Thu Sep 13 15:56:54 2018 R8LIB_TEST Python version: 3.6.5 Test the R8LIB library. AGM_VALUES_TEST: Python version: 3.6.5 AGM_VALUES stores values of the arithmetic geometric mean function. A B AGM(A,B) 22.000000 96.000000 52.2746411987042379 83.000000 56.000000 68.8365300598585179 42.000000 7.000000 20.6593011967340097 26.000000 11.000000 17.6968548737436500 4.000000 63.000000 23.8670497217533004 6.000000 45.000000 20.7170159828059930 40.000000 75.000000 56.1278422556166845 80.000000 0.000000 0.0000000000000000 90.000000 35.000000 59.2695650812296364 9.000000 1.000000 3.9362355036495553 53.000000 53.000000 53.0000000000000000 1.000000 2.000000 1.4567910310469068 1.000000 4.000000 2.2430285802876027 1.000000 8.000000 3.6157561775973628 AGM_VALUES_TEST: Normal end of execution. GAMMA_VALUES_TEST: Python version: 3.6.5 GAMMA_VALUES stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322 -0.010000 -100.5871979644108052 0.010000 99.4325851191506018 0.100000 9.5135076986687324 0.200000 4.5908437119988026 0.400000 2.2181595437576882 0.500000 1.7724538509055161 0.600000 1.4891922488128171 0.800000 1.1642297137253030 1.000000 1.0000000000000000 1.100000 0.9513507698668732 1.200000 0.9181687423997607 1.300000 0.8974706963062772 1.400000 0.8872638175030753 1.500000 0.8862269254527581 1.600000 0.8935153492876903 1.700000 0.9086387328532904 1.800000 0.9313837709802427 1.900000 0.9617658319073874 2.000000 1.0000000000000000 3.000000 2.0000000000000000 4.000000 6.0000000000000000 10.000000 362880.0000000000000000 20.000000 121645100408832000.0000000000000000 30.000000 8841761993739701898620088352768.0000000000000000 GAMMA_VALUES_TEST: Normal end of execution. GAMMA_LOG_VALUES: Python version: 3.6.5 GAMMA_LOG_VALUES stores values of the logarithm of the Gamma function. X GAMMA_LOG(X) 0.200000 1.5240638224307841 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.000000 0.0000000000000000 1.100000 -0.0498724412598397 1.200000 -0.0853740900033158 1.300000 -0.1081748095078604 1.400000 -0.1196129141723712 1.500000 -0.1207822376352452 1.600000 -0.1125917656967557 1.700000 -0.0958076974070659 1.800000 -0.0710838729143722 1.900000 -0.0389842759230833 2.000000 0.0000000000000000 3.000000 0.6931471805599453 4.000000 1.7917594692280550 10.000000 12.8018274800814691 20.000000 39.3398841871994946 30.000000 71.2570389671680147 GAMMA_LOG_VALUES_TEST: Normal end of execution. I4_LOG_10_TEST Python version: 3.6.5 I4_LOG_10: whole part of log base 10, X, I4_LOG_10 0 0 1 0 2 0 3 0 9 0 10 1 11 1 99 1 101 2 -1 0 -2 0 -3 0 -9 0 I4_LOG_10_TEST Normal end of execution. I4_MODP_TEST Python version: 3.6.5 I4_MODP factors a number into a multiple M and a positive remainder R. Number Divisor Multiple Remainder 107 50 2 7 107 -50 -2 7 -107 50 -3 43 -107 -50 3 43 Repeat using Python % Operator: 107 50 2 7 107 -50 -3 -43 -107 50 -3 43 -107 -50 2 -7 I4_MODP_TEST Normal end of execution. I4_SIGN_TEST Python version: 3.6.5 I4_SIGN returns the sign of an I4. I4 I4_SIGN(I4) -10 -1 -7 -1 0 1 5 1 9 1 I4_SIGN_TEST Normal end of execution. I4_UNIFORM_AB_TEST Python version: 3.6.5 I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 I4_UNIFORM_AB_TEST: Normal end of execution. I4_WRAP_TEST Python version: 3.6.5 I4_WRAP forces an integer to lie within given limits. ILO = 4 IHI = 8 I I4_WRAP(I) -10 5 -9 6 -8 7 -7 8 -6 4 -5 5 -4 6 -3 7 -2 8 -1 4 0 5 1 6 2 7 3 8 4 4 5 5 6 6 7 7 8 8 9 4 10 5 11 6 12 7 13 8 14 4 15 5 16 6 17 7 18 8 19 4 20 5 I4_WRAP_TEST Normal end of execution. I4VEC_INDICATOR0_TEST Python version: 3.6.5 I4VEC_INDICATOR0 returns an indicator vector. The indicator0 vector: 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 I4VEC_INDICATOR0_TEST Normal end of execution. I4VEC_INDICATOR1_TEST Python version: 3.6.5 I4VEC_INDICATOR1 returns an indicator vector. The indicator1 vector: 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 I4VEC_INDICATOR1_TEST Normal end of execution. I4VEC_PRINT_TEST Python version: 3.6.5 I4VEC_PRINT prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 I4VEC_PRINT_TEST: Normal end of execution. I4VEC_TRANSPOSE_PRINT_TEST Python version: 3.6.5 I4VEC_TRANSPOSE_PRINT prints an I4VEC with 5 entries to a row, and an optional title. My array: 1 2 3 4 5 6 7 8 9 10 11 12 I4VEC_TRANSPOSE_PRINT_TEST: Normal end of execution. I4VEC_UNIFORM_AB_TEST Python version: 3.6.5 I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 The random vector: 0 -35 1 187 2 149 3 69 4 25 5 -81 6 -23 7 -67 8 -87 9 90 10 -82 11 35 12 20 13 127 14 139 15 -100 16 170 17 5 18 -72 19 -96 I4VEC_UNIFORM_AB_TEST: Normal end of execution. PERM0_CHECK_TEST Python version: 3.6.5 PERM0_CHECK checks a permutation of 0,...,N-1. Permutation 1: 5 2 3 4 1 PERM0_CHECK - Warning! Permutation is missing the value 0. Permutation 2: 4 1 3 0 2 Permutation 3: 0 2 1 3 2 PERM0_CHECK - Warning! Permutation is missing the value 4. PERM0_CHECK_TEST: Normal end of execution. PERM0_UNIFORM_TEST Python version: 3.6.5 PERM0_UNIFORM randomly selects a permutation of 0,...,N-1. 2 9 8 6 3 5 7 4 0 1 6 1 5 2 8 4 0 9 3 7 0 1 8 2 4 5 7 9 3 6 3 8 4 7 0 9 2 5 6 1 1 7 5 4 0 6 8 2 3 9 PERM0_UNIFORM_TEST Normal end of execution. PERM1_CHECK_TEST Python version: 3.6.5 PERM1_CHECK checks a permutation of 1,...,N. Permutation 1: 5 2 3 4 1 Permutation 2: 4 1 3 0 2 PERM1_CHECK - Warning! Permutation is missing the value 5. Permutation 3: 0 2 1 3 2 PERM1_CHECK - Warning! Permutation is missing the value 4. PERM1_CHECK_TEST: Normal end of execution. PERM1_UNIFORM_TEST Python version: 3.6.5 PERM1_UNIFORM randomly selects a permutation of 1,...,N. 3 10 9 7 4 6 8 5 1 2 7 2 6 3 9 5 1 10 4 8 1 2 9 3 5 6 8 10 4 7 4 9 5 8 1 10 3 6 7 2 2 8 6 5 1 7 9 3 4 10 PERM1_UNIFORM_TEST Normal end of execution. R8_ABS_TEST Python version: 3.6.5 R8_ABS returns the absolute value of an R8. X R8_ABS(X) -2.815817 2.815817 4.563176 4.563176 3.295092 3.295092 0.616954 0.616954 -0.846929 0.846929 -4.338813 4.338813 -2.424222 2.424222 -3.900432 3.900432 -4.561710 4.561710 1.339657 1.339657 R8_ABS_TEST Normal end of execution. R8_ACOS_TEST Python version: 3.6.5 R8_ACOS computes the arc-cosine of an angle. C R8_ACOS(C) ACOS(C) -1.16667 3.14159 -1 3.14159 3.14159 -0.833333 2.55591 2.55591 -0.666667 2.30052 2.30052 -0.5 2.0944 2.0944 -0.333333 1.91063 1.91063 -0.166667 1.73824 1.73824 0 1.5708 1.5708 0.166667 1.40335 1.40335 0.333333 1.23096 1.23096 0.5 1.0472 1.0472 0.666667 0.841069 0.841069 0.833333 0.585686 0.585686 1 0 0 1.16667 0 R8_ACOS_TEST Normal end of execution. R8_ACOSH_TEST Python version: 3.6.5 R8_ACOSH computes the arc-hyperbolic-cosine of an angle. X A=R8_ACOSH(X) COSH(A) 1 0 1 1.5 0.962424 1.5 2 1.31696 2 2.5 1.5668 2.5 3 1.76275 3 3.5 1.92485 3.5 4 2.06344 4 4.5 2.18464 4.5 5 2.29243 5 R8_ACOSH_TEST Normal end of execution. R8_ADD_TEST Python version: 3.6.5 R8_ADD adds two R8's. R1 R2 R3 R4 R1+R2 R8_ADD(R1,R2) -281.582 456.318 174.736 174.736 329.509 61.6954 391.205 391.205 -84.6929 -433.881 -518.574 -518.574 -242.422 -390.043 -632.465 -632.465 -456.171 133.966 -322.205 -322.205 R8_ADD_TEST Normal end of execution. R8_AGM_TEST: Python version: 3.6.5 R8_AGM computes the arithmetic geometric mean. X Y AGM AGM Exact Computed 22.000000 96.000000 52.27464119870424 52.27464119870424 83.000000 56.000000 68.83653005985852 68.83653005985852 42.000000 7.000000 20.65930119673401 20.65930119673401 26.000000 11.000000 17.69685487374365 17.69685487374367 4.000000 63.000000 23.8670497217533 23.8670497217533 6.000000 45.000000 20.71701598280599 20.71701598280599 40.000000 75.000000 56.12784225561668 56.12784225561668 80.000000 0.000000 0 0 90.000000 35.000000 59.26956508122964 59.26956508122989 9.000000 1.000000 3.936235503649555 3.936235503649556 53.000000 53.000000 53 53 1.000000 2.000000 1.456791031046907 1.456791031046907 1.000000 4.000000 2.243028580287603 2.243028580287603 1.000000 8.000000 3.615756177597363 3.615756177597363 R8_AGM_TEST Normal end of execution. R8_AINT_TEST Python version: 3.6.5 R8_AINT truncates a real number to its integer part. X R8_AINT(X) -5.631634 -5.000000 9.126352 9.000000 6.590185 6.000000 1.233909 1.000000 -1.693858 -1.000000 -8.677625 -8.000000 -4.848444 -4.000000 -7.800864 -7.000000 -9.123420 -9.000000 2.679314 2.000000 R8_AINT_TEST Normal end of execution. R8_ASIN_TEST Python version: 3.6.5 R8_ASIN computes the arc-sine of an angle. S R8_ASIN(S) ARCSIN(S) -1.16667 -1.5708 -1 -1.5708 -1.5708 -0.833333 -0.985111 -0.985111 -0.666667 -0.729728 -0.729728 -0.5 -0.523599 -0.523599 -0.333333 -0.339837 -0.339837 -0.166667 -0.167448 -0.167448 0 0 0 0.166667 0.167448 0.167448 0.333333 0.339837 0.339837 0.5 0.523599 0.523599 0.666667 0.729728 0.729728 0.833333 0.985111 0.985111 1 1.5708 1.5708 1.16667 1.5708 R8_ASIN_TEST Normal end of execution. R8_ASINH_TEST Python version: 3.6.5 R8_ASINH computes the inverse hyperbolic sine. X R8_ASINH(X) SINH(R8_SINH(X)) 1.000000 0.881374 1.000000 1.200000 1.015973 1.200000 1.400000 1.137982 1.400000 1.600000 1.248983 1.600000 1.800000 1.350441 1.800000 2.000000 1.443635 2.000000 2.200000 1.529660 2.200000 2.400000 1.609438 2.400000 2.600000 1.683743 2.600000 2.800000 1.753229 2.800000 R8_ASINH_TEST Normal end of execution. R8_ATAN_TEST Python version: 3.6.5 R8_ATAN computes the arc-tangent given Y and X; ATAN2 is the system version of this routine. X Y ATAN2(Y,X) R8_ATAN(Y,X) 1.000000 0.000000 0.000000 0.000000 1.000000 1.000000 0.785398 0.785398 0.000000 1.000000 1.570796 1.570796 -1.000000 1.000000 2.356194 2.356194 -1.000000 0.000000 3.141593 3.141593 -1.000000 -1.000000 -2.356194 3.926991 0.000000 -1.000000 -1.570796 4.712389 1.000000 -1.000000 -0.785398 5.497787 R8_ATAN_TEST Normal end of execution R8_ATANH_TEST Python version: 3.6.5 R8_ATANH computes the inverse hyperbolic tangent. X R8_ATANH(X) TANH(R8_TANH(X)) -0.200000 -0.202733 -0.200000 -0.100000 -0.100335 -0.100000 0.000000 0.000000 0.000000 0.100000 0.100335 0.100000 0.200000 0.202733 0.200000 0.300000 0.309520 0.300000 0.400000 0.423649 0.400000 0.500000 0.549306 0.500000 0.600000 0.693147 0.600000 0.700000 0.867301 0.700000 0.800000 1.098612 0.800000 0.900000 1.472219 0.900000 R8_ATANH_TEST Normal end of execution. R8_BIG_TEST Python version: 3.6.5 R8_BIG returns a "big" R8; R8_BIG = 1e+30 R8_BIG_TEST Normal end of execution. R8_CAS_TEST Python version: 3.6.5 R8_CAS evaluates the casine of a number. X R8_CAS ( X ) 0.000000 1.000000 0.261799 1.224745 0.523599 1.366025 0.785398 1.414214 1.047198 1.366025 1.308997 1.224745 1.570796 1.000000 1.832596 0.707107 2.094395 0.366025 2.356194 0.000000 2.617994 -0.366025 2.879793 -0.707107 3.141593 -1.000000 R8_CAS_TEST Normal end of execution. R8_CEILING_TEST Python version: 3.6.5 R8_CEILING rounds a value up. X R8_CEILING(X) -1.200000 -1 -1.000000 -1 -0.800000 0 -0.600000 0 -0.400000 0 -0.200000 0 0.000000 0 0.200000 1 0.400000 1 0.600000 1 0.800000 1 1.000000 1 1.200000 2 R8_CEILING_TEST Normal end of execution. R8_CHOOSE_TEST Python version: 3.6.5 R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 5 0 1 5 1 5 5 2 10 5 3 10 5 4 5 5 5 1 R8_CHOOSE_TEST Normal end of execution. R8_CHOP_TEST Python version: 3.6.5 R8_CHOP chops an R8 to IPLACE places PLACE X R8_CHOP 0 3.141592653589793 0 1 3.141592653589793 2 2 3.141592653589793 3 3 3.141592653589793 3 4 3.141592653589793 3 5 3.141592653589793 3.125 6 3.141592653589793 3.125 7 3.141592653589793 3.125 8 3.141592653589793 3.140625 9 3.141592653589793 3.140625 10 3.141592653589793 3.140625 11 3.141592653589793 3.140625 12 3.141592653589793 3.140625 13 3.141592653589793 3.14111328125 14 3.141592653589793 3.141357421875 15 3.141592653589793 3.1414794921875 16 3.141592653589793 3.14154052734375 17 3.141592653589793 3.141571044921875 18 3.141592653589793 3.141586303710938 19 3.141592653589793 3.141586303710938 20 3.141592653589793 3.141590118408203 21 3.141592653589793 3.141592025756836 22 3.141592653589793 3.141592025756836 23 3.141592653589793 3.141592502593994 24 3.141592653589793 3.141592502593994 25 3.141592653589793 3.141592621803284 26 3.141592653589793 3.141592621803284 27 3.141592653589793 3.141592651605606 28 3.141592653589793 3.141592651605606 29 3.141592653589793 3.141592651605606 30 3.141592653589793 3.141592651605606 31 3.141592653589793 3.141592653468251 32 3.141592653589793 3.141592653468251 R8_CHOP_TEST Normal end of execution. R8_COSD_TEST Python version: 3.6.5 R8_COSD computes the cosine of an angle given in degrees. ANGLE R8_COSD(ANGLE) 0.00 1 15.00 