 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ clatm6()

 subroutine clatm6 ( integer TYPE, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( lda, * ) B, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldy, * ) Y, integer LDY, complex ALPHA, complex BETA, complex WX, complex WY, real, dimension( * ) S, real, dimension( * ) DIF )

CLATM6

Purpose:
``` CLATM6 generates test matrices for the generalized eigenvalue
problem, their corresponding right and left eigenvector matrices,
and also reciprocal condition numbers for all eigenvalues and
the reciprocal condition numbers of eigenvectors corresponding to
the 1th and 5th eigenvalues.

Test Matrices
=============

Two kinds of test matrix pairs
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:

Type 1:
Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
0   2+a   0    0    0         0   1   0   0   0
0    0   3+a   0    0         0   0   1   0   0
0    0    0   4+a   0         0   0   0   1   0
0    0    0    0   5+a ,      0   0   0   0   1
and Type 2:
Da = 1+i   0    0       0       0    Db = 1   0   0   0   0
0   1-i   0       0       0         0   1   0   0   0
0    0    1       0       0         0   0   1   0   0
0    0    0 (1+a)+(1+b)i  0         0   0   0   1   0
0    0    0       0 (1+a)-(1+b)i,   0   0   0   0   1 .

In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):

YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
0    1   -y    y   -y         0   1   x  -x  -x
0    0    1    0    0         0   0   1   0   0
0    0    0    1    0         0   0   0   1   0
0    0    0    0    1,        0   0   0   0   1 , where

a, b, x and y will have all values independently of each other.```
Parameters
 [in] TYPE ``` TYPE is INTEGER Specifies the problem type (see further details).``` [in] N ``` N is INTEGER Size of the matrices A and B.``` [out] A ``` A is COMPLEX array, dimension (LDA, N). On exit A N-by-N is initialized according to TYPE.``` [in] LDA ``` LDA is INTEGER The leading dimension of A and of B.``` [out] B ``` B is COMPLEX array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE.``` [out] X ``` X is COMPLEX array, dimension (LDX, N). On exit X is the N-by-N matrix of right eigenvectors.``` [in] LDX ``` LDX is INTEGER The leading dimension of X.``` [out] Y ``` Y is COMPLEX array, dimension (LDY, N). On exit Y is the N-by-N matrix of left eigenvectors.``` [in] LDY ``` LDY is INTEGER The leading dimension of Y.``` [in] ALPHA ` ALPHA is COMPLEX` [in] BETA ``` BETA is COMPLEX Weighting constants for matrix A.``` [in] WX ``` WX is COMPLEX Constant for right eigenvector matrix.``` [in] WY ``` WY is COMPLEX Constant for left eigenvector matrix.``` [out] S ``` S is REAL array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i.``` [out] DIF ``` DIF is REAL array, dimension (N) DIF(i) is the reciprocal condition number for eigenvector i.```

Definition at line 172 of file clatm6.f.

174*
175* -- LAPACK computational routine --
176* -- LAPACK is a software package provided by Univ. of Tennessee, --
177* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178*
179* .. Scalar Arguments ..
180 INTEGER LDA, LDX, LDY, N, TYPE
181 COMPLEX ALPHA, BETA, WX, WY
182* ..
183* .. Array Arguments ..
184 REAL DIF( * ), S( * )
185 COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
186 \$ Y( LDY, * )
187* ..
188*
189* =====================================================================
