LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ ssyt01_3()

 subroutine ssyt01_3 ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) E, integer, dimension( * ) IPIV, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID )

SSYT01_3

Purpose:
``` SSYT01_3 reconstructs a symmetric indefinite matrix A from its
block L*D*L' or U*D*U' factorization computed by SSYTRF_RK
(or SSYTRF_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 SSYTRF_RK and SSYTRF_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 SSYTRF_RK (or SSYTRF_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 ssyt01_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  REAL RESID
149 * ..
150 * .. Array Arguments ..
151  INTEGER IPIV( * )
152  REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
153  \$ E( * ), RWORK( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ZERO, ONE
160  parameter( zero = 0.0e+0, one = 1.0e+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER I, INFO, J
164  REAL ANORM, EPS
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  REAL SLAMCH, SLANSY
169  EXTERNAL lsame, slamch, slansy
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL slaset, slavsy_rook, ssyconvf_rook
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC real
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 ssyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
189 *
190 * 1) Determine EPS and the norm of A.
191 *
192  eps = slamch( 'Epsilon' )
193  anorm = slansy( '1', uplo, n, a, lda, rwork )
194 *
195 * 2) Initialize C to the identity matrix.
196 *
197  CALL slaset( 'Full', n, n, zero, one, c, ldc )
198 *
199 * 3) Call SLAVSY_ROOK to form the product D * U' (or D * L' ).
200 *
201  CALL slavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
202  \$ ldafac, ipiv, c, ldc, info )
203 *
204 * 4) Call SLAVSY_ROOK again to multiply by U (or L ).
205 *
206  CALL slavsy_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 = slansy( '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 / real( n ) ) / anorm ) / eps
234  END IF
235
236 *
237 * b) Convert to factor of L (or U)
238 *
239  CALL ssyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
240 *
241  RETURN
242 *
243 * End of SSYT01_3
244 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine slavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SLAVSY_ROOK
Definition: slavsy_rook.f:157
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine ssyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
SSYCONVF_ROOK
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