136 lines
3.8 KiB
FortranFixed
136 lines
3.8 KiB
FortranFixed
SUBROUTINE CPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
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$ RESID )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDB, LDX, N, NRHS
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL RWORK( * )
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COMPLEX A( * ), B( LDB, * ), X( LDX, * )
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* ..
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*
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* Purpose
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* =======
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*
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* CPPT02 computes the residual in the solution of a Hermitian system
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* of linear equations A*x = b when packed storage is used for the
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* coefficient matrix. The ratio computed is
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*
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* RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
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*
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* where EPS is the machine precision.
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* Hermitian matrix A is stored:
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The number of rows and columns of the matrix A. N >= 0.
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*
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* NRHS (input) INTEGER
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* The number of columns of B, the matrix of right hand sides.
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* NRHS >= 0.
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*
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* A (input) COMPLEX array, dimension (N*(N+1)/2)
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* The original Hermitian matrix A, stored as a packed
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* triangular matrix.
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*
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* X (input) COMPLEX array, dimension (LDX,NRHS)
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* The computed solution vectors for the system of linear
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* equations.
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*
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* LDX (input) INTEGER
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* The leading dimension of the array X. LDX >= max(1,N).
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*
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* B (input/output) COMPLEX array, dimension (LDB,NRHS)
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* On entry, the right hand side vectors for the system of
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* linear equations.
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* On exit, B is overwritten with the difference B - A*X.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* RWORK (workspace) REAL array, dimension (N)
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*
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* RESID (output) REAL
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* The maximum over the number of right hand sides of
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* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER J
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REAL ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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REAL CLANHP, SCASUM, SLAMCH
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EXTERNAL CLANHP, SCASUM, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CHPMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = CLANHP( '1', UPLO, N, A, RWORK )
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IF( ANORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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*
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* Compute B - A*X for the matrix of right hand sides B.
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*
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DO 10 J = 1, NRHS
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CALL CHPMV( UPLO, N, -CONE, A, X( 1, J ), 1, CONE, B( 1, J ),
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$ 1 )
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10 CONTINUE
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*
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* Compute the maximum over the number of right hand sides of
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* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
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*
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RESID = ZERO
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DO 20 J = 1, NRHS
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BNORM = SCASUM( N, B( 1, J ), 1 )
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XNORM = SCASUM( N, X( 1, J ), 1 )
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IF( XNORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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ELSE
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RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS )
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END IF
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20 CONTINUE
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*
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RETURN
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*
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* End of CPPT02
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*
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END
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