 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sptt02()

 subroutine sptt02 ( integer N, integer NRHS, real, dimension( * ) D, real, dimension( * ) E, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real RESID )

SPTT02

Purpose:
``` SPTT02 computes the residual for the solution to a symmetric
tridiagonal system of equations:
RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
where EPS is the machine epsilon.```
Parameters
 [in] N ``` N is INTEGTER The order of the matrix A.``` [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] D ``` D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.``` [in] E ``` E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.``` [in] X ``` X is REAL array, dimension (LDX,NRHS) The n by nrhs matrix of 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 n by nrhs matrix of right hand side vectors B. On exit, B is overwritten with the difference B - 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 - A*X) / (norm(A) * norm(X) * EPS)```

Definition at line 103 of file sptt02.f.

104 *
105 * -- LAPACK test routine --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 *
109 * .. Scalar Arguments ..
110  INTEGER LDB, LDX, N, NRHS
111  REAL RESID
112 * ..
113 * .. Array Arguments ..
114  REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Parameters ..
120  REAL ONE, ZERO
121  parameter( one = 1.0e+0, zero = 0.0e+0 )
122 * ..
123 * .. Local Scalars ..
124  INTEGER J
125  REAL ANORM, BNORM, EPS, XNORM
126 * ..
127 * .. External Functions ..
128  REAL SASUM, SLAMCH, SLANST
129  EXTERNAL sasum, slamch, slanst
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC max
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL slaptm
136 * ..
137 * .. Executable Statements ..
138 *
139 * Quick return if possible
140 *
141  IF( n.LE.0 ) THEN
142  resid = zero
143  RETURN
144  END IF
145 *
146 * Compute the 1-norm of the tridiagonal matrix A.
147 *
148  anorm = slanst( '1', n, d, e )
149 *
150 * Exit with RESID = 1/EPS if ANORM = 0.
151 *
152  eps = slamch( 'Epsilon' )
153  IF( anorm.LE.zero ) THEN
154  resid = one / eps
155  RETURN
156  END IF
157 *
158 * Compute B - A*X.
159 *
160  CALL slaptm( n, nrhs, -one, d, e, x, ldx, one, b, ldb )
161 *
162 * Compute the maximum over the number of right hand sides of
163 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
164 *
165  resid = zero
166  DO 10 j = 1, nrhs
167  bnorm = sasum( n, b( 1, j ), 1 )
168  xnorm = sasum( n, x( 1, j ), 1 )
169  IF( xnorm.LE.zero ) THEN
170  resid = one / eps
171  ELSE
172  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
173  END IF
174  10 CONTINUE
175 *
176  RETURN
177 *
178 * End of SPTT02
179 *
real function slanst(NORM, N, D, E)
SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slanst.f:100
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine slaptm(N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
SLAPTM
Definition: slaptm.f:116
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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