0.965926 30.00 0.866025 45.00 0.707107 60.00 0.5 75.00 0.258819 90.00 6.12323e-17 105.00 -0.258819 120.00 -0.5 135.00 -0.707107 150.00 -0.866025 165.00 -0.965926 180.00 -1 195.00 -0.965926 210.00 -0.866025 225.00 -0.707107 240.00 -0.5 255.00 -0.258819 270.00 -1.83697e-16 285.00 0.258819 300.00 0.5 315.00 0.707107 330.00 0.866025 345.00 0.965926 360.00 1 R8_COSD_TEST Normal end of execution. R8_COTD_TEST Python version: 3.6.5 R8_COTD computes the cotangent of an angle given in degrees. ANGLE R8_COTD(ANGLE) 0.00 Undefined 15.00 3.73205 30.00 1.73205 45.00 1 60.00 0.57735 75.00 0.267949 90.00 6.12323e-17 105.00 -0.267949 120.00 -0.57735 135.00 -1 150.00 -1.73205 165.00 -3.73205 180.00 Undefined 195.00 3.73205 210.00 1.73205 225.00 1 240.00 0.57735 255.00 0.267949 270.00 1.83697e-16 285.00 -0.267949 300.00 -0.57735 315.00 -1 330.00 -1.73205 345.00 -3.73205 360.00 Undefined R8_COTD_TEST Normal end of execution. R8_CSC_TEST Python version: 3.6.5 R8_CSC computes the cosecant of an angle. ANGLE R8_CSC(ANGLE) 0.00 Undefined 15.00 1.46037 30.00 -1.00194 45.00 1.29876 60.00 -8.05172 75.00 -1.69796 90.00 1.0177 105.00 -1.18588 120.00 4.05727 135.00 2.06607 150.00 -1.05049 165.00 1.10683 180.00 Undefined 195.00 -2.69119 210.00 1.10311 225.00 -1.05294 240.00 2.09321 255.00 3.94632 270.00 -1.18053 285.00 1.0191 300.00 -1.71484 315.00 -7.61642 330.00 1.29113 345.00 -1.00241 360.00 Undefined R8_CSC_TEST Normal end of execution. R8_CSCD_TEST Python version: 3.6.5 R8_CSCD computes the cosecant of an angle given in degrees. ANGLE R8_CSCD(ANGLE) 0.00 Undefined 15.00 3.8637 30.00 2 45.00 1.41421 60.00 1.1547 75.00 1.03528 90.00 1 105.00 1.03528 120.00 1.1547 135.00 1.41421 150.00 2 165.00 3.8637 180.00 Undefined 195.00 -3.8637 210.00 -2 225.00 -1.41421 240.00 -1.1547 255.00 -1.03528 270.00 -1 285.00 -1.03528 300.00 -1.1547 315.00 -1.41421 330.00 -2 345.00 -3.8637 360.00 Undefined R8_CSCD_TEST Normal end of execution. R8_CUBE_ROOT_TEST Python version: 3.6.5 R8_CUBE_ROOT computes the cube root of an R8. X Y Y^3 -5.63163 -1.77915 -5.63163 9.12635 2.08977 9.12635 6.59018 1.87485 6.59018 1.23391 1.07258 1.23391 -1.69386 -1.19204 -1.69386 -8.67763 -2.05495 -8.67763 -4.84844 -1.69252 -4.84844 -7.80086 -1.98327 -7.80086 -9.12342 -2.08955 -9.12342 2.67931 1.38891 2.67931 R8_CUBE_ROOT_TEST Normal end of execution. R8_DEGREES_TEST Python version: 3.6.5 R8_DEGREES converts an angle from radians to degrees.. Radians Degrees 0.000000 0.000000 0.261799 15.000000 0.523599 30.000000 0.785398 45.000000 1.047198 60.000000 1.308997 75.000000 1.570796 90.000000 1.832596 105.000000 2.094395 120.000000 2.356194 135.000000 2.617994 150.000000 2.879793 165.000000 3.141593 180.000000 R8_DEGREES_TEST Normal end of execution. R8_DIFF_TEST Python version: 3.6.5 R8_DIFF computes a difference X-Y to a given number of binary places. For this test, we use 3 binary places. X Y X-Y R8_DIFF(X,Y) 1.000000 0.062500 0.937500 0.875000 1.000000 0.125000 0.875000 0.875000 1.000000 0.250000 0.750000 0.750000 1.000000 0.500000 0.500000 0.500000 1.000000 0.874000 0.126000 0.125000 1.000000 0.876000 0.124000 0.125000 1.000000 0.900000 0.100000 0.125000 1.000000 0.950000 0.050000 0.000000 1.000000 0.990000 0.010000 0.000000 1.000000 1.000000 0.000000 0.000000 1.000000 1.010000 -0.010000 0.000000 1.000000 1.050000 -0.050000 0.000000 1.000000 1.100000 -0.100000 -0.137500 1.000000 3.000000 -2.000000 -1.875000 1.000000 10.000000 -9.000000 -8.750000 R8_DIFF_TEST Normal end of execution. R8_DIGIT_TEST Python version: 3.6.5 R8_DIGIT extracts decimal digits. Here, we get digits of 3.14159 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 R8_DIGIT_TEST Normal end of execution. R8_DIVIDE_I4_TEST Python version: 3.6.5 R8_DIVIDE_I4 computes an integer ratio as a real number. I J I/J I//J R8_DIVIDE_I4(I,J) -3 -2 1 1 1.5 -3 -1 3 3 3 -3 1 -3 -3 -3 -3 2 -1 -2 -1.5 -3 3 -1 -1 -1 -3 4 0 -1 -0.75 -2 -2 1 1 1 -2 -1 2 2 2 -2 1 -2 -2 -2 -2 2 -1 -1 -1 -2 3 0 -1 -0.666667 -2 4 0 -1 -0.5 -1 -2 0 0 0.5 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 2 0 -1 -0.5 -1 3 0 -1 -0.333333 -1 4 0 -1 -0.25 0 -2 0 0 -0 0 -1 0 0 -0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 1 -2 0 -1 -0.5 1 -1 -1 -1 -1 1 1 1 1 1 1 2 0 0 0.5 1 3 0 0 0.333333 1 4 0 0 0.25 2 -2 -1 -1 -1 2 -1 -2 -2 -2 2 1 2 2 2 2 2 1 1 1 2 3 0 0 0.666667 2 4 0 0 0.5 3 -2 -1 -2 -1.5 3 -1 -3 -3 -3 3 1 3 3 3 3 2 1 1 1.5 3 3 1 1 1 3 4 0 0 0.75 4 -2 -2 -2 -2 4 -1 -4 -4 -4 4 1 4 4 4 4 2 2 2 2 4 3 1 1 1.33333 4 4 1 1 1 5 -2 -2 -3 -2.5 5 -1 -5 -5 -5 5 1 5 5 5 5 2 2 2 2.5 5 3 1 1 1.66667 5 4 1 1 1.25 6 -2 -3 -3 -3 6 -1 -6 -6 -6 6 1 6 6 6 6 2 3 3 3 6 3 2 2 2 6 4 1 1 1.5 7 -2 -3 -4 -3.5 7 -1 -7 -7 -7 7 1 7 7 7 7 2 3 3 3.5 7 3 2 2 2.33333 7 4 1 1 1.75 R8_DIVIDE_I4_TEST Normal end of execution. R8_E_TEST Python version: 3.6.5 R8_E returns the value of E. Compare E to (1+1/n)^n R8_E = 2.71828 N Estimate Error 1 2 0.718282 2 2.25 0.468282 4 2.44141 0.276876 8 2.56578 0.152497 16 2.63793 0.0803533 32 2.67699 0.0412917 64 2.69734 0.0209369 128 2.70774 0.0105428 256 2.71299 0.0052902 512 2.71563 0.00264983 1024 2.71696 0.0013261 2048 2.71762 0.000663346 4096 2.71795 0.000331747 8192 2.71812 0.000165892 16384 2.7182 8.29507e-05 32768 2.71824 4.14765e-05 65536 2.71826 2.07386e-05 131072 2.71827 1.03693e-05 262144 2.71828 5.18469e-06 524288 2.71828 2.59235e-06 1048576 2.71828 1.29618e-06 R8_E_TEST Normal end of execution. R8_EPSILON_TEST Python version: 3.6.5 R8_EPSILON produces the R8 roundoff unit. R = R8_EPSILON() = 2.220446e-16 ( 1 + R ) - 1 = 2.220446e-16 ( 1 + (R/2) ) - 1 = 0.000000e+00 R8_EPSILON_TEST Normal end of execution. R8_EPSILON_COMPUTE_TEST Python version: 3.6.5 R8_EPSILON_COMPUTE computes the R8 roundoff unit. R = R8_EPSILON_COMPUTE() = 2.220446e-16 ( 1 + R ) - 1 = 2.220446e-16 ( 1 + (R/2) ) - 1 = 0.000000e+00 R8_EPSILON_COMPUTE_TEST Normal end of execution. R8_EXP_TEST Python version: 3.6.5 R8_EXP returns the exponential of a real number. X R8_EXP(X) -80 0 -70 0 -60 8.75651e-27 -50 1.92875e-22 -40 4.24835e-18 -30 9.35762e-14 -20 2.06115e-09 -10 4.53999e-05 0 1 10 22026.5 20 4.85165e+08 30 1.06865e+13 40 2.35385e+17 50 5.18471e+21 60 1.14201e+26 70 1e+30 80 1e+30 R8_EXP_TEST Normal end of execution. R8_FACTORIAL_TEST Python version: 3.6.5 R8_FACTORIAL evaluates the factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 6 6 4 24 24 5 120 120 6 720 720 7 5040 5040 8 40320 40320 9 362880 362880 10 3628800 3628800 11 39916800 39916800 12 479001600 479001600 13 6227020800 6227020800 14 87178291200 87178291200 15 1307674368000 1307674368000 16 20922789888000 20922789888000 17 355687428096000 355687428096000 18 6402373705728000 6402373705728000 19 1.21645100408832e+17 1.21645100408832e+17 20 2.43290200817664e+18 2.43290200817664e+18 25 1.551121004333099e+25 1.551121004333099e+25 50 3.041409320171338e+64 3.041409320171338e+64 100 9.332621544394415e+157 9.33262154439441e+157 150 5.713383956445855e+262 5.71338395644585e+262 R8_FACTORIAL_TEST Normal end of execution. R8_FACTORIAL_STIRLING_TEST Python version: 3.6.5 R8_FACTORIAL_STIRLING computes Stirling's approximate factorial function N Factorial Factorial Stirling 1 1.00227 1 2 2.00065 2 3 6.0006 6 4 24.001 24 5 120.003 120 6 720.009 720 7 5040.04 5040 8 40320.2 40320 9 362881 362880 10 3.62881e+06 3.6288e+06 11 3.99169e+07 3.99168e+07 12 4.79002e+08 4.79002e+08 13 6.22703e+09 6.22702e+09 14 8.71784e+10 8.71783e+10 15 1.30768e+12 1.30767e+12 16 2.09228e+13 2.09228e+13 17 3.55688e+14 3.55687e+14 18 6.40238e+15 6.40237e+15 19 1.21645e+17 1.21645e+17 20 2.4329e+18 2.4329e+18 R8_FACTORIAL_STIRLING_TEST Normal end of execution. R8_FACTORIAL_VALUES_TEST: Python version: 3.6.5 R8_FACTORIAL_VALUES returns values of the real factorial function. N R8_FACTORIAL(N) 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 11 3.99168e+07 12 4.79002e+08 13 6.22702e+09 14 8.71783e+10 15 1.30767e+12 16 2.09228e+13 17 3.55687e+14 18 6.40237e+15 19 1.21645e+17 20 2.4329e+18 25 1.55112e+25 50 3.04141e+64 100 9.33262e+157 150 5.71338e+262 R8_FACTORIAL_VALUES_TEST: Normal end of execution. R8_FACTORIAL2_TEST Python version: 3.6.5 R8_FACTORIAL2 evaluates the double factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 3 3 4 8 8 5 15 15 6 48 48 7 105 105 8 384 384 9 945 945 10 3840 3840 11 10395 10395 12 46080 46080 13 135135 135135 14 645120 645120 15 2027025 2027025 R8_FACTORIAL2_TEST Normal end of execution. R8_FACTORIAL2_VALUES_TEST: Python version: 3.6.5 R8_FACTORIAL2_VALUES returns values of the double factorial function. N N!! 0 1 1 1 2 2 3 3 4 8 5 15 6 48 7 105 8 384 9 945 10 3840 11 10395 12 46080 13 135135 14 645120 15 2.02702e+06 R8_FACTORIAL2_VALUES_TEST: Normal end of execution. R8_FALL_TEST Python version: 3.6.5 R8_FALL evaluates the falling factorial Fall(X,N). X N Exact Computed 5 4 120 120 5.25 4 163.16015625 163.16015625 5.5 4 216.5625 216.5625 5.75 4 281.66015625 281.66015625 6 4 360 360 7.5 0 1 1 7.5 1 7.5 7.5 7.5 2 48.75 48.75 7.5 3 268.125 268.125 7.5 4 1206.5625 1206.5625 7.5 5 4222.96875 4222.96875 7.5 6 10557.421875 10557.421875 7.5 7 15836.1328125 15836.1328125 7.5 8 7918.06640625 7918.06640625 7.5 9 -3959.033203125 -3959.033203125 R8_FALL_TEST Normal end of execution. R8_FALL_VALUES_TEST: Python version: 3.6.5 R8_FALL_VALUES returns values of the falling factorial. X N R8_FALL(X,N) 5.0000 4 120 5.2500 4 163.16015625 5.5000 4 216.5625 5.7500 4 281.66015625 6.0000 4 360 7.5000 0 1 7.5000 1 7.5 7.5000 2 48.75 7.5000 3 268.125 7.5000 4 1206.5625 7.5000 5 4222.96875 7.5000 6 10557.421875 7.5000 7 15836.1328125 7.5000 8 7918.06640625 7.5000 9 -3959.033203125 R8_FALL_VALUES_TEST: Normal end of execution. R8_FLOOR_TEST Python version: 3.6.5 R8_FLOOR returns the "floor" of a real number. X R8_FLOOR(X) -5.631634 -6.000000 9.126352 9.000000 6.590185 6.000000 1.233909 1.000000 -1.693858 -2.000000 -8.677625 -9.000000 -4.848444 -5.000000 -7.800864 -8.000000 -9.123420 -10.000000 2.679314 2.000000 R8_FLOOR_TEST Normal end of execution. R8_FRACTION_TEST: Python version: 3.6.5 R8_FRACTION computes a ratio of integers using real arithmetic. I J I/J R8_FRACTION(I,J) 5 20 0 0.25 17 12 1 1.41667 9 2 4 4.5 6 3 2 2 1 13 0 0.0769231 2 9 0 0.222222 9 16 0 0.5625 16 1 16 16 18 8 2 2.25 2 1 2 2 R8_FRACTION_TEST Normal end of execution. R8_FRACTIONAL_TEST Python version: 3.6.5 R8_FRACTIONAL returns the fractional part of an R8. X R8_FRACTIONAL(X) -1.252654 0.252654 4.650541 0.650541 3.636074 0.636074 1.493564 0.493564 0.322457 0.322457 -2.471050 0.471050 -0.939378 0.939378 -2.120346 0.120346 -2.649368 0.649368 2.071726 0.071726 R8_FRACTIONAL_TEST Normal end of execution. R8_GAMMA_TEST: Python version: 3.6.5 R8_GAMMA evaluates the Gamma function. X GAMMA(X) R8_GAMMA(X) -0.5 -3.544907701811032 -3.544907701811032 -0.01 -100.5871979644108 -100.5871979644108 0.01 99.4325851191506 99.4325851191506 0.1 9.513507698668732 9.513507698668731 0.2 4.590843711998803 4.590843711998803 0.4 2.218159543757688 2.218159543757688 0.5 1.772453850905516 1.772453850905516 0.6 1.489192248812817 1.489192248812817 0.8 1.164229713725303 1.164229713725303 1 1 1 1.1 0.9513507698668732 0.9513507698668732 1.2 0.9181687423997607 0.9181687423997607 1.3 0.8974706963062772 0.8974706963062772 1.4 0.8872638175030753 0.8872638175030754 1.5 0.8862269254527581 0.8862269254527581 1.6 0.8935153492876903 0.8935153492876903 1.7 0.9086387328532904 0.9086387328532904 1.8 0.9313837709802427 0.9313837709802427 1.9 0.9617658319073874 0.9617658319073874 2 1 1 3 2 2 4 6 6 10 362880 362880 20 1.21645100408832e+17 1.216451004088321e+17 30 8.841761993739702e+30 8.841761993739751e+30 R8_GAMMA_TEST Normal end of execution. R8_GAMMA_LOG_TEST: Python version: 3.6.5 R8_GAMMA_LOG evaluates the logarithm of the Gamma function. X GAMMA_LOG(X) R8_GAMMA_LOG(X) 0.2 1.524063822430784 1.524063822430784 0.4 0.7966778177017837 0.7966778177017837 0.6 0.3982338580692348 0.3982338580692349 0.8 0.1520596783998375 0.1520596783998376 1 0 0 1.1 -0.04987244125983972 -0.04987244125983976 1.2 -0.08537409000331583 -0.08537409000331585 1.3 -0.1081748095078604 -0.1081748095078605 1.4 -0.1196129141723712 -0.1196129141723713 1.5 -0.1207822376352452 -0.1207822376352453 1.6 -0.1125917656967557 -0.1125917656967558 1.7 -0.09580769740706586 -0.09580769740706586 1.8 -0.07108387291437215 -0.07108387291437215 1.9 -0.03898427592308333 -0.03898427592308337 2 0 0 3 0.6931471805599453 0.6931471805599454 4 1.791759469228055 1.791759469228055 10 12.80182748008147 12.80182748008147 20 39.33988418719949 39.33988418719949 30 71.25703896716801 71.257038967168 R8_GAMMA_LOG_TEST Normal end of execution. R8_HUGE_TEST Python version: 3.6.5 R8_HUGE returns a "huge" R8; R8_HUGE = 1.79769e+308 R8_HUGE_TEST Normal end of execution. R8_HYPOT_TEST Python version: 3.6.5 R8_HYPOT returns an accurate value for sqrt(A^2+B^2). A B R8_HYPOT sqrt(A^2+B^2) 1 1 1.414213562373095 1.414213562373095 1 0.5 1.118033988749895 1.118033988749895 1 0.25 1.030776406404415 1.030776406404415 1 0.125 1.007782218537319 1.007782218537319 1 0.0625 1.001951221367587 1.001951221367587 1 0.03125 1.000488162098883 1.000488162098883 1 0.015625 1.000122062862829 1.000122062862829 1 0.0078125 1.000030517112478 1.000030517112478 1 0.00390625 1.000007629365428 1.000007629365428 1 0.00195312 1.000001907346814 1.000001907346814 1 0.000976562 1.000000476837045 1.000000476837045 1 0.000488281 1.000000119209282 1.000000119209282 1 0.000244141 1.000000029802322 1.000000029802322 1 0.00012207 1.000000007450581 1.000000007450581 1 6.10352e-05 1.000000001862645 1.000000001862645 1 3.05176e-05 1.000000000465661 1.000000000465661 1 1.52588e-05 1.000000000116415 1.000000000116415 1 7.62939e-06 1.000000000029104 1.000000000029104 1 3.8147e-06 1.000000000007276 1.000000000007276 1 1.90735e-06 1.000000000001819 1.000000000001819 R8_HYPOT_TEST Normal end of execution. R8_IS_IN_01_TEST Python version: 3.6.5 R8_IS_IN_01 reports whether an R8 is in [0,1]. R8 R8_IS_IN_01? -0.34 False 1.87 False 1.49 False 0.69 True 0.25 True -0.80 False -0.23 False -0.67 False -0.87 False 0.90 True R8_IS_IN_01_TEST Normal end of execution. R8_IS_INF_TEST Python version: 3.6.5 R8_IS_INF reports whether an R8 is infinite. These tests are wasted, since all the arithmetic operations return run time errors. R8_IS_INF(1.0) = False In Python, 1.0/0.0 causes a run time error! In Python, 0.0/0.0 causes a run time error! R8_IS_INF(0^0) = False In Python, arccos(-2.0) causes a run time error! In Python, exp(1000) causes a run time overflow warning! In Python, log(0) causes a run time error! In Python, sqrt(-1) causes a run time error! R8_IS_INF_TEST Normal end of execution. R8_IS_INSIGNIFICANT_TEST: R8_IS_INSIGNIFICANT ( R, S ) is TRUE is S is insignificant compared to R. R S Insignificant? 1e-30 1e-30 False 2.22045e-16 1e-30 False 1 1e-30 True 1e+30 1e-30 True 1e-30 2.22045e-16 False 2.22045e-16 2.22045e-16 False 1 2.22045e-16 True 1e+30 2.22045e-16 True 1e-30 1 False 2.22045e-16 1 False 1 1 False 1e+30 1 True 1e-30 1e+30 False 2.22045e-16 1e+30 False 1 1e+30 False 1e+30 1e+30 False R8_IS_INSIGNIFICANT_TEST: Normal end of execution. R8_IS_INTEGER_TEST Python version: 3.6.5 R8_IS_INTEGER reports whether an R8 stores an integer value. -1.1429 False -1.0000 True -0.8571 False -0.7143 False -0.5714 False -0.4286 False -0.2857 False -0.1429 False 0.0000 True 0.1429 False 0.2857 False 0.4286 False 0.5714 False 0.7143 False 0.8571 False 1.0000 True 1.1429 False 1.2857 False 1.4286 False 1.5714 False 1.7143 False 1.8571 False 2.0000 True 2.1429 False R8_IS_INTEGER_TEST Normal end of execution. R8_IS_NAN_TEST Python version: 3.6.5 R8_IS_NAN reports whether an R8 is a NaN. These tests are wasted, since all the arithmetic operations return run time errors. R8_IS_NAN(1.0) = 0 In Python, 1.0/0.0 just sets a run time error. In Python, 0.0/0.0 just sets a run time error. R8_IS_NAN(0^0) = 0 In Python, arccos(-2.0) just sets a run time warning. In Python, exp(1000) just sets a run time warning. In Python, log(0.0) just sets a run time warning. In Python, sqrt(-1.0) just sets a run time warning. R8_IS_NAN_TEST Normal end of execution. R8_LOG_10_TEST Python version: 3.6.5 R8_LOG_10 computes the logarithm base 10. X R8_LOG_10 0.000000 -inf 1.000000 0.000000 2.000000 0.301030 3.000000 0.477121 9.000000 0.954243 10.000000 1.000000 11.000000 1.041393 99.000000 1.995635 101.000000 2.004321 -1.000000 0.000000 -2.000000 0.301030 -3.000000 0.477121 -9.000000 0.954243 0.500000 -0.301030 0.330000 -0.481486 0.250000 -0.602060 0.200000 -0.698970 0.010000 -2.000000 R8_LOG_10_TEST Normal end of execution. R8_LOG_2_TEST Python version: 3.6.5 R8_LOG_2 computes the logarithm base 2. X R8_LOG_2 0.000000 -inf 1.000000 0.000000 2.000000 1.000000 3.000000 1.584963 9.000000 3.169925 10.000000 3.321928 11.000000 3.459432 99.000000 6.629357 101.000000 6.658211 -1.000000 0.000000 -2.000000 1.000000 -3.000000 1.584963 -9.000000 3.169925 0.500000 -1.000000 0.330000 -1.599462 0.250000 -2.000000 0.200000 -2.321928 0.010000 -6.643856 R8_LOG_2_TEST Normal end of execution. R8_LOG_B_TEST Python version: 3.6.5 R8_LOG_B computes the logarithm base B. X B R8_LOG_B 16.000000 2.000000 4.000000 16.000000 3.000000 2.523719 16.000000 4.000000 2.000000 16.000000 5.000000 1.722706 16.000000 6.000000 1.547411 16.000000 7.000000 1.424829 16.000000 8.000000 1.333333 16.000000 16.000000 1.000000 16.000000 32.000000 0.800000 16.000000 256.000000 0.500000 R8_LOG_B_TEST Normal end of execution. R8_MANT_TEST Python version: 3.6.5 R8_MANT decomposes a value. Number to be decomposed: -314.159 R8_MANT: X = -1 * 1.227184 * 2^ 8 R8_MANT_TEST Normal end of execution. R8_MAX_TEST Python version: 3.6.5 R8_MAX computes the maximum of two R8's. A B C=R8_MAX(A,B) -5.63163 9.12635 9.12635 6.59018 1.23391 6.59018 -1.69386 -8.67763 -1.69386 -4.84844 -7.80086 -4.84844 -9.12342 2.67931 2.67931 -8.76546 -1.00922 -1.00922 -1.97387 5.09347 5.09347 5.94574 -9.96323 5.94574 7.95008 -2.98495 7.95008 -8.1091 -9.72766 -8.1091 R8_MAX_TEST: Normal end of execution. R8_MIN_TEST Python version: 3.6.5 R8_MIN computes the minimum of two R8's. A B C=R8_MIN(A,B) -5.63163 9.12635 -5.63163 6.59018 1.23391 1.23391 -1.69386 -8.67763 -8.67763 -4.84844 -7.80086 -7.80086 -9.12342 2.67931 -9.12342 -8.76546 -1.00922 -8.76546 -1.97387 5.09347 -1.97387 5.94574 -9.96323 -9.96323 7.95008 -2.98495 -2.98495 -8.1091 -9.72766 -9.72766 R8_MIN_TEST: Normal end of execution. R8_MOD_TEST Python version: 3.6.5 R8_MOD returns the remainder after division. X Y (X%Y) R8_MOD(X,Y) -5.631634 9.126352 3.494717 -5.631634 6.590185 1.233909 0.420640 0.420640 -1.693858 -8.677625 -1.693858 -1.693858 -4.848444 -7.800864 -4.848444 -4.848444 -9.123420 2.679314 1.593837 -1.085477 -8.765455 -1.009221 -0.691689 -0.691689 -1.973874 5.093470 3.119595 -1.973874 5.945739 -9.963233 -4.017493 5.945739 7.950081 -2.984953 -1.004779 1.980175 -8.109105 -9.727662 -8.109105 -8.109105 R8_MOD_TEST Normal end of execution. R8_MODP_TEST Python version: 3.6.5 R8_MODP returns the remainder after division. Unlike the MATLAB MOD, R8_MODP ( X, Y ) is positive. X Y MOD(X,Y) R8_MODP(X,Y) -5.631634 9.126352 3.494717 3.494717 6.590185 1.233909 0.420640 0.420640 -1.693858 -8.677625 -1.693858 6.983767 -4.848444 -7.800864 -4.848444 2.952420 -9.123420 2.679314 1.593837 1.593837 -8.765455 -1.009221 -0.691689 0.317532 -1.973874 5.093470 3.119595 3.119595 5.945739 -9.963233 -4.017493 5.945739 7.950081 -2.984953 -1.004779 1.980175 -8.109105 -9.727662 -8.109105 1.618557 R8_MODP_TEST Normal end of execution. R8_MOP_TEST Python version: 3.6.5 R8_MOP evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) -57 -1.0 92 1.0 66 1.0 12 1.0 -17 -1.0 -87 -1.0 -49 -1.0 -78 1.0 -92 1.0 27 -1.0 R8_MOP_TEST Normal end of execution. R8_NINT_TEST Python version: 3.6.5 R8_NINT produces the nearest integer. X R8_NINT(X) -5.631634 -6 9.126352 10 6.590185 7 1.233909 2 -1.693858 -2 -8.677625 -9 -4.848444 -5 -7.800864 -8 -9.123420 -10 2.679314 3 R8_NINT_TEST Normal end of execution. R8_NORMAL_01_TEST Python version: 3.6.5 R8_NORMAL_01 generates normally distributed random values. Using initial random number seed = 123456789 1.679040 -0.566060 1.212934 1.269381 -1.666087 -2.242464 0.039675 0.673068 -0.275127 2.164005 0.297785 2.044536 1.398819 -1.242985 -0.067084 -0.794396 -0.523768 -0.350567 0.131700 0.537380 R8_NORMAL_01_TEST Normal end of execution. R8_NORMAL_AB_TEST Python version: 3.6.5 R8_NORMAL_AB generates normally distributed values with given mean and standard deviation. Using initial random number seed = 123456789 MEAN = 100 STD = 10 116.79 94.3394 112.129 112.694 83.3391 77.5754 100.397 106.731 97.2487 121.64 102.978 120.445 113.988 87.5701 99.3292 92.056 94.7623 96.4943 101.317 105.374 R8_NORMAL_AB_TEST Normal end of execution. R8_NTH_ROOT_TEST Python version: 3.6.5 R8_NTH_ROOT computes the nth root of an R8. X -3 -2 -1 0 1 2 3 -3 -0.6934 -0.5774 -0.3333 1 -3 nan -1.442 -2 -0.7937 -0.7071 -0.5 1 -2 nan -1.26 -1 -1 -1 -1 1 -1 nan -1 0 inf inf inf 1 0 0 0 1 1 1 1 1 1 1 1 2 0.7937 0.7071 0.5 1 2 1.414 1.26 3 0.6934 0.5774 0.3333 1 3 1.732 1.442 R8_NTH_ROOT_TEST Normal end of execution. R8_PI_TEST Python version: 3.6.5 R8_PI returns the value of PI. R8_PI = 3.1415926535897931 4 * Atan(1) = 3.1415926535897931 np.pi = 3.1415926535897931 R8_PI_TEST Normal end of execution. R8_PI_SQRT_TEST Python version: 3.6.5 R8_PI_SQRT returns the square root of PI. R8_PI_SQRT = 1.7724538509055161 sqrt ( 4 * Atan(1) ) = 1.7724538509055159 sqrt ( NP.PI ) = 1.7724538509055159 NP.PI = 3.1415926535897931 R8_PI_SQRT ** 2 = 3.1415926535897936 R8_PI_SQRT_TEST Normal end of execution. R8_POWER_TEST Python version: 3.6.5 R8_POWER computes R^P. R P R8_POWER 2.000000 -5 0.031250 2.000000 -4 0.062500 2.000000 -3 0.125000 2.000000 -2 0.250000 2.000000 -1 0.500000 2.000000 0 1.000000 2.000000 1 2.000000 2.000000 2 4.000000 2.000000 3 8.000000 2.000000 4 16.000000 2.000000 5 32.000000 R8_POWER_TEST Normal end of execution. R8_POWER_FAST_TEST Python version: 3.6.5 R8_POWER_FAST computes R^P, economizing on multiplications. R P R^P Mults 2.000000 -10 0.000977 7 2.000000 -9 0.001953 7 2.000000 -8 0.003906 6 2.000000 -7 0.007812 7 2.000000 -6 0.015625 6 2.000000 -5 0.031250 6 2.000000 -4 0.062500 5 2.000000 -3 0.125000 5 2.000000 -2 0.250000 4 2.000000 -1 0.500000 1 2.000000 0 1.000000 0 2.000000 1 2.000000 0 2.000000 2 4.000000 3 2.000000 3 8.000000 4 2.000000 4 16.000000 4 2.000000 5 32.000000 5 2.000000 6 64.000000 5 2.000000 7 128.000000 6 2.000000 8 256.000000 5 2.000000 9 512.000000 6 2.000000 10 1024.000000 6 2.000000 11 2048.000000 7 2.000000 12 4096.000000 6 2.000000 13 8192.000000 7 2.000000 14 16384.000000 7 2.000000 15 32768.000000 8 2.000000 16 65536.000000 6 2.000000 17 131072.000000 7 2.000000 18 262144.000000 7 2.000000 19 524288.000000 8 2.000000 20 1048576.000000 7 2.000000 21 2097152.000000 8 2.000000 22 4194304.000000 8 2.000000 23 8388608.000000 9 2.000000 24 16777216.000000 7 2.000000 25 33554432.000000 8 2.000000 26 67108864.000000 8 2.000000 27 134217728.000000 9 2.000000 28 268435456.000000 8 2.000000 29 536870912.000000 9 2.000000 30 1073741824.000000 9 2.000000 31 2147483648.000000 10 2.000000 32 4294967296.000000 7 2.000000 33 8589934592.000000 8 2.000000 34 17179869184.000000 8 2.000000 35 34359738368.000000 9 2.000000 36 68719476736.000000 8 2.000000 37 137438953472.000000 9 2.000000 38 274877906944.000000 9 2.000000 39 549755813888.000000 10 2.000000 40 1099511627776.000000 8 R8_POWER_FAST_TEST Normal end of execution. R8_PRINT_TEST Python version: 3.6.5 R8_PRINT prints an R8 with a label. The value np.pi: 3.14159 The value 1.0: 1 The value -123456789: -1.23457e+08 The value 1.23456789: 1.23457 R8_PRINT_TEST Normal end of execution. R8_RADIANS_TEST Python version: 3.6.5 R8_RADIANS converts an angle from degrees to radians. Degrees Radians 0.000000 0.000000 15.000000 0.261799 30.000000 0.523599 45.000000 0.785398 60.000000 1.047198 75.000000 1.308997 90.000000 1.570796 105.000000 1.832596 120.000000 2.094395 135.000000 2.356194 150.000000 2.617994 165.000000 2.879793 180.000000 3.141593 R8_RADIANS_TEST Normal end of execution. R8_RISE_TEST Python version: 3.6.5 R8_RISE evaluates the rising factorial Rise(X,N). X N Exact Computed 5 4 1680 1680 5.25 4 1962.59765625 1962.59765625 5.5 4 2279.0625 2279.0625 5.75 4 2631.97265625 2631.97265625 6 4 3024 3024 7.5 0 1 1 7.5 1 7.5 7.5 7.5 2 63.75 63.75 7.5 3 605.625 605.625 7.5 4 6359.0625 6359.0625 7.5 5 73129.21875 73129.21875 7.5 6 914115.234375 914115.234375 7.5 7 12340555.6640625 12340555.6640625 7.5 8 178938057.1289063 178938057.1289062 7.5 9 2773539885.498047 2773539885.498047 R8_RISE_TEST Normal end of execution. R8_RISE_VALUES_TEST: Python version: 3.6.5 R8_RISE_VALUES returns values of the rising factorial. X N R8_RISE(X,N) 5.0000 4 1680 5.2500 4 1962.59765625 5.5000 4 2279.0625 5.7500 4 2631.97265625 6.0000 4 3024 7.5000 0 1 7.5000 1 7.5 7.5000 2 63.75 