N and
          at least 1.
[out]WORK
          WORK is COMPLEX*16 array, dimension (2*N**2)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESULT
          RESULT is DOUBLE PRECISION
          The values computed by the test specified by ITYPE.  The
          value is currently limited to 1/ulp, to avoid overflow.
          Errors are flagged by RESULT=10/ulp.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 153 of file zget51.f.

155 *
156 * -- LAPACK test routine --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 *
160 * .. Scalar Arguments ..
161  INTEGER ITYPE, LDA, LDB, LDU, LDV, N
162  DOUBLE PRECISION RESULT
163 * ..
164 * .. Array Arguments ..
165  DOUBLE PRECISION RWORK( * )
166  COMPLEX*16 A( LDA, * ), B( LDB, * ), U( LDU, * ),
167  $ V( LDV, * ), WORK( * )
168 * ..
169 *
170 * =====================================================================
171 *
172 * .. Parameters ..
173  DOUBLE PRECISION ZERO, ONE, TEN
174  parameter( zero = 0.0d+0, one = 1.0d+0, ten = 10.0d+0 )
175  COMPLEX*16 CZERO, CONE
176  parameter( czero = ( 0.0d+0, 0.0d+0 ),
177  $ cone = ( 1.0d+0, 0.0d+0 ) )
178 * ..
179 * .. Local Scalars ..
180  INTEGER JCOL, JDIAG, JROW
181  DOUBLE PRECISION ANORM, ULP, UNFL, WNORM
182 * ..
183 * .. External Functions ..
184  DOUBLE PRECISION DLAMCH, ZLANGE
185  EXTERNAL dlamch, zlange
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL zgemm, zlacpy
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC dble, max, min
192 * ..
193 * .. Executable Statements ..
194 *
195  result = zero
196  IF( n.LE.0 )
197  $ RETURN
198 *
199 * Constants
200 *
201  unfl = dlamch( 'Safe minimum' )
202  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
203 *
204 * Some Error Checks
205 *
206  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
207  result = ten / ulp
208  RETURN
209  END IF
210 *
211  IF( itype.LE.2 ) THEN
212 *
213 * Tests scaled by the norm(A)
214 *
215  anorm = max( zlange( '1', n, n, a, lda, rwork ), unfl )
216 *
217  IF( itype.EQ.1 ) THEN
218 *
219 * ITYPE=1: Compute W = A - U B V**H
220 *
221  CALL zlacpy( ' ', n, n, a, lda, work, n )
222  CALL zgemm( 'N', 'N', n, n, n, cone, u, ldu, b, ldb, czero,
223  $ work( n**2+1 ), n )
224 *
225  CALL zgemm( 'N', 'C', n, n, n, -cone, work( n**2+1 ), n, v,
226  $ ldv, cone, work, n )
227 *
228  ELSE
229 *
230 * ITYPE=2: Compute W = A - B
231 *
232  CALL zlacpy( ' ', n, n, b, ldb, work, n )
233 *
234  DO 20 jcol = 1, n
235  DO 10 jrow = 1, n
236  work( jrow+n*( jcol-1 ) ) = work( jrow+n*( jcol-1 ) )
237  $ - a( jrow, jcol )
238  10 CONTINUE
239  20 CONTINUE
240  END IF
241 *
242 * Compute norm(W)/ ( ulp*norm(A) )
243 *
244  wnorm = zlange( '1', n, n, work, n, rwork )
245 *
246  IF( anorm.GT.wnorm ) THEN
247  result = ( wnorm / anorm ) / ( n*ulp )
248  ELSE
249  IF( anorm.LT.one ) THEN
250  result = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
251  ELSE
252  result = min( wnorm / anorm, dble( n ) ) / ( n*ulp )
253  END IF
254  END IF
255 *
256  ELSE
257 *
258 * Tests not scaled by norm(A)
259 *
260 * ITYPE=3: Compute U U**H - I
261 *
262  CALL zgemm( 'N', 'C', n, n, n, cone, u, ldu, u, ldu, czero,
263  $ work, n )
264 *
265  DO 30 jdiag = 1, n
266  work( ( n+1 )*( jdiag-1 )+1 ) = work( ( n+1 )*( jdiag-1 )+
267  $ 1 ) - cone
268  30 CONTINUE
269 *
270  result = min( zlange( '1', n, n, work, n, rwork ),
271  $ dble( n ) ) / ( n*ulp )
272  END IF
273 *
274  RETURN
275 *
276 * End of ZGET51
277 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
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:115
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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