LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ csgt01()

 subroutine csgt01 ( integer ITYPE, character UPLO, integer N, integer M, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldz, * ) Z, integer LDZ, real, dimension( * ) D, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

CSGT01

Purpose:
``` CSGT01 checks a decomposition of the form

A Z   =  B Z D or
A B Z =  Z D or
B A Z =  Z D

where A is a Hermitian matrix, B is Hermitian positive definite,
Z is unitary, and D is diagonal.

One of the following test ratios is computed:

ITYPE = 1:  RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )

ITYPE = 2:  RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )

ITYPE = 3:  RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER The form of the Hermitian generalized eigenproblem. = 1: A*z = (lambda)*B*z = 2: A*B*z = (lambda)*z = 3: B*A*z = (lambda)*z``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrices A and B is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] M ``` M is INTEGER The number of eigenvalues found. M >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA, N) The original Hermitian matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] B ``` B is COMPLEX array, dimension (LDB, N) The original Hermitian positive definite matrix B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [in] Z ``` Z is COMPLEX array, dimension (LDZ, M) The computed eigenvectors of the generalized eigenproblem.``` [in] LDZ ``` LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,N).``` [in] D ``` D is REAL array, dimension (M) The computed eigenvalues of the generalized eigenproblem.``` [out] WORK ` WORK is COMPLEX array, dimension (N*N)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESULT ``` RESULT is REAL array, dimension (1) The test ratio as described above.```
Date
December 2016

Definition at line 154 of file csgt01.f.

154 *
155 * -- LAPACK test routine (version 3.7.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * December 2016
159 *
160 * .. Scalar Arguments ..
161  CHARACTER uplo
162  INTEGER itype, lda, ldb, ldz, m, n
163 * ..
164 * .. Array Arguments ..
165  REAL d( * ), result( * ), rwork( * )
166  COMPLEX a( lda, * ), b( ldb, * ), work( * ),
167  \$ z( ldz, * )
168 * ..
169 *
170 * =====================================================================
171 *
172 * .. Parameters ..
173  REAL zero, one
174  parameter( zero = 0.0e+0, one = 1.0e+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 i
181  REAL anorm, ulp
182 * ..
183 * .. External Functions ..
184  REAL clange, clanhe, slamch
185  EXTERNAL clange, clanhe, slamch
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL chemm, csscal
189 * ..
190 * .. Executable Statements ..
191 *
192  result( 1 ) = zero
193  IF( n.LE.0 )
194  \$ RETURN
195 *
196  ulp = slamch( 'Epsilon' )
197 *
198 * Compute product of 1-norms of A and Z.
199 *
200  anorm = clanhe( '1', uplo, n, a, lda, rwork )*
201  \$ clange( '1', n, m, z, ldz, rwork )
202  IF( anorm.EQ.zero )
203  \$ anorm = one
204 *
205  IF( itype.EQ.1 ) THEN
206 *
207 * Norm of AZ - BZD
208 *
209  CALL chemm( 'Left', uplo, n, m, cone, a, lda, z, ldz, czero,
210  \$ work, n )
211  DO 10 i = 1, m
212  CALL csscal( n, d( i ), z( 1, i ), 1 )
213  10 CONTINUE
214  CALL chemm( 'Left', uplo, n, m, cone, b, ldb, z, ldz, -cone,
215  \$ work, n )
216 *
217  result( 1 ) = ( clange( '1', n, m, work, n, rwork ) / anorm ) /
218  \$ ( n*ulp )
219 *
220  ELSE IF( itype.EQ.2 ) THEN
221 *
222 * Norm of ABZ - ZD
223 *
224  CALL chemm( 'Left', uplo, n, m, cone, b, ldb, z, ldz, czero,
225  \$ work, n )
226  DO 20 i = 1, m
227  CALL csscal( n, d( i ), z( 1, i ), 1 )
228  20 CONTINUE
229  CALL chemm( 'Left', uplo, n, m, cone, a, lda, work, n, -cone,
230  \$ z, ldz )
231 *
232  result( 1 ) = ( clange( '1', n, m, z, ldz, rwork ) / anorm ) /
233  \$ ( n*ulp )
234 *
235  ELSE IF( itype.EQ.3 ) THEN
236 *
237 * Norm of BAZ - ZD
238 *
239  CALL chemm( 'Left', uplo, n, m, cone, a, lda, z, ldz, czero,
240  \$ work, n )
241  DO 30 i = 1, m
242  CALL csscal( n, d( i ), z( 1, i ), 1 )
243  30 CONTINUE
244  CALL chemm( 'Left', uplo, n, m, cone, b, ldb, work, n, -cone,
245  \$ z, ldz )
246 *
247  result( 1 ) = ( clange( '1', n, m, z, ldz, rwork ) / anorm ) /
248  \$ ( n*ulp )
249  END IF
250 *
251  RETURN
252 *
253 * End of CSGT01
254 *
subroutine chemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CHEMM
Definition: chemm.f:193
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:117
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: clanhe.f:126
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:80
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