 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 *
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(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SLAVSY
Definition: slavsy.f:155
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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