 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ csyt03()

 subroutine csyt03 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID )

CSYT03

Purpose:
``` CSYT03 computes the residual for a complex symmetric matrix times
its inverse:
norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
where EPS is the machine epsilon.```
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 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,out] AINV ``` AINV is COMPLEX array, dimension (LDAINV,N) On entry, the inverse of the matrix A, stored as a symmetric matrix in the same format as A. In this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed; i.e., if the upper triangular part of AINV is stored, the lower triangular part will be used as work space.``` [in] LDAINV ``` LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).``` [out] WORK ` WORK is COMPLEX array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of A, computed as RCOND = 1/ (norm(A) * norm(AINV)).``` [out] RESID ``` RESID is REAL norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 124 of file csyt03.f.

126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  CHARACTER UPLO
133  INTEGER LDA, LDAINV, LDWORK, N
134  REAL RCOND, RESID
135 * ..
136 * .. Array Arguments ..
137  REAL RWORK( * )
138  COMPLEX A( LDA, * ), AINV( LDAINV, * ),
139  \$ WORK( LDWORK, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 *
145 * .. Parameters ..
146  REAL ZERO, ONE
147  parameter( zero = 0.0e+0, one = 1.0e+0 )
148  COMPLEX CZERO, CONE
149  parameter( czero = ( 0.0e+0, 0.0e+0 ),
150  \$ cone = ( 1.0e+0, 0.0e+0 ) )
151 * ..
152 * .. Local Scalars ..
153  INTEGER I, J
154  REAL AINVNM, ANORM, EPS
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  REAL CLANGE, CLANSY, SLAMCH
159  EXTERNAL lsame, clange, clansy, slamch
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL csymm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC real
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0
170 *
171  IF( n.LE.0 ) THEN
172  rcond = one
173  resid = zero
174  RETURN
175  END IF
176 *
177 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
178 *
179  eps = slamch( 'Epsilon' )
180  anorm = clansy( '1', uplo, n, a, lda, rwork )
181  ainvnm = clansy( '1', uplo, n, ainv, ldainv, rwork )
182  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
183  rcond = zero
184  resid = one / eps
185  RETURN
186  END IF
187  rcond = ( one/anorm ) / ainvnm
188 *
189 * Expand AINV into a full matrix and call CSYMM to multiply
190 * AINV on the left by A (store the result in WORK).
191 *
192  IF( lsame( uplo, 'U' ) ) THEN
193  DO 20 j = 1, n
194  DO 10 i = 1, j - 1
195  ainv( j, i ) = ainv( i, j )
196  10 CONTINUE
197  20 CONTINUE
198  ELSE
199  DO 40 j = 1, n
200  DO 30 i = j + 1, n
201  ainv( j, i ) = ainv( i, j )
202  30 CONTINUE
203  40 CONTINUE
204  END IF
205  CALL csymm( 'Left', uplo, n, n, -cone, a, lda, ainv, ldainv,
206  \$ czero, work, ldwork )
207 *
208 * Add the identity matrix to WORK .
209 *
210  DO 50 i = 1, n
211  work( i, i ) = work( i, i ) + cone
212  50 CONTINUE
213 *
214 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
215 *
216  resid = clange( '1', n, n, work, ldwork, rwork )
217 *
218  resid = ( ( resid*rcond )/eps ) / real( n )
219 *
220  RETURN
221 *
222 * End of CSYT03
223 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine csymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CSYMM
Definition: csymm.f:189
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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