LAPACK  3.9.0
LAPACK: Linear Algebra PACKage

◆ 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.
Date
December 2016

Definition at line 176 of file zlatm6.f.

176 *
177 * -- LAPACK computational routine (version 3.7.0) --
178 * -- LAPACK is a software package provided by Univ. of Tennessee, --
179 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
180 * December 2016
181 *
182 * .. Scalar Arguments ..
183  INTEGER LDA, LDX, LDY, N, TYPE
184  COMPLEX*16 ALPHA, BETA, WX, WY
185 * ..
186 * .. Array Arguments ..
187  DOUBLE PRECISION DIF( * ), S( * )
188  COMPLEX*16 A( LDA, * ), B( LDA, * ), X( LDX, * ),
189  $ Y( LDY, * )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  DOUBLE PRECISION RONE, TWO, THREE
196  parameter( rone = 1.0d+0, two = 2.0d+0, three = 3.0d+0 )
197  COMPLEX*16 ZERO, ONE
198  parameter( zero = ( 0.0d+0, 0.0d+0 ),
199  $ one = ( 1.0d+0, 0.0d+0 ) )
200 * ..
201 * .. Local Scalars ..
202  INTEGER I, INFO, J
203 * ..
204 * .. Local Arrays ..
205  DOUBLE PRECISION RWORK( 50 )
206  COMPLEX*16 WORK( 26 ), Z( 8, 8 )
207 * ..
208 * .. Intrinsic Functions ..
209  INTRINSIC cdabs, dble, dcmplx, dconjg, sqrt
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL zgesvd, zlacpy, zlakf2
213 * ..
214 * .. Executable Statements ..
215 *
216 * Generate test problem ...
217 * (Da, Db) ...
218 *
219  DO 20 i = 1, n
220  DO 10 j = 1, n
221 *
222  IF( i.EQ.j ) THEN
223  a( i, i ) = dcmplx( i ) + alpha
224  b( i, i ) = one
225  ELSE
226  a( i, j ) = zero
227  b( i, j ) = zero
228  END IF
229 *
230  10 CONTINUE
231  20 CONTINUE
232  IF( type.EQ.2 ) THEN
233  a( 1, 1 ) = dcmplx( rone, rone )
234  a( 2, 2 ) = dconjg( a( 1, 1 ) )
235  a( 3, 3 ) = one
236  a( 4, 4 ) = dcmplx( dble( one+alpha ), dble( one+beta ) )
237  a( 5, 5 ) = dconjg( a( 4, 4 ) )
238  END IF
239 *
240 * Form X and Y
241 *
242  CALL zlacpy( 'F', n, n, b, lda, y, ldy )
243  y( 3, 1 ) = -dconjg( wy )
244  y( 4, 1 ) = dconjg( wy )
245  y( 5, 1 ) = -dconjg( wy )
246  y( 3, 2 ) = -dconjg( wy )
247  y( 4, 2 ) = dconjg( wy )
248  y( 5, 2 ) = -dconjg( wy )
249 *
250  CALL zlacpy( 'F', n, n, b, lda, x, ldx )
251  x( 1, 3 ) = -wx
252  x( 1, 4 ) = -wx
253  x( 1, 5 ) = wx
254  x( 2, 3 ) = wx
255  x( 2, 4 ) = -wx
256  x( 2, 5 ) = -wx
257 *
258 * Form (A, B)
259 *
260  b( 1, 3 ) = wx + wy
261  b( 2, 3 ) = -wx + wy
262  b( 1, 4 ) = wx - wy
263  b( 2, 4 ) = wx - wy
264  b( 1, 5 ) = -wx + wy
265  b( 2, 5 ) = wx + wy
266  a( 1, 3 ) = wx*a( 1, 1 ) + wy*a( 3, 3 )
267  a( 2, 3 ) = -wx*a( 2, 2 ) + wy*a( 3, 3 )
268  a( 1, 4 ) = wx*a( 1, 1 ) - wy*a( 4, 4 )
269  a( 2, 4 ) = wx*a( 2, 2 ) - wy*a( 4, 4 )
270  a( 1, 5 ) = -wx*a( 1, 1 ) + wy*a( 5, 5 )
271  a( 2, 5 ) = wx*a( 2, 2 ) + wy*a( 5, 5 )
272 *
273 * Compute condition numbers
274 *
275  s( 1 ) = rone / sqrt( ( rone+three*cdabs( wy )*cdabs( wy ) ) /
276  $ ( rone+cdabs( a( 1, 1 ) )*cdabs( a( 1, 1 ) ) ) )
277  s( 2 ) = rone / sqrt( ( rone+three*cdabs( wy )*cdabs( wy ) ) /
278  $ ( rone+cdabs( a( 2, 2 ) )*cdabs( a( 2, 2 ) ) ) )
279  s( 3 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
280  $ ( rone+cdabs( a( 3, 3 ) )*cdabs( a( 3, 3 ) ) ) )
281  s( 4 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
282  $ ( rone+cdabs( a( 4, 4 ) )*cdabs( a( 4, 4 ) ) ) )
283  s( 5 ) = rone / sqrt( ( rone+two*cdabs( wx )*cdabs( wx ) ) /
284  $ ( rone+cdabs( a( 5, 5 ) )*cdabs( a( 5, 5 ) ) ) )
285 *
286  CALL zlakf2( 1, 4, a, lda, a( 2, 2 ), b, b( 2, 2 ), z, 8 )
287  CALL zgesvd( 'N', 'N', 8, 8, z, 8, rwork, work, 1, work( 2 ), 1,
288  $ work( 3 ), 24, rwork( 9 ), info )
289  dif( 1 ) = rwork( 8 )
290 *
291  CALL zlakf2( 4, 1, a, lda, a( 5, 5 ), b, b( 5, 5 ), z, 8 )
292  CALL zgesvd( 'N', 'N', 8, 8, z, 8, rwork, work, 1, work( 2 ), 1,
293  $ work( 3 ), 24, rwork( 9 ), info )
294  dif( 5 ) = rwork( 8 )
295 *
296  RETURN
297 *
298 * End of ZLATM6
299 *
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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:216
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:105
zlakf2
subroutine zlakf2(M, N, A, LDA, B, D, E, Z, LDZ)
ZLAKF2
Definition: zlakf2.f:107