7.5000 3 605.625 7.5000 4 6359.0625 7.5000 5 73129.21875 7.5000 6 914115.234375 7.5000 7 12340555.6640625 7.5000 8 178938057.1289063 7.5000 9 2773539885.498047 R8_RISE_VALUES_TEST: Normal end of execution. R8_ROUND_TEST Python version: 3.6.5 R8_ROUND rounds a real number to a real number with integer value. X XROUND 21.841830 22.000000 -95.631758 -96.000000 82.950923 83.000000 -56.169544 -56.000000 41.530708 42.000000 -6.611873 -7.000000 25.757779 26.000000 -10.995679 -11.000000 4.382900 4.000000 -63.396571 -63.000000 R8_ROUND_TEST Normal end of execution. R8_ROUND2_TEST Python version: 3.6.5 R8_ROUND2 rounds a number to a specified number of base 2 digits. Test effect on PI. X = 3.141593 NPLACE XROUND 0 0.000000 1 2.000000 2 3.000000 3 3.000000 4 3.000000 5 3.125000 6 3.125000 7 3.125000 8 3.140625 9 3.140625 10 3.140625 11 3.140625 12 3.140625 13 3.141113 14 3.141357 15 3.141479 16 3.141541 17 3.141571 18 3.141586 19 3.141586 20 3.141590 R8_ROUND2_TEST Normal end of execution. R8_ROUNDB_TEST Python version: 3.6.5 R8_ROUNDB rounds a number to a specified number of base BASE digits. Here, we will use BASE = 3 Test effect on PI: X = 3.141593 NPLACE XROUND 0 0.000000 1 3.000000 2 3.000000 3 3.000000 4 3.111111 5 3.111111 6 3.135802 7 3.139918 8 3.141289 9 3.141289 10 3.141442 11 3.141543 12 3.141577 13 3.141589 14 3.141592 15 3.141592 16 3.141593 17 3.141593 18 3.141593 19 3.141593 20 3.141593 Try with a negative base: Input quantity is X = 121.000000 to be rounded in base -3 Output value to 1 places is 81.000000 Output value to 2 places is 108.000000 Output value to 3 places is 117.000000 Output value to 4 places is 120.000000 Output value to 5 places is 121.000000 R8_ROUNDB_TEST Normal end of execution. R8_ROUNDX_TEST Python version: 3.6.5 R8_ROUNDX rounds a number to a specified number of decimal digits. Test effect on PI: X = 3.141593 NPLACE XROUND 0 0.000000 1 3.000000 2 3.100000 3 3.140000 4 3.141000 5 3.141500 6 3.141590 7 3.141592 8 3.141593 9 3.141593 10 3.141593 Test effect on random values: NPLACE X XROUND 0 0.218418 0.000000 2 0.218418 0.210000 4 0.218418 0.218400 6 0.218418 0.218418 8 0.218418 0.218418 10 0.218418 0.218418 0 0.956318 0.000000 2 0.956318 0.950000 4 0.956318 0.956300 6 0.956318 0.956317 8 0.956318 0.956318 10 0.956318 0.956318 0 0.829509 0.000000 2 0.829509 0.820000 4 0.829509 0.829500 6 0.829509 0.829509 8 0.829509 0.829509 10 0.829509 0.829509 0 0.561695 0.000000 2 0.561695 0.560000 4 0.561695 0.561600 6 0.561695 0.561695 8 0.561695 0.561695 10 0.561695 0.561695 0 0.415307 0.000000 2 0.415307 0.410000 4 0.415307 0.415300 6 0.415307 0.415307 8 0.415307 0.415307 10 0.415307 0.415307 R8_ROUNDX_TEST Normal end of execution. R8_SECD_TEST Python version: 3.6.5 R8_SECD computes the secant of an angle given in degrees. ANGLE R8_SECD(ANGLE) 0.00 1 15.00 1.03528 30.00 1.1547 45.00 1.41421 60.00 2 75.00 3.8637 90.00 Undefined 105.00 -3.8637 120.00 -2 135.00 -1.41421 150.00 -1.1547 165.00 -1.03528 180.00 -1 195.00 -1.03528 210.00 -1.1547 225.00 -1.41421 240.00 -2 255.00 -3.8637 270.00 Undefined 285.00 3.8637 300.00 2 315.00 1.41421 330.00 1.1547 345.00 1.03528 360.00 1 R8_SECD_TEST Normal end of execution. R8_SECH_TEST Python version: 3.6.5 R8_SECH computes the hyperbolic secant. X R8_SECH(X) -1 0.648054 -0.9 0.697795 -0.8 0.7477 -0.7 0.796705 -0.6 0.843551 -0.5 0.886819 -0.4 0.925007 -0.3 0.956628 -0.2 0.980328 -0.1 0.995021 0 1 0.1 0.995021 0.2 0.980328 0.3 0.956628 0.4 0.925007 0.5 0.886819 0.6 0.843551 0.7 0.796705 0.8 0.7477 0.9 0.697795 1 0.648054 R8_SECH_TEST Normal end of execution. R8_SIGMOID_TEST Python version: 3.6.5 R8_SIGMOID evaluates the sigmoid function of R8. X R8_SIGMOID(X) -4 0.0179862 -2 0.119203 -1 0.268941 -0.5 0.377541 -0.25 0.437823 0 0.5 0.25 0.562177 0.5 0.622459 1 0.731059 2 0.880797 4 0.982014 R8_SIGMOID_TEST Normal end of execution. R8_SIGN_TEST Python version: 3.6.5 R8_SIGN returns the sign of an R8. R8 R8_SIGN(R8) -1.2500 -1 -0.2500 -1 0.0000 1 0.5000 1 9.0000 1 R8_SIGN_TEST Normal end of execution. R8_SIGN_CHAR_TEST Python version: 3.6.5 R8_SIGN_CHAR returns the sign of an R8 as a character. R8 R8_SIGNCHAR(R8) -2.815817 - 4.563176 + 3.295092 + 0.616954 + -0.846929 - -4.338813 - -2.424222 - -3.900432 - -4.561710 - 1.339657 + R8_SIGN_CHAR_TEST Normal end of execution. R8_SIGN_MATCH_TEST Python version: 3.6.5 R8_SIGN_MATCH is TRUE if two R8's have matching signs. R1 R2 Match(R1,R2)? 0.0000 0.0000 True -5.6316 9.1264 False 6.5902 1.2339 True -1.6939 -8.6776 True 0.0000 -4.8484 True -7.8009 -9.1234 True 2.6793 -8.7655 False -1.0092 -1.9739 True 0.0000 5.0935 True 5.9457 -9.9632 False 7.9501 0.0000 True -2.9850 -8.1091 True 0.0000 -9.7277 True 7.1819 6.8169 True -7.5379 -9.8498 True -4.7939 8.2497 False 0.0000 -7.7267 True -2.9674 6.4577 False -4.6574 3.8413 False 1.2332 7.2243 True 0.0000 0.0000 True R8_SIGN_MATCH_TEST Normal end of execution. R8_SIGN_MATCH_STRICT_TEST Python version: 3.6.5 R8_SIGN_MATCH_STRICT is TRUE if two R8's have matching signs. R1 R2 MatchStrict(R1,R2)? 0.0000 0.0000 True -5.6316 9.1264 False 6.5902 1.2339 True -1.6939 -8.6776 True 0.0000 -4.8484 False -7.8009 -9.1234 True 2.6793 -8.7655 False -1.0092 -1.9739 True 0.0000 5.0935 False 5.9457 -9.9632 False 7.9501 0.0000 False -2.9850 -8.1091 True 0.0000 -9.7277 False 7.1819 6.8169 True -7.5379 -9.8498 True -4.7939 8.2497 False 0.0000 -7.7267 False -2.9674 6.4577 False -4.6574 3.8413 False 1.2332 7.2243 True 0.0000 0.0000 True R8_SIGN_MATCH_STRICT_TEST Normal end of execution. R8_SIGN_OPPOSITE_TEST Python version: 3.6.5 R8_SIGN_OPPOSITE is TRUE if two R8's have opposite signs. R1 R2 Opposite(R1,R2)? 0.0000 0.0000 True -5.6316 9.1264 True 6.5902 1.2339 False -1.6939 -8.6776 False 0.0000 -4.8484 True -7.8009 -9.1234 False 2.6793 -8.7655 True -1.0092 -1.9739 False 0.0000 5.0935 True 5.9457 -9.9632 True 7.9501 0.0000 True -2.9850 -8.1091 False 0.0000 -9.7277 True 7.1819 6.8169 False -7.5379 -9.8498 False -4.7939 8.2497 True 0.0000 -7.7267 True -2.9674 6.4577 True -4.6574 3.8413 True 1.2332 7.2243 False 0.0000 0.0000 True R8_SIGN_OPPOSITE_TEST Normal end of execution. R8_SIGN_OPPOSITE_STRICT_TEST Python version: 3.6.5 R8_SIGN_OPPOSITE_STRICT is TRUE if two R8's have opposite signs. R1 R2 OppositeStrict(R1,R2)? 0.0000 0.0000 False -5.6316 9.1264 True 6.5902 1.2339 False -1.6939 -8.6776 False 0.0000 -4.8484 False -7.8009 -9.1234 False 2.6793 -8.7655 True -1.0092 -1.9739 False 0.0000 5.0935 False 5.9457 -9.9632 True 7.9501 0.0000 False -2.9850 -8.1091 False 0.0000 -9.7277 False 7.1819 6.8169 False -7.5379 -9.8498 False -4.7939 8.2497 True 0.0000 -7.7267 False -2.9674 6.4577 True -4.6574 3.8413 True 1.2332 7.2243 False 0.0000 0.0000 False R8_SIGN_OPPOSITE_STRICT_TEST Normal end of execution. R8_SIGN3_TEST Python version: 3.6.5 R8_SIGN3 returns the three-way sign of an R8. R8 R8_SIGN3(R8) -1.25 -1 -0.25 -1 0 0 0.5 1 9 1 R8_SIGN3_TEST Normal end of execution. R8_SINCOS_SUM_TEST Python version: 3.6.5 R8_SINCOS_SUM simplifies a linear sine and cosine sum -2.81582 * sin ( 3.29509 * x ) + 4.56318 * cos ( 3.29509 * x ) = 5.36203 * sin ( 3.29509 * x + 2.12368 ) = 5.36203 * cos ( 3.29509 * x + 0.552879 ) I X form 1 form 2 form 3 0 0.000000 4.56318 4.56318 4.56318 1 0.314159 -0.0925808 -0.0925808 -0.0925808 2 0.628319 -4.65768 -4.65768 -4.65768 3 0.942478 -4.66168 -4.66168 -4.66168 4 1.256637 -0.100663 -0.100663 -0.100663 5 1.570796 4.55893 4.55893 4.55893 6 1.884956 4.75412 4.75412 4.75412 7 2.199115 0.293777 0.293777 0.293777 8 2.513274 -4.45425 -4.45425 -4.45425 9 2.827433 -4.84039 -4.84039 -4.84039 10 3.141593 -0.486508 -0.486508 -0.486508 R8_SINCOS_SUM_TEST Normal end of execution. R8_SIND_TEST Python version: 3.6.5 R8_SIND computes the sine of an angle given in degrees. ANGLE R8_SIND(ANGLE) 0.00 0 15.00 0.258819 30.00 0.5 45.00 0.707107 60.00 0.866025 75.00 0.965926 90.00 1 105.00 0.965926 120.00 0.866025 135.00 0.707107 150.00 0.5 165.00 0.258819 180.00 1.22465e-16 195.00 -0.258819 210.00 -0.5 225.00 -0.707107 240.00 -0.866025 255.00 -0.965926 270.00 -1 285.00 -0.965926 300.00 -0.866025 315.00 -0.707107 330.00 -0.5 345.00 -0.258819 360.00 -2.44929e-16 R8_SIND_TEST Normal end of execution. R8_SOFTPLUS_TEST Python version: 3.6.5 R8_SOFTPLUS evaluates the softplus function of an R8. This is a smoothed version of max(x,0). X R8_SOFTPLUS(X) -500 0 -50 0 -5 0.00671535 -4 0.0181499 -3 0.0485874 -2 0.126928 -1 0.313262 -0.5 0.474077 -0.05 0.66846 -0.005 0.69065 -0.0005 0.692897 0 0.693147 0.0005 0.693397 0.005 0.69565 0.05 0.71846 0.5 0.974077 1 1.31326 2 2.12693 3 3.04859 4 4.01815 5 5.00672 50 50 500 500 5000 5000 50000 50000 R8_SOFTPLUS_TEST Normal end of execution. R8_SQRT_I4_TEST Python version: 3.6.5 R8_SQRT_I4 returns the square root of an I4 as an R8. I4 R8_SQRT_I4(I4) 218418 467.352 956318 977.915 829510 910.774 561696 749.464 415307 644.443 66118 257.134 257578 507.521 109956 331.596 43829 209.354 633966 796.22 R8_SQRT_I4_TEST Normal end of execution. R8_SWAP_TEST Python version: 3.6.5 R8_SWAP swaps two reals. Before swapping: X = 1.000000 Y = 3.141590 After swapping: X = 3.141590 Y = 1.000000 R8_SWAP_TEST Normal end of execution. R8_SWAP3_TEST Python version: 3.6.5 R8_SWAP3 swaps three reals. Before 1 3.14159 1952 Swap 0: 3.14159 1952 1 Swap 1: 1952 1 3.14159 Swap 2: 1 3.14159 1952 R8_SWAP3_TEST Normal end of execution. R8_TAND_TEST Python version: 3.6.5 R8_TAND computes the tangent of an angle given in degrees. ANGLE R8_TAND(ANGLE) 0.00 0 15.00 0.267949 30.00 0.57735 45.00 1 60.00 1.73205 75.00 3.73205 90.00 Undefined 105.00 -3.73205 120.00 -1.73205 135.00 -1 150.00 -0.57735 165.00 -0.267949 180.00 -1.22465e-16 195.00 0.267949 210.00 0.57735 225.00 1 240.00 1.73205 255.00 3.73205 270.00 Undefined 285.00 -3.73205 300.00 -1.73205 315.00 -1 330.00 -0.57735 345.00 -0.267949 360.00 -2.44929e-16 R8_TAND_TEST Normal end of execution. R8_TINY_TEST Python version: 3.6.5 R8_TINY returns a "tiny" R8; R8_TINY = 1e-30 R8_TINY_TEST Normal end of execution. R8_TO_DHMS_TEST Python version: 3.6.5 R8_TO_DHMS converts a real day measure into days, hours, minutes, seconds. X D H M S 0.62102 0 14 54 16.0903 9.47581 9 11 25 10.0633 7.95411 7 22 53 55.1737 4.74035 4 17 46 5.83506 2.98368 2 23 36 30.3821 -1.20658 -1 -4 -57 -28.0956 1.09093 1 2 10 56.6551 -0.680518 0 -16 -19 -56.7965 -1.47405 -1 -11 -22 -38.0951 5.60759 5 14 34 55.6505 R8_TO_DHMS_TEST Normal end of execution. R8_TO_I4_TEST Python version: 3.6.5 R8_TO_I4 finds an integer IX in [IXMIN,IXMAX] corresponding to X in [XMIN,XMAX]. XMIN = 2.500000, X = 3.500000, XMAX = 5.500000 IXMIN = 10, IX = 20, IXMAX = 40 R8_TO_I4_TEST Normal end of execution. R8_TO_R8_DISCRETE_TEST Python version: 3.6.5 R8_TO_R8_DISCRETE maps numbers to a discrete set of equally spaced numbers in an interval. Number of discrete values = 19 Real interval: [1.000000, 10.000000] R RD 1.839438 1.947368 11.432128 10.000000 9.783620 10.000000 6.302041 6.210526 4.398992 4.315789 -0.140456 1.000000 2.348511 2.421053 0.429438 1.000000 -0.430223 1.000000 7.241554 7.157895 -0.197546 1.000000 4.844006 4.789474 4.216982 4.315789 8.810755 8.578947 9.364730 9.526316 R8_TO_R8_DISCRETE_TEST Normal end of execution. R8_UNIFORM_01_TEST Python version: 3.6.5 R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 R8_UNIFORM_01_TEST Normal end of execution. R8_UNIFORM_AB_TEST Python version: 3.6.5 R8_UNIFORM_AB returns random values in a given range: [ A, B ] For this problem: A = 10.000000 B = 20.000000 12.184183 19.563176 18.295092 15.616954 14.153071 10.661187 12.575778 11.099568 10.438290 16.339657 R8_UNIFORM_AB_TEST Normal end of execution R8_UNSWAP3_TEST Python version: 3.6.5 R8_UNSWAP3 unswaps three reals. Data : 1 3.14159 1952 Swap : 3.14159 1952 1 Unswap : 1 3.14159 1952 R8_UNSWAP3_TEST Normal end of execution. R8_WALSH_1D_TEST Python version: 3.6.5 R8_WALSH_1D evaluates 1D Walsh functions: X W(+2) W(+1) W(0) W(-1) W(-2) W(-3) 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.250000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.500000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.750000 0.000000 0.000000 0.000000 1.000000 1.000000 0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.250000 0.000000 0.000000 1.000000 0.000000 1.000000 0.000000 1.500000 0.000000 0.000000 1.000000 1.000000 0.000000 0.000000 1.750000 0.000000 0.000000 1.000000 1.000000 1.000000 0.000000 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 2.250000 0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 2.500000 0.000000 1.000000 0.000000 1.000000 0.000000 0.000000 2.750000 0.000000 1.000000 0.000000 1.000000 1.000000 0.000000 3.000000 0.000000 1.000000 1.000000 0.000000 0.000000 0.000000 3.250000 0.000000 1.000000 1.000000 0.000000 1.000000 0.000000 3.500000 0.000000 1.000000 1.000000 1.000000 0.000000 0.000000 3.750000 0.000000 1.000000 1.000000 1.000000 1.000000 0.000000 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 4.250000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 4.500000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 4.750000 1.000000 0.000000 0.000000 1.000000 1.000000 0.000000 5.000000 1.000000 0.000000 1.000000 0.000000 0.000000 0.000000 5.250000 1.000000 0.000000 1.000000 0.000000 1.000000 0.000000 5.500000 1.000000 0.000000 1.000000 1.000000 0.000000 0.000000 5.750000 1.000000 0.000000 1.000000 1.000000 1.000000 0.000000 6.000000 1.000000 1.000000 0.000000 0.000000 0.000000 0.000000 6.250000 1.000000 1.000000 0.000000 0.000000 1.000000 0.000000 6.500000 1.000000 1.000000 0.000000 1.000000 0.000000 0.000000 6.750000 1.000000 1.000000 0.000000 1.000000 1.000000 0.000000 7.000000 1.000000 1.000000 1.000000 0.000000 0.000000 0.000000 7.250000 1.000000 1.000000 1.000000 0.000000 1.000000 0.000000 7.500000 1.000000 1.000000 1.000000 1.000000 0.000000 0.000000 7.750000 1.000000 1.000000 1.000000 1.000000 1.000000 0.000000 8.