 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zsyt01_aa()

 subroutine zsyt01_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 )

ZSYT01

Purpose:
``` ZSYT01 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 ZSYTRF.``` [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 ZSYTRF.``` [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 zsyt01_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  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
137  DOUBLE PRECISION RWORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145  COMPLEX*16 CZERO, CONE
146  parameter( czero = 0.0e+0, cone = 1.0e+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER I, J
150  DOUBLE PRECISION ANORM, EPS
151 * ..
152 * .. External Functions ..
153  LOGICAL LSAME
154  DOUBLE PRECISION DLAMCH, ZLANSY
155  EXTERNAL lsame, dlamch, zlansy
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL zlaset, zlavsy
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC dble
162 * ..
163 * .. Executable Statements ..
164 *
165 * Quick exit if N = 0.
166 *
167  IF( n.LE.0 ) THEN
168  resid = zero
169  RETURN
170  END IF
171 *
172 * Determine EPS and the norm of A.
173 *
174  eps = dlamch( 'Epsilon' )
175  anorm = zlansy( '1', uplo, n, a, lda, rwork )
176 *
177 * Initialize C to the tridiagonal matrix T.
178 *
179  CALL zlaset( 'Full', n, n, czero, czero, c, ldc )
180  CALL zlacpy( 'F', 1, n, afac( 1, 1 ), ldafac+1, c( 1, 1 ), ldc+1 )
181  IF( n.GT.1 ) THEN
182  IF( lsame( uplo, 'U' ) ) THEN
183  CALL zlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 1, 2 ),
184  \$ ldc+1 )
185  CALL zlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 2, 1 ),
186  \$ ldc+1 )
187  ELSE
188  CALL zlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 1, 2 ),
189  \$ ldc+1 )
190  CALL zlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 2, 1 ),
191  \$ ldc+1 )
192  ENDIF
193 *
194 * Call ZTRMM to form the product U' * D (or L * D ).
195 *
196  IF( lsame( uplo, 'U' ) ) THEN
197  CALL ztrmm( 'Left', uplo, 'Transpose', 'Unit', n-1, n,
198  \$ cone, afac( 1, 2 ), ldafac, c( 2, 1 ), ldc )
199  ELSE
200  CALL ztrmm( 'Left', uplo, 'No transpose', 'Unit', n-1, n,
201  \$ cone, afac( 2, 1 ), ldafac, c( 2, 1 ), ldc )
202  END IF
203 *
204 * Call ZTRMM again to multiply by U (or L ).
205 *
206  IF( lsame( uplo, 'U' ) ) THEN
207  CALL ztrmm( 'Right', uplo, 'No transpose', 'Unit', n, n-1,
208  \$ cone, afac( 1, 2 ), ldafac, c( 1, 2 ), ldc )
209  ELSE
210  CALL ztrmm( 'Right', uplo, 'Transpose', 'Unit', n, n-1,
211  \$ cone, afac( 2, 1 ), ldafac, c( 1, 2 ), ldc )
212  END IF
213  ENDIF
214 *
215 * Apply symmetric pivots
216 *
217  DO j = n, 1, -1
218  i = ipiv( j )
219  IF( i.NE.j )
220  \$ CALL zswap( n, c( j, 1 ), ldc, c( i, 1 ), ldc )
221  END DO
222  DO j = n, 1, -1
223  i = ipiv( j )
224  IF( i.NE.j )
225  \$ CALL zswap( n, c( 1, j ), 1, c( 1, i ), 1 )
226  END DO
227 *
228 *
229 * Compute the difference C - A .
230 *
231  IF( lsame( uplo, 'U' ) ) THEN
232  DO j = 1, n
233  DO i = 1, j
234  c( i, j ) = c( i, j ) - a( i, j )
235  END DO
236  END DO
237  ELSE
238  DO j = 1, n
239  DO i = j, n
240  c( i, j ) = c( i, j ) - a( i, j )
241  END DO
242  END DO
243  END IF
244 *
245 * Compute norm( C - A ) / ( N * norm(A) * EPS )
246 *
247  resid = zlansy( '1', uplo, n, c, ldc, rwork )
248 *
249  IF( anorm.LE.zero ) THEN
250  IF( resid.NE.zero )
251  \$ resid = one / eps
252  ELSE
253  resid = ( ( resid / dble( n ) ) / anorm ) / eps
254  END IF
255 *
256  RETURN
257 *
258 * End of ZSYT01_AA
259 *
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 zlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVSY
Definition: zlavsy.f:153
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
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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