June 24 2002 1:25:27.811 PM NMS_PRB Run the NMS tests. TEST001: ALNGAM evaluates the log of the Gamma function. X Exact F ALNGAM(X) 0.2000 1.52406 1.52406 0.4000 0.796678 0.796678 0.6000 0.398234 0.398234 0.8000 0.152060 0.152060 1.0000 0.00000 0.00000 1.1000 -0.498725E-01 -0.498725E-01 1.2000 -0.853741E-01 -0.853741E-01 1.3000 -0.108175 -0.108175 1.4000 -0.119613 -0.119613 1.5000 -0.120782 -0.120782 1.6000 -0.112592 -0.112592 1.7000 -0.958077E-01 -0.958076E-01 1.8000 -0.710839E-01 -0.710839E-01 1.9000 -0.389843E-01 -0.389843E-01 2.0000 0.00000 0.00000 10.0000 12.8018 12.8018 20.0000 39.3399 39.3399 30.0000 71.2570 71.2570 TEST002: BESI0 evaluates the Bessel I0 function. X Exact F BESI0(X) 0.0000 1.00000 1.00000 0.2000 1.01003 1.01003 0.4000 1.04040 1.04040 0.6000 1.09205 1.09205 0.8000 1.16651 1.16651 1.0000 1.26607 1.26607 1.2000 1.39373 1.39373 1.4000 1.55340 1.55340 1.6000 1.74998 1.74998 1.8000 1.98956 1.98956 2.0000 2.27959 2.27959 2.5000 3.28984 3.28984 3.0000 4.88079 4.88079 3.5000 7.37820 7.37820 4.0000 11.3019 11.3019 4.5000 17.4812 17.4812 5.0000 27.2399 27.2399 6.0000 67.2344 67.2344 8.0000 427.564 427.564 10.0000 2815.72 2815.72 TEST003: BESJ evaluates the Bessel function. X Exact F BESJ(0)(X) 0.0000 1.00000 1.00000 1.0000 0.765198 0.765198 2.0000 0.223891 0.223891 3.0000 -0.260052 -0.260052 4.0000 -0.397150 -0.397150 5.0000 -0.177597 -0.177597 6.0000 0.150645 0.150645 7.0000 0.300079 0.300080 8.0000 0.171651 0.171651 9.0000 -0.903336E-01 -0.903338E-01 10.0000 -0.245936 -0.245937 11.0000 -0.171190 -0.171190 12.0000 0.476893E-01 0.476891E-01 13.0000 0.206926 0.206926 14.0000 0.171073 0.171073 15.0000 -0.142245E-01 -0.142243E-01 TEST004: BESJ evaluates the Bessel function. X Exact F BESJ(1)(X) 0.0000 0.00000 0.00000 1.0000 0.440051 0.440051 2.0000 0.576725 0.576725 3.0000 0.339059 0.339059 4.0000 -0.660433E-01 -0.660433E-01 5.0000 -0.327579 -0.327579 6.0000 -0.276684 -0.276684 7.0000 -0.468280E-02 -0.468293E-02 8.0000 0.234636 0.234637 9.0000 0.245312 0.245312 10.0000 0.434728E-01 0.434730E-01 11.0000 -0.176785 -0.176785 12.0000 -0.223447 -0.223447 13.0000 -0.703181E-01 -0.703180E-01 14.0000 0.133375 0.133375 15.0000 0.205104 0.205105 TEST005: BESJ evaluates the Bessel function. NU X Exact F BESJ(NU)(X) 2 1.0000 0.114903 0.114903 2 2.0000 0.352834 0.352834 2 5.0000 0.465651E-01 0.465651E-01 2 10.0000 0.254630 0.254631 2 50.0000 -0.597128E-01 -0.597128E-01 5 1.0000 0.249758E-03 0.249758E-03 5 2.0000 0.703963E-02 0.703963E-02 5 5.0000 0.261141 0.261140 5 10.0000 -0.234062 -0.234062 5 50.0000 -0.814002E-01 -0.814001E-01 10 1.0000 0.263062E-09 0.263061E-09 10 2.0000 0.251539E-06 0.251539E-06 10 5.0000 0.146780E-02 0.146780E-02 10 10.0000 0.207486 0.207487 10 50.0000 -0.113848 -0.113848 20 1.0000 0.387350E-24 0.387349E-24 20 2.0000 0.391897E-18 0.391897E-18 20 5.0000 0.277033E-10 0.277033E-10 20 10.0000 0.115134E-04 0.115134E-04 20 50.0000 -0.116704 -0.116704 TEST006 For Fourier transforms of complex data, CFFTI initializes, CFFTF forward transforms data, CFFTB backward transforms coefficient. Autocorrelation by the complex FFT method. 