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 R8_WALSH_1D_TEST Normal end of execution R8_WRAP_TEST Python version: 3.6.5 R8_WRAP "wraps" an R8 to lie within an interval: Wrapping interval is 3.000000, 6.500000 R R8_WRAP ( R ) 1.05786 4.55786 11.3884 4.38845 9.61313 6.11313 5.86374 5.86374 3.8143 3.8143 -1.07434 5.92566 1.60609 5.10609 -0.460605 3.0394 -1.38639 5.61361 6.87552 3.37552 -1.13582 5.86418 4.29355 4.29355 3.61829 3.61829 8.56543 5.06543 9.16202 5.66202 -1.97426 5.02574 10.5651 3.56506 2.91053 6.41053 -0.676373 6.32363 -1.80936 5.19064 R8_WRAP_TEST Normal end of execution. R82COL_PRINT_PART_TEST Python version: 3.6.5 R82COL_PRINT_PART prints an R82COL. Output with MAX_PRINT = 2 0 11 12 1 21 22 ...more entries... Output with MAX_PRINT = 5 0 11 12 1 21 22 2 31 32 .... .............. .............. 9 101 102 Output with MAX_PRINT = 25 0 11 12 1 21 22 2 31 32 3 41 42 4 51 52 5 61 62 6 71 72 7 81 82 8 91 92 9 101 102 R82COL_PRINT_PART_TEST: Normal end of execution. R82ROW_PRINT_PART_TEST R82ROW_PRINT_PART prints part of an R82ROW, a real array of 2 rows. Output with MAX_PRINT = 2 0 11 21 1 12 22 ...more entries... Output with MAX_PRINT = 5 0 11 21 1 12 22 2 13 23 .... .............. .............. 9 20 30 Output with MAX_PRINT = 25 0 11 21 1 12 22 2 13 23 3 14 24 4 15 25 5 16 26 6 17 27 7 18 28 8 19 29 9 20 30 R82ROW_PRINT_PART_TEST: Normal end of execution. R82VEC_PRINT_PART_TEST Python version: 3.6.5 R82VEC_PRINT_PART prints an R8VEC. Output with MAX_PRINT = 2 0 11.000000 21.000000 1 12.000000 22.000000 ...more entries... Output with MAX_PRINT = 5 0 11.000000 21.000000 1 12.000000 22.000000 2 13.000000 23.000000 .... .............. .............. 9 20.000000 30.000000 Output with MAX_PRINT = 25 0 11.000000 21.000000 1 12.000000 22.000000 2 13.000000 23.000000 3 14.000000 24.000000 4 15.000000 25.000000 5 16.000000 26.000000 6 17.000000 27.000000 7 18.000000 28.000000 8 19.000000 29.000000 9 20.000000 30.000000 R82VEC_PRINT_PART_TEST: Normal end of execution. R83COL_PRINT_PART_TEST Python version: 3.6.5 R83COL_PRINT_PART prints part of an R83COL. Output with MAX_PRINT = 2 0 11 12 13 1 21 22 23 ...more entries... Output with MAX_PRINT = 5 0 11 12 13 1 21 22 23 2 31 32 33 .... .............. .............. .............. 9 101 102 103 Output with MAX_PRINT = 25 0 11 12 13 1 21 22 23 2 31 32 33 3 41 42 43 4 51 52 53 5 61 62 63 6 71 72 73 7 81 82 83 8 91 92 93 9 101 102 103 R83COL_PRINT_PART_TEST: Normal end of execution. R83ROW_PRINT_PART_TEST Python version: 3.6.5 R83ROW_PRINT_PART prints part of an R83ROW, a real array of 3 rows. Output with MAX_PRINT = 2 0 11 21 31 1 12 22 32 ...more entries... Output with MAX_PRINT = 5 0 11 21 31 1 12 22 32 2 13 23 33 .... .............. .............. 9 20 30 40 Output with MAX_PRINT = 25 0 11 21 31 1 12 22 32 2 13 23 33 3 14 24 34 4 15 25 35 5 16 26 36 6 17 27 37 7 18 28 38 8 19 29 39 9 20 30 40 R83ROW_PRINT_PART_TEST: Normal end of execution. R8MAT_ADD_TEST Python version: 3.6.5 R8MAT_ADD computes C = alpha * A + beta * B for R8MATs. A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 B: Col: 0 1 2 3 Row 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 3 : 14 24 34 44 ALPHA = 3, BETA = 0.5 C = alpha * A + beta * B: Col: 0 1 2 3 Row 0 : 38.5 46.5 54.5 62.5 1 : 69 77 85 93 2 : 99.5 107.5 115.5 123.5 3 : 130 138 146 154 R8MAT_ADD_TEST: Normal end of execution. R8MAT_CHOLESKY_FACTOR_TEST Python version: 3.6.5 R8MAT_CHOLESKY_FACTOR determines the lower triangular Cholesky factorization of a positive definite symmetric matrix, Matrix to be factored: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1.41421 0 0 0 0 1 : -0.707107 1.22474 0 0 0 2 : 0 -0.816497 1.1547 0 0 3 : 0 0 -0.866025 1.11803 0 4 : 0 0 0 -0.894427 1.09545 Product L * L': Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 R8MAT_CHOLESKY_FACTOR_TEST: Normal end of execution. R8MAT_CHOLESKY_FACTOR_UPPER_TEST Python version: 3.6.5 R8MAT_CHOLESKY_FACTOR_UPPER determines the upper triangular Cholesky factorization of a positive definite symmetric matrix, Matrix to be factored: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 Cholesky factor R: Col: 0 1 2 3 4 Row 0 : 1.41421 -0.707107 0 0 0 1 : 0 1.22474 -0.816497 0 0 2 : 0 0 1.1547 -0.866025 0 3 : 0 0 0 1.11803 -0.894427 4 : 0 0 0 0 1.09545 Product R' * R: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 R8MAT_CHOLESKY_FACTOR_UPPER_TEST: Normal end of execution. R8MAT_CHOLESKY_SOLVE_TEST Python version: 3.6.5 R8MAT_CHOLESKY_SOLVE solves a linear system using the lower triangular Cholesky factorization, for a positive definite symmetric matrix. Matrix to be factored: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 Cholesky factor L: Col: 0 1 2 3 4 Row 0 : 1.41421 0 0 0 0 1 : -0.707107 1.22474 0 0 0 2 : 0 -0.816497 1.1547 0 0 3 : 0 0 -0.866025 1.11803 0 4 : 0 0 0 -0.894427 1.09545 Product L * L': Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 Right hand side b: 0: 0 1: 0 2: 0 3: 0 4: 6 Computed solution x: 0: 1 1: 2 2: 3 3: 4 4: 5 R8MAT_CHOLESKY_SOLVE_TEST: Normal end of execution. R8MAT_DET_2D_TEST Python version: 3.6.5 R8MAT_DET_2D: determinant of a 2 by 2 matrix; Matrix: Col: 0 1 Row 0 : 1 1 1 : 1 10 R8MAT_DET_2D computes determinant: 9 Exact determinant is 9 R8MAT_DET_2D_TEST Normal end of execution. R8MAT_DET_3D_TEST Python version: 3.6.5 R8MAT_DET_3D: determinant of a 3 by 3 matrix Matrix: Col: 0 1 2 Row 0 : 1 1 1 1 : 1 10 100 2 : 1 4 16 R8MAT_DET_3D computes determinant: -162 Exact determinant is -162 R8MAT_DET_3D_TEST Normal end of execution. R8MAT_DET_4D_TEST Python version: 3.6.5 R8MAT_DET_4D determinant of a 4 by 4 matrix Matrix: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 10 100 1000 2 : 1 4 16 64 3 : 1 2 4 8 R8MAT_DET_4D computes determinant: -2592 Exact determinant is -2592 R8MAT_DET_4D_TEST Normal end of execution. R8MAT_DIAG_GET_VECTOR_TEST Python version: 3.6.5 R8MAT_DIAG_GET_VECTOR retrieves the diagonal from an R8MAT. Random R8MAT: Col: 0 1 2 3 4 Row 0 : 0.218418 0.0661187 0.0617272 0.00183837 0.859097 1 : 0.956318 0.257578 0.449539 0.897504 0.840847 2 : 0.829509 0.109957 0.401306 0.350752 0.123104 3 : 0.561695 0.043829 0.754673 0.0945448 0.00751236 4 : 0.415307 0.633966 0.797287 0.0136169 0.260303 Diagonal vector: 0: 0.218418 1: 0.257578 2: 0.401306 3: 0.0945448 4: 0.260303 R8MAT_DIAG_GET_VECTOR_TEST: Normal end of execution. R8MAT_HOUSE_AXH_TEST Python version: 3.6.5 R8MAT_HOUSE_AXH multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : 3.29509 -3.90043 -0.986937 -1.49248 -3.76896 3 : 0.616954 -4.56171 2.54673 -4.05455 -4.92488 4 : -0.846929 1.33966 2.97287 -4.86383 -2.39697 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.788819 3: 0.399863 4: 0.466771 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 -0.244469 0.630839 0.736395 3 : 0 0 0.630839 0.680219 -0.373289 4 : 0 0 0.736395 -0.373289 0.56425 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : -1.04002 -0.937652 4.03706 -5.7746 -3.95052 3 : 2.81449 -6.06358 -4.44089e-16 -1.88388 -4.83284 4 : 1.71831 -0.41352 -4.44089e-16 -2.32995 -2.28953 R8MAT_HOUSE_AXH_TEST Normal end of execution. R8MAT_HOUSE_FORM_TEST Python version: 3.6.5 R8MAT_HOUSE_FORM forms a Householder matrix from its compact form. Compact vector form V: 0: 0 1: 0 2: 1 3: 2 4: 3 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 0.857143 -0.285714 -0.428571 3 : 0 0 -0.285714 0.428571 -0.857143 4 : 0 0 -0.428571 -0.857143 -0.285714 R8MAT_HOUSE_FORM_TEST Normal end of execution. R8MAT_IDENTITY_TEST Python version: 3.6.5 R8MAT_IDENTITY creates an identity matrix. The identity matrix: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 1 0 0 3 : 0 0 0 1 0 4 : 0 0 0 0 1 R8MAT_IDENTITY_TEST Normal end of execution. R8MAT_INDICATOR_TEST Python version: 3.6.5 R8MAT_INDICATOR creates an "indicator" R8MAT. The indicator matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 R8MAT_INDICATOR_TEST Normal end of execution. R8MAT_INVERSE_3D_TEST R8MAT_INVERSE_3D inverts a 3 by 3 matrix. Matrix A to be inverted: Col: 0 1 2 Row 0 : 1 2 3 1 : 4 5 6 2 : 7 8 0 Inverse matrix B: Col: 0 1 2 Row 0 : -1.77778 0.888889 -0.111111 1 : 1.55556 -0.777778 0.222222 2 : -0.111111 0.222222 -0.111111 Product C = A * B: Col: 0 1 2 Row 0 : 1 -1.11022e-16 0 1 : 3.33067e-16 1 1.11022e-16 2 : 1.77636e-15 -8.88178e-16 1 R8MAT_INVERSE_3D_TEST: Normal end of execution. R8MAT_IS_BINARY_TEST Python version: 3.6.5 R8MAT_IS_BINARY is TRUE if an R8MAT only contains 0 or 1 entries. X: Col: 0 1 2 Row 0 : 0 1 0 1 : 1 0 1 X is binary X: Col: 0 1 2 Row 0 : 1 1 1 1 : 1 1 1 X is binary X: Col: 0 1 2 Row 0 : 0 1 0 1 : 1 2 1 X is NOT binary. R8MAT_IS_BINARY_TEST Normal end of execution. R8MAT_L_SOLVE_TEST Python version: 3.6.5 R8MAT_L_SOLVE solves a lower triangular system. Input matrix A: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 2 3 0 0 2 : 4 5 6 0 3 : 7 8 9 10 Right hand side b: 0: 1 1: 8 2: 32 3: 90 Computed solution x: 0: 1 1: 2 2: 3 3: 4 Norm of A*x-b = 0 R8MAT_L_SOLVE_TEST Normal end of execution. R8MAT_LT_SOLVE_TEST Python version: 3.6.5 R8MAT_LT_SOLVE solves a transposed lower triangular system. Input matrix A: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 2 3 0 0 2 : 4 5 6 0 3 : 7 8 9 10 Right hand side b: 0: 45 1: 53 2: 54 3: 40 Computed solution x: 0: 1 1: 2 2: 3 3: 4 Norm of A'*x-b = 0 R8MAT_LT_SOLVE_TEST Normal end of execution. R8MAT_MM_TEST Python version: 3.6.5 R8MAT_MM computes a matrix-matrix product C = A * B; A: Col: 0 1 2 Row 0 : 1 0 0 1 : 1 1 0 2 : 1 2 1 3 : 1 3 3 B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 0 1 2 3 2 : 0 0 1 3 C = A*B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 3 4 2 : 1 3 6 10 3 : 1 4 10 19 R8MAT_MM_TEST Normal end of execution. R8MAT_MTM_TEST Python version: 3.6.5 R8MAT_MTM computes a matrix-matrix product C = A' * B; A: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 C = A'*B: Col: 0 1 2 3 Row 0 : 3 3 1 0 1 : 3 5 2 0 2 : 1 2 1 0 3 : 0 0 0 0 R8MAT_MTM_TEST Normal end of execution. R8MAT_MTV_TEST Python version: 3.6.5 R8MAT_MTV computes a matrix-vector product b = A' * x; A: Col: 0 1 Row 0 : 1 1 1 : 2 1 2 : 3 1 3 : 4 1 X: 0: 1 1: 2 2: 3 3: 4 B = A'*X: 0: 30 1: 10 R8MAT_MTV_TEST Normal end of execution. R8MAT_MV_TEST Python version: 3.6.5 R8MAT_MV computes a matrix-vector product b = A * x; A: Col: 0 1 Row 0 : 1 1 1 : 2 1 2 : 3 1 3 : 4 1 X: 0: 1 1: 2 B = A*X: 0: 3 1: 4 2: 5 3: 6 R8MAT_MV_TEST Normal end of execution. R8MAT_NINT_TEST Python version: 3.6.5 R8MAT_NINT rounds an R8MAT. Matrix A: Col: 0 1 2 3 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 1 : 4.56318 -2.42422 -0.50461 3.97504 2 : 3.29509 -3.90043 -0.986937 -1.49248 3 : 0.616954 -4.56171 2.54673 -4.05455 4 : -0.846929 1.33966 2.97287 -4.86383 Rounded matrix A: Col: 0 1 2 3 Row 0 : -3 -4 -4 -5 1 : 5 -2 -1 4 2 : 3 -4 -1 -1 3 : 1 -5 3 -4 4 : -1 1 3 -5 R8MAT_NINT_TEST Normal end of execution. R8MAT_NONZEROS_TEST Python version: 3.6.5 R8MAT_NONZEROS counts nonzeros in an R8MAT. Matrix A: Col: 0 1 2 3 Row 0 : 1 0 1 0 1 : 0 0 0 0 2 : 1 