 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhet01_3()

 subroutine zhet01_3 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

ZHET01_3

Purpose:
``` ZHET01_3 reconstructs a Hermitian indefinite matrix A from its
block L*D*L' or U*D*U' factorization computed by ZHETRF_RK
(or ZHETRF_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*16 array, dimension (LDAFAC,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_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*16 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 ZHETRF_RK (or ZHETRF_BK).``` [out] C ` C is COMPLEX*16 array, dimension (LDC,N)` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION 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 139 of file zhet01_3.f.

141 *
142 * -- LAPACK test routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  CHARACTER UPLO
148  INTEGER LDA, LDAFAC, LDC, N
149  DOUBLE PRECISION RESID
150 * ..
151 * .. Array Arguments ..
152  INTEGER IPIV( * )
153  DOUBLE PRECISION RWORK( * )
154  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
155  \$ E( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  DOUBLE PRECISION ZERO, ONE
162  parameter( zero = 0.0d+0, one = 1.0d+0 )
163  COMPLEX*16 CZERO, CONE
164  parameter( czero = ( 0.0d+0, 0.0d+0 ),
165  \$ cone = ( 1.0d+0, 0.0d+0 ) )
166 * ..
167 * .. Local Scalars ..
168  INTEGER I, INFO, J
169  DOUBLE PRECISION ANORM, EPS
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  DOUBLE PRECISION ZLANHE, DLAMCH
174  EXTERNAL lsame, zlanhe, dlamch
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL zlaset, zlavhe_rook, zsyconvf_rook
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC dimag, dble
181 * ..
182 * .. Executable Statements ..
183 *
184 * Quick exit if N = 0.
185 *
186  IF( n.LE.0 ) THEN
187  resid = zero
188  RETURN
189  END IF
190 *
191 * a) Revert to multiplyers of L
192 *
193  CALL zsyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
194 *
195 * 1) Determine EPS and the norm of A.
196 *
197  eps = dlamch( 'Epsilon' )
198  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
199 *
200 * Check the imaginary parts of the diagonal elements and return with
201 * an error code if any are nonzero.
202 *
203  DO j = 1, n
204  IF( dimag( afac( j, j ) ).NE.zero ) THEN
205  resid = one / eps
206  RETURN
207  END IF
208  END DO
209 *
210 * 2) Initialize C to the identity matrix.
211 *
212  CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
213 *
214 * 3) Call ZLAVHE_ROOK to form the product D * U' (or D * L' ).
215 *
216  CALL zlavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
217  \$ ldafac, ipiv, c, ldc, info )
218 *
219 * 4) Call ZLAVHE_RK again to multiply by U (or L ).
220 *
221  CALL zlavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
222  \$ ldafac, ipiv, c, ldc, info )
223 *
224 * 5) Compute the difference C - A .
225 *
226  IF( lsame( uplo, 'U' ) ) THEN
227  DO j = 1, n
228  DO i = 1, j - 1
229  c( i, j ) = c( i, j ) - a( i, j )
230  END DO
231  c( j, j ) = c( j, j ) - dble( a( j, j ) )
232  END DO
233  ELSE
234  DO j = 1, n
235  c( j, j ) = c( j, j ) - dble( a( j, j ) )
236  DO i = j + 1, n
237  c( i, j ) = c( i, j ) - a( i, j )
238  END DO
239  END DO
240  END IF
241 *
242 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
243 *
244  resid = zlanhe( '1', uplo, n, c, ldc, rwork )
245 *
246  IF( anorm.LE.zero ) THEN
247  IF( resid.NE.zero )
248  \$ resid = one / eps
249  ELSE
250  resid = ( ( resid/dble( n ) )/anorm ) / eps
251  END IF
252 *
253 * b) Convert to factor of L (or U)
254 *
255  CALL zsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
256 *
257  RETURN
258 *
259 * End of ZHET01_3
260 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVHE_ROOK
Definition: zlavhe_rook.f:153
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhe.f:124
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zsyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
ZSYCONVF_ROOK
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