 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dppt03()

 subroutine dppt03 ( character UPLO, integer N, double precision, dimension( * ) A, double precision, dimension( * ) AINV, double precision, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision RCOND, double precision RESID )

DPPT03

Purpose:
``` DPPT03 computes the residual for a symmetric packed 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 (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.``` [in] AINV ``` AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2) The (symmetric) inverse of the matrix A, stored as a packed triangular matrix.``` [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 108 of file dppt03.f.

110 *
111 * -- LAPACK test routine --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 *
115 * .. Scalar Arguments ..
116  CHARACTER UPLO
117  INTEGER LDWORK, N
118  DOUBLE PRECISION RCOND, RESID
119 * ..
120 * .. Array Arguments ..
121  DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ),
122  \$ WORK( LDWORK, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ZERO, ONE
129  parameter( zero = 0.0d+0, one = 1.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER I, J, JJ
133  DOUBLE PRECISION AINVNM, ANORM, EPS
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME
137  DOUBLE PRECISION DLAMCH, DLANGE, DLANSP
138  EXTERNAL lsame, dlamch, dlange, dlansp
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC dble
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL dcopy, dspmv
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick exit if N = 0.
149 *
150  IF( n.LE.0 ) THEN
151  rcond = one
152  resid = zero
153  RETURN
154  END IF
155 *
156 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157 *
158  eps = dlamch( 'Epsilon' )
159  anorm = dlansp( '1', uplo, n, a, rwork )
160  ainvnm = dlansp( '1', uplo, n, ainv, rwork )
161  IF( anorm.LE.zero .OR. ainvnm.EQ.zero ) THEN
162  rcond = zero
163  resid = one / eps
164  RETURN
165  END IF
166  rcond = ( one / anorm ) / ainvnm
167 *
168 * UPLO = 'U':
169 * Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
170 * expand it to a full matrix, then multiply by A one column at a
171 * time, moving the result one column to the left.
172 *
173  IF( lsame( uplo, 'U' ) ) THEN
174 *
175 * Copy AINV
176 *
177  jj = 1
178  DO 10 j = 1, n - 1
179  CALL dcopy( j, ainv( jj ), 1, work( 1, j+1 ), 1 )
180  CALL dcopy( j-1, ainv( jj ), 1, work( j, 2 ), ldwork )
181  jj = jj + j
182  10 CONTINUE
183  jj = ( ( n-1 )*n ) / 2 + 1
184  CALL dcopy( n-1, ainv( jj ), 1, work( n, 2 ), ldwork )
185 *
186 * Multiply by A
187 *
188  DO 20 j = 1, n - 1
189  CALL dspmv( 'Upper', n, -one, a, work( 1, j+1 ), 1, zero,
190  \$ work( 1, j ), 1 )
191  20 CONTINUE
192  CALL dspmv( 'Upper', n, -one, a, ainv( jj ), 1, zero,
193  \$ work( 1, n ), 1 )
194 *
195 * UPLO = 'L':
196 * Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
197 * and multiply by A, moving each column to the right.
198 *
199  ELSE
200 *
201 * Copy AINV
202 *
203  CALL dcopy( n-1, ainv( 2 ), 1, work( 1, 1 ), ldwork )
204  jj = n + 1
205  DO 30 j = 2, n
206  CALL dcopy( n-j+1, ainv( jj ), 1, work( j, j-1 ), 1 )
207  CALL dcopy( n-j, ainv( jj+1 ), 1, work( j, j ), ldwork )
208  jj = jj + n - j + 1
209  30 CONTINUE
210 *
211 * Multiply by A
212 *
213  DO 40 j = n, 2, -1
214  CALL dspmv( 'Lower', n, -one, a, work( 1, j-1 ), 1, zero,
215  \$ work( 1, j ), 1 )
216  40 CONTINUE
217  CALL dspmv( 'Lower', n, -one, a, ainv( 1 ), 1, zero,
218  \$ work( 1, 1 ), 1 )
219 *
220  END IF
221 *
222 * Add the identity matrix to WORK .
223 *
224  DO 50 i = 1, n
225  work( i, i ) = work( i, i ) + one
226  50 CONTINUE
227 *
228 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
229 *
230  resid = dlange( '1', n, n, work, ldwork, rwork )
231 *
232  resid = ( ( resid*rcond ) / eps ) / dble( n )
233 *
234  RETURN
235 *
236 * End of DPPT03
237 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
DSPMV
Definition: dspmv.f:147
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 dlansp(NORM, UPLO, N, AP, WORK)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansp.f:114
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