LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dtpt01()

 subroutine dtpt01 ( character UPLO, character DIAG, integer N, double precision, dimension( * ) AP, double precision, dimension( * ) AINVP, double precision RCOND, double precision, dimension( * ) WORK, double precision RESID )

DTPT01

Purpose:
``` DTPT01 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 DOUBLE PRECISION 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,out] AINVP ``` AINVP is DOUBLE PRECISION 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] WORK ` WORK 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 107 of file dtpt01.f.

108*
109* -- LAPACK test routine --
110* -- LAPACK is a software package provided by Univ. of Tennessee, --
111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112*
113* .. Scalar Arguments ..
114 CHARACTER DIAG, UPLO
115 INTEGER N
116 DOUBLE PRECISION RCOND, RESID
117* ..
118* .. Array Arguments ..
119 DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 DOUBLE PRECISION ZERO, ONE
126 parameter( zero = 0.0d+0, one = 1.0d+0 )
127* ..
128* .. Local Scalars ..
129 LOGICAL UNITD
130 INTEGER J, JC
131 DOUBLE PRECISION AINVNM, ANORM, EPS
132* ..
133* .. External Functions ..
134 LOGICAL LSAME
135 DOUBLE PRECISION DLAMCH, DLANTP
136 EXTERNAL lsame, dlamch, dlantp
137* ..
138* .. External Subroutines ..
139 EXTERNAL dtpmv
140* ..
141* .. Intrinsic Functions ..
142 INTRINSIC dble
143* ..
144* .. Executable Statements ..
145*
146* Quick exit if N = 0.
147*
148 IF( n.LE.0 ) THEN
149 rcond = one
150 resid = zero
151 RETURN
152 END IF
153*
154* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
155*
156 eps = dlamch( 'Epsilon' )
157 anorm = dlantp( '1', uplo, diag, n, ap, work )
158 ainvnm = dlantp( '1', uplo, diag, n, ainvp, work )
159 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
160 rcond = zero
161 resid = one / eps
162 RETURN
163 END IF
164 rcond = ( one / anorm ) / ainvnm
165*
166* Compute A * AINV, overwriting AINV.
167*
168 unitd = lsame( diag, 'U' )
169 IF( lsame( uplo, 'U' ) ) THEN
170 jc = 1
171 DO 10 j = 1, n
172 IF( unitd )
173 \$ ainvp( jc+j-1 ) = one
174*
175* Form the j-th column of A*AINV
176*
177 CALL dtpmv( 'Upper', 'No transpose', diag, j, ap,
178 \$ ainvp( jc ), 1 )
179*
180* Subtract 1 from the diagonal
181*
182 ainvp( jc+j-1 ) = ainvp( jc+j-1 ) - one
183 jc = jc + j
184 10 CONTINUE
185 ELSE
186 jc = 1
187 DO 20 j = 1, n
188 IF( unitd )
189 \$ ainvp( jc ) = one
190*
191* Form the j-th column of A*AINV
192*
193 CALL dtpmv( 'Lower', 'No transpose', diag, n-j+1, ap( jc ),
194 \$ ainvp( jc ), 1 )
195*
196* Subtract 1 from the diagonal
197*
198 ainvp( jc ) = ainvp( jc ) - one
199 jc = jc + n - j + 1
200 20 CONTINUE
201 END IF
202*
203* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
204*
205 resid = dlantp( '1', uplo, 'Non-unit', n, ainvp, work )
206*
207 resid = ( ( resid*rcond ) / dble( n ) ) / eps
208*
209 RETURN
210*
211* End of DTPT01
212*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142
double precision function dlantp(NORM, UPLO, DIAG, N, AP, WORK)
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantp.f:124
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