LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ 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 )```

Definition at line 124 of file chet01.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 CHARACTER UPLO
133 INTEGER LDA, LDAFAC, LDC, N
134 REAL RESID
135* ..
136* .. Array Arguments ..
137 INTEGER IPIV( * )
138 REAL RWORK( * )
139 COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 REAL ZERO, ONE
146 parameter( zero = 0.0e+0, one = 1.0e+0 )
147 COMPLEX CZERO, CONE
148 parameter( czero = ( 0.0e+0, 0.0e+0 ),
149 \$ cone = ( 1.0e+0, 0.0e+0 ) )
150* ..
151* .. Local Scalars ..
152 INTEGER I, INFO, J
153 REAL ANORM, EPS
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 REAL CLANHE, SLAMCH
158 EXTERNAL lsame, clanhe, slamch
159* ..
160* .. External Subroutines ..
161 EXTERNAL clavhe, claset
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC aimag, real
165* ..
166* .. Executable Statements ..
167*
168* Quick exit if N = 0.
169*
170 IF( n.LE.0 ) THEN
171 resid = zero
172 RETURN
173 END IF
174*
175* Determine EPS and the norm of A.
176*
177 eps = slamch( 'Epsilon' )
178 anorm = clanhe( '1', uplo, n, a, lda, rwork )
179*
180* Check the imaginary parts of the diagonal elements and return with
181* an error code if any are nonzero.
182*
183 DO 10 j = 1, n
184 IF( aimag( afac( j, j ) ).NE.zero ) THEN
185 resid = one / eps
186 RETURN
187 END IF
188 10 CONTINUE
189*
190* Initialize C to the identity matrix.
191*
192 CALL claset( 'Full', n, n, czero, cone, c, ldc )
193*
194* Call CLAVHE to form the product D * U' (or D * L' ).
195*
196 CALL clavhe( uplo, 'Conjugate', 'Non-unit', n, n, afac, ldafac,
197 \$ ipiv, c, ldc, info )
198*
199* Call CLAVHE again to multiply by U (or L ).
200*
201 CALL clavhe( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
202 \$ ipiv, c, ldc, info )
203*
204* Compute the difference C - A .
205*
206 IF( lsame( uplo, 'U' ) ) THEN
207 DO 30 j = 1, n
208 DO 20 i = 1, j - 1
209 c( i, j ) = c( i, j ) - a( i, j )
210 20 CONTINUE
211 c( j, j ) = c( j, j ) - real( a( j, j ) )
212 30 CONTINUE
213 ELSE
214 DO 50 j = 1, n
215 c( j, j ) = c( j, j ) - real( a( j, j ) )
216 DO 40 i = j + 1, n
217 c( i, j ) = c( i, j ) - a( i, j )
218 40 CONTINUE
219 50 CONTINUE
220 END IF
221*
222* Compute norm( C - A ) / ( N * norm(A) * EPS )
223*
224 resid = clanhe( '1', uplo, n, c, ldc, rwork )
225*
226 IF( anorm.LE.zero ) THEN
227 IF( resid.NE.zero )
228 \$ resid = one / eps
229 ELSE
230 resid = ( ( resid / real( n ) ) / anorm ) / eps
231 END IF
232*
233 RETURN
234*
235* End of CHET01
236*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clavhe(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE
Definition: clavhe.f:153
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
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: