LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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 op(A)*X = B, when the
 triangular matrix A is stored in packed format. The test ratio is
 the maximum over
    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
 where op(A) = A or A**T, b is the column of B, x is the solution
 vector, 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**T * X = B  (Transpose)
          = 'C':  A**H * 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 op(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*
real function sasum(n, sx, incx)
SASUM
Definition sasum.f:72
subroutine saxpy(n, sa, sx, incx, sy, incy)
SAXPY
Definition saxpy.f:89
subroutine scopy(n, sx, incx, sy, incy)
SCOPY
Definition scopy.f:82
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine stpmv(uplo, trans, diag, n, ap, x, incx)
STPMV
Definition stpmv.f:142
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