LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ csyt01_3()

subroutine csyt01_3 ( character  UPLO,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
complex, dimension( * )  E,
integer, dimension( * )  IPIV,
complex, dimension( ldc, * )  C,
integer  LDC,
real, dimension( * )  RWORK,
real  RESID 
)

CSYT01_3

Purpose:
 CSYT01_3 reconstructs a symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization computed by CSYTRF_RK
 (or CSYTRF_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 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 array, dimension (LDAFAC,N)
          Diagonal of the block diagonal matrix D and factors U or L
          as computed by CSYTRF_RK and CSYTRF_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 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 CSYTRF_RK (or CSYTRF_BK).
[out]C
          C is COMPLEX array, dimension (LDC,N)
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 139 of file csyt01_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  REAL RESID
150 * ..
151 * .. Array Arguments ..
152  INTEGER IPIV( * )
153  REAL RWORK( * )
154  COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
155  $ E( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  REAL ZERO, ONE
162  parameter( zero = 0.0e+0, one = 1.0e+0 )
163  COMPLEX CZERO, CONE
164  parameter( czero = ( 0.0e+0, 0.0e+0 ),
165  $ cone = ( 1.0e+0, 0.0e+0 ) )
166 * ..
167 * .. Local Scalars ..
168  INTEGER I, INFO, J
169  REAL ANORM, EPS
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  REAL SLAMCH, CLANSY
174  EXTERNAL lsame, slamch, clansy
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL claset, clavsy_rook, csyconvf_rook
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC real
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 csyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
194 *
195 * 1) Determine EPS and the norm of A.
196 *
197  eps = slamch( 'Epsilon' )
198  anorm = clansy( '1', uplo, n, a, lda, rwork )
199 *
200 * 2) Initialize C to the identity matrix.
201 *
202  CALL claset( '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 clavsy_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 clavsy_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 = clansy( '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 / real( n ) ) / anorm ) / eps
239  END IF
240 
241 *
242 * b) Convert to factor of L (or U)
243 *
244  CALL csyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
245 *
246  RETURN
247 *
248 * End of CSYT01_3
249 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVSY_ROOK
Definition: clavsy_rook.f:155
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
subroutine csyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
CSYCONVF_ROOK
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: