LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zlatm6()

subroutine zlatm6 ( integer  type,
integer  n,
complex*16, dimension( lda, * )  a,
integer  lda,
complex*16, dimension( lda, * )  b,
complex*16, dimension( ldx, * )  x,
integer  ldx,
complex*16, dimension( ldy, * )  y,
integer  ldy,
complex*16  alpha,
complex*16  beta,
complex*16  wx,
complex*16  wy,
double precision, dimension( * )  s,
double precision, dimension( * )  dif 
)

ZLATM6

Purpose:
 ZLATM6 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*16 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*16 array, dimension (LDA, N).
          On exit B N-by-N is initialized according to TYPE.
[out]X
          X is COMPLEX*16 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*16 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*16
[in]BETA
          BETA is COMPLEX*16
 \verbatim
          Weighting constants for matrix A.
[in]WX
          WX is COMPLEX*16
          Constant for right eigenvector matrix.
[in]WY
          WY is COMPLEX*16
          Constant for left eigenvector matrix.
[out]S
          S is DOUBLE PRECISION array, dimension (N)
          S(i) is the reciprocal condition number for eigenvalue i.
[out]DIF
          DIF is DOUBLE PRECISION array, dimension (N)
          DIF(i) is the reciprocal condition number for eigenvector i.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 172 of file zlatm6.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*16 ALPHA, BETA, WX, WY
182* ..
183* .. Array Arguments ..
184 DOUBLE PRECISION DIF( * ), S( * )
185 COMPLEX*16 A( LDA, * ), B( LDA, * ), X( LDX, * ),
186 $ Y( LDY, * )
187* ..
188*
189* =====================================================================
190*
191* .. Parameters ..
192 DOUBLE PRECISION RONE, TWO, THREE
193 parameter( rone = 1.0d+0, two = 2.0d+0, three = 3.0d+0 )
194 COMPLEX*16 ZERO, ONE
195 parameter( zero = ( 0.0d+0, 0.0d+0 ),
196 $ one = ( 1.0d+0, 0.0d+0 ) )
197* ..
198* .. Local Scalars ..
199 INTEGER I, INFO, J
200* ..
201* .. Local Arrays ..
202 DOUBLE PRECISION RWORK( 50 )
203 COMPLEX*16 WORK( 26 ), Z( 8, 8 )
204* ..
205* .. Intrinsic Functions ..
206 INTRINSIC cdabs, dble, dcmplx, dconjg, sqrt
207* ..
208* .. External Subroutines ..
209 EXTERNAL zgesvd, zlacpy, zlakf2
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 ) = dcmplx( 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 ) = dcmplx( rone, rone )
231 a( 2, 2 ) = dconjg( a( 1, 1 ) )
232 a( 3, 3 ) = one
233 a( 4, 4 ) = dcmplx( dble( one+alpha ), dble( one+beta ) )
234 a( 5, 5 ) = dconjg( a( 4, 4 ) )
235 END IF
236*
237* Form X and Y
238*
239 CALL zlacpy( 'F', n, n, b, lda, y, ldy )
240 y( 3, 1 ) = -dconjg( wy )
241 y( 4, 1 ) = dconjg( wy )
242 y( 5, 1 ) = -dconjg( wy )
243 y( 3, 2 ) = -dconjg( wy )
244 y( 4, 2 ) = dconjg( wy )
245 y( 5, 2 ) = -dconjg( wy )
246*
247 CALL zlacpy( '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*cdabs( wy )*cdabs( wy ) ) /
273 $ ( rone+cdabs( a( 1, 1 ) )*cdabs( a( 1, 1 ) ) ) )
274 s( 2 ) = rone / sqrt( ( rone+three*cdabs( wy )*cdabs( wy ) ) /
275 $ ( rone+cdabs( a( 2, 2 ) )*cdabs( a( 2, 2 ) ) ) )
276 s( 3 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
277 $ ( rone+cdabs( a( 3, 3 ) )*cdabs( a( 3, 3 ) ) ) )
278 s( 4 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
279 $ ( rone+cdabs( a( 4, 4 ) )*cdabs( a( 4, 4 ) ) ) )
280 s( 5 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
281 $ ( rone+cdabs( a( 5, 5 ) )*cdabs( a( 5, 5 ) ) ) )
282*
283 CALL zlakf2( 1, 4, a, lda, a( 2, 2 ), b, b( 2, 2 ), z, 8 )
284 CALL zgesvd( '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 zlakf2( 4, 1, a, lda, a( 5, 5 ), b, b( 5, 5 ), z, 8 )
289 CALL zgesvd( '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 ZLATM6
296*
zgesvd
subroutine zgesvd(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, info)
ZGESVD computes the singular value decomposition (SVD) for GE matrices
Definition zgesvd.f:214
zlacpy
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
zlakf2
subroutine zlakf2(m, n, a, lda, b, d, e, z, ldz)
ZLAKF2
Definition zlakf2.f:105
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