 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dpot03()

 subroutine dpot03 ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldainv, * ) AINV, integer LDAINV, double precision, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision RCOND, double precision RESID )

DPOT03

Purpose:
``` DPOT03 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).``` [out] RESID ``` RESID is DOUBLE PRECISION norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 123 of file dpot03.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  DOUBLE PRECISION RCOND, RESID
134 * ..
135 * .. Array Arguments ..
136  DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
137  \$ WORK( LDWORK, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER I, J
148  DOUBLE PRECISION AINVNM, ANORM, EPS
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
153  EXTERNAL lsame, dlamch, dlange, dlansy
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL dsymm
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC dble
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 = dlamch( 'Epsilon' )
174  anorm = dlansy( '1', uplo, n, a, lda, rwork )
175  ainvnm = dlansy( '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 DSYMM 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 dsymm( '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 = dlange( '1', n, n, work, ldwork, rwork )
211 *
212  resid = ( ( resid*rcond ) / eps ) / dble( n )
213 *
214  RETURN
215 *
216 * End of DPOT03
217 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:189
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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