LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrt01()

 subroutine ztrt01 ( character UPLO, character DIAG, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldainv, * ) AINV, integer LDAINV, double precision RCOND, double precision, dimension( * ) RWORK, double precision RESID )

ZTRT01

Purpose:
``` ZTRT01 computes the residual for a triangular matrix A times its
inverse:
RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] AINV ``` AINV is COMPLEX*16 array, dimension (LDAINV,N) On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.``` [in] LDAINV ``` LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).``` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 123 of file ztrt01.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 DIAG, UPLO
132 INTEGER LDA, LDAINV, N
133 DOUBLE PRECISION RCOND, RESID
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION RWORK( * )
137 COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 DOUBLE PRECISION AINVNM, ANORM, EPS
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 DOUBLE PRECISION DLAMCH, ZLANTR
153 EXTERNAL lsame, dlamch, zlantr
154* ..
155* .. External Subroutines ..
156 EXTERNAL ztrmv
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC dble
160* ..
161* .. Executable Statements ..
162*
163* Quick exit if N = 0
164*
165 IF( n.LE.0 ) THEN
166 rcond = one
167 resid = zero
168 RETURN
169 END IF
170*
171* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
172*
173 eps = dlamch( 'Epsilon' )
174 anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
175 ainvnm = zlantr( '1', uplo, diag, n, n, ainv, ldainv, rwork )
176 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
177 rcond = zero
178 resid = one / eps
179 RETURN
180 END IF
181 rcond = ( one / anorm ) / ainvnm
182*
183* Set the diagonal of AINV to 1 if AINV has unit diagonal.
184*
185 IF( lsame( diag, 'U' ) ) THEN
186 DO 10 j = 1, n
187 ainv( j, j ) = one
188 10 CONTINUE
189 END IF
190*
191* Compute A * AINV, overwriting AINV.
192*
193 IF( lsame( uplo, 'U' ) ) THEN
194 DO 20 j = 1, n
195 CALL ztrmv( 'Upper', 'No transpose', diag, j, a, lda,
196 \$ ainv( 1, j ), 1 )
197 20 CONTINUE
198 ELSE
199 DO 30 j = 1, n
200 CALL ztrmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
201 \$ lda, ainv( j, j ), 1 )
202 30 CONTINUE
203 END IF
204*
205* Subtract 1 from each diagonal element to form A*AINV - I.
206*
207 DO 40 j = 1, n
208 ainv( j, j ) = ainv( j, j ) - one
209 40 CONTINUE
210*
211* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
212*
213 resid = zlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, rwork )
214*
215 resid = ( ( resid*rcond ) / dble( n ) ) / eps
216*
217 RETURN
218*
219* End of ZTRT01
220*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
double precision function zlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlantr.f:142
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