LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ chet01_rook()

 subroutine chet01_rook ( 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_ROOK

Purpose:
``` CHET01_ROOK reconstructs a complex 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 transpose of L, and U' is the transpose of U.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the complex 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 complex 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 CSYTRF_ROOK.``` [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 CSYTRF_ROOK.``` [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 123 of file chet01_rook.f.

125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER UPLO
132 INTEGER LDA, LDAFAC, LDC, N
133 REAL RESID
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * )
137 REAL RWORK( * )
138 COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 REAL ZERO, ONE
145 parameter( zero = 0.0e+0, one = 1.0e+0 )
146 COMPLEX CZERO, CONE
147 parameter( czero = ( 0.0e+0, 0.0e+0 ),
148 \$ cone = ( 1.0e+0, 0.0e+0 ) )
149* ..
150* .. Local Scalars ..
151 INTEGER I, INFO, J
152 REAL ANORM, EPS
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 REAL CLANHE, SLAMCH
157 EXTERNAL lsame, clanhe, slamch
158* ..
159* .. External Subroutines ..
160 EXTERNAL claset, clavhe_rook
161* ..
162* .. Intrinsic Functions ..
163 INTRINSIC aimag, real
164* ..
165* .. Executable Statements ..
166*
167* Quick exit if N = 0.
168*
169 IF( n.LE.0 ) THEN
170 resid = zero
171 RETURN
172 END IF
173*
174* Determine EPS and the norm of A.
175*
176 eps = slamch( 'Epsilon' )
177 anorm = clanhe( '1', uplo, n, a, lda, rwork )
178*
179* Check the imaginary parts of the diagonal elements and return with
180* an error code if any are nonzero.
181*
182 DO 10 j = 1, n
183 IF( aimag( afac( j, j ) ).NE.zero ) THEN
184 resid = one / eps
185 RETURN
186 END IF
187 10 CONTINUE
188*
189* Initialize C to the identity matrix.
190*
191 CALL claset( 'Full', n, n, czero, cone, c, ldc )
192*
193* Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
194*
195 CALL clavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
196 \$ ldafac, ipiv, c, ldc, info )
197*
198* Call CLAVHE_ROOK again to multiply by U (or L ).
199*
200 CALL clavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
201 \$ ldafac, ipiv, c, ldc, info )
202*
203* Compute the difference C - A .
204*
205 IF( lsame( uplo, 'U' ) ) THEN
206 DO 30 j = 1, n
207 DO 20 i = 1, j - 1
208 c( i, j ) = c( i, j ) - a( i, j )
209 20 CONTINUE
210 c( j, j ) = c( j, j ) - real( a( j, j ) )
211 30 CONTINUE
212 ELSE
213 DO 50 j = 1, n
214 c( j, j ) = c( j, j ) - real( a( j, j ) )
215 DO 40 i = j + 1, n
216 c( i, j ) = c( i, j ) - a( i, j )
217 40 CONTINUE
218 50 CONTINUE
219 END IF
220*
221* Compute norm( C - A ) / ( N * norm(A) * EPS )
222*
223 resid = clanhe( '1', uplo, n, c, ldc, rwork )
224*
225 IF( anorm.LE.zero ) THEN
226 IF( resid.NE.zero )
227 \$ resid = one / eps
228 ELSE
229 resid = ( ( resid/real( n ) )/anorm ) / eps
230 END IF
231*
232 RETURN
233*
234* End of CHET01_ROOK
235*
subroutine clavhe_rook(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
CLAVHE_ROOK
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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