LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ stpt01()

subroutine stpt01 ( character  uplo,
character  diag,
integer  n,
real, dimension( * )  ap,
real, dimension( * )  ainvp,
real  rcond,
real, dimension( * )  work,
real  resid 
)

STPT01

Purpose:
 STPT01 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 REAL 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 REAL 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 REAL
          The reciprocal condition number of A, computed as
          1/(norm(A) * norm(AINV)).
[out]WORK
          WORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 107 of file stpt01.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 REAL RCOND, RESID
117* ..
118* .. Array Arguments ..
119 REAL AINVP( * ), AP( * ), WORK( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 REAL ZERO, ONE
126 parameter( zero = 0.0e+0, one = 1.0e+0 )
127* ..
128* .. Local Scalars ..
129 LOGICAL UNITD
130 INTEGER J, JC
131 REAL AINVNM, ANORM, EPS
132* ..
133* .. External Functions ..
134 LOGICAL LSAME
135 REAL SLAMCH, SLANTP
136 EXTERNAL lsame, slamch, slantp
137* ..
138* .. External Subroutines ..
139 EXTERNAL stpmv
140* ..
141* .. Intrinsic Functions ..
142 INTRINSIC real
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 = slamch( 'Epsilon' )
157 anorm = slantp( '1', uplo, diag, n, ap, work )
158 ainvnm = slantp( '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 stpmv( '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 stpmv( '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 = slantp( '1', uplo, 'Non-unit', n, ainvp, work )
206*
207 resid = ( ( resid*rcond ) / real( n ) ) / eps
208*
209 RETURN
210*
211* End of STPT01
212*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slantp(norm, uplo, diag, n, ap, work)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slantp.f:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine stpmv(uplo, trans, diag, n, ap, x, incx)
STPMV
Definition stpmv.f:142
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