LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ chet01_3()

subroutine chet01_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 
)

CHET01_3

Purpose:
 CHET01_3 reconstructs a Hermitian indefinite matrix A from its
 block L*D*L' or U*D*U' factorization computed by CHETRF_RK
 (or CHETRF_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
          Hermitian 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 Hermitian 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 CHETRF_RK and CHETRF_BK:
            a) ONLY diagonal elements of the Hermitian 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 Hermitian 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 CHETRF_RK (or CHETRF_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 chet01_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 CLANHE, SLAMCH
174  EXTERNAL lsame, clanhe, slamch
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL claset, clavhe_rook, csyconvf_rook
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC aimag, 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 = clanhe( '1', uplo, n, a, lda, rwork )
199 *
200 * Check the imaginary parts of the diagonal elements and return with
201 * an error code if any are nonzero.
202 *
203  DO j = 1, n
204  IF( aimag( afac( j, j ) ).NE.zero ) THEN
205  resid = one / eps
206  RETURN
207  END IF
208  END DO
209 *
210 * 2) Initialize C to the identity matrix.
211 *
212  CALL claset( 'Full', n, n, czero, cone, c, ldc )
213 *
214 * 3) Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
215 *
216  CALL clavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
217  $ ldafac, ipiv, c, ldc, info )
218 *
219 * 4) Call ZLAVHE_RK again to multiply by U (or L ).
220 *
221  CALL clavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
222  $ ldafac, ipiv, c, ldc, info )
223 *
224 * 5) Compute the difference C - A .
225 *
226  IF( lsame( uplo, 'U' ) ) THEN
227  DO j = 1, n
228  DO i = 1, j - 1
229  c( i, j ) = c( i, j ) - a( i, j )
230  END DO
231  c( j, j ) = c( j, j ) - real( a( j, j ) )
232  END DO
233  ELSE
234  DO j = 1, n
235  c( j, j ) = c( j, j ) - real( a( j, j ) )
236  DO i = j + 1, n
237  c( i, j ) = c( i, j ) - a( i, j )
238  END DO
239  END DO
240  END IF
241 *
242 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
243 *
244  resid = clanhe( '1', uplo, n, c, ldc, rwork )
245 *
246  IF( anorm.LE.zero ) THEN
247  IF( resid.NE.zero )
248  $ resid = one / eps
249  ELSE
250  resid = ( ( resid/real( n ) )/anorm ) / eps
251  END IF
252 *
253 * b) Convert to factor of L (or U)
254 *
255  CALL csyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
256 *
257  RETURN
258 *
259 * End of CHET01_3
260 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE_ROOK
Definition: clavhe_rook.f:156
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,...
Definition: clanhe.f:124
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
subroutine csyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
CSYCONVF_ROOK
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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