LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cspt02()

subroutine cspt02 ( character  UPLO,
integer  N,
integer  NRHS,
complex, dimension( * )  A,
complex, dimension( ldx, * )  X,
integer  LDX,
complex, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  RWORK,
real  RESID 
)

CSPT02

Purpose:
 CSPT02 computes the residual in the solution of a complex symmetric
 system of linear equations  A*x = b  when packed storage is used for
 the coefficient matrix.  The ratio computed is

    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).

 where EPS is the machine precision.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is COMPLEX array, dimension (N*(N+1)/2)
          The original complex symmetric matrix A, stored as a packed
          triangular matrix.
[in]X
          X is COMPLEX 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,out]B
          B is COMPLEX 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 - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 121 of file cspt02.f.

123 *
124 * -- LAPACK test routine --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 *
128 * .. Scalar Arguments ..
129  CHARACTER UPLO
130  INTEGER LDB, LDX, N, NRHS
131  REAL RESID
132 * ..
133 * .. Array Arguments ..
134  REAL RWORK( * )
135  COMPLEX A( * ), B( LDB, * ), X( LDX, * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL ZERO, ONE
142  parameter( zero = 0.0e+0, one = 1.0e+0 )
143  COMPLEX CONE
144  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  REAL ANORM, BNORM, EPS, XNORM
149 * ..
150 * .. External Functions ..
151  REAL CLANSP, SCASUM, SLAMCH
152  EXTERNAL clansp, scasum, slamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL cspmv
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if N = 0 or NRHS = 0
163 *
164  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
165  resid = zero
166  RETURN
167  END IF
168 *
169 * Exit with RESID = 1/EPS if ANORM = 0.
170 *
171  eps = slamch( 'Epsilon' )
172  anorm = clansp( '1', uplo, n, a, rwork )
173  IF( anorm.LE.zero ) THEN
174  resid = one / eps
175  RETURN
176  END IF
177 *
178 * Compute B - A*X for the matrix of right hand sides B.
179 *
180  DO 10 j = 1, nrhs
181  CALL cspmv( uplo, n, -cone, a, x( 1, j ), 1, cone, b( 1, j ),
182  $ 1 )
183  10 CONTINUE
184 *
185 * Compute the maximum over the number of right hand sides of
186 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
187 *
188  resid = zero
189  DO 20 j = 1, nrhs
190  bnorm = scasum( n, b( 1, j ), 1 )
191  xnorm = scasum( n, x( 1, j ), 1 )
192  IF( xnorm.LE.zero ) THEN
193  resid = one / eps
194  ELSE
195  resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
196  END IF
197  20 CONTINUE
198 *
199  RETURN
200 *
201 * End of CSPT02
202 *
real function clansp(NORM, UPLO, N, AP, WORK)
CLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansp.f:115
subroutine cspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
Definition: cspmv.f:151
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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