 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztpt01()

 subroutine ztpt01 ( character UPLO, character DIAG, integer N, complex*16, dimension( * ) AP, complex*16, dimension( * ) AINVP, double precision RCOND, double precision, dimension( * ) RWORK, double precision RESID )

ZTPT01

Purpose:
``` ZTPT01 computes the residual for a triangular matrix A times its
inverse when A is stored in packed format:
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] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) The original upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.``` [in] AINVP ``` AINVP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the (triangular) inverse of the matrix A, packed columnwise in a linear array as in AP. On exit, the contents of AINVP are destroyed.``` [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 108 of file ztpt01.f.

109*
110* -- LAPACK test routine --
111* -- LAPACK is a software package provided by Univ. of Tennessee, --
112* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*
114* .. Scalar Arguments ..
115 CHARACTER DIAG, UPLO
116 INTEGER N
117 DOUBLE PRECISION RCOND, RESID
118* ..
119* .. Array Arguments ..
120 DOUBLE PRECISION RWORK( * )
121 COMPLEX*16 AINVP( * ), AP( * )
122* ..
123*
124* =====================================================================
125*
126* .. Parameters ..
127 DOUBLE PRECISION ZERO, ONE
128 parameter( zero = 0.0d+0, one = 1.0d+0 )
129* ..
130* .. Local Scalars ..
131 LOGICAL UNITD
132 INTEGER J, JC
133 DOUBLE PRECISION AINVNM, ANORM, EPS
134* ..
135* .. External Functions ..
136 LOGICAL LSAME
137 DOUBLE PRECISION DLAMCH, ZLANTP
138 EXTERNAL lsame, dlamch, zlantp
139* ..
140* .. External Subroutines ..
141 EXTERNAL ztpmv
142* ..
143* .. Intrinsic Functions ..
144 INTRINSIC dble
145* ..
146* .. Executable Statements ..
147*
148* Quick exit if N = 0.
149*
150 IF( n.LE.0 ) THEN
151 rcond = one
152 resid = zero
153 RETURN
154 END IF
155*
156* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157*
158 eps = dlamch( 'Epsilon' )
159 anorm = zlantp( '1', uplo, diag, n, ap, rwork )
160 ainvnm = zlantp( '1', uplo, diag, n, ainvp, rwork )
161 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
162 rcond = zero
163 resid = one / eps
164 RETURN
165 END IF
166 rcond = ( one / anorm ) / ainvnm
167*
168* Compute A * AINV, overwriting AINV.
169*
170 unitd = lsame( diag, 'U' )
171 IF( lsame( uplo, 'U' ) ) THEN
172 jc = 1
173 DO 10 j = 1, n
174 IF( unitd )
175 \$ ainvp( jc+j-1 ) = one
176*
177* Form the j-th column of A*AINV.
178*
179 CALL ztpmv( 'Upper', 'No transpose', diag, j, ap,
180 \$ ainvp( jc ), 1 )
181*
182* Subtract 1 from the diagonal to form A*AINV - I.
183*
184 ainvp( jc+j-1 ) = ainvp( jc+j-1 ) - one
185 jc = jc + j
186 10 CONTINUE
187 ELSE
188 jc = 1
189 DO 20 j = 1, n
190 IF( unitd )
191 \$ ainvp( jc ) = one
192*
193* Form the j-th column of A*AINV.
194*
195 CALL ztpmv( 'Lower', 'No transpose', diag, n-j+1, ap( jc ),
196 \$ ainvp( jc ), 1 )
197*
198* Subtract 1 from the diagonal to form A*AINV - I.
199*
200 ainvp( jc ) = ainvp( jc ) - one
201 jc = jc + n - j + 1
202 20 CONTINUE
203 END IF
204*
205* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
206*
207 resid = zlantp( '1', uplo, 'Non-unit', n, ainvp, rwork )
208*
209 resid = ( ( resid*rcond ) / dble( n ) ) / eps
210*
211 RETURN
212*
213* End of ZTPT01
214*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
double precision function zlantp(NORM, UPLO, DIAG, N, AP, WORK)
ZLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlantp.f:125
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