LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 )```
Date
November 2011

Definition at line 127 of file dpot03.f.

127 *
128 * -- LAPACK test routine (version 3.4.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * November 2011
132 *
133 * .. Scalar Arguments ..
134  CHARACTER uplo
135  INTEGER lda, ldainv, ldwork, n
136  DOUBLE PRECISION rcond, resid
137 * ..
138 * .. Array Arguments ..
139  DOUBLE PRECISION a( lda, * ), ainv( ldainv, * ), rwork( * ),
140  \$ work( ldwork, * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION zero, one
147  parameter ( zero = 0.0d+0, one = 1.0d+0 )
148 * ..
149 * .. Local Scalars ..
150  INTEGER i, j
151  DOUBLE PRECISION ainvnm, anorm, eps
152 * ..
153 * .. External Functions ..
154  LOGICAL lsame
155  DOUBLE PRECISION dlamch, dlange, dlansy
156  EXTERNAL lsame, dlamch, dlange, dlansy
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL dsymm
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC dble
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick exit if N = 0.
167 *
168  IF( n.LE.0 ) THEN
169  rcond = one
170  resid = zero
171  RETURN
172  END IF
173 *
174 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
175 *
176  eps = dlamch( 'Epsilon' )
177  anorm = dlansy( '1', uplo, n, a, lda, rwork )
178  ainvnm = dlansy( '1', uplo, n, ainv, ldainv, rwork )
179  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
180  rcond = zero
181  resid = one / eps
182  RETURN
183  END IF
184  rcond = ( one / anorm ) / ainvnm
185 *
186 * Expand AINV into a full matrix and call DSYMM to multiply
187 * AINV on the left by A.
188 *
189  IF( lsame( uplo, 'U' ) ) THEN
190  DO 20 j = 1, n
191  DO 10 i = 1, j - 1
192  ainv( j, i ) = ainv( i, j )
193  10 CONTINUE
194  20 CONTINUE
195  ELSE
196  DO 40 j = 1, n
197  DO 30 i = j + 1, n
198  ainv( j, i ) = ainv( i, j )
199  30 CONTINUE
200  40 CONTINUE
201  END IF
202  CALL dsymm( 'Left', uplo, n, n, -one, a, lda, ainv, ldainv, zero,
203  \$ work, ldwork )
204 *
205 * Add the identity matrix to WORK .
206 *
207  DO 50 i = 1, n
208  work( i, i ) = work( i, i ) + one
209  50 CONTINUE
210 *
211 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
212 *
213  resid = dlange( '1', n, n, work, ldwork, rwork )
214 *
215  resid = ( ( resid*rcond ) / eps ) / dble( n )
216 *
217  RETURN
218 *
219 * End of DPOT03
220 *
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, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:191
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:116
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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