190*
191* .. Parameters ..
192 REAL RONE, TWO, THREE
193 parameter( rone = 1.0e+0, two = 2.0e+0, three = 3.0e+0 )
194 COMPLEX ZERO, ONE
195 parameter( zero = ( 0.0e+0, 0.0e+0 ),
196 \$ one = ( 1.0e+0, 0.0e+0 ) )
197* ..
198* .. Local Scalars ..
199 INTEGER I, INFO, J
200* ..
201* .. Local Arrays ..
202 REAL RWORK( 50 )
203 COMPLEX WORK( 26 ), Z( 8, 8 )
204* ..
205* .. Intrinsic Functions ..
206 INTRINSIC cabs, cmplx, conjg, real, sqrt
207* ..
208* .. External Subroutines ..
209 EXTERNAL cgesvd, clacpy, clakf2
210* ..
211* .. Executable Statements ..
212*
213* Generate test problem ...
214* (Da, Db) ...
215*
216 DO 20 i = 1, n
217 DO 10 j = 1, n
218*
219 IF( i.EQ.j ) THEN
220 a( i, i ) = cmplx( i ) + alpha
221 b( i, i ) = one
222 ELSE
223 a( i, j ) = zero
224 b( i, j ) = zero
225 END IF
226*
227 10 CONTINUE
228 20 CONTINUE
229 IF( type.EQ.2 ) THEN
230 a( 1, 1 ) = cmplx( rone, rone )
231 a( 2, 2 ) = conjg( a( 1, 1 ) )
232 a( 3, 3 ) = one
233 a( 4, 4 ) = cmplx( real( one+alpha ), real( one+beta ) )
234 a( 5, 5 ) = conjg( a( 4, 4 ) )
235 END IF
236*
237* Form X and Y
238*
239 CALL clacpy( 'F', n, n, b, lda, y, ldy )
240 y( 3, 1 ) = -conjg( wy )
241 y( 4, 1 ) = conjg( wy )
242 y( 5, 1 ) = -conjg( wy )
243 y( 3, 2 ) = -conjg( wy )
244 y( 4, 2 ) = conjg( wy )
245 y( 5, 2 ) = -conjg( wy )
246*
247 CALL clacpy( 'F', n, n, b, lda, x, ldx )
248 x( 1, 3 ) = -wx
249 x( 1, 4 ) = -wx
250 x( 1, 5 ) = wx
251 x( 2, 3 ) = wx
252 x( 2, 4 ) = -wx
253 x( 2, 5 ) = -wx
254*
255* Form (A, B)
256*
257 b( 1, 3 ) = wx + wy
258 b( 2, 3 ) = -wx + wy
259 b( 1, 4 ) = wx - wy
260 b( 2, 4 ) = wx - wy
261 b( 1, 5 ) = -wx + wy
262 b( 2, 5 ) = wx + wy
263 a( 1, 3 ) = wx*a( 1, 1 ) + wy*a( 3, 3 )
264 a( 2, 3 ) = -wx*a( 2, 2 ) + wy*a( 3, 3 )
265 a( 1, 4 ) = wx*a( 1, 1 ) - wy*a( 4, 4 )
266 a( 2, 4 ) = wx*a( 2, 2 ) - wy*a( 4, 4 )
267 a( 1, 5 ) = -wx*a( 1, 1 ) + wy*a( 5, 5 )
268 a( 2, 5 ) = wx*a( 2, 2 ) + wy*a( 5, 5 )
269*
270* Compute condition numbers
271*
272 s( 1 ) = rone / sqrt( ( rone+three*cabs( wy )*cabs( wy ) ) /
273 \$ ( rone+cabs( a( 1, 1 ) )*cabs( a( 1, 1 ) ) ) )
274 s( 2 ) = rone / sqrt( ( rone+three*cabs( wy )*cabs( wy ) ) /
275 \$ ( rone+cabs( a( 2, 2 ) )*cabs( a( 2, 2 ) ) ) )
276 s( 3 ) = rone / sqrt( ( rone+two*cabs( wx )*cabs( wx ) ) /
277 \$ ( rone+cabs( a( 3, 3 ) )*cabs( a( 3, 3 ) ) ) )
278 s( 4 ) = rone / sqrt( ( rone+two*cabs( wx )*cabs( wx ) ) /
279 \$ ( rone+cabs( a( 4, 4 ) )*cabs( a( 4, 4 ) ) ) )
280 s( 5 ) = rone / sqrt( ( rone+two*cabs( wx )*cabs( wx ) ) /
281 \$ ( rone+cabs( a( 5, 5 ) )*cabs( a( 5, 5 ) ) ) )
282*
283 CALL clakf2( 1, 4, a, lda, a( 2, 2 ), b, b( 2, 2 ), z, 8 )
284 CALL cgesvd( 'N', 'N', 8, 8, z, 8, rwork, work, 1, work( 2 ), 1,
285 \$ work( 3 ), 24, rwork( 9 ), info )
286 dif( 1 ) = rwork( 8 )
287*
288 CALL clakf2( 4, 1, a, lda, a( 5, 5 ), b, b( 5, 5 ), z, 8 )
289 CALL cgesvd( 'N', 'N', 8, 8, z, 8, rwork, work, 1, work( 2 ), 1,
290 \$ work( 3 ), 24, rwork( 9 ), info )
291 dif( 5 ) = rwork( 8 )
292*
293 RETURN
294*
295* End of CLATM6
296*
subroutine clakf2(M, N, A, LDA, B, D, E, Z, LDZ)
CLAKF2
Definition: clakf2.f:105
subroutine cgesvd(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO)
CGESVD computes the singular value decomposition (SVD) for GE matrices
Definition: cgesvd.f:214
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
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