00001 SUBROUTINE CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT ) 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 DIAG, UPLO 00009 INTEGER N 00010 REAL RAT, RCOND, RCONDC 00011 * .. 00012 * .. Array Arguments .. 00013 REAL RWORK( * ) 00014 COMPLEX AP( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CTPT06 computes a test ratio comparing RCOND (the reciprocal 00021 * condition number of the triangular matrix A) and RCONDC, the estimate 00022 * computed by CTPCON. Information about the triangular matrix is used 00023 * if one estimate is zero and the other is non-zero to decide if 00024 * underflow in the estimate is justified. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * RCOND (input) REAL 00030 * The estimate of the reciprocal condition number obtained by 00031 * forming the explicit inverse of the matrix A and computing 00032 * RCOND = 1/( norm(A) * norm(inv(A)) ). 00033 * 00034 * RCONDC (input) REAL 00035 * The estimate of the reciprocal condition number computed by 00036 * CTPCON. 00037 * 00038 * UPLO (input) CHARACTER 00039 * Specifies whether the matrix A is upper or lower triangular. 00040 * = 'U': Upper triangular 00041 * = 'L': Lower triangular 00042 * 00043 * DIAG (input) CHARACTER 00044 * Specifies whether or not the matrix A is unit triangular. 00045 * = 'N': Non-unit triangular 00046 * = 'U': Unit triangular 00047 * 00048 * N (input) INTEGER 00049 * The order of the matrix A. N >= 0. 00050 * 00051 * AP (input) COMPLEX array, dimension (N*(N+1)/2) 00052 * The upper or lower triangular matrix A, packed columnwise in 00053 * a linear array. The j-th column of A is stored in the array 00054 * AP as follows: 00055 * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; 00056 * if UPLO = 'L', 00057 * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. 00058 * 00059 * RWORK (workspace) REAL array, dimension (N) 00060 * 00061 * RAT (output) REAL 00062 * The test ratio. If both RCOND and RCONDC are nonzero, 00063 * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. 00064 * If RAT = 0, the two estimates are exactly the same. 00065 * 00066 * ===================================================================== 00067 * 00068 * .. Parameters .. 00069 REAL ZERO, ONE 00070 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00071 * .. 00072 * .. Local Scalars .. 00073 REAL ANORM, BIGNUM, EPS, RMAX, RMIN 00074 * .. 00075 * .. External Functions .. 00076 REAL CLANTP, SLAMCH 00077 EXTERNAL CLANTP, SLAMCH 00078 * .. 00079 * .. Intrinsic Functions .. 00080 INTRINSIC MAX, MIN 00081 * .. 00082 * .. Executable Statements .. 00083 * 00084 EPS = SLAMCH( 'Epsilon' ) 00085 RMAX = MAX( RCOND, RCONDC ) 00086 RMIN = MIN( RCOND, RCONDC ) 00087 * 00088 * Do the easy cases first. 00089 * 00090 IF( RMIN.LT.ZERO ) THEN 00091 * 00092 * Invalid value for RCOND or RCONDC, return 1/EPS. 00093 * 00094 RAT = ONE / EPS 00095 * 00096 ELSE IF( RMIN.GT.ZERO ) THEN 00097 * 00098 * Both estimates are positive, return RMAX/RMIN - 1. 00099 * 00100 RAT = RMAX / RMIN - ONE 00101 * 00102 ELSE IF( RMAX.EQ.ZERO ) THEN 00103 * 00104 * Both estimates zero. 00105 * 00106 RAT = ZERO 00107 * 00108 ELSE 00109 * 00110 * One estimate is zero, the other is non-zero. If the matrix is 00111 * ill-conditioned, return the nonzero estimate multiplied by 00112 * 1/EPS; if the matrix is badly scaled, return the nonzero 00113 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum 00114 * element in absolute value in A. 00115 * 00116 BIGNUM = ONE / SLAMCH( 'Safe minimum' ) 00117 ANORM = CLANTP( 'M', UPLO, DIAG, N, AP, RWORK ) 00118 * 00119 RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) ) 00120 END IF 00121 * 00122 RETURN 00123 * 00124 * End of CTPT06 00125 * 00126 END
1.7.2