LAPACK  3.8.0
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.
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.
Date
December 2016

Definition at line 143 of file stpt02.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  REAL resid
153 * ..
154 * .. Array Arguments ..
155  REAL ap( * ), b( ldb, * ), work( * ), x( ldx, * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  REAL zero, one
162  parameter( zero = 0.0e+0, one = 1.0e+0 )
163 * ..
164 * .. Local Scalars ..
165  INTEGER j
166  REAL anorm, bnorm, eps, xnorm
167 * ..
168 * .. External Functions ..
169  LOGICAL lsame
170  REAL sasum, slamch, slantp
171  EXTERNAL lsame, sasum, slamch, slantp
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL saxpy, scopy, stpmv
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 = slantp( '1', uplo, diag, n, ap, work )
192  ELSE
193  anorm = slantp( 'I', uplo, diag, n, ap, work )
194  END IF
195 *
196 * Exit with RESID = 1/EPS if ANORM = 0.
197 *
198  eps = slamch( '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 scopy( n, x( 1, j ), 1, work, 1 )
210  CALL stpmv( uplo, trans, diag, n, ap, work, 1 )
211  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
212  bnorm = sasum( n, work, 1 )
213  xnorm = sasum( 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 STPT02
224 *
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:144
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: slantp.f:126
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
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