LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dtpt02()

 subroutine dtpt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, double precision, dimension( * ) AP, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, double precision RESID )

DTPT02

Purpose:
``` DTPT02 computes the residual for the computed solution to a
triangular system of linear equations  A*x = b  or  A'*x = b  when
the triangular matrix A is stored in packed format.  Here A' is the
transpose of A and x and b are N by NRHS matrices.  The test ratio is
the maximum over the number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] TRANS ``` TRANS is CHARACTER*1 Specifies the operation applied to A. = 'N': A *x = b (No transpose) = 'T': A'*x = b (Transpose) = 'C': A'*x = b (Conjugate transpose = Transpose)``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.``` [in] AP ``` AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.``` [in] X ``` X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in] B ``` B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).```
Date
December 2016

Definition at line 143 of file dtpt02.f.

143 *
144 * -- LAPACK test routine (version 3.7.0) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * December 2016
148 *
149 * .. Scalar Arguments ..
150  CHARACTER diag, trans, uplo
151  INTEGER ldb, ldx, n, nrhs
152  DOUBLE PRECISION resid
153 * ..
154 * .. Array Arguments ..
155  DOUBLE PRECISION ap( * ), b( ldb, * ), work( * ), x( ldx, * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  DOUBLE PRECISION zero, one
162  parameter( zero = 0.0d+0, one = 1.0d+0 )
163 * ..
164 * .. Local Scalars ..
165  INTEGER j
166  DOUBLE PRECISION anorm, bnorm, eps, xnorm
167 * ..
168 * .. External Functions ..
169  LOGICAL lsame
170  DOUBLE PRECISION dasum, dlamch, dlantp
171  EXTERNAL lsame, dasum, dlamch, dlantp
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL daxpy, dcopy, dtpmv
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC max
178 * ..
179 * .. Executable Statements ..
180 *
181 * Quick exit if N = 0 or NRHS = 0
182 *
183  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
184  resid = zero
185  RETURN
186  END IF
187 *
188 * Compute the 1-norm of A or A'.
189 *
190  IF( lsame( trans, 'N' ) ) THEN
191  anorm = dlantp( '1', uplo, diag, n, ap, work )
192  ELSE
193  anorm = dlantp( 'I', uplo, diag, n, ap, work )
194  END IF
195 *
196 * Exit with RESID = 1/EPS if ANORM = 0.
197 *
198  eps = dlamch( 'Epsilon' )
199  IF( anorm.LE.zero ) THEN
200  resid = one / eps
201  RETURN
202  END IF
203 *
204 * Compute the maximum over the number of right hand sides of
205 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
206 *
207  resid = zero
208  DO 10 j = 1, nrhs
209  CALL dcopy( n, x( 1, j ), 1, work, 1 )
210  CALL dtpmv( uplo, trans, diag, n, ap, work, 1 )
211  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
212  bnorm = dasum( n, work, 1 )
213  xnorm = dasum( n, x( 1, j ), 1 )
214  IF( xnorm.LE.zero ) THEN
215  resid = one / eps
216  ELSE
217  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
218  END IF
219  10 CONTINUE
220 *
221  RETURN
222 *
223 * End of DTPT02
224 *
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:91
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlantp(NORM, UPLO, DIAG, N, AP, WORK)
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: dlantp.f:126
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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