LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ spot03()

subroutine spot03 ( character  uplo,
integer  n,
real, dimension( lda, * )  a,
integer  lda,
real, dimension( ldainv, * )  ainv,
integer  ldainv,
real, dimension( ldwork, * )  work,
integer  ldwork,
real, dimension( * )  rwork,
real  rcond,
real  resid 
)

SPOT03

Purpose:
 SPOT03 computes the residual for a 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
          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 REAL array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in,out]AINV
          AINV is REAL 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 REAL array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RCOND
          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).
[out]RESID
          RESID is REAL
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file spot03.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 UPLO
132 INTEGER LDA, LDAINV, LDWORK, N
133 REAL RCOND, RESID
134* ..
135* .. Array Arguments ..
136 REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
137 $ WORK( LDWORK, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER I, J
148 REAL AINVNM, ANORM, EPS
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 REAL SLAMCH, SLANGE, SLANSY
153 EXTERNAL lsame, slamch, slange, slansy
154* ..
155* .. External Subroutines ..
156 EXTERNAL ssymm
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC real
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 = slamch( 'Epsilon' )
174 anorm = slansy( '1', uplo, n, a, lda, rwork )
175 ainvnm = slansy( '1', uplo, 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* Expand AINV into a full matrix and call SSYMM to multiply
184* AINV on the left by A.
185*
186 IF( lsame( uplo, 'U' ) ) THEN
187 DO 20 j = 1, n
188 DO 10 i = 1, j - 1
189 ainv( j, i ) = ainv( i, j )
190 10 CONTINUE
191 20 CONTINUE
192 ELSE
193 DO 40 j = 1, n
194 DO 30 i = j + 1, n
195 ainv( j, i ) = ainv( i, j )
196 30 CONTINUE
197 40 CONTINUE
198 END IF
199 CALL ssymm( 'Left', uplo, n, n, -one, a, lda, ainv, ldainv, zero,
200 $ work, ldwork )
201*
202* Add the identity matrix to WORK .
203*
204 DO 50 i = 1, n
205 work( i, i ) = work( i, i ) + one
206 50 CONTINUE
207*
208* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
209*
210 resid = slange( '1', n, n, work, ldwork, rwork )
211*
212 resid = ( ( resid*rcond ) / eps ) / real( n )
213*
214 RETURN
215*
216* End of SPOT03
217*
subroutine ssymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
SSYMM
Definition ssymm.f:189
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
real function slansy(norm, uplo, n, a, lda, work)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansy.f:122
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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