LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssyt01()

 subroutine ssyt01 ( character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldafac, * ) afac, integer ldafac, integer, dimension( * ) ipiv, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) rwork, real resid )

SSYT01

Purpose:
``` SSYT01 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 REAL 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 REAL 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 SSYTRF.``` [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 SSYTRF.``` [out] C ` C is REAL array, dimension (LDC,N)` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL 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 ssyt01.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 REAL RESID
133* ..
134* .. Array Arguments ..
135 INTEGER IPIV( * )
136 REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
137 \$ RWORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER I, INFO, J
148 REAL ANORM, EPS
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 REAL SLAMCH, SLANSY
153 EXTERNAL lsame, slamch, slansy
154* ..
155* .. External Subroutines ..
156 EXTERNAL slaset, slavsy
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC real
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 = slamch( 'Epsilon' )
173 anorm = slansy( '1', uplo, n, a, lda, rwork )
174*
175* Initialize C to the identity matrix.
176*
177 CALL slaset( 'Full', n, n, zero, one, c, ldc )
178*
179* Call SLAVSY to form the product D * U' (or D * L' ).
180*
181 CALL slavsy( uplo, 'Transpose', 'Non-unit', n, n, afac, ldafac,
182 \$ ipiv, c, ldc, info )
183*
184* Call SLAVSY again to multiply by U (or L ).
185*
186 CALL slavsy( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
187 \$ ipiv, c, ldc, info )
188*
189* Compute the difference C - A .
190*
191 IF( lsame( uplo, 'U' ) ) THEN
192 DO 20 j = 1, n
193 DO 10 i = 1, j
194 c( i, j ) = c( i, j ) - a( i, j )
195 10 CONTINUE
196 20 CONTINUE
197 ELSE
198 DO 40 j = 1, n
199 DO 30 i = j, n
200 c( i, j ) = c( i, j ) - a( i, j )
201 30 CONTINUE
202 40 CONTINUE
203 END IF
204*
205* Compute norm( C - A ) / ( N * norm(A) * EPS )
206*
207 resid = slansy( '1', uplo, n, c, ldc, rwork )
208*
209 IF( anorm.LE.zero ) THEN
210 IF( resid.NE.zero )
211 \$ resid = one / eps
212 ELSE
213 resid = ( ( resid / real( n ) ) / anorm ) / eps
214 END IF
215*
216 RETURN
217*
218* End of SSYT01
219*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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 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:48
subroutine slavsy(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
SLAVSY
Definition slavsy.f:155
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