LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgtt02()

subroutine sgtt02 ( character  TRANS,
integer  N,
integer  NRHS,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real  RESID 
)

SGTT02

Purpose:
 SGTT02 computes the residual for the solution to a tridiagonal
 system of equations:
    RESID = norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS),
 where EPS is the machine epsilon.
 The norm used is the 1-norm.
Parameters
[in]TRANS
          TRANS is CHARACTER
          Specifies the form of the residual.
          = 'N':  B - A    * X  (No transpose)
          = 'T':  B - A**T * X  (Transpose)
          = 'C':  B - A**H * X  (Conjugate transpose = Transpose)
[in]N
          N is INTEGTER
          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 B and X.  NRHS >= 0.
[in]DL
          DL is REAL array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.
[in]D
          D is REAL array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is REAL array, dimension (N-1)
          The (n-1) super-diagonal elements of A.
[in]X
          X is REAL array, dimension (LDX,NRHS)
          The computed solution vectors X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - op(A)*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RESID
          RESID is REAL
          norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file sgtt02.f.

125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  CHARACTER TRANS
132  INTEGER LDB, LDX, N, NRHS
133  REAL RESID
134 * ..
135 * .. Array Arguments ..
136  REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
137  $ X( LDX, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL ONE, ZERO
144  parameter( one = 1.0e+0, zero = 0.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  REAL ANORM, BNORM, EPS, XNORM
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  REAL SASUM, SLAMCH, SLANGT
153  EXTERNAL lsame, sasum, slamch, slangt
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL slagtm
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC max
160 * ..
161 * .. Executable Statements ..
162 *
163 * Quick exit if N = 0 or NRHS = 0
164 *
165  resid = zero
166  IF( n.LE.0 .OR. nrhs.EQ.0 )
167  $ RETURN
168 *
169 * Compute the maximum over the number of right hand sides of
170 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
171 *
172  IF( lsame( trans, 'N' ) ) THEN
173  anorm = slangt( '1', n, dl, d, du )
174  ELSE
175  anorm = slangt( 'I', n, dl, d, du )
176  END IF
177 *
178 * Exit with RESID = 1/EPS if ANORM = 0.
179 *
180  eps = slamch( 'Epsilon' )
181  IF( anorm.LE.zero ) THEN
182  resid = one / eps
183  RETURN
184  END IF
185 *
186 * Compute B - op(A)*X and store in B.
187 *
188  CALL slagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
189  $ ldb )
190 *
191  DO 10 j = 1, nrhs
192  bnorm = sasum( n, b( 1, j ), 1 )
193  xnorm = sasum( n, x( 1, j ), 1 )
194  IF( xnorm.LE.zero ) THEN
195  resid = one / eps
196  ELSE
197  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
198  END IF
199  10 CONTINUE
200 *
201  RETURN
202 *
203 * End of SGTT02
204 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slangt(NORM, N, DL, D, DU)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangt.f:106
subroutine slagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: slagtm.f:145
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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