LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ strt02()

subroutine strt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
real  RESID 
)

STRT02

Purpose:
 STRT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b.
 Here A is a triangular matrix, 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]A
          A is REAL array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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 152 of file strt02.f.

152 *
153 * -- LAPACK test routine (version 3.7.0) --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 * December 2016
157 *
158 * .. Scalar Arguments ..
159  CHARACTER diag, trans, uplo
160  INTEGER lda, ldb, ldx, n, nrhs
161  REAL resid
162 * ..
163 * .. Array Arguments ..
164  REAL a( lda, * ), b( ldb, * ), work( * ),
165  $ x( ldx, * )
166 * ..
167 *
168 * =====================================================================
169 *
170 * .. Parameters ..
171  REAL zero, one
172  parameter( zero = 0.0e+0, one = 1.0e+0 )
173 * ..
174 * .. Local Scalars ..
175  INTEGER j
176  REAL anorm, bnorm, eps, xnorm
177 * ..
178 * .. External Functions ..
179  LOGICAL lsame
180  REAL sasum, slamch, slantr
181  EXTERNAL lsame, sasum, slamch, slantr
182 * ..
183 * .. External Subroutines ..
184  EXTERNAL saxpy, scopy, strmv
185 * ..
186 * .. Intrinsic Functions ..
187  INTRINSIC max
188 * ..
189 * .. Executable Statements ..
190 *
191 * Quick exit if N = 0 or NRHS = 0
192 *
193  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
194  resid = zero
195  RETURN
196  END IF
197 *
198 * Compute the 1-norm of A or A'.
199 *
200  IF( lsame( trans, 'N' ) ) THEN
201  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
202  ELSE
203  anorm = slantr( 'I', uplo, diag, n, n, a, lda, work )
204  END IF
205 *
206 * Exit with RESID = 1/EPS if ANORM = 0.
207 *
208  eps = slamch( 'Epsilon' )
209  IF( anorm.LE.zero ) THEN
210  resid = one / eps
211  RETURN
212  END IF
213 *
214 * Compute the maximum over the number of right hand sides of
215 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
216 *
217  resid = zero
218  DO 10 j = 1, nrhs
219  CALL scopy( n, x( 1, j ), 1, work, 1 )
220  CALL strmv( uplo, trans, diag, n, a, lda, work, 1 )
221  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
222  bnorm = sasum( n, work, 1 )
223  xnorm = sasum( n, x( 1, j ), 1 )
224  IF( xnorm.LE.zero ) THEN
225  resid = one / eps
226  ELSE
227  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
228  END IF
229  10 CONTINUE
230 *
231  RETURN
232 *
233 * End of STRT02
234 *
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
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 slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: slantr.f:143
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
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