LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cget51()

 subroutine cget51 ( integer ITYPE, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESULT )

CGET51

Purpose:
```      CGET51  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, CGET51 does nothing. It must be at least zero.``` [in] A ``` A is COMPLEX 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 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 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 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 array, dimension (2*N**2)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESULT ``` RESULT is REAL 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.```

Definition at line 153 of file cget51.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 REAL RESULT
163* ..
164* .. Array Arguments ..
165 REAL RWORK( * )
166 COMPLEX A( LDA, * ), B( LDB, * ), U( LDU, * ),
167 \$ V( LDV, * ), WORK( * )
168* ..
169*
170* =====================================================================
171*
172* .. Parameters ..
173 REAL ZERO, ONE, TEN
174 parameter( zero = 0.0e+0, one = 1.0e+0, ten = 10.0e+0 )
175 COMPLEX CZERO, CONE
176 parameter( czero = ( 0.0e+0, 0.0e+0 ),
177 \$ cone = ( 1.0e+0, 0.0e+0 ) )
178* ..
179* .. Local Scalars ..
180 INTEGER JCOL, JDIAG, JROW
181 REAL ANORM, ULP, UNFL, WNORM
182* ..
183* .. External Functions ..
184 REAL CLANGE, SLAMCH
185 EXTERNAL clange, slamch
186* ..
187* .. External Subroutines ..
188 EXTERNAL cgemm, clacpy
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max, min, real
192* ..
193* .. Executable Statements ..
194*
195 result = zero
196 IF( n.LE.0 )
197 \$ RETURN
198*
199* Constants
200*
201 unfl = slamch( 'Safe minimum' )
202 ulp = slamch( 'Epsilon' )*slamch( '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( clange( '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 clacpy( ' ', n, n, a, lda, work, n )
222 CALL cgemm( 'N', 'N', n, n, n, cone, u, ldu, b, ldb, czero,
223 \$ work( n**2+1 ), n )
224*
225 CALL cgemm( '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 clacpy( ' ', 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 = clange( '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, real( 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 cgemm( '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( clange( '1', n, n, work, n, rwork ),
271 \$ real( n ) ) / ( n*ulp )
272 END IF
273*
274 RETURN
275*
276* End of CGET51
277*
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
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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