 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zsyt03()

 subroutine zsyt03 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldainv, * ) AINV, integer LDAINV, complex*16, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision RCOND, double precision RESID )

ZSYT03

Purpose:
``` ZSYT03 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*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,out] AINV ``` AINV is COMPLEX*16 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*16 array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as RCOND = 1/ (norm(A) * norm(AINV)).``` [out] RESID ``` RESID is DOUBLE PRECISION norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 124 of file zsyt03.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  DOUBLE PRECISION RCOND, RESID
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION RWORK( * )
138  COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
139  \$ WORK( LDWORK, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION ZERO, ONE
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  COMPLEX*16 CZERO, CONE
149  parameter( czero = ( 0.0d+0, 0.0d+0 ),
150  \$ cone = ( 1.0d+0, 0.0d+0 ) )
151 * ..
152 * .. Local Scalars ..
153  INTEGER I, J
154  DOUBLE PRECISION AINVNM, ANORM, EPS
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
159  EXTERNAL lsame, dlamch, zlange, zlansy
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zsymm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC dble
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 = dlamch( 'Epsilon' )
180  anorm = zlansy( '1', uplo, n, a, lda, rwork )
181  ainvnm = zlansy( '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 ZSYMM 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 zsymm( '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 = zlange( '1', n, n, work, ldwork, rwork )
217 *
218  resid = ( ( resid*rcond ) / eps ) / dble( n )
219 *
220  RETURN
221 *
222 * End of ZSYT03
223 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:189
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
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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