 LAPACK  3.8.0 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 )```
Date
June 2017

Definition at line 143 of file chet01_3.f.

143 *
144 * -- LAPACK test routine (version 3.7.1) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * June 2017
148 *
149 * .. Scalar Arguments ..
150  CHARACTER uplo
151  INTEGER lda, ldafac, ldc, n
152  REAL resid
153 * ..
154 * .. Array Arguments ..
155  INTEGER ipiv( * )
156  REAL rwork( * )
157  COMPLEX a( lda, * ), afac( ldafac, * ), c( ldc, * ),
158  \$ e( * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  REAL zero, one
165  parameter( zero = 0.0e+0, one = 1.0e+0 )
166  COMPLEX czero, cone
167  parameter( czero = ( 0.0e+0, 0.0e+0 ),
168  \$ cone = ( 1.0e+0, 0.0e+0 ) )
169 * ..
170 * .. Local Scalars ..
171  INTEGER i, info, j
172  REAL anorm, eps
173 * ..
174 * .. External Functions ..
175  LOGICAL lsame
176  REAL clanhe, slamch
177  EXTERNAL lsame, clanhe, slamch
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL claset, clavhe_rook, csyconvf_rook
181 * ..
182 * .. Intrinsic Functions ..
183  INTRINSIC aimag, real
184 * ..
185 * .. Executable Statements ..
186 *
187 * Quick exit if N = 0.
188 *
189  IF( n.LE.0 ) THEN
190  resid = zero
191  RETURN
192  END IF
193 *
194 * a) Revert to multiplyers of L
195 *
196  CALL csyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
197 *
198 * 1) Determine EPS and the norm of A.
199 *
200  eps = slamch( 'Epsilon' )
201  anorm = clanhe( '1', uplo, n, a, lda, rwork )
202 *
203 * Check the imaginary parts of the diagonal elements and return with
204 * an error code if any are nonzero.
205 *
206  DO j = 1, n
207  IF( aimag( afac( j, j ) ).NE.zero ) THEN
208  resid = one / eps
209  RETURN
210  END IF
211  END DO
212 *
213 * 2) Initialize C to the identity matrix.
214 *
215  CALL claset( 'Full', n, n, czero, cone, c, ldc )
216 *
217 * 3) Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
218 *
219  CALL clavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
220  \$ ldafac, ipiv, c, ldc, info )
221 *
222 * 4) Call ZLAVHE_RK again to multiply by U (or L ).
223 *
224  CALL clavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
225  \$ ldafac, ipiv, c, ldc, info )
226 *
227 * 5) Compute the difference C - A .
228 *
229  IF( lsame( uplo, 'U' ) ) THEN
230  DO j = 1, n
231  DO i = 1, j - 1
232  c( i, j ) = c( i, j ) - a( i, j )
233  END DO
234  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
235  END DO
236  ELSE
237  DO j = 1, n
238  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
239  DO i = j + 1, n
240  c( i, j ) = c( i, j ) - a( i, j )
241  END DO
242  END DO
243  END IF
244 *
245 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
246 *
247  resid = clanhe( '1', uplo, n, c, ldc, rwork )
248 *
249  IF( anorm.LE.zero ) THEN
250  IF( resid.NE.zero )
251  \$ resid = one / eps
252  ELSE
253  resid = ( ( resid/REAL( N ) )/anorm ) / eps
254  END IF
255 *
256 * b) Convert to factor of L (or U)
257 *
258  CALL csyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
259 *
260  RETURN
261 *
262 * End of CHET01_3
263 *
subroutine csyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
CSYCONVF_ROOK
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:108
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine clavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE_ROOK
Definition: clavhe_rook.f:158
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
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