0 1 0 3 : 0 0 0 0 4 : 1 0 1 0 Expected nonzeros = 6 Computed nonzeros = 6 R8MAT_NONZEROS_TEST Normal end of execution. R8MAT_NORM_FRO_TEST Python version: 3.6.5 R8MAT_NORM_FRO computes the Frobenius norm of an R8MAT; A: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 3 : 13 14 15 16 4 : 17 18 19 20 Expected Frobenius norm = 53.5724 Computed Frobenius norm = 53.5724 R8MAT_NORM_FRO_TEST Normal end of execution. R8MAT_NORM_FRO_AFFINE_TEST Python version: 3.6.5 R8MAT_NORM_FRO_AFFINE computes the Frobenius norm of the difference of two R8MAT's; Expected norm = 2.1594 Computed norm = 2.1594 R8MAT_NORM_FRO_AFFINE_TEST Normal end of execution. R8MAT_NORM_L1_TEST Python version: 3.6.5 R8MAT_NORM_L1 computes the L1 norm of an R8MAT; A: Col: 0 1 2 3 Row 0 : -3 -4 -4 -5 1 : 5 -2 -1 4 2 : 3 -4 -1 -1 3 : 1 -5 3 -4 4 : -1 1 3 -5 Computed L1 norm = 19 R8MAT_NORM_L1_TEST Normal end of execution. R8MAT_NORMAL_01_TEST Python version: 3.6.5 R8MAT_NORMAL_01 returns a matrix of Normal 01 values SEED = 123456789 Matrix: Col: 0 1 2 3 Row 0 : 1.67904 -0.56606 1.21293 1.26938 1 : -1.66609 -2.24246 0.0396749 0.673068 2 : -0.275127 2.164 0.297785 2.04454 3 : 1.39882 -1.24299 -0.0670837 -0.794396 4 : -0.523768 -0.350567 0.1317 0.53738 R8MAT_NORMAL_01_TEST: Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8MAT_PRODUCT_ELEMENTWISE_TEST Python version: 3.6.5 R8MAT_PRODUCT_ELEMENTWISE computes the elementwise product of two R8MATs. A: Col: 0 1 2 Row 0 : 1 2 3 1 : 4 5 6 B: Col: 0 1 2 Row 0 : 1 3 5 1 : 2 4 6 Elementwise product = 86 R8MAT_PRODUCT_ELEMENTWISE_TEST Normal end of execution. R8MAT_REF_TEST R8MAT_REF computes the row echelon form of a matrix. Input A: Col: 0 1 2 3 4 Row 0 : 1 3 0 2 6 1 : -2 -6 0 -2 -8 2 : 3 9 0 0 6 3 : -1 -3 0 1 0 Col: 5 6 Row 0 : 3 1 1 : 3 1 2 : 6 2 3 : 9 3 Pseudo-determinat = 48 REF form: Col: 0 1 2 3 4 Row 0 : 1 3 0 2 6 1 : 0 0 0 1 2 2 : 0 0 0 0 0 3 : 0 0 0 0 0 Col: 5 6 Row 0 : 3 1 1 : 4.5 1.5 2 : 1 0.333333 3 : 0 0 R8MAT_REF_TEST Normal end of execution. R8MAT_RREF_TEST R8MAT_RREF computes the reduced row echelon form of a matrix. Input A: Col: 0 1 2 3 4 Row 0 : 1 3 0 2 6 1 : -2 -6 0 -2 -8 2 : 3 9 0 0 6 3 : -1 -3 0 1 0 Col: 5 6 Row 0 : 3 1 1 : 3 1 2 : 6 2 3 : 9 3 Pseudo-determinant = 48 RREF form: Col: 0 1 2 3 4 Row 0 : 1 3 0 0 2 1 : 0 0 0 1 2 2 : 0 0 0 0 0 3 : 0 0 0 0 0 Col: 5 6 Row 0 : 0 0 1 : 0 0 2 : 1 0.333333 3 : 0 0 R8MAT_RREF_TEST Normal end of execution. R8MAT_SOLVE_TEST Python version: 3.6.5 R8MAT_SOLVE solves linear systems. The linear system: Col: 0 1 2 3 4 Row 0 : 1 2 3 14 7 1 : 4 5 6 32 16 2 : 7 8 0 23 7 Factored matrix and solutions: Col: 0 1 2 3 4 Row 0 : 1 0 0 1 1 1 : 0 1 0 2 0 2 : 0 0 1 3 2 R8MAT_SOLVE_TEST: Normal end of execution. R8MAT_TRANSPOSE_TEST Python version: 3.6.5 R8MAT_TRANSPOSE transposes an R8MAT. Matrix A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 Transposed matrix At: Col: 0 1 2 3 4 Row 0 : 11 21 31 41 51 1 : 12 22 32 42 52 2 : 13 23 33 43 53 3 : 14 24 34 44 54 R8MAT_TRANSPOSE_TEST Normal end of execution. R8MAT_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT prints an R8MAT. Here is an R8MAT, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 R8MAT_TRANSPOSE_PRINT_TEST: Normal end of execution. R8MAT_TRANSPOSE_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed. R8MAT, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 R8MAT_TRANSPOSE_PRINT_SOME_TEST: Normal end of execution. R8MAT_U_INVERSE_TEST R8MAT_U_INVERSE inverts an upper triangular matrix. Input matrix A Col: 0 1 2 3 Row 0 : 1 2 4 7 1 : 0 3 5 8 2 : 0 0 6 9 3 : 0 0 0 10 Inverse matrix B: Col: 0 1 2 3 Row 0 : 1 -0.666667 -0.111111 -0.0666667 1 : 0 0.333333 -0.277778 -0.0166667 2 : 0 0 0.166667 -0.15 3 : 0 0 0 0.1 Product C = A * B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 1.11022e-16 3 : 0 0 0 1 R8MAT_U_SOLVE_TEST Python version: 3.6.5 R8MAT_U_SOLVE solves an upper triangular system. Input matrix A: Col: 0 1 2 3 Row 0 : 1 2 4 7 1 : 0 3 5 8 2 : 0 0 6 9 3 : 0 0 0 10 Right hand side b: 0: 45 1: 53 2: 54 3: 40 Computed solution x: 0: 1 1: 2 2: 3 3: 4 Norm of A*x-b = 0 R8MAT_U_SOLVE_TEST Normal end of execution. R8MAT_UNIFORM_01_TEST Python version: 3.6.5 R8MAT_UNIFORM_01 computes a random R8MAT. 0 <= X <= 1 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.218418 0.0661187 0.0617272 0.00183837 1 : 0.956318 0.257578 0.449539 0.897504 2 : 0.829509 0.109957 0.401306 0.350752 3 : 0.561695 0.043829 0.754673 0.0945448 4 : 0.415307 0.633966 0.797287 0.0136169 R8MAT_UNIFORM_01_TEST: Normal end of execution. R8MAT_UNIFORM_AB_TEST Python version: 3.6.5 R8MAT_UNIFORM_AB computes a random R8MAT. -1 <= X <= 5 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.31051 -0.603288 -0.629637 -0.98897 1 : 4.73791 0.545467 1.69723 4.38502 2 : 3.97706 -0.340259 1.40784 1.10451 3 : 2.37017 -0.737026 3.52804 -0.432731 4 : 1.49184 2.80379 3.78372 -0.918299 R8MAT_UNIFORM_AB_TEST: Normal end of execution. R8MAT_UNIFORM_ABVEC_TEST Python version: 3.6.5 R8MAT_UNIFORM_ABVEC computes a random R8MAT. Initial seed is 123456789 Lower and upper row limits: 0: 2 10 1: 0 1 2: -1 0 3: 100 110 4: 0.1 0.2 Random R8MAT: Col: 0 1 2 3 Row 0 : 3.74735 2.52895 2.49382 2.01471 1 : 0.956318 0.257578 0.449539 0.897504 2 : -0.170491 -0.890043 -0.598694 -0.649248 3 : 105.617 100.438 107.547 100.945 4 : 0.141531 0.163397 0.179729 0.101362 R8MAT_UNIFORM_ABVEC_TEST: Normal end of execution. R8MAT_UT_SOLVE_TEST Python version: 3.6.5 R8MAT_UT_SOLVE solves a transposed upper triangular system. Input matrix A: Col: 0 1 2 3 Row 0 : 1 2 4 7 1 : 0 3 5 8 2 : 0 0 6 9 3 : 0 0 0 10 Right hand side b: 0: 1 1: 8 2: 32 3: 90 Computed solution x: 0: 1 1: 2 2: 3 3: 4 Norm of A'*x-b = 0 R8MAT_UT_SOLVE_TEST Normal end of execution. R8MAT_VAND2_TEST Python version: 3.6.5 R8MAT_VAND2 returns a row Vandermonde matrix. The factor vector X: 0: 1 1: 2 2: 3 3: 4 4: 5 The row Vandermonde matrix: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 4 8 2 : 1 3 9 27 3 : 1 4 16 64 4 : 1 5 25 125 R8MAT_VAND2_TEST Normal end of execution. R8ROWS_TO_R8MAT_TEST Python version: 3.6.5 R8ROWS_TO_R8MAT allows an R8MAT to be initialized by data stored ROW-WISE in a vector. The data vector: 0: 11 1: 12 2: 13 3: 14 4: 21 5: 22 6: 23 7: 24 8: 31 9: 32 10: 33 11: 34 The data copied into an array: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 R8ROWS_TO_R8MAT_TEST: Normal end of execution. R8VEC_AMAX_TEST Python version: 3.6.5 R8VEC_AMAX computes the maximum absolute value entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Max Abs = 9.12635 R8VEC_AMAX_TEST: Normal end of execution. R8VEC_AMAX_INDEX_TEST Python version: 3.6.5 R8VEC_AMAX_INDEX computes the index of the entry of maximum absolute value in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 AMAX = A[1] = 9.12635 R8VEC_AMAX_INDEX_TEST: Normal end of execution. R8VEC_AMIN_TEST Python version: 3.6.5 R8VEC_AMIN computes the minimum absolute entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Min Abs = 1.23391 R8VEC_AMIN_TEST: Normal end of execution. R8VEC_AMIN_INDEX_TEST Python version: 3.6.5 R8VEC_AMIN_INDEX computes the index of the entry of minimum absolute value in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 AMIN = A[3] = 1.23391 R8VEC_AMIN_INDEX_TEST: Normal end of execution. R8VEC_ASUM_TEST Python version: 3.6.5 R8VEC_ASUM sums the absolute values of the entries in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Sum of absolute values of entries = 57.4056 R8VEC_ASUM_TEST: Normal end of execution. R8VEC_BINARY_NEXT_TEST Python version: 3.6.5 R8VEC_BINARY_NEXT generates the next binary vector. 000 001 010 011 100 101 110 111 R8VEC_BINARY_NEXT_TEST Normal end of execution. R8VEC_BRACKET_TEST Python version: 3.6.5 R8VEC_BRACKET finds, for a given value R, the nearest interval [low,high] in a sorted R8VEC that "brackets" the value. Sorted R8VEC: 0: 0 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 R = 1.62102 is bracketed by ( S[1] = 1, S[2] = 2 R = 10.4758 is bracketed by ( S[9] = 9, S[10] = 10 R = 8.95411 is bracketed by ( S[8] = 8, S[9] = 9 R = 5.74035 is bracketed by ( S[5] = 5, S[6] = 6 R = 3.98368 is bracketed by ( S[3] = 3, S[4] = 4 R = -0.206575 is bracketed by ( S[0] = 0, S[1] = 1 R = 2.09093 is bracketed by ( S[2] = 2, S[3] = 3 R = 0.319482 is bracketed by ( S[0] = 0, S[1] = 1 R = -0.474052 is bracketed by ( S[0] = 0, S[1] = 1 R = 6.60759 is bracketed by ( S[6] = 6, S[7] = 7 R = -0.259273 is bracketed by ( S[0] = 0, S[1] = 1 R = 4.39447 is bracketed by ( S[4] = 4, S[5] = 5 R = 3.81568 is bracketed by ( S[3] = 3, S[4] = 4 R = 8.05608 is bracketed by ( S[8] = 8, S[9] = 9 R = 8.56744 is bracketed by ( S[8] = 8, S[9] = 9 R8VEC_BRACKET_TEST: Normal end of execution. R8VEC_BRACKET5_TEST R8VEC_BRACKET5 finds a pair of entries in a sorted R8VEC which bracket a value. Sorted array: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 5 6: 7 7: 8 8: 9 9: 10 LEFT RIGHT X(LEFT) XVAL X(RIGHT) -1 -10.0000 (Not bracketed!) 0 1 1.0000 1.0000 2.0000 3 4 4.0000 4.5000 5.0000 5 6 5.0000 5.0000 7.0000 8 9 9.0000 10.0000 10.0000 -1 12.0000 (Not bracketed!) R8VEC_BRACKET5_TEST Normal end of execution. R8VEC_CHEBY_EXTREME_TEST Python version: 3.6.5 R8VEC_CHEBY_EXTREME returns Chebyshev Extreme values between A and B. The vector: 0: 10 1: 11.4645 2: 15 3: 18.5355 4: 20 R8VEC_CHEBY_EXTREME_TEST Normal end of execution. R8VEC_CHEBY_ZERO_TEST Python version: 3.6.5 R8VEC_CHEBY_ZERO returns Chebyshev Zero values between A and B. The vector: 0: 10.2447 1: 12.0611 2: 15 3: 17.9389 4: 19.7553 R8VEC_CHEBY_ZERO_TEST Normal end of execution. R8VEC_CHEBY1SPACE_TEST Python version: 3.6.5 R8VEC_CHEBY1SPACE returns Type 1 Chebyshev values in [A,B]. The vector: 0: 10 1: 11.4645 2: 15 3: 18.5355 4: 20 R8VEC_CHEBY1SPACE_TEST Normal end of execution. R8VEC_CONCATENATE_TEST Python version: 3.6.5 R8VEC_CONCATENATE concatenates two R8VECs Array 1: 0: 91.1 1: 31.2 2: 71.3 3: 51.4 4: 31.5 Array 2: 0: 42.6 1: 22.7 2: 12.8 Array 3 = Array 1 + Array 2: 0: 91.1 1: 31.2 2: 71.3 3: 51.4 4: 31.5 5: 42.6 6: 22.7 7: 12.8 R8VEC_CONCATENATE_TEST Normal end of execution. R8VEC_COPY_TEST Python version: 3.6.5 R8VEC_COPY copies an R8VEC. Array 1: 0: 91.1 1: 31.2 2: 71.3 3: 51.4 4: 31.5 Array 2: 0: 91.1 1: 31.2 2: 71.3 3: 51.4 4: 31.5 R8VEC_COPY_TEST Normal end of execution. R8VEC_COVARIANCE_TEST: R8VEC_COVARIANCE computes the covariance of two R8VECs. Vector V1:10 Vector V2:0.2184180 Covariance(V1,V2) = 0.109209 Vector V2:0.8281950.478159 Covariance(V1,V2) = 0.175018 Vector V2:0.4147550.718376 Covariance(V1,V2) = -0.151811 Vector V2:3.43939e-170.561695 Covariance(V1,V2) = -0.280848 Vector V2:-0.2076540.359666 Covariance(V1,V2) = -0.28366 Vector V2:-0.05726050.0330594 Covariance(V1,V2) = -0.0451599 Vector V2:-0.2575783.15442e-17 Covariance(V1,V2) = -0.128789 Vector V2:-0.0952254-0.0549784 Covariance(V1,V2) = -0.0201235 Vector V2:-0.0219145-0.037957 Covariance(V1,V2) = 0.00802126 Vector V2:-1.16458e-16-0.633966 Covariance(V1,V2) = 0.316983 Vector V2:0.0308636-0.0534573 Covariance(V1,V2) = 0.0421605 Vector V2:0.389312-0.224769 Covariance(V1,V2) = 0.307041 R8VEC_COVARIANCE_TEST Normal end of execution. R8VEC_DIFF_NORM_TEST Python version: 3.6.5 R8VEC_DIFF_NORM: L2 norm of the difference of two R8VECs. I V[I] W[I] 0 0.000000 1.000000 1 1.000000 2.000000 2 2.000000 3.000000 3 3.000000 5.000000 4 4.000000 5.000000 5 5.000000 6.000000 L2 norm of vector difference ||V-W|| is 3 R8VEC_DIFF_NORM_TEST: Normal end of execution. R8VEC_DIFF_NORM_LI_TEST Python version: 3.6.5 R8VEC_DIFF_NORM_LI: L-infinity norm of the difference of two R8VEC's. Vector V1: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 Vector V2: 0: -8.67763 1: -4.84844 2: -7.80086 3: -9.12342 4: 2.67931 L-Infinity norm of V1-V2: 14.391 R8VEC_DIFF_NORM_LI_TEST Normal end of execution. R8VEC_DIRECT_PRODUCT_TEST Python version: 3.6.5 R8VEC_DIRECT_PRODUCT forms the entries of a direct product of a given number of R8VEC factors. Matrix (transposed) Row: 0 1 2 Col 0 : 1 50 800 1 : 2 50 800 2 : 3 50 800 3 : 4 50 800 4 : 1 60 800 5 : 2 60 800 6 : 3 60 800 7 : 4 60 800 8 : 1 70 800 9 : 2 70 800 10 : 3 70 800 11 : 4 70 800 12 : 1 50 900 13 : 2 50 900 14 : 3 50 900 15 : 4 50 900 16 : 1 60 900 17 : 2 60 900 18 : 3 60 900 19 : 4 60 900 20 : 1 70 900 21 : 2 70 900 22 : 3 70 900 23 : 4 70 900 R8VEC_DIRECT_PRODUCT_TEST: Normal end of execution. R8VEC_DOT_PRODUCT_TEST: Python version: 3.6.5 R8VEC_DOT_PRODUCT computes the dot product of two