LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zsyt01()

subroutine zsyt01 ( 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

Purpose:
 ZSYT01 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.
[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.
[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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file zsyt01.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
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 to form the product D * U' (or D * L' ).
184*
185 CALL zlavsy( uplo, 'Transpose', 'Non-unit', n, n, afac, ldafac,
186 $ ipiv, c, ldc, info )
187*
188* Call ZLAVSY again to multiply by U (or L ).
189*
190 CALL zlavsy( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
191 $ 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
223*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine zlavsy(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
ZLAVSY
Definition zlavsy.f:153
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