0.100000E+01 0.606740E+00 0.353857E+00 0.184303E+00 -0.152912E-01 -0.219872E+00 -0.296218E+00 -0.291458E+00 -0.155056E+00 0.368080E-01 0.173559E+00 0.266597E+00 0.304990E+00 0.201169E+00 0.178036E-01 -0.210367E+00 -0.377387E+00 -0.437960E+00 -0.460333E+00 -0.425589E+00 TEST007 For two dimensional complex data: CFFTF_2D computes the forward FFT transform; CFFTB_2D computes the backward FFT transform. Maximum error in CFFT2D calculation: 0.119605E-06 TEST008 CFFTI initializes the complex FFT routines. CFFTF does a forward Fourier transform on complex data. Results for n= 16 czero= 0.549222 0.00000 j output from cfftf, scaled coeffs 1 -0.275492E+01 0.298023E-07 0.344365E+00 -0.338306E-07 2 0.140523E+01 0.000000E+00 0.175654E+00 -0.307123E-07 3 -0.778358E+00 0.000000E+00 0.972947E-01 -0.232046E-08 4 0.401056E+00 0.000000E+00 0.501320E-01 -0.175307E-07 5 -0.228722E+00 0.000000E+00 0.285903E-01 -0.193137E-07 6 0.119966E+00 0.000000E+00 0.149957E-01 -0.715290E-09 7 -0.841548E-01 -0.298023E-07 0.105194E-01 -0.102362E-07 8 0.614042E-01 0.000000E+00 0.767553E-02 -0.536813E-08 9 -0.841548E-01 -0.298023E-07 0.105194E-01 0.297264E-08 10 0.119966E+00 0.000000E+00 0.149957E-01 -0.202602E-07 11 -0.228722E+00 0.000000E+00 0.285903E-01 -0.752090E-07 12 0.401056E+00 0.000000E+00 0.501320E-01 -0.478254E-08 13 -0.778358E+00 0.000000E+00 0.972947E-01 -0.133772E-06 14 0.140523E+01 0.000000E+00 0.175654E+00 -0.466262E-06 15 -0.275492E+01 0.298023E-07 0.344365E+00 -0.447904E-07 Results for n= 17 czero= 0.549161 0.00000 j output from cfftf, scaled coeffs 1 -0.292606E+01 -0.228505E-06 0.344243E+00 -0.321169E-08 2 0.149192E+01 0.327057E-06 0.175520E+00 0.778845E-08 3 -0.824417E+00 -0.294977E-06 0.969903E-01 0.323900E-07 4 0.421975E+00 0.231923E-06 0.496441E-01 0.992501E-08 5 -0.234573E+00 -0.203721E-06 0.275968E-01 0.532464E-08 6 0.112482E+00 0.184924E-06 0.132331E-01 0.211245E-07 7 -0.603454E-01 -0.135952E-06 0.709946E-02 0.657184E-08 8 0.120123E-01 0.830954E-07 0.141321E-02 0.878756E-08 9 0.120123E-01 -0.830954E-07 -0.141321E-02 0.987705E-08 10 -0.603454E-01 0.135952E-06 -0.709946E-02 0.255862E-07 11 0.112482E+00 -0.184924E-06 -0.132331E-01 0.565666E-07 12 -0.234573E+00 0.203721E-06 -0.275968E-01 0.265999E-07 13 0.421975E+00 -0.231923E-06 -0.496441E-01 0.955415E-07 14 -0.824417E+00 0.294977E-06 -0.969903E-01 0.292157E-06 15 0.149192E+01 -0.327057E-06 -0.175520E+00 0.594078E-07 16 -0.292606E+01 0.228505E-06 -0.344243E+00 0.508397E-06 TEST009 CHKDER compares a user supplied jacobian and a finite difference approximation to it and judges whether the jacobian is correct. On the first test, use a correct jacobian. Evaluation point X: 0.500000 0.500000 0.500000 0.500000 0.500000 Sampled function values F(X) and F(XP) 1 -3.00000 -2.99896 2 -3.00000 -2.99896 3 -3.00000 -2.99896 4 -3.00000 -2.99896 5 -0.968750 -0.968696 Computed jacobian 2.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 0.625000E-01 0.625000E-01 0.625000E-01 0.625000E-01 0.625000E-01 CHKDER error estimates: > 0.5, gradient component is probably correct. < 0.5, gradient component is probably incorrect. 1 1.00000 2 1.00000 3 1.00000 4 1.00000 5 1.00000 Repeat the test, but use a "bad" jacobian and see if the routine notices! Evaluation point X: 0.500000 0.500000 0.500000 0.500000 0.500000 Sampled function values F(X) and F(XP) 1 -3.00000 -2.99896 2 -3.00000 -2.99896 3 -3.00000 -2.99896 4 -3.00000 -2.99896 5 -0.968750 -0.968696 Computed jacobian 2.02000 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 0.625000E-01 0.625000E-01 0.625000E-01 0.625000E-01 0.625000E-01 CHKDER error estimates: > 0.5, gradient component is probably correct. < 0.5, gradient component is probably incorrect. 1 0.798528 2 0.224798 3 1.00000 4 1.00000 5 1.00000 TEST010: ERF evaluates the Error function. X Exact F ERF(X) 0.0000 0.00000 0.00000 0.1000 0.112463 0.112463 0.2000 0.222703 0.222703 0.3000 0.328627 0.328627 0.4000 0.428392 0.428392 0.5000 0.520500 0.520500 0.6000 0.603856 0.603856 0.7000 0.677801 0.677801 0.8000 0.742101 0.742101 0.9000 0.796908 0.796908 1.0000 0.842701 0.842701 1.1000 0.880205 0.880205 1.2000 0.910314 0.910314 1.3000 0.934008 0.934008 1.4000 0.952285 0.952285 1.5000 0.966105 0.966105 1.6000 0.976348 0.976348 1.7000 0.983790 0.983790 1.8000 0.989091 0.989091 1.9000 0.992790 0.992790 2.0000 0.995322 0.995322 TEST011: ERFC evaluates the Complementary Error function. X Exact F ERFC(X) 0.0000 1.00000 1.00000 0.1000 0.887537 0.887537 0.2000 0.777297 0.777297 0.3000 0.671373 0.671373 0.4000 0.571608 0.571608 0.5000 0.479500 0.479500 0.6000 0.396144 0.396144 0.7000 0.322199 0.322199 0.8000 0.257899 0.257899 0.9000 0.203092 0.203092 1.0000 0.157299 0.157299 1.1000 0.119795 0.119795 1.2000 0.896860E-01 0.896860E-01 1.3000 0.659921E-01 0.659921E-01 1.4000 0.477149E-01 0.477149E-01 1.5000 0.338948E-01 0.338949E-01 1.6000 0.236516E-01 0.236516E-01 1.7000 0.162095E-01 0.162095E-01 1.8000 0.109095E-01 0.109095E-01 1.9000 0.720960E-02 0.720957E-02 2.0000 0.467771E-02 0.467774E-02 TEST012 For the FFT of a real data sequence: EZFFTI initializes, EZFFTF does forward transforms, EZFFTB does backward transforms. Autocorrelation (real fft) output reduced. 