00001 SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID ) 00002 * 00003 * -- LAPACK test routine (version 3.1) -- 00004 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00005 * November 2006 00006 * 00007 * .. Scalar Arguments .. 00008 INTEGER LDB, LDX, N, NRHS 00009 DOUBLE PRECISION RESID 00010 * .. 00011 * .. Array Arguments .. 00012 DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * DPTT02 computes the residual for the solution to a symmetric 00019 * tridiagonal system of equations: 00020 * RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS), 00021 * where EPS is the machine epsilon. 00022 * 00023 * Arguments 00024 * ========= 00025 * 00026 * N (input) INTEGTER 00027 * The order of the matrix A. 00028 * 00029 * NRHS (input) INTEGER 00030 * The number of right hand sides, i.e., the number of columns 00031 * of the matrices B and X. NRHS >= 0. 00032 * 00033 * D (input) DOUBLE PRECISION array, dimension (N) 00034 * The n diagonal elements of the tridiagonal matrix A. 00035 * 00036 * E (input) DOUBLE PRECISION array, dimension (N-1) 00037 * The (n-1) subdiagonal elements of the tridiagonal matrix A. 00038 * 00039 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) 00040 * The n by nrhs matrix of solution vectors X. 00041 * 00042 * LDX (input) INTEGER 00043 * The leading dimension of the array X. LDX >= max(1,N). 00044 * 00045 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) 00046 * On entry, the n by nrhs matrix of right hand side vectors B. 00047 * On exit, B is overwritten with the difference B - A*X. 00048 * 00049 * LDB (input) INTEGER 00050 * The leading dimension of the array B. LDB >= max(1,N). 00051 * 00052 * RESID (output) DOUBLE PRECISION 00053 * norm(B - A*X) / (norm(A) * norm(X) * EPS) 00054 * 00055 * ===================================================================== 00056 * 00057 * .. Parameters .. 00058 DOUBLE PRECISION ONE, ZERO 00059 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00060 * .. 00061 * .. Local Scalars .. 00062 INTEGER J 00063 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM 00064 * .. 00065 * .. External Functions .. 00066 DOUBLE PRECISION DASUM, DLAMCH, DLANST 00067 EXTERNAL DASUM, DLAMCH, DLANST 00068 * .. 00069 * .. Intrinsic Functions .. 00070 INTRINSIC MAX 00071 * .. 00072 * .. External Subroutines .. 00073 EXTERNAL DLAPTM 00074 * .. 00075 * .. Executable Statements .. 00076 * 00077 * Quick return if possible 00078 * 00079 IF( N.LE.0 ) THEN 00080 RESID = ZERO 00081 RETURN 00082 END IF 00083 * 00084 * Compute the 1-norm of the tridiagonal matrix A. 00085 * 00086 ANORM = DLANST( '1', N, D, E ) 00087 * 00088 * Exit with RESID = 1/EPS if ANORM = 0. 00089 * 00090 EPS = DLAMCH( 'Epsilon' ) 00091 IF( ANORM.LE.ZERO ) THEN 00092 RESID = ONE / EPS 00093 RETURN 00094 END IF 00095 * 00096 * Compute B - A*X. 00097 * 00098 CALL DLAPTM( N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB ) 00099 * 00100 * Compute the maximum over the number of right hand sides of 00101 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00102 * 00103 RESID = ZERO 00104 DO 10 J = 1, NRHS 00105 BNORM = DASUM( N, B( 1, J ), 1 ) 00106 XNORM = DASUM( N, X( 1, J ), 1 ) 00107 IF( XNORM.LE.ZERO ) THEN 00108 RESID = ONE / EPS 00109 ELSE 00110 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00111 END IF 00112 10 CONTINUE 00113 * 00114 RETURN 00115 * 00116 * End of DPTT02 00117 * 00118 END
1.7.2