LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine ssyt01_rook ( 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_ROOK

Purpose:
``` SSYT01_ROOK 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_ROOK.``` [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_ROOK.``` [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 )```
Date
November 2013

Definition at line 126 of file ssyt01_rook.f.

126 *
127 * -- LAPACK test routine (version 3.5.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * November 2013
131 *
132 * .. Scalar Arguments ..
133  CHARACTER uplo
134  INTEGER lda, ldafac, ldc, n
135  REAL resid
136 * ..
137 * .. Array Arguments ..
138  INTEGER ipiv( * )
139  REAL a( lda, * ), afac( ldafac, * ), c( ldc, * ),
140  \$ rwork( * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL zero, one
147  parameter ( zero = 0.0e+0, one = 1.0e+0 )
148 * ..
149 * .. Local Scalars ..
150  INTEGER i, info, j
151  REAL anorm, eps
152 * ..
153 * .. External Functions ..
154  LOGICAL lsame
155  REAL slamch, slansy
156  EXTERNAL lsame, slamch, slansy
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL slaset, slavsy_rook
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC real
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick exit if N = 0.
167 *
168  IF( n.LE.0 ) THEN
169  resid = zero
170  RETURN
171  END IF
172 *
173 * Determine EPS and the norm of A.
174 *
175  eps = slamch( 'Epsilon' )
176  anorm = slansy( '1', uplo, n, a, lda, rwork )
177 *
178 * Initialize C to the identity matrix.
179 *
180  CALL slaset( 'Full', n, n, zero, one, c, ldc )
181 *
182 * Call SLAVSY_ROOK to form the product D * U' (or D * L' ).
183 *
184  CALL slavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
185  \$ ldafac, ipiv, c, ldc, info )
186 *
187 * Call SLAVSY_ROOK again to multiply by U (or L ).
188 *
189  CALL slavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
190  \$ ldafac, ipiv, c, ldc, info )
191 *
192 * Compute the difference C - A .
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 20 j = 1, n
196  DO 10 i = 1, j
197  c( i, j ) = c( i, j ) - a( i, j )
198  10 CONTINUE
199  20 CONTINUE
200  ELSE
201  DO 40 j = 1, n
202  DO 30 i = j, n
203  c( i, j ) = c( i, j ) - a( i, j )
204  30 CONTINUE
205  40 CONTINUE
206  END IF
207 *
208 * Compute norm( C - A ) / ( N * norm(A) * EPS )
209 *
210  resid = slansy( '1', uplo, n, c, ldc, rwork )
211 *
212  IF( anorm.LE.zero ) THEN
213  IF( resid.NE.zero )
214  \$ resid = one / eps
215  ELSE
216  resid = ( ( resid / REAL( N ) ) / anorm ) / eps
217  END IF
218 *
219  RETURN
220 *
221 * End of SSYT01_ROOK
222 *
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:112
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine slavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SLAVSY_ROOK
Definition: slavsy_rook.f:159
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, or the element of largest absolute value of a real symmetric matrix.
Definition: slansy.f:124

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