 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dsyt01_aa()

 subroutine dsyt01_aa ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

DSYT01

Purpose:
``` DSYT01 reconstructs a symmetric 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 symmetric 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 DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)``` [in] AFAC ``` AFAC is DOUBLE PRECISION 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 DSYTRF.``` [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 DSYTRF.``` [out] C ` C is DOUBLE PRECISION 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 122 of file dsyt01_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 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
137  \$ RWORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER I, J
148  DOUBLE PRECISION ANORM, EPS
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  DOUBLE PRECISION DLAMCH, DLANSY
153  EXTERNAL lsame, dlamch, dlansy
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL dlaset, dlavsy
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC dble
160 * ..
161 * .. Executable Statements ..
162 *
163 * Quick exit if N = 0.
164 *
165  IF( n.LE.0 ) THEN
166  resid = zero
167  RETURN
168  END IF
169 *
170 * Determine EPS and the norm of A.
171 *
172  eps = dlamch( 'Epsilon' )
173  anorm = dlansy( '1', uplo, n, a, lda, rwork )
174 *
175 * Initialize C to the tridiagonal matrix T.
176 *
177  CALL dlaset( 'Full', n, n, zero, zero, c, ldc )
178  CALL dlacpy( 'F', 1, n, afac( 1, 1 ), ldafac+1, c( 1, 1 ), ldc+1 )
179  IF( n.GT.1 ) THEN
180  IF( lsame( uplo, 'U' ) ) THEN
181  CALL dlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 1, 2 ),
182  \$ ldc+1 )
183  CALL dlacpy( 'F', 1, n-1, afac( 1, 2 ), ldafac+1, c( 2, 1 ),
184  \$ ldc+1 )
185  ELSE
186  CALL dlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 1, 2 ),
187  \$ ldc+1 )
188  CALL dlacpy( 'F', 1, n-1, afac( 2, 1 ), ldafac+1, c( 2, 1 ),
189  \$ ldc+1 )
190  ENDIF
191 *
192 * Call DTRMM to form the product U' * D (or L * D ).
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195  CALL dtrmm( 'Left', uplo, 'Transpose', 'Unit', n-1, n,
196  \$ one, afac( 1, 2 ), ldafac, c( 2, 1 ), ldc )
197  ELSE
198  CALL dtrmm( 'Left', uplo, 'No transpose', 'Unit', n-1, n,
199  \$ one, afac( 2, 1 ), ldafac, c( 2, 1 ), ldc )
200  END IF
201 *
202 * Call DTRMM again to multiply by U (or L ).
203 *
204  IF( lsame( uplo, 'U' ) ) THEN
205  CALL dtrmm( 'Right', uplo, 'No transpose', 'Unit', n, n-1,
206  \$ one, afac( 1, 2 ), ldafac, c( 1, 2 ), ldc )
207  ELSE
208  CALL dtrmm( 'Right', uplo, 'Transpose', 'Unit', n, n-1,
209  \$ one, afac( 2, 1 ), ldafac, c( 1, 2 ), ldc )
210  END IF
211  ENDIF
212 *
213 * Apply symmetric pivots
214 *
215  DO j = n, 1, -1
216  i = ipiv( j )
217  IF( i.NE.j )
218  \$ CALL dswap( n, c( j, 1 ), ldc, c( i, 1 ), ldc )
219  END DO
220  DO j = n, 1, -1
221  i = ipiv( j )
222  IF( i.NE.j )
223  \$ CALL dswap( n, c( 1, j ), 1, c( 1, i ), 1 )
224  END DO
225 *
226 *
227 * Compute the difference C - A .
228 *
229  IF( lsame( uplo, 'U' ) ) THEN
230  DO j = 1, n
231  DO i = 1, j
232  c( i, j ) = c( i, j ) - a( i, j )
233  END DO
234  END DO
235  ELSE
236  DO j = 1, n
237  DO i = j, n
238  c( i, j ) = c( i, j ) - a( i, j )
239  END DO
240  END DO
241  END IF
242 *
243 * Compute norm( C - A ) / ( N * norm(A) * EPS )
244 *
245  resid = dlansy( '1', uplo, n, c, ldc, rwork )
246 *
247  IF( anorm.LE.zero ) THEN
248  IF( resid.NE.zero )
249  \$ resid = one / eps
250  ELSE
251  resid = ( ( resid / dble( n ) ) / anorm ) / eps
252  END IF
253 *
254  RETURN
255 *
256 * End of DSYT01_AA
257 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
Definition: dlavsy.f:155
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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