LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ chet01()

 subroutine chet01 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID )

CHET01

Purpose:
``` CHET01 reconstructs a Hermitian indefinite matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix, EPS is the machine epsilon,
L' is the conjugate transpose of L, and U' is the conjugate transpose
of U.```
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 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) The factored form of the matrix A. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by CHETRF.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from CHETRF.``` [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
November 2013

Definition at line 128 of file chet01.f.

128 *
129 * -- LAPACK test routine (version 3.5.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2013
133 *
134 * .. Scalar Arguments ..
135  CHARACTER uplo
136  INTEGER lda, ldafac, ldc, n
137  REAL resid
138 * ..
139 * .. Array Arguments ..
140  INTEGER ipiv( * )
141  REAL rwork( * )
142  COMPLEX a( lda, * ), afac( ldafac, * ), c( ldc, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  REAL zero, one
149  parameter( zero = 0.0e+0, one = 1.0e+0 )
150  COMPLEX czero, cone
151  parameter( czero = ( 0.0e+0, 0.0e+0 ),
152  \$ cone = ( 1.0e+0, 0.0e+0 ) )
153 * ..
154 * .. Local Scalars ..
155  INTEGER i, info, j
156  REAL anorm, eps
157 * ..
158 * .. External Functions ..
159  LOGICAL lsame
160  REAL clanhe, slamch
161  EXTERNAL lsame, clanhe, slamch
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL clavhe, claset
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC aimag, real
168 * ..
169 * .. Executable Statements ..
170 *
171 * Quick exit if N = 0.
172 *
173  IF( n.LE.0 ) THEN
174  resid = zero
175  RETURN
176  END IF
177 *
178 * Determine EPS and the norm of A.
179 *
180  eps = slamch( 'Epsilon' )
181  anorm = clanhe( '1', uplo, n, a, lda, rwork )
182 *
183 * Check the imaginary parts of the diagonal elements and return with
184 * an error code if any are nonzero.
185 *
186  DO 10 j = 1, n
187  IF( aimag( afac( j, j ) ).NE.zero ) THEN
188  resid = one / eps
189  RETURN
190  END IF
191  10 CONTINUE
192 *
193 * Initialize C to the identity matrix.
194 *
195  CALL claset( 'Full', n, n, czero, cone, c, ldc )
196 *
197 * Call CLAVHE to form the product D * U' (or D * L' ).
198 *
199  CALL clavhe( uplo, 'Conjugate', 'Non-unit', n, n, afac, ldafac,
200  \$ ipiv, c, ldc, info )
201 *
202 * Call CLAVHE again to multiply by U (or L ).
203 *
204  CALL clavhe( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
205  \$ ipiv, c, ldc, info )
206 *
207 * Compute the difference C - A .
208 *
209  IF( lsame( uplo, 'U' ) ) THEN
210  DO 30 j = 1, n
211  DO 20 i = 1, j - 1
212  c( i, j ) = c( i, j ) - a( i, j )
213  20 CONTINUE
214  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
215  30 CONTINUE
216  ELSE
217  DO 50 j = 1, n
218  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
219  DO 40 i = j + 1, n
220  c( i, j ) = c( i, j ) - a( i, j )
221  40 CONTINUE
222  50 CONTINUE
223  END IF
224 *
225 * Compute norm( C - A ) / ( N * norm(A) * EPS )
226 *
227  resid = clanhe( '1', uplo, n, c, ldc, rwork )
228 *
229  IF( anorm.LE.zero ) THEN
230  IF( resid.NE.zero )
231  \$ resid = one / eps
232  ELSE
233  resid = ( ( resid / REAL( N ) ) / anorm ) / eps
234  END IF
235 *
236  RETURN
237 *
238 * End of CHET01
239 *
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
subroutine clavhe(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE
Definition: clavhe.f:155
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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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