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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE CPTT02( UPLO, 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 CHARACTER UPLO 00009 INTEGER LDB, LDX, N, NRHS 00010 REAL RESID 00011 * .. 00012 * .. Array Arguments .. 00013 REAL D( * ) 00014 COMPLEX B( LDB, * ), E( * ), X( LDX, * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CPTT02 computes the residual for the solution to a symmetric 00021 * tridiagonal system of equations: 00022 * RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS), 00023 * where EPS is the machine epsilon. 00024 * 00025 * Arguments 00026 * ========= 00027 * 00028 * UPLO (input) CHARACTER*1 00029 * Specifies whether the superdiagonal or the subdiagonal of the 00030 * tridiagonal matrix A is stored. 00031 * = 'U': E is the superdiagonal of A 00032 * = 'L': E is the subdiagonal of A 00033 * 00034 * N (input) INTEGTER 00035 * The order of the matrix A. 00036 * 00037 * NRHS (input) INTEGER 00038 * The number of right hand sides, i.e., the number of columns 00039 * of the matrices B and X. NRHS >= 0. 00040 * 00041 * D (input) REAL array, dimension (N) 00042 * The n diagonal elements of the tridiagonal matrix A. 00043 * 00044 * E (input) COMPLEX array, dimension (N-1) 00045 * The (n-1) subdiagonal elements of the tridiagonal matrix A. 00046 * 00047 * X (input) COMPLEX array, dimension (LDX,NRHS) 00048 * The n by nrhs matrix of solution vectors X. 00049 * 00050 * LDX (input) INTEGER 00051 * The leading dimension of the array X. LDX >= max(1,N). 00052 * 00053 * B (input/output) COMPLEX array, dimension (LDB,NRHS) 00054 * On entry, the n by nrhs matrix of right hand side vectors B. 00055 * On exit, B is overwritten with the difference B - A*X. 00056 * 00057 * LDB (input) INTEGER 00058 * The leading dimension of the array B. LDB >= max(1,N). 00059 * 00060 * RESID (output) REAL 00061 * norm(B - A*X) / (norm(A) * norm(X) * EPS) 00062 * 00063 * ===================================================================== 00064 * 00065 * .. Parameters .. 00066 REAL ONE, ZERO 00067 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00068 * .. 00069 * .. Local Scalars .. 00070 INTEGER J 00071 REAL ANORM, BNORM, EPS, XNORM 00072 * .. 00073 * .. External Functions .. 00074 REAL CLANHT, SCASUM, SLAMCH 00075 EXTERNAL CLANHT, SCASUM, SLAMCH 00076 * .. 00077 * .. Intrinsic Functions .. 00078 INTRINSIC MAX 00079 * .. 00080 * .. External Subroutines .. 00081 EXTERNAL CLAPTM 00082 * .. 00083 * .. Executable Statements .. 00084 * 00085 * Quick return if possible 00086 * 00087 IF( N.LE.0 ) THEN 00088 RESID = ZERO 00089 RETURN 00090 END IF 00091 * 00092 * Compute the 1-norm of the tridiagonal matrix A. 00093 * 00094 ANORM = CLANHT( '1', N, D, E ) 00095 * 00096 * Exit with RESID = 1/EPS if ANORM = 0. 00097 * 00098 EPS = SLAMCH( 'Epsilon' ) 00099 IF( ANORM.LE.ZERO ) THEN 00100 RESID = ONE / EPS 00101 RETURN 00102 END IF 00103 * 00104 * Compute B - A*X. 00105 * 00106 CALL CLAPTM( UPLO, N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB ) 00107 * 00108 * Compute the maximum over the number of right hand sides of 00109 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00110 * 00111 RESID = ZERO 00112 DO 10 J = 1, NRHS 00113 BNORM = SCASUM( N, B( 1, J ), 1 ) 00114 XNORM = SCASUM( N, X( 1, J ), 1 ) 00115 IF( XNORM.LE.ZERO ) THEN 00116 RESID = ONE / EPS 00117 ELSE 00118 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00119 END IF 00120 10 CONTINUE 00121 * 00122 RETURN 00123 * 00124 * End of CPTT02 00125 * 00126 END
1.7.3 
