 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dsyt01_3()

 subroutine dsyt01_3 ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, double precision, dimension( * ) E, integer, dimension( * ) IPIV, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

DSYT01_3

Purpose:
``` DSYT01_3 reconstructs a symmetric indefinite matrix A from its
block L*D*L' or U*D*U' factorization computed by DSYTRF_RK
(or DSYTRF_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 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) Diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_BK: a) ONLY diagonal elements of the symmetric 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 DOUBLE PRECISION array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric 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 DSYTRF_RK (or DSYTRF_BK).``` [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 138 of file dsyt01_3.f.

140*
141* -- LAPACK test routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 CHARACTER UPLO
147 INTEGER LDA, LDAFAC, LDC, N
148 DOUBLE PRECISION RESID
149* ..
150* .. Array Arguments ..
151 INTEGER IPIV( * )
152 DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
153 \$ E( * ), RWORK( * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 DOUBLE PRECISION ZERO, ONE
160 parameter( zero = 0.0d+0, one = 1.0d+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER I, INFO, J
164 DOUBLE PRECISION ANORM, EPS
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 DOUBLE PRECISION DLAMCH, DLANSY
169 EXTERNAL lsame, dlamch, dlansy
170* ..
171* .. External Subroutines ..
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC dble
176* ..
177* .. Executable Statements ..
178*
179* Quick exit if N = 0.
180*
181 IF( n.LE.0 ) THEN
182 resid = zero
183 RETURN
184 END IF
185*
186* a) Revert to multiplyers of L
187*
188 CALL dsyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
189*
190* 1) Determine EPS and the norm of A.
191*
192 eps = dlamch( 'Epsilon' )
193 anorm = dlansy( '1', uplo, n, a, lda, rwork )
194*
195* 2) Initialize C to the identity matrix.
196*
197 CALL dlaset( 'Full', n, n, zero, one, c, ldc )
198*
199* 3) Call DLAVSY_ROOK to form the product D * U' (or D * L' ).
200*
201 CALL dlavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
202 \$ ldafac, ipiv, c, ldc, info )
203*
204* 4) Call DLAVSY_ROOK again to multiply by U (or L ).
205*
206 CALL dlavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
207 \$ ldafac, ipiv, c, ldc, info )
208*
209* 5) Compute the difference C - A.
210*
211 IF( lsame( uplo, 'U' ) ) THEN
212 DO j = 1, n
213 DO i = 1, j
214 c( i, j ) = c( i, j ) - a( i, j )
215 END DO
216 END DO
217 ELSE
218 DO j = 1, n
219 DO i = j, n
220 c( i, j ) = c( i, j ) - a( i, j )
221 END DO
222 END DO
223 END IF
224*
225* 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
226*
227 resid = dlansy( '1', uplo, n, c, ldc, rwork )
228*
229 IF( anorm.LE.zero ) THEN
230 IF( resid.NE.zero )
231 \$ resid = one / eps
232 ELSE
233 resid = ( ( resid / dble( n ) ) / anorm ) / eps
234 END IF
235
236*
237* b) Convert to factor of L (or U)
238*
239 CALL dsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
240*
241 RETURN
242*
243* End of DSYT01_3
244*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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 dlavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY_ROOK
Definition: dlavsy_rook.f:157
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
subroutine dsyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
DSYCONVF_ROOK
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