 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 )```

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 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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
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