 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zsyt01_rook()

 subroutine zsyt01_rook ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex*16, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

ZSYT01_ROOK

Purpose:
``` ZSYT01_ROOK reconstructs a complex 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, EPS is the machine epsilon,
L' is the transpose of L, and U' is the transpose of U.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the complex 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 COMPLEX*16 array, dimension (LDA,N) The original complex symmetric matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)``` [in] AFAC ``` AFAC is COMPLEX*16 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 ZSYTRF_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 ZSYTRF_ROOK.``` [out] C ` C is COMPLEX*16 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 123 of file zsyt01_rook.f.

125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER UPLO
132 INTEGER LDA, LDAFAC, LDC, N
133 DOUBLE PRECISION RESID
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * )
137 DOUBLE PRECISION RWORK( * )
138 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 DOUBLE PRECISION ZERO, ONE
145 parameter( zero = 0.0d+0, one = 1.0d+0 )
146 COMPLEX*16 CZERO, CONE
147 parameter( czero = ( 0.0d+0, 0.0d+0 ),
148 \$ cone = ( 1.0d+0, 0.0d+0 ) )
149* ..
150* .. Local Scalars ..
151 INTEGER I, INFO, J
152 DOUBLE PRECISION ANORM, EPS
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 DOUBLE PRECISION DLAMCH, ZLANSY
157 EXTERNAL lsame, dlamch, zlansy
158* ..
159* .. External Subroutines ..
160 EXTERNAL zlaset, zlavsy_rook
161* ..
162* .. Intrinsic Functions ..
163 INTRINSIC dble
164* ..
165* .. Executable Statements ..
166*
167* Quick exit if N = 0.
168*
169 IF( n.LE.0 ) THEN
170 resid = zero
171 RETURN
172 END IF
173*
174* Determine EPS and the norm of A.
175*
176 eps = dlamch( 'Epsilon' )
177 anorm = zlansy( '1', uplo, n, a, lda, rwork )
178*
179* Initialize C to the identity matrix.
180*
181 CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
182*
183* Call ZLAVSY_ROOK to form the product D * U' (or D * L' ).
184*
185 CALL zlavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
186 \$ ldafac, ipiv, c, ldc, info )
187*
188* Call ZLAVSY_ROOK again to multiply by U (or L ).
189*
190 CALL zlavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
191 \$ ldafac, ipiv, c, ldc, info )
192*
193* Compute the difference C - A .
194*
195 IF( lsame( uplo, 'U' ) ) THEN
196 DO 20 j = 1, n
197 DO 10 i = 1, j
198 c( i, j ) = c( i, j ) - a( i, j )
199 10 CONTINUE
200 20 CONTINUE
201 ELSE
202 DO 40 j = 1, n
203 DO 30 i = j, n
204 c( i, j ) = c( i, j ) - a( i, j )
205 30 CONTINUE
206 40 CONTINUE
207 END IF
208*
209* Compute norm( C - A ) / ( N * norm(A) * EPS )
210*
211 resid = zlansy( '1', uplo, n, c, ldc, rwork )
212*
213 IF( anorm.LE.zero ) THEN
214 IF( resid.NE.zero )
215 \$ resid = one / eps
216 ELSE
217 resid = ( ( resid / dble( n ) ) / anorm ) / eps
218 END IF
219*
220 RETURN
221*
222* End of ZSYT01_ROOK
223*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlavsy_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVSY_ROOK
Definition: zlavsy_rook.f:155
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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