LAPACK  3.10.0
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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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
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