 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhet01_aa()

 subroutine zhet01_aa ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex*16, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

ZHET01_AA

Purpose:
``` ZHET01_AA 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 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) 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 ZHETRF.``` [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 ZHETRF.``` [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 COMPLEX*16 array, dimension (N)` [out] RESID ``` RESID is COMPLEX*16 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 122 of file zhet01_aa.f.

124 *
125 * -- LAPACK test routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER UPLO
131  INTEGER LDA, LDAFAC, LDC, N
132  DOUBLE PRECISION RESID
133 * ..
134 * .. Array Arguments ..
135  INTEGER IPIV( * )
136  DOUBLE PRECISION RWORK( * )
137  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  COMPLEX*16 CZERO, CONE
144  parameter( czero = ( 0.0d+0, 0.0d+0 ),
145  \$ cone = ( 1.0d+0, 0.0d+0 ) )
146  DOUBLE PRECISION ZERO, ONE
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148 * ..
149 * .. Local Scalars ..
150  INTEGER I, J
151  DOUBLE PRECISION ANORM, EPS
152 * ..
153 * .. External Functions ..
154  LOGICAL LSAME
155  DOUBLE PRECISION DLAMCH, ZLANHE
156  EXTERNAL lsame, dlamch, zlanhe
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL zlaset, zlavhe
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC dble
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick exit if N = 0.
167 *
168  IF( n.LE.0 ) THEN
169  resid = zero
170  RETURN
171  END IF
172 *
173 * Determine EPS and the norm of A.
174 *
175  eps = dlamch( 'Epsilon' )
176  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
177 *
178 * Initialize C to the tridiagonal matrix T.
179 *
180  CALL zlaset( 'Full', n, n, czero, czero, c, ldc )
181  CALL zlacpy( 'F', 1, n, afac( 1, 1 ), ldafac+1, c( 1, 1 ), ldc+1 )
182  IF( n.GT.1 ) THEN
183  IF( lsame( uplo, 'U' ) ) THEN
184  CALL zlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 1, 2 ),
185  \$ ldc+1 )
186  CALL zlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 2, 1 ),
187  \$ ldc+1 )
188  CALL zlacgv( n-1, c( 2, 1 ), ldc+1 )
189  ELSE
190  CALL zlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 1, 2 ),
191  \$ ldc+1 )
192  CALL zlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 2, 1 ),
193  \$ ldc+1 )
194  CALL zlacgv( n-1, c( 1, 2 ), ldc+1 )
195  ENDIF
196 *
197 * Call ZTRMM to form the product U' * D (or L * D ).
198 *
199  IF( lsame( uplo, 'U' ) ) THEN
200  CALL ztrmm( 'Left', uplo, 'Conjugate transpose', 'Unit',
201  \$ n-1, n, cone, afac( 1, 2 ), ldafac, c( 2, 1 ),
202  \$ ldc )
203  ELSE
204  CALL ztrmm( 'Left', uplo, 'No transpose', 'Unit', n-1, n,
205  \$ cone, afac( 2, 1 ), ldafac, c( 2, 1 ), ldc )
206  END IF
207 *
208 * Call ZTRMM again to multiply by U (or L ).
209 *
210  IF( lsame( uplo, 'U' ) ) THEN
211  CALL ztrmm( 'Right', uplo, 'No transpose', 'Unit', n, n-1,
212  \$ cone, afac( 1, 2 ), ldafac, c( 1, 2 ), ldc )
213  ELSE
214  CALL ztrmm( 'Right', uplo, 'Conjugate transpose', 'Unit', n,
215  \$ n-1, cone, afac( 2, 1 ), ldafac, c( 1, 2 ),
216  \$ ldc )
217  END IF
218 *
219 * Apply hermitian pivots
220 *
221  DO j = n, 1, -1
222  i = ipiv( j )
223  IF( i.NE.j )
224  \$ CALL zswap( n, c( j, 1 ), ldc, c( i, 1 ), ldc )
225  END DO
226  DO j = n, 1, -1
227  i = ipiv( j )
228  IF( i.NE.j )
229  \$ CALL zswap( n, c( 1, j ), 1, c( 1, i ), 1 )
230  END DO
231  ENDIF
232 *
233 *
234 * Compute the difference C - A .
235 *
236  IF( lsame( uplo, 'U' ) ) THEN
237  DO j = 1, n
238  DO i = 1, j
239  c( i, j ) = c( i, j ) - a( i, j )
240  END DO
241  END DO
242  ELSE
243  DO j = 1, n
244  DO i = j, n
245  c( i, j ) = c( i, j ) - a( i, j )
246  END DO
247  END DO
248  END IF
249 *
250 * Compute norm( C - A ) / ( N * norm(A) * EPS )
251 *
252  resid = zlanhe( '1', uplo, n, c, ldc, rwork )
253 *
254  IF( anorm.LE.zero ) THEN
255  IF( resid.NE.zero )
256  \$ resid = one / eps
257  ELSE
258  resid = ( ( resid / dble( n ) ) / anorm ) / eps
259  END IF
260 *
261  RETURN
262 *
263 * End of ZHET01_AA
264 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:177
subroutine zlavhe(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVHE
Definition: zlavhe.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 zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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 zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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