 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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