0.100000E+01 0.606740E+00 0.353858E+00 0.184303E+00 -0.152918E-01 -0.219873E+00 -0.296219E+00 -0.291460E+00 -0.155057E+00 0.368083E-01 0.173560E+00 0.266599E+00 0.304990E+00 0.201170E+00 0.178039E-01 -0.210368E+00 -0.377387E+00 -0.437961E+00 -0.460334E+00 -0.425591E+00 TEST013 The "EZ" FFT package: EZFFTI initializes, EZFFTF does forward transforms, EZFFTB does backward transforms. EZFFTF results N = 16 AZERO = 0.274611 j dfta(j) dftb(j) 1 0.344365 -0.338306E-07 2 0.175654 -0.307123E-07 3 0.972947E-01 -0.977104E-08 4 0.501320E-01 -0.175307E-07 5 0.285903E-01 -0.267642E-07 6 0.149957E-01 -0.715290E-09 7 0.105193E-01 -0.176867E-07 8 0.383776E-02 -0.268406E-08 Trigonometric polynomial order n= 16 X Interpolant Runge Error -1.00000 0.384616E-01 0.384615E-01 0.372529E-07 -0.900000 0.459555E-01 0.470588E-01 -0.110334E-02 -0.800000 0.606973E-01 0.588235E-01 0.187382E-02 -0.700000 0.732069E-01 0.754717E-01 -0.226480E-02 -0.600000 0.101743 0.100000 0.174331E-02 -0.500000 0.137931 0.137931 0.298023E-07 -0.400000 0.197306 0.200000 -0.269373E-02 -0.300000 0.312975 0.307692 0.528318E-02 -0.200000 0.494078 0.500000 -0.592190E-02 -0.100000 0.802987 0.800000 0.298691E-02 0.00000 1.00000 1.00000 -0.596046E-07 0.100000 0.802987 0.800000 0.298691E-02 0.200000 0.494078 0.500000 -0.592178E-02 0.300000 0.312976 0.307692 0.528321E-02 0.400000 0.197306 0.200000 -0.269382E-02 0.500000 0.137931 0.137931 -0.596046E-07 0.600000 0.101743 0.100000 0.174325E-02 0.700000 0.732069E-01 0.754717E-01 -0.226477E-02 0.800000 0.606974E-01 0.588235E-01 0.187386E-02 0.900000 0.459554E-01 0.470588E-01 -0.110340E-02 1.00000 0.384616E-01 0.384615E-01 0.372529E-07 EZFFTF results N = 17 AZERO = 0.274581 j dfta(j) dftb(j) 1 0.344243 -0.569776E-07 2 0.175520 -0.691661E-07 3 0.969902E-01 -0.370164E-07 4 0.496441E-01 -0.446452E-07 5 0.275968E-01 -0.426097E-07 6 0.132331E-01 -0.223870E-07 7 0.709944E-02 -0.254168E-07 8 0.141322E-02 -0.107643E-07 Trigonometric polynomial order n= 17 X Interpolant Runge Error -1.00000 0.384615E-01 0.384615E-01 -0.745058E-08 -0.900000 0.464566E-01 0.470588E-01 -0.602257E-03 -0.800000 0.596512E-01 0.588235E-01 0.827666E-03 -0.700000 0.744720E-01 0.754717E-01 -0.999704E-03 -0.600000 0.101106 0.100000 0.110563E-02 -0.500000 0.136885 0.137931 -0.104587E-02 -0.400000 0.200633 0.200000 0.632524E-03 -0.300000 0.308171 0.307692 0.478953E-03 -0.200000 0.497123 0.500000 -0.287676E-02 -0.100000 0.806918 0.800000 0.691843E-02 0.00000 0.990320 1.00000 -0.968003E-02 0.100000 0.806918 0.800000 0.691795E-02 0.200000 0.497123 0.500000 -0.287703E-02 0.300000 0.308171 0.307692 0.478953E-03 0.400000 0.200632 0.200000 0.632375E-03 0.500000 0.136885 0.137931 -0.104594E-02 0.600000 0.101106 0.100000 0.110554E-02 0.700000 0.744720E-01 0.754717E-01 -0.999689E-03 0.800000 0.596512E-01 