LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ ssgt01()

subroutine ssgt01 ( integer  ITYPE,
character  UPLO,
integer  N,
integer  M,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldz, * )  Z,
integer  LDZ,
real, dimension( * )  D,
real, dimension( * )  WORK,
real, dimension( * )  RESULT 
)

SSGT01

Purpose:
 SSGT01 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 symmetric matrix, B is
 symmetric positive definite, Z is orthogonal, 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 symmetric 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
          symmetric 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.  0 <= M <= N.
[in]A
          A is REAL array, dimension (LDA, N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]B
          B is REAL array, dimension (LDB, N)
          The original symmetric positive definite matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]Z
          Z is REAL 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 REAL array, dimension (N*N)
[out]RESULT
          RESULT is REAL array, dimension (1)
          The test ratio as described above.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 144 of file ssgt01.f.

146*
147* -- LAPACK test routine --
148* -- LAPACK is a software package provided by Univ. of Tennessee, --
149* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150*
151* .. Scalar Arguments ..
152 CHARACTER UPLO
153 INTEGER ITYPE, LDA, LDB, LDZ, M, N
154* ..
155* .. Array Arguments ..
156 REAL A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ),
157 $ WORK( * ), Z( LDZ, * )
158* ..
159*
160* =====================================================================
161*
162* .. Parameters ..
163 REAL ZERO, ONE
164 parameter( zero = 0.0e0, one = 1.0e0 )
165* ..
166* .. Local Scalars ..
167 INTEGER I
168 REAL ANORM, ULP
169* ..
170* .. External Functions ..
171 REAL SLAMCH, SLANGE, SLANSY
172 EXTERNAL slamch, slange, slansy
173* ..
174* .. External Subroutines ..
175 EXTERNAL sscal, ssymm
176* ..
177* .. Executable Statements ..
178*
179 result( 1 ) = zero
180 IF( n.LE.0 )
181 $ RETURN
182*
183 ulp = slamch( 'Epsilon' )
184*
185* Compute product of 1-norms of A and Z.
186*
187 anorm = slansy( '1', uplo, n, a, lda, work )*
188 $ slange( '1', n, m, z, ldz, work )
189 IF( anorm.EQ.zero )
190 $ anorm = one
191*
192 IF( itype.EQ.1 ) THEN
193*
194* Norm of AZ - BZD
195*
196 CALL ssymm( 'Left', uplo, n, m, one, a, lda, z, ldz, zero,
197 $ work, n )
198 DO 10 i = 1, m
199 CALL sscal( n, d( i ), z( 1, i ), 1 )
200 10 CONTINUE
201 CALL ssymm( 'Left', uplo, n, m, one, b, ldb, z, ldz, -one,
202 $ work, n )
203*
204 result( 1 ) = ( slange( '1', n, m, work, n, work ) / anorm ) /
205 $ ( n*ulp )
206*
207 ELSE IF( itype.EQ.2 ) THEN
208*
209* Norm of ABZ - ZD
210*
211 CALL ssymm( 'Left', uplo, n, m, one, b, ldb, z, ldz, zero,
212 $ work, n )
213 DO 20 i = 1, m
214 CALL sscal( n, d( i ), z( 1, i ), 1 )
215 20 CONTINUE
216 CALL ssymm( 'Left', uplo, n, m, one, a, lda, work, n, -one, z,
217 $ ldz )
218*
219 result( 1 ) = ( slange( '1', n, m, z, ldz, work ) / anorm ) /
220 $ ( n*ulp )
221*
222 ELSE IF( itype.EQ.3 ) THEN
223*
224* Norm of BAZ - ZD
225*
226 CALL ssymm( 'Left', uplo, n, m, one, a, lda, z, ldz, zero,
227 $ work, n )
228 DO 30 i = 1, m
229 CALL sscal( n, d( i ), z( 1, i ), 1 )
230 30 CONTINUE
231 CALL ssymm( 'Left', uplo, n, m, one, b, ldb, work, n, -one, z,
232 $ ldz )
233*
234 result( 1 ) = ( slange( '1', n, m, z, ldz, work ) / anorm ) /
235 $ ( n*ulp )
236 END IF
237*
238 RETURN
239*
240* End of SSGT01
241*
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine ssymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SSYMM
Definition: ssymm.f:189
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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