LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ stpt02()

subroutine stpt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
real, dimension( * )  AP,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
real  RESID 
)

STPT02

Purpose:
 STPT02 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.
 The norm used is the 1-norm.
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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]RESID
          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 140 of file stpt02.f.

142 *
143 * -- LAPACK test routine --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 *
147 * .. Scalar Arguments ..
148  CHARACTER DIAG, TRANS, UPLO
149  INTEGER LDB, LDX, N, NRHS
150  REAL RESID
151 * ..
152 * .. Array Arguments ..
153  REAL AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ZERO, ONE
160  parameter( zero = 0.0e+0, one = 1.0e+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER J
164  REAL ANORM, BNORM, EPS, XNORM
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  REAL SASUM, SLAMCH, SLANTP
169  EXTERNAL lsame, sasum, slamch, slantp
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL saxpy, scopy, stpmv
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC max
176 * ..
177 * .. Executable Statements ..
178 *
179 * Quick exit if N = 0 or NRHS = 0
180 *
181  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
182  resid = zero
183  RETURN
184  END IF
185 *
186 * Compute the 1-norm of A or A'.
187 *
188  IF( lsame( trans, 'N' ) ) THEN
189  anorm = slantp( '1', uplo, diag, n, ap, work )
190  ELSE
191  anorm = slantp( 'I', uplo, diag, n, ap, work )
192  END IF
193 *
194 * Exit with RESID = 1/EPS if ANORM = 0.
195 *
196  eps = slamch( 'Epsilon' )
197  IF( anorm.LE.zero ) THEN
198  resid = one / eps
199  RETURN
200  END IF
201 *
202 * Compute the maximum over the number of right hand sides of
203 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
204 *
205  resid = zero
206  DO 10 j = 1, nrhs
207  CALL scopy( n, x( 1, j ), 1, work, 1 )
208  CALL stpmv( uplo, trans, diag, n, ap, work, 1 )
209  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
210  bnorm = sasum( n, work, 1 )
211  xnorm = sasum( n, x( 1, j ), 1 )
212  IF( xnorm.LE.zero ) THEN
213  resid = one / eps
214  ELSE
215  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
216  END IF
217  10 CONTINUE
218 *
219  RETURN
220 *
221 * End of STPT02
222 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slantp(NORM, UPLO, DIAG, N, AP, WORK)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantp.f:124
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:142
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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