0.588235E-01 0.827655E-03 0.900000 0.464566E-01 0.470588E-01 -0.602257E-03 1.00000 0.384615E-01 0.384615E-01 -0.745058E-08 TEST014 FMIN, function minimizer. Find a minimizer of F(X) = X^3 - 2 * X - 5. Results: X* = 0.816793 F(X*) = -6.08866 F'(X*) = 0.145149E-02 TEST015 FZERO, single nonlinear equation solver. F(X) = X^3 - 2 * X - 5 Initial interval: 2.00000 3.00000 Absolute error tolerance= 0.100000E-05 Relative error tolerance= 0.100000E-05 FZERO results Estimate of zero = 2.09455 Function value= 0.143051E-05 TEST016: GAMMA evaluates the Gamma function. X Exact F GAMMA(X) 0.2000 4.59085 4.59084 0.4000 2.21816 2.21816 0.6000 1.48919 1.48919 0.8000 1.16423 1.16423 1.0000 1.00000 1.00000 1.1000 0.951351 0.951351 1.2000 0.918169 0.918169 1.3000 0.897471 0.897471 1.4000 0.887264 0.887264 1.5000 0.886227 0.886227 1.6000 0.893515 0.893515 1.7000 0.908639 0.908639 1.8000 0.931384 0.931384 1.9000 0.961766 0.961766 2.0000 1.00000 1.00000 10.0000 362880. 362880. 20.0000 0.121645E+18 0.121645E+18 30.0000 0.884176E+31 0.884179E+31 TEST017 PCHEZ carries out piecewise cubic Hermite interpolation. PCHEV evaluates the interpolant. PCHQA integrates the interpolant. PCHEZ has set up the interpolant. PCHEV has evaluated the interpolant. -1.0000 0.0385 0.000 -0.7396E-01 -0.9900 0.0385 -0.7503E-03 -0.7611E-01 -0.9800 0.0385 -0.1522E-02 -0.7834E-01 -0.9700 0.0385 -0.2317E-02 -0.8065E-01 -0.9600 0.0385 -0.3136E-02 -0.8306E-01 -0.9500 0.0385 -0.3979E-02 -0.8556E-01 -0.9400 0.0385 -0.4847E-02 -0.8816E-01 -0.9300 0.0385 -0.5742E-02 -0.9086E-01 -0.9200 0.0385 -0.6665E-02 -0.9367E-01 -0.9100 0.0385 -0.7616E-02 -0.9660E-01 -0.9000 0.0385 -0.8597E-02 -0.9965E-01 -0.8900 0.0385 -0.9610E-02 -0.1028 -0.8800 0.0385 -0.1065E-01 -0.1061 -0.8700 0.0385 -0.1173E-01 -0.1096 -0.8600 0.0385 -0.1285E-01 -0.1132 -0.8500 0.0385 -0.1400E-01 -0.1170 -0.8400 0.0385 -0.1519E-01 -0.1209 -0.8300 0.0385 -0.1642E-01 -0.1250 -0.8200 0.0385 -0.1769E-01 -0.1293 -0.8100 0.0385 -0.1900E-01 -0.1337 -0.8000 0.0385 -0.2036E-01 -0.1384 -0.7900 0.0385 -0.2177E-01 -0.1433 -0.7800 0.0385 -0.2323E-01 -0.1484 -0.7700 0.0385 -0.2474E-01 -0.1538 -0.7600 0.0385 -0.2631E-01 -0.1594 -0.7500 0.0385 -0.2793E-01 -0.1653 -0.7400 0.0385 -0.2961E-01 -0.1715 -0.7300 0.0385 -0.3136E-01 -0.1779 -0.7200 0.0385 -0.3317E-01 -0.1847 -0.7100 0.0385 -0.3505E-01 -0.1919 -0.7000 0.0385 -0.3701E-01 -0.1994 -0.6900 0.0385 -0.3904E-01 -0.2072 -0.6800 0.0385 -0.4116E-01 -0.2155 -0.6700 0.0385 -0.4335E-01 -0.2242 -0.6600 0.0385 -0.4564E-01 -0.2334 -0.6500 0.0385 -0.4802E-01 -0.2431 -0.6400 0.0385 -0.5051E-01 -0.2533 -0.6300 0.0385 -0.5309E-01 -0.2640 -0.6200 0.0385 -0.5579E-01 -0.2754 -0.6100 0.0385 -0.5860E-01 -0.2874 -0.6000 0.0385 -0.6154E-01 -0.3000 -0.5900 0.0385 -0.6460E-01 -0.3134 -0.5800 0.0385 -0.6781E-01 -0.3275 -0.5700 0.0385 -0.7116E-01 -0.3425 -0.5600 0.0385 -0.7466E-01 -0.3583 -0.5500 0.0385 -0.7833E-01 -0.3751 -0.5400 0.0385 -0.8217E-01 -0.3929 -0.5300 0.0385 -0.8619E-01 -0.4117 -0.5200 0.0385 -0.9040E-01 -0.4318 -0.5100 0.0385 -0.9483E-01 -0.4530 -0.5000 0.0385 -0.9947E-01 -0.4756 -0.4900 0.0385 -0.1043 -0.4996 -0.4800 0.0385 -0.1095 -0.5252 -0.4700 0.0385 -0.1149 -0.5524 -0.4600 0.0385 -0.1205 -0.5813 -0.4500 0.0385 -0.1265 -0.6122 -0.4400 0.0385 -0.1328 -0.6451 -0.4300 0.0385 -0.1394 -0.6801 -0.4200 0.0385 -0.1464 -0.7175 -0.4100 0.0385 -0.1538 -0.7574 -0.4000 0.0385 -0.1615 -0.8000 -0.3900 0.0385 -0.1698 -0.8455 -0.3800 0.0385 -0.1785 -0.8940 -0.3700 0.0385 -0.1877 -0.9459 -0.3600 0.0385 -0.1974 -1.001 -0.3500 0.0385 -0.2077 -1.060 -0.3400 0.0385 -0.2186 -1.123 -0.3300 0.0385 -0.2302 -1.191 -0.3200 0.0385 -0.2424 -1.262 -0.3100 0.0385 -0.2554 -1.339 -0.3000 0.0385 -0.2692 -1.420 -0.2900 0.0385 -0.2839 -1.506 -0.2800 0.0385 -0.2994 -1.598 -0.2700 0.0385 -0.3158 -1.695 -0.2600 0.0385 -0.3333 -1.797 -0.2500 0.0385 -0.3518 -1.904 -0.2400 0.0385 -0.3714 -2.016 -0.2300 0.0385 -0.3921 -2.132 -0.2200 0.0385 -0.4140 -2.252 -0.2100 0.0385 -0.4372 -2.375 -0.2000 0.0385 -0.4615 -2.500 -0.1900 0.0385 -0.4872 -2.625 -0.1800 0.0385 -0.5140 -2.747 -0.1700 0.0385 -0.5421 -2.865 -0.1600 0.0385 -0.5713 -2.974 -0.1500 0.0385 -0.6015 -3.072 -0.1400 0.0385 -0.6327 -3.153 -0.1300 0.0385 -0.6645 -3.212 -0.1200 0.0385 -0.6968 -3.244 -0.1100 0.0385 -0.7293 -3.242 -0.1000 0.0385 -0.7615 -3.200 -0.0900 0.0385 -0.7931 -3.112 -0.0800 0.0385 -0.8236 -2.973 -0.0700 0.0385 -0.8524 -2.778 -0.0600 0.0385 -0.8790 -2.525 -0.0500 0.0385 -0.9027 -2.215 -0.0400 0.0385 -0.9231 -1.849 -0.0300 0.0385 -0.9395 -1.435 -0.0200 0.0385 -0.9516 -0.9803 -0.0100 0.0385 -0.9590 -0.4975 0.0000 0.0385 -0.9615 0.000 PCHQA estimates the integral from A to B. A = 0.00000 B = 1.00000 Integral estiamte = 0.384615E-01 Return code IERR = 0 TEST018 Q1DA, quadrature routine. Q1DA results: a, b, eps, r, e, kf, iflag 0.0000 1.0000 0.0010 0.41406754E-01 0.55436726E-06 30 0 TEST019 Q1DAX estimates the integral of a function over a a finite interval, allowing more flexibility than Q1DA. Error tolerance 0.100000E-02 Integral estimate 0.147020E-01 Error estimate 0.707938E-05 Q1DAX error flag = 4 TEST020 QAGI estimates an integral on a semi-infinite interval. Estimated integral = 0.702604 Estimated error = 0.683043E-05 Function evaluations = 1215 Return code IER = 0 TEST021 QK15 estimates an integral using Gauss-Kronrod integration. QK15 estimate of ERF(1) 2.0/sqrt(pi())*result, abserr 0.842701 0.445142E-05 TEST023 RNOR, normal random number generator. Number of normal values to compute is 10000 Number of bins is 32 Histogram for rnor: number in bin 1,...,32 (-infinity,-3],(-3,-2.8],...,(2.8,3],(3,infinity) (values are slightly computer dependent) 16 10 20 34 56 104 125 181 267 317 442 542 621 706 751 787 814 768 665 622 536 441 339 289 199 131 84 39 35 31 11 17 TEST024 RNOR generates random normal numbers. ISEED = 305 RSEED = 305.000 0.335785 0.230143 1.02517 TEST025 SDRIV1 is a simple interface to the ODE solver. Results t y(1) y(2) sin(t) cos(t) error error 0.00000 0.00000 1.00000 0.00000 1.00000 0.00000 0.00000 0.52360 0.50000 0.86602 0.50000 0.86603 0.00000 -0.00001 1.04720 0.86603 0.49999 0.86603 0.50000 0.00000 -0.00001 1.57080 1.00000 -0.00002 1.00000 0.00000 0.00000 -0.00002 2.09440 0.86601 -0.50002 0.86603 -0.50000 -0.00002 -0.00002 2.61799 0.49997 -0.86603 0.50000 -0.86603 -0.00003 -0.00001 3.14159 -0.00003 -0.99998 0.00000 -1.00000 -0.00003 0.00002 3.66519 -0.50002 -0.86600 -0.50000 -0.86603 -0.00002 0.00003 4.18879 -0.86602 -0.49996 -0.86603 -0.50000 0.00000 0.00004 4.71239 -0.99998 0.00003 -1.00000 0.00000 0.00002 0.00003 5.23599 -0.86599 0.50002 -0.86603 0.50000 0.00004 0.00002 5.75959 -0.49996 0.86602 -0.50000 0.86603 0.00004 -0.00001 6.28319 0.00003 0.99997 0.00000 1.00000 0.00003 -0.00003 TEST026 SDRIV2 is an ODE solver. sdriv2 results t, y(1), y(2), ms 0.00000 10.00000 0.00000 1 0.10000 9.87534 -2.20271 2 0.20000 9.59906 -3.19246 2 0.30000 9.25464 -3.63713 2 0.40000 8.87961 -3.83690 2 0.50000 8.49084 -3.92670 2 0.60000 8.09588 -3.96706 2 0.70000 7.69815 -3.98519 2 0.80000 7.29917 -3.99334 2 0.90000 6.89962 -3.99700 2 1.00000 6.49983 -3.99864 2 1.10000 6.09992 -3.99938 2 1.20000 5.69996 -3.99972 2 1.30000 5.29998 -3.99987 2 1.40000 4.89999 -3.99994 2 1.50000 4.50000 -3.99997 2 1.60000 4.10000 -3.99999 2 1.70000 3.70000 -4.00000 2 1.80000 3.30000 -4.00000 2 1.90000 2.90000 -4.00000 2 2.00000 2.50000 -4.00000 2 2.10000 2.10000 -4.00000 2 2.20000 1.70000 -4.00000 2 2.30000 1.30000 -4.00000 2 2.40000 0.90000 -4.00000 2 2.50000 0.50000 -4.00000 2 2.60000 0.10000 -4.00000 2 2.62500 0.00000 -4.00000 5 <-- y=0 at t= 2.62500 TEST027 For sine analysis of real data, SINTI initializes the FFT routines. SINT does a forward or backward FFT. The number of data items is N = 4096 NOTE THAT SOMETHING IS WRONG, EITHER WITH THE PROBLEM, OR THE CODE. THE TRANSFORM IS NOT PROPERLY INVERTED. The first 10 data values: 4.94322 0.693425 4.39877 0.493461E-01 4.36019 1.77878 0.880901 0.306925 3.49322 0.596004 Compute the sine coefficients from data. The first 10 sine coefficients: 13130.7 115.001 4442.99 366.450 2822.33 -30.2218 1733.38 69.5665 1486.38 70.6744 Retrieve data from coeficients. The first 10 data values: 4.95556 0.692717 4.40323 0.493243E-01 4.36270 1.77853 0.882799 0.306711 3.49468 0.595789 TEST028 SNSQE, nonlinear equation system solver. Initial solution estimate X0: 