R8VEC's. V1 and V2: 0: 0.218418 0.0617272 1: 0.956318 0.449539 2: 0.829509 0.401306 3: 0.561695 0.754673 4: 0.415307 0.797287 5: 0.0661187 0.00183837 6: 0.257578 0.897504 7: 0.109957 0.350752 8: 0.043829 0.0945448 9: 0.633966 0.0136169 V1 dot V2 = 1.81393 R8VEC_DOT_PRODUCT_TEST: Normal end of execution. R8VEC_EQ_TEST Python version: 3.6.5 R8VEC_EQ is TRUE if two R8VECs are equal. Vectors A and B: 0: 1.1 1.1 1: 3.2 3.2 2: 2.3 2.3 3: 4.4 4.4 R8VEC_EQ(A,B) = True Vectors A and B: 0: 2.1 2.1 1: 2.2 2.2 2: 2.3 1.3 3: 2.4 2.4 R8VEC_EQ(A,B) = False Vectors A and B: 0: 1.1 4.1 1: 2.2 1.2 2: 2.3 1.3 3: 4.4 3.4 R8VEC_EQ(A,B) = False Vectors A and B: 0: 1.1 1.1 1: 2.2 2.2 2: 3.3 3.3 3: 4.4 4.4 R8VEC_EQ(A,B) = True R8VEC_EQ_TEST Normal end of execution. R8VEC_EVEN_TEST R8VEC_EVEN computes N evenly spaced values between XLO and XHI. XLO = 0.000000 XHI = 99.000000 while N = 10 Resulting array: 0: 0 1: 11 2: 22 3: 33 4: 44 5: 55 6: 66 7: 77 8: 88 9: 99 R8VEC_EVEN_TEST: Normal end of execution. R8VEC_EVEN_SELECT_TEST R8VEC_EVEN_SELECT returns the I-th of N evenly spaced values between XLO and XHI. XLO = 0.000000 XHI = 99.000000 while N = 10 X(2) = 11 X(5) = 44 X(8) = 77 R8VEC_EVEN_SELECT_TEST: Normal end of execution. R8VEC_FILL_TEST Python version: 3.6.5 R8VEC_FILL sets all entries of an array to a given value. x=r8vec_fill(5,1.2): 0: 1.2 1: 1.2 2: 1.2 3: 1.2 4: 1.2 x=r8vec_fill(3,123.456): 0: -123.456 1: -123.456 2: -123.456 R8VEC_FILL_TEST Normal end of execution. R8VEC_FRAC_TEST Python version: 3.6.5 R8VEC_FRAC: K-th smallest real vector entry; The real array to search: 0: 2.18418 1: 9.56318 2: 8.29509 3: 5.61695 4: 4.15307 5: 0.661187 6: 2.57578 7: 1.09957 8: 0.43829 9: 6.33966 Frac R8VEC_FRAC 1 0.438290 2 0.661187 3 1.099568 4 2.184183 5 2.575778 6 4.153071 7 5.616954 8 6.339657 9 8.295092 10 9.563176 R8VEC_FRAC_TEST Normal end of execution. R8VEC_HOUSE_COLUMN_TEST Python version: 3.6.5 R8VEC_HOUSE_COLUMN returns the compact form of a Householder matrix that "packs" a column of a matrix. Matrix A: Col: 0 1 2 3 Row 0 : 1.09209 2.07654 0.219145 2.00653 1 : 4.78159 0.330594 3.16983 3.77337 2 : 4.14755 1.28789 0.308636 3.98643 3 : 2.80848 0.549784 2.24769 0.00919186 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.155781 -0.682069 -0.591626 -0.400615 1 : -0.682069 0.597486 -0.34914 -0.236418 2 : -0.591626 -0.34914 0.697156 -0.205068 3 : -0.400615 -0.236418 -0.205068 0.86114 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 :-8.88178e-16 -1.79845 1.1053 -0.508058 2 :-1.77636e-15 -0.558841 -1.48213 0.272729 3 :-8.88178e-16 -0.700714 1.03509 -2.50551 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.895014 -0.278112 -0.348717 2 : 0 -0.278112 0.959184 -0.0511776 3 : 0 -0.348717 -0.0511776 0.93583 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.59868e-15 2.00941 -0.938018 1.25258 2 :-1.41139e-15 7.63278e-17 -1.78201 0.531121 3 :-4.30552e-16 0 0.659083 -2.18152 Working on column K = 2 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 -0.937906 0.346889 3 : 0 0 0.346889 0.937906 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.59868e-15 2.00941 -0.938018 1.25258 2 : 1.17439e-15 -7.15884e-17 1.89999 -1.25489 3 : -8.9341e-16 2.64773e-17 1.11022e-16 -1.86183 R8VEC_HOUSE_COLUMN_TEST Normal end of execution. R8VEC_IDENTITY_ROW_TEST R8VEC_IDENTITY_ROW returns a row of the identity matrix. -1: 0 0 0 0 0 0: 1 0 0 0 0 1: 0 1 0 0 0 2: 0 0 1 0 0 3: 0 0 0 1 0 4: 0 0 0 0 1 5: 0 0 0 0 0 R8VEC_IDENTITY_ROW_TEST: Normal end of execution. R8VEC_INDICATOR0_TEST Python version: 3.6.5 R8VEC_INDICATOR0 returns an indicator matrix. The indicator0 vector: 0: 0 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 R8VEC_INDICATOR0_TEST Normal end of execution. R8VEC_INDICATOR1_TEST Python version: 3.6.5 R8VEC_INDICATOR1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8VEC_INDICATOR1_TEST Normal end of execution. R8VEC_IS_ASCENDING_TEST Python version: 3.6.5 R8VEC_IS_ASCENDING is TRUE if the entries of an R8VEC are ascending. X: 1 2 0 9 X is NOT ascending. X: 1 2 2 9 X is ascending. X: 1 2 4 9 X is ascending. R8VEC_IS_ASCENDING_TEST Normal end of execution. R8VEC_IS_ASCENDING_STRICTLY_TEST Python version: 3.6.5 R8VEC_IS_ASCENDING_STRICTLY is TRUE if the entries of an R8VEC are strictly ascending. X: 1 2 0 9 X is NOT strictly ascending. X: 1 2 2 9 X is NOT strictly ascending. X: 1 2 4 9 X is strictly ascending. R8VEC_IS_ASCENDING_STRICTLY_TEST Normal end of execution. R8VEC_IS_BINARY_TEST Python version: 3.6.5 R8VEC_IS_BINARY is TRUE if an R8VEC only contains 0 or 1 entries. X: 0 0 0 X is binary X: 1 0 1 X is binary X: 0 2 1 X is NOT binary. R8VEC_IS_BINARY_TEST Normal end of execution. R8VEC_IS_DISTINCT_TEST Python version: 3.6.5 R8VEC_IS_DISTINCT computes the maximum entry in an R8VEC. Input vector: 0: 1 1: 2 2: 5 3: 3 4: 4 Array entries are distinct. Input vector: 0: 1 1: 2 2: 5 3: 2 4: 4 Array entries are NOT distinct. R8VEC_IS_DISTINCT_TEST: Normal end of execution. R8VEC_IS_IN_01_TEST Python version: 3.6.5 R8VEC_IS_IN_01 is TRUE if an R8VEC only contains entries in [0,1]. X: 0 1 2 At least one entry is NOT in [0,1]. X: 0.5 0.1 0.9 All entries are in [0,1]. X: -0.5 0.5 0.4 At least one entry is NOT in [0,1]. R8VEC_IS_IN_01_TEST Normal end of execution. R8VEC_IS_IN_AB_TEST Python version: 3.6.5 R8VEC_IS_IN_AB is TRUE if an R8VEC only contains entries in [A,B]. X: 0 1 2 At least one entry is NOT in [0.500000,2.000000]. X: 0.5 1.1 0.9 All entries are in [0.500000,2.000000]. X: -0.5 0.5 0.4 At least one entry is NOT in [0.500000,2.000000]. R8VEC_IS_IN_AB_TEST Normal end of execution. R8VEC_IS_INSIGNIFICANT_TEST Python version: 3.6.5 R8VEC_IS_INSIGNIFICANT is TRUE if an R8VEC only contains negative entries. X: 1 2 100 Y: 2.22045e-11 4.44089e-11 2.22045e-09 Y is NOT insignificant compared to X. X: 1 2 100 Y: 2.22045e-15 0 0 Y is NOT insignificant compared to X. X: 1 2 100 Y: 2.22045e-20 4.44089e-20 2.22045e-18 Y is insignificant compared to X. R8VEC_IS_INSIGNIFICANT_TEST Normal end of execution. R8VEC_IS_INTEGER_TEST Python version: 3.6.5 R8VEC_IS_INTEGER is TRUE if an R8VEC contains only integer entries. X: 0 1 100 X contains only integer entries. X: 1 2.5 3 X contains at least one noninteger entry. X: -3 -99 -87.3 X contains at least one noninteger entry. R8VEC_IS_INTEGER_TEST Normal end of execution. R8VEC_IS_NEGATIVE_TEST Python version: 3.6.5 R8VEC_IS_NEGATIVE is TRUE if an R8VEC only contains negative entries. X: 0 1 2 X does NOT contain only negative entries. X: -1 0 1 X does NOT contain only negative entries. X: -3 -99 -87.3 X contains only negative entries. R8VEC_IS_NEGATIVE_TEST Normal end of execution. R8VEC_IS_NEGATIVE_ANY_TEST Python version: 3.6.5 R8VEC_IS_NEGATIVE_ANY is TRUE if an R8VEC contains any negative entries. X: 0 1 2 X does NOT contain any negative entries. X: -1 0 1 X contains at least one negative entry. X: -3 -99 -87.3 X contains at least one negative entry. R8VEC_IS_NEGATIVE_ANY_TEST Normal end of execution. R8VEC_IS_NONNEGATIVE_TEST Python version: 3.6.5 R8VEC_IS_NONNEGATIVE is TRUE if an R8VEC only contains nonnegative entries. X: 0 1 2 X contains only nonnegative entries. X: -1 0 1 X does NOT contain only nonnegative entries. X: -3 -99 -87.3 X does NOT contain only nonnegative entries. R8VEC_IS_NONNEGATIVE_TEST Normal end of execution. R8VEC_IS_NONPOSITIVE_TEST Python version: 3.6.5 R8VEC_IS_NONPOSITIVE is TRUE if an R8VEC only contains nonpositive entries. X: 0 1 2 X does NOT contain only nonpositive entries. X: -2 -1 0 X contains only nonpositive entries. X: -3 -99 -87.3 X contains only nonpositive entries. R8VEC_IS_NONPOSITIVE_TEST Normal end of execution. R8VEC_IS_NONZERO_ANY_TEST Python version: 3.6.5 R8VEC_IS_NONZERO_ANY is TRUE if an R8VEC contains any nonzero entry. X: 0 1 0 X contains at least one nonzero entry. X: 0 0 0 X contains NO nonzero entries. X: -3 -99 -87.3 X contains at least one nonzero entry. R8VEC_IS_NONZERO_ANY_TEST Normal end of execution. R8VEC_IS_ONE_TEST Python version: 3.6.5 R8VEC_IS_ONE is TRUE if an R8VEC contains only one entries. X: 0 1 0 X contains at least one nonone entry. X: 1 1 1 X contains only one entries. X: -3 -99 -87.3 X contains at least one nonone entry. R8VEC_IS_ONE_TEST Normal end of execution. R8VEC_IS_POSITIVE_TEST Python version: 3.6.5 R8VEC_IS_POSITIVE is TRUE if an R8VEC only contains strictly positive entries. X: 1 2 3 X contains only positive entries. X: 2 1 0 X does NOT contain only positive entries. X: -3 -99 -87.3 X does NOT contain only positive entries. R8VEC_IS_POSITIVE_TEST Normal end of execution. R8VEC_IS_ZERO_TEST Python version: 3.6.5 R8VEC_IS_ZERO is TRUE if an R8VEC contains only zero entries. X: 0 1 0 X contains at least one nonzero entry. X: 0 0 0 X contains only zero entries. X: -3 -99 -87.3 X contains at least one nonzero entry. R8VEC_IS_ZERO_TEST Normal end of execution. R8VEC_LINSPACE_TEST Python version: 3.6.5 R8VEC_LINSPACE returns evenly spaced values between A and B. The linspace vector: 0: 10 1: 12.5 2: 15 3: 17.5 4: 20 R8VEC_LINSPACE_TEST Normal end of execution. R8VEC_LINSPACE2_TEST Python version: 3.6.5 R8VEC_LINSPACE2 returns evenly spaced values between A and B omitting the endpoints. The linspace2 vector: 0: 12 1: 14 2: 16 3: 18 R8VEC_LINSPACE2_TEST Normal end of execution. R8VEC_MAX_TEST Python version: 3.6.5 R8VEC_MAX computes the maximum entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Max = 9.12635 R8VEC_MAX_TEST: Normal end of execution. R8VEC_MAX_ABS_INDEX_TEST Python version: 3.6.5 R8VEC_MAX_ABS_INDEX: index of entry of maximum absolute value Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Maximum index: 1 R8VEC_MAX_ABS_INDEX_TEST: Normal end of execution. R8VEC_MAX_INDEX_TEST Python version: 3.6.5 R8VEC_MAX_INDEX: index of maximum entry Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Maximum index: 1 R8VEC_MAX_INDEX_TEST: Normal end of execution. R8VEC_MEAN_TEST Python version: 3.6.5 R8VEC_MEAN computes the mean of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = -0.907304 R8VEC_MEAN_TEST: Normal end of execution. R8VEC_MEAN_GEOMETRIC_TEST Python version: 3.6.5 R8VEC_MEAN_GEOMETRIC computes the geometric mean of an R8VEC. Input vector: 0: 1.09209 1: 4.78159 2: 4.14755 3: 2.80848 4: 2.07654 5: 0.330594 6: 1.28789 7: 0.549784 8: 0.219145 9: 3.16983 Geometric mean = 1.35287 R8VEC_MEAN_GEOMETRIC_TEST: Normal end of execution. R8VEC_MEAN_RUNNING_TEST Python version: 3.6.5 R8VEC_MEAN_RUNNING returns the running means of an R8VEC. Random R8VEC: 0: -1.72373 1: 9.34476 2: 7.44264 3: 3.42543 4: 1.22961 5: -4.00822 6: -1.13633 7: -3.35065 8: -4.34257 9: 4.50949 Running means: 0: 0 1: -1.72373 2: 3.81052 3: 5.02123 4: 4.62228 5: 3.94374 6: 2.61842 7: 2.08202 8: 1.40294 9: 0.76455 10: 1.13904 R8VEC_MEAN_RUNNING_TEST: Normal end of execution. R8VEC_MEAN_UPDATE_TEST Python version: 3.6.5 R8VEC_MEAN_UPDATE updates the mean of a vector when one more element is added. N R MEAN MEAN_UPDATE 1 0.218418 0.218418 0.218418 2 0.956318 0.587368 0.587368 3 0.829509 0.668082 0.668082 4 0.561695 0.641485 0.641485 5 0.415307 0.59625 0.59625 6 0.0661187 0.507894 0.507894 7 0.257578 0.472135 0.472135 8 0.109957 0.426863 0.426863 9 0.043829 0.384303 0.384303 R8VEC_MEAN_UPDATE_TEST: Normal end of execution. R8VEC_MIDSPACE_TEST Python version: 3.6.5 R8VEC_MIDSPACE returns the midpoints of N intervals in [A,B]. The midspace vector: 0: 11 1: 13 2: 15 3: 17 4: 19 R8VEC_MIDSPACE_TEST Normal end of execution. R8VEC_MIN_TEST Python version: 3.6.5 R8VEC_MIN computes the minimum entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Min = -9.12342 R8VEC_MIN_TEST: Normal end of execution. R8VEC_MIRROR_NEXT_TEST Python version: 3.6.5 R8VEC_MIRROR_NEXT generates all sign variations of a real vector. 