 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ zsyt01_3()

 subroutine zsyt01_3 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

ZSYT01_3

Purpose:
ZSYT01_3 reconstructs a symmetric indefinite matrix A from its
block L*D*L' or U*D*U' factorization computed by ZSYTRF_RK
(or ZSYTRF_BK) and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters
 [in] UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular [in] N N is INTEGER The number of rows and columns of the matrix A. N >= 0. [in] A A is COMPLEX*16 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] AFAC AFAC is COMPLEX*16 array, dimension (LDAFAC,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. [in] LDAFAC LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N). [in] E E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. [in] IPIV IPIV is INTEGER array, dimension (N) The pivot indices from ZSYTRF_RK (or ZSYTRF_BK). [out] C C is COMPLEX*16 array, dimension (LDC,N) [in] LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N). [out] RWORK RWORK is DOUBLE PRECISION array, dimension (N) [out] RESID RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Definition at line 139 of file zsyt01_3.f.

141 *
142 * -- LAPACK test routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  CHARACTER UPLO
148  INTEGER LDA, LDAFAC, LDC, N
149  DOUBLE PRECISION RESID
150 * ..
151 * .. Array Arguments ..
152  INTEGER IPIV( * )
153  DOUBLE PRECISION RWORK( * )
154  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
155  \$ E( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  DOUBLE PRECISION ZERO, ONE
162  parameter( zero = 0.0d+0, one = 1.0d+0 )
163  COMPLEX*16 CZERO, CONE
164  parameter( czero = ( 0.0d+0, 0.0d+0 ),
165  \$ cone = ( 1.0d+0, 0.0d+0 ) )
166 * ..
167 * .. Local Scalars ..
168  INTEGER I, INFO, J
169  DOUBLE PRECISION ANORM, EPS
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  DOUBLE PRECISION DLAMCH, ZLANSY
174  EXTERNAL lsame, dlamch, zlansy
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL zlaset, zlavsy_rook, zsyconvf_rook
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC dble
181 * ..
182 * .. Executable Statements ..
183 *
184 * Quick exit if N = 0.
185 *
186  IF( n.LE.0 ) THEN
187  resid = zero
188  RETURN
189  END IF
190 *
191 * a) Revert to multiplyers of L
192 *
193  CALL zsyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
194 *
195 * 1) Determine EPS and the norm of A.
196 *
197  eps = dlamch( 'Epsilon' )
198  anorm = zlansy( '1', uplo, n, a, lda, rwork )
199 *
200 * 2) Initialize C to the identity matrix.
201 *
202  CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
203 *
204 * 3) Call ZLAVSY_ROOK to form the product D * U' (or D * L' ).
205 *
206  CALL zlavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
207  \$ ldafac, ipiv, c, ldc, info )
208 *
209 * 4) Call ZLAVSY_ROOK again to multiply by U (or L ).
210 *
211  CALL zlavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
212  \$ ldafac, ipiv, c, ldc, info )
213 *
214 * 5) Compute the difference C - A .
215 *
216  IF( lsame( uplo, 'U' ) ) THEN
217  DO j = 1, n
218  DO i = 1, j
219  c( i, j ) = c( i, j ) - a( i, j )
220  END DO
221  END DO
222  ELSE
223  DO j = 1, n
224  DO i = j, n
225  c( i, j ) = c( i, j ) - a( i, j )
226  END DO
227  END DO
228  END IF
229 *
230 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
231 *
232  resid = zlansy( '1', uplo, n, c, ldc, rwork )
233 *
234  IF( anorm.LE.zero ) THEN
235  IF( resid.NE.zero )
236  \$ resid = one / eps
237  ELSE
238  resid = ( ( resid / dble( n ) ) / anorm ) / eps
239  END IF
240
241 *
242 * b) Convert to factor of L (or U)
243 *
244  CALL zsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
245 *
246  RETURN
247 *
248 * End of ZSYT01_3
249 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVSY_ROOK
Definition: zlavsy_rook.f:155
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
subroutine zsyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
ZSYCONVF_ROOK
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