0 1 2 3 0 -1 2 3 0 1 -2 3 0 -1 -2 3 0 1 2 -3 0 -1 2 -3 0 1 -2 -3 0 -1 -2 -3 Done. 0 1 0 3 0 -1 0 3 0 1 -0 -3 0 -1 -0 -3 Done. R8VEC_MIRROR_NEXT_TEST: Normal end of execution. R8VEC_MIRROR_AB_NEXT_TEST Python version: 3.6.5 R8VEC_MIRROR_AB_NEXT generates all versions of of a real vector X mirrored by A and B. Case 1: 3x3x3 possibilities: A: -0.5 -0.5 -0.5 X: 0 0 0 B: 0.5 0.5 0.5 1 -1 -1 -1 2 -1 -1 0 3 -1 -1 1 4 -1 0 -1 5 -1 0 0 6 -1 0 1 7 -1 1 -1 8 -1 1 0 9 -1 1 1 10 0 -1 -1 11 0 -1 0 12 0 -1 1 13 0 0 -1 14 0 0 0 15 0 0 1 16 0 1 -1 17 0 1 0 18 0 1 1 19 1 -1 -1 20 1 -1 0 21 1 -1 1 22 1 0 -1 23 1 0 0 24 1 0 1 25 1 1 -1 26 1 1 0 27 1 1 1 Done. Case 2: 3x2x3 possibilities: A: -0.5 -0.5 -0.5 X: 0 0.5 0 B: 0.5 0.5 0.5 1 -1 -1.5 -1 2 -1 -1.5 0 3 -1 -1.5 1 4 -1 0.5 -1 5 -1 0.5 0 6 -1 0.5 1 7 0 -1.5 -1 8 0 -1.5 0 9 0 -1.5 1 10 0 0.5 -1 11 0 0.5 0 12 0 0.5 1 13 1 -1.5 -1 14 1 -1.5 0 15 1 -1.5 1 16 1 0.5 -1 17 1 0.5 0 18 1 0.5 1 Done. Case 3: 1x3x3 possibilities: A: 0 -0.5 -0.5 X: 0 0 0 B: 0 0.5 0.5 1 0 -1 -1 2 0 -1 0 3 0 -1 1 4 0 0 -1 5 0 0 0 6 0 0 1 7 0 1 -1 8 0 1 0 9 0 1 1 Done. R8VEC_MIRROR_AB_NEXT_TEST: Normal end of execution. R8VEC_NINT_TEST Python version: 3.6.5 R8VEC_NINT rounds an R8VEC. Vector A: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 Rounded vector A: 0: -3 1: 5 2: 3 3: 1 4: -1 R8VEC_NINT_TEST: Normal end of execution. R8VEC_NORM_TEST Python version: 3.6.5 R8VEC_NORM computes the L2 norm of an R8VEC. Input vector: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 L2 norm = 1.62017 R8VEC_NORM_TEST: Normal end of execution. R8VEC_NORM_AFFINE_TEST Python version: 3.6.5 R8VEC_NORM_AFFINE computes the L2 norm of the difference of two R8VECs. R8VEC_NORM_AFFINE(X,Y) = 1.22756 R8VEC_NORM (X-Y): 1.22756 R8VEC_NORM_AFFINE_TEST: Normal end of execution. R8VEC_NORM_L0_TEST Python version: 3.6.5 R8VEC_NORM_L0 computes the L0 "norm" of an R8VEC. Input vector: 0: -1 1: 2 2: 1 3: 0 4: -0 5: -2 6: -1 7: -2 8: -2 9: 1 L0 norm = 8 R8VEC_NORM_L0_TEST: Normal end of execution. R8VEC_NORM_L1_TEST Python version: 3.6.5 R8VEC_NORM_L1 computes the L1 norm of an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 L1 norm = 57.4056 R8VEC_NORM_L1_TEST: Normal end of execution. R8VEC_NORM_L2_TEST Python version: 3.6.5 R8VEC_NORM_L2 computes the L2 norm of an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 L2 norm = 20.3201 R8VEC_NORM_L2_TEST: Normal end of execution. R8VEC_NORM_LI_TEST Python version: 3.6.5 R8VEC_NORM_LI computes the Loo norm of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Loo norm = 4.56318 R8VEC_NORM_LI_TEST: Normal end of execution. R8VEC_NORM_RMS_TEST Python version: 3.6.5 R8VEC_NORM_RMS computes the RMS norm of an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 RMS norm = 6.42577 R8VEC_NORM_RMS_TEST: Normal end of execution. R8VEC_NORMAL_01_TEST Python version: 3.6.5 R8VEC_NORMAL_01 returns a vector of Normal 01 values SEED = 123456789 Vector: 0: 1.67904 1: -0.56606 2: 1.21293 3: 1.26938 4: -1.66609 5: -2.24246 6: 0.0396749 7: 0.673068 8: -0.275127 9: 2.164 R8VEC_NORMAL_01_TEST: Normal end of execution. R8VEC_NORMAL_AB_TEST Python version: 3.6.5 R8VEC_NORMAL_AB returns a vector of Normal AB values Mean = 15 Standard deviation = 0.25 SEED = 123456789 Vector: 0: 15.4198 1: 14.8585 2: 15.3032 3: 15.3173 4: 14.5835 5: 14.4394 6: 15.0099 7: 15.1683 8: 14.9312 9: 15.541 R8VEC_NORMAL_AB_TEST: Normal end of execution. R8VEC_NORMALIZE_L1_TEST Python version: 3.6.5 R8VEC_NORMALIZE_L1 normalizes an R8VEC in the L1 norm. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 After calling R8VEC_NORMALIZE_L1: 0: -0.0981025 1: 0.15898 2: 0.1148 3: 0.0214946 4: -0.0295068 5: -0.151163 6: -0.0844594 7: -0.13589 8: -0.158929 9: 0.0466734 R8VEC_NORMALIZE_L1_TEST: Normal end of execution. R8VEC_PERMUTE_TEST Python version: 3.6.5 R8VEC_PERMUTE permutes an R8VEC. Original array X[]: 0: 1.1 1: 2.2 2: 3.3 3: 4.4 4: 5.5 Permutation vector P[]: 0 1 1 3 2 4 3 0 4 2 Permuted array X[P[*]]: 0: 2.2 1: 4.4 2: 5.5 3: 1.1 4: 3.3 R8VEC_PERMUTE_TEST: Normal end of execution. R8VEC_PERMUTE_CYCLIC_TEST Python version: 3.6.5 R8VEC_PERMUTE_CYCLIC performa a cyclic permutation of K positions on an R8VEC. K = 4 Original array X: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Array after permutation: 0: 5 1: 6 2: 7 3: 8 4: 9 5: 10 6: 1 7: 2 8: 3 9: 4 R8VEC_PERMUTE_CYCLIC_TEST: Normal end of execution. R8VEC_PERMUTE_UNIFORM_TEST Python version: 3.6.5 R8VEC_PERMUTE_UNIFORM randomly reorders an R8VEC. A, before rearrangement: 0: 101 1: 102 2: 103 3: 104 4: 105 5: 106 6: 107 7: 108 8: 109 9: 110 10: 111 11: 112 A, after rearrangement: 0: 103 1: 112 2: 111 3: 109 4: 108 5: 106 6: 105 7: 107 8: 104 9: 101 10: 110 11: 102 R8VEC_PERMUTE_UNIFORM_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_PRINT_PART_TEST Python version: 3.6.5 R8VEC_PRINT_PART prints part of an R8VEC. Lines 10:20 of the vector: 10: 11 11: 12 12: 13 13: 14 14: 15 15: 16 16: 17 17: 18 18: 19 19: 20 20: 21 R8VEC_PRINT_PART_TEST: Normal end of execution. R8VEC_PRINT_SOME_TEST Python version: 3.6.5 R8VEC_PRINT_SOME prints some of an R8VEC. No more than 10 lines of this vector: 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 ...... .............. 99 100 R8VEC_PRINT_SOME_TEST: Normal end of execution. R8VEC_PRODUCT_TEST Python version: 3.6.5 R8VEC_PRODUCT computes the product of the entries in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Product of entries = 5.67959e+06 R8VEC_PRODUCT_TEST: Normal end of execution. R8VEC_REVERSE_TEST Python version: 3.6.5 R8VEC_REVERSE reverses an R8VEC. Original array: 0: 1 1: 2 2: 3 3: 4 4: 5 Reversed array: 0: 5 1: 4 2: 3 3: 2 4: 1 R8VEC_REVERSE_TEST: Normal end of execution. R8VEC_ROTATE_TEST Python version: 3.6.5 R8VEC_ROTATE rotates an R8VEC in place. Rotate entries 2 places to the right Original array: 0: 1 1: 2 2: 3 3: 4 4: 5 Rotated array: 0: 4 1: 5 2: 1 3: 2 4: 3 R8VEC_ROTATE_TEST: Normal end of execution. R8VEC_SIGN3_RUNNING_TEST Python version: 3.6.5 R8VEC_SIGN3_RUNNING returns the running sign3 of an R8VEC. Random R8VEC: 0: -1.72373 1: 9.34476 2: 7.44264 3: 3.42543 4: 1.22961 5: -4.00822 6: -1.13633 7: -3.35065 8: -4.34257 9: 4.50949 Running sign3: 0: 0 1: -1 2: 1 3: 1 4: 1 5: 1 6: 1 7: 1 8: 1 9: 1 10: 1 R8VEC_SIGN3_RUNNING_TEST: Normal end of execution. R8VEC_SOFTMAX_TEST Python version: 3.6.5 R8VEC_SOFTMAX evaluates the softmax function. X, Softmax(X): 0: 2.03712 0.169954 1: -4.69818 0.000201943 2: 0.638803 0.0419808 3: 0.808142 0.0497272 4: -7.99826 7.4477e-06 5: -9.72739 1.32151e-06 6: -2.88098 0.00124288 7: -0.980795 0.00831128 8: -3.82538 0.00048337 9: 3.49201 0.728089 R8VEC_SOFTMAX_TEST: Normal end of execution. R8VEC_SORTED_NEAREST_TEST Python version: 3.6.5 R8VEC_SORTED_NEAREST finds, for a given value R, the nearest element in a sorted R8VEC. Sorted R8VEC: 0: 0 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 R = 1.62102 is nearest S[2] = 2 R = 10.4758 is nearest S[10] = 10 R = 8.95411 is nearest S[9] = 9 R = 5.74035 is nearest S[6] = 6 R = 3.98368 is nearest S[4] = 4 R = -0.206575 is nearest S[0] = 0 R = 2.09093 is nearest S[2] = 2 R = 0.319482 is nearest S[0] = 0 R = -0.474052 is nearest S[0] = 0 R = 6.60759 is nearest S[7] = 7 R = -0.259273 is nearest S[0] = 0 R = 4.39447 is nearest S[4] = 4 R = 3.81568 is nearest S[4] = 4 R = 8.05608 is nearest S[8] = 8 R = 8.56744 is nearest S[9] = 9 R8VEC_SORTED_NEAREST_TEST: Normal end of execution. R8VEC_STD_TEST Python version: 3.6.5 R8VEC_STD computes the standard deviation of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = 3.08212 R8VEC_STD_TEST: Normal end of execution. R8VEC_STD_SAMPLE_TEST Python version: 3.6.5 R8VEC_STD_SAMPLE computes the sample standard deviation of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = 3.24883 R8VEC_STD_SAMPLE_TEST: Normal end of execution. R8VEC_STD_UPDATE_TEST Python version: 3.6.5 R8VEC_STD_UPDATE updates the standard deviation of a vector when one more element is added. N R STD STD_UPDATE 1 0.218418 0 0 2 0.956318 0.36895 0.36895 3 0.829509 0.322147 0.322147 4 0.561695 0.282765 0.282765 5 0.415307 0.268607 0.268607 6 0.0661187 0.314894 0.314894 7 0.257578 0.304409 0.304409 8 0.109957 0.308916 0.308916 9 0.043829 0.315145 0.315145 R8VEC_STD_UPDATE_TEST: Normal end of execution. R8VEC_STEP_TEST Python version: 3.6.5 R8VEC_STEP evaluates a step function. X0 X STEP(X0,X) Step function with X0 = 0.31 0: 0 0 1: 0.05 0 2: 0.1 0 3: 0.15 0 4: 0.2 0 5: 0.25 0 6: 0.3 0 7: 0.35 1 8: 0.4 1 9: 0.45 1 10: 0.5 1 11: 0.55 1 12: 0.6 1 13: 0.65 1 14: 0.7 1 15: 0.75 1 16: 0.8 1 17: 0.85 1 18: 0.9 1 19: 0.95 1 20: 1 1 R8VEC_STEP_TEST Normal end of execution. R8VEC_SUM_TEST Python version: 3.6.5 R8VEC_SUM sums the entries in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Sum of entries = -18.1461 R8VEC_SUM_TEST: Normal end of execution. R8VEC_SUM_RUNNING_TEST Python version: 3.6.5 R8VEC_SUM_RUNNING returns the running sums of an R8VEC. Random R8VEC: 0: -1.72373 1: 9.34476 2: 7.44264 3: 3.42543 4: 1.22961 5: -4.00822 6: -1.13633 7: -3.35065 8: -4.34257 9: 4.50949 Running sums: 0: 0 1: -1.72373 2: 7.62104 3: 15.0637 4: 18.4891 5: 19.7187 6: 15.7105 7: 14.5742 8: 11.2235 9: 6.88095 10: 11.3904 R8VEC_SUM_RUNNING_TEST: Normal end of execution. R8VEC_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8VEC_TRANSPOSE_PRINT prints an R8VEC "tranposed", that is, placing multiple entries on a line. The vector X: 1 2.1 3.2 4.3 5.4 6.5 7.6 8.7 9.8 10.9 11 R8VEC_TRANSPOSE_PRINT_TEST Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. R8VEC_UNIFORM_AB_TEST Python version: 3.6.5 R8VEC_UNIFORM_AB computes a random R8VEC. -1 <= X <= 5 Initial seed is 123456789 Random R8VEC: 0: 0.31051 1: 4.73791 2: 3.97706 3: 2.37017 4: 1.49184 5: -0.603288 6: 0.545467 7: -0.340259 8: -0.737026 9: 2.80379 R8VEC_UNIFORM_AB_TEST: Normal end of execution. R8VEC_UNIFORM_UNIT_TEST Python version: 3.6.5 R8VEC_UNIFORM_UNIT returns a random R8VEC on the surface of the unit M sphere. Vector: 0: 0.559743 1: -0.188708 2: 0.404357 3: 0.423174 4: -0.555425 Vector: 0: -0.700707 1: 0.0123973 2: 0.210315 3: -0.0859695 4: 0.67619 Vector: 0: 0.106795 1: 0.733237 2: 0.501662 3: -0.445775 4: -0.0240584 Vector: 0: -0.687688 1: -0.453412 2: -0.303477 3: 0.114009 4: 0.465195 Vector: 0: -0.571363 1: -0.512344 2: -0.314941 3: -0.510312 4: 0.226806 R8VEC_UNIFORM_UNIT_TEST: Normal end of execution. R8VEC_VARIANCE_TEST Python version: 3.6.5 R8VEC_VARIANCE computes the variance of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = 9.49943 R8VEC_VARIANCE_TEST: Normal end of execution. R8VEC_VARIANCE_CIRCULAR_TEST Python version: 3.6.5 R8VEC_VARIANCE_CIRCULAR computes the circular variance of an R8VEC. Uniform Vector in [-PI,+PI]: 0: -1.76923 1: 2.86713 2: 2.07037 3: 0.387644 4: -0.532141 5: -2.72616 6: -1.52318 7: -2.45071 8: -2.86621 9: 0.841731 Circular variance: 0.765084 Normal vector, mean 0, variance 1 0: 1.67904 1: -0.56606 2: 1.21293 3: 1.26938 4: -1.66609 5: -2.24246 6: 0.0396749 7: 0.673068 8: -0.275127 9: 2.164 Circular variance: 0.663344 R8VEC_VARIANCE_CIRCULAR_TEST Normal end of execution. R8VEC_VARIANCE_SAMPLE_TEST Python version: 3.6.5 R8VEC_VARIANCE_SAMPLE computes the sample variance of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Sample variance = 10.5549 R8VEC_VARIANCE_SAMPLE_TEST: Normal end of execution. R8VEC_VARIANCE_UPDATE_TEST Python version: 3.6.5 R8VEC_VARIANCE_UPDATE updates the variance of a vector when one more element is added. N R VARIANCE VARIANCE_UPDATE 1 0.218418 0 0 2 0.956318 0.136124 0.136124 3 0.829509 0.103779 0.103779 4 0.561695 0.0799561 0.0799561 5 0.415307 0.0721499 0.0721499 6 0.0661187 0.0991581 0.0991581 7 0.257578 0.0926651 0.0926651 8 0.109957 0.095429 0.095429 9 0.043829 0.0993161 0.0993161 R8VEC_VARIANCE_UPDATE_TEST: Normal end of execution. R8VEC2_PRINT_TEST Python version: 3.6.5 R8VEC2_PRINT prints a pair of R8VEC's. Print a pair of R8VEC's: 0: 0 0 1: 0.2 0.04 2: 0.4 0.16 3: 0.6 0.36 4: 0.8 0.64 5: 1 1 R8VEC2_PRINT_TEST: Normal end of execution. R8VEC2_PRINT_SOME_TEST Python version: 3.6.5 R8VEC2_PRINT_SOME prints some of a pair of R8VEC's. Square and square root: 0: 1 1 1: 4 1.41421 2: 9 1.73205 3: 16 2 4: 25 2.23607 5: 36 2.44949 6: 49 2.64575 7: 64 2.82843 ...... .............. .............. 99: 10000 10 R8VEC2_PRINT_SOME_TEST: Normal end of execution. R8VEC3_PRINT_TEST Python version: 3.6.5 R8VEC3_PRINT prints an R8VEC. X, X^2, X+X^2's: 0: 0 0 0 1: 0.2 0.04 0.24 2: 0.4 0.16 0.56 3: 0.6 0.36 0.96 4: 0.8 0.64 1.44 5: 1 1 2 R8VEC3_PRINT_TEST: Normal end of execution. SORT_HEAP_EXTERNAL_TEST Python version: 3.6.5 SORT_HEAP_EXTERNAL sorts objects externally. Unsorted array: 0 5 1 20 2 17 3 12 4 9 5 2 6 6 7 3 8 1 9 13 10 2 11 9 12 9 13 16 14 16 15 1 16 18 17 8 18 2 19 1 Sorted array: 0 1 1 1 2 1 3 2 4 2 5 2 6 3 7 5 8 6 9 8 10 9 11 9 12 9 13 12 14 13 15 16 16 16 17 17 18 18 19 20 SORT_HEAP_EXTERNAL_TEST: Normal end of execution. TIMESTAMP_TEST: Python version: 3.6.5 TIMESTAMP prints a timestamp of the current date and time. Thu Sep 13 15:56:54 2018 TIMESTAMP_TEST: Normal end of execution. R8LIB_TEST: Normal end of execution. Thu Sep 13 15:56:54 2018