2.00000 3.00000 Function value F(X0): -22.0000 10.0000 SNSQE solution estimate X: 2.00000 1.00000 Function value F(X): -0.119209E-06 -0.476837E-06 TEST029 SQRLS solves linear systems in the least squares sense. Coefficient matrix 1.000000 1.000000 1.000000 1.000000 2.000000 4.000000 1.000000 3.000000 9.000000 1.000000 4.000000 16.000000 1.000000 5.000000 25.000000 Right-hand side 1.000000 2.300000 4.600000 3.100000 1.200000 Error code = 0 Estimated matrix rank = 3 Parameters -3.020015 4.491437 -0.728573 Residuals 0.257142 -0.748570 0.702856 -0.188573 -0.022856 TEST030 SSVDC computes the singular value decomposition. Computed singular values: 0.1059E+08 64.77 0.3421E-03 Computed polynomial coefficients: -0.1672E-02 -1.617 0.8711E-03 Model True Year Population Population Error 1900 72.19 75.99 3.81 1910 89.20 91.97 2.77 1920 106.40 105.71 -0.69 1930 123.76 122.78 -0.99 1940 141.30 131.67 -9.63 1950 159.02 150.70 -8.32 1960 176.90 179.32 2.42 1970 194.97 203.24 8.27 1980 213.202 RMS error is 16.1182 TEST031 SGEFS solves a system of linear equations. Coefficient matrix A: 10.000000 -7.000000 0.000000 -3.000000 2.000000 6.000000 5.000000 -1.000000 5.000000 Right-hand side B: 7.000000 4.000000 6.000000 SGEFS results: Estimated number of accurate digits = 5 Solution: 0.000000 -1.000000 1.000000 TEST032 UNCMIN, unconstrained minimization code. 0optstp relative gradient close to zero. optstp current iterate is probably solution. UNCMIN - Note! INFO = 1. The iteration probably converged. The gradient is very small. UNCMIN return code = 1 f(x*) = 91.0001 x* = 19.9899 -20.6233 TEST033 UNCMIN carries out unconstrained minimization of a scalar function of several variables. optdrv shift from forward to central differences in iteration 63 0optstp last global step failed to locate a point lower than x. optstp either x is an approximate local minimum of the function optstp the function is too non-linear for this algorithm, optstp or steptl is too large. UNCMIN - Warning! INFO = 3. Cannot find a point with lower value. (But not completely happy with the current value.) Return code = 3 f(x*) = 1.00113 x* = 0.999714 0.999606 0.999347 0.998917 0.997969 0.996220 0.992660 0.985613 0.971682 0.943797 TEST034 UNI is a uniform random number generator. The seed value ISEED is 305 The starting value is 305.000 The 1000-th random number generated is 0.512760 TEST035 Compute the autocorrelation of El Nino data using a direct method. Autocorrelation by the direct method. 0.100000E+01 0.606740E+00 0.353857E+00 0.184303E+00 -0.152912E-01 -0.219872E+00 -0.296218E+00 -0.291458E+00 -0.155056E+00 0.368081E-01 0.173559E+00 0.266598E+00 0.304990E+00 0.201169E+00 0.178036E-01 -0.210367E+00 -0.377387E+00 -0.437960E+00 -0.460333E+00 -0.425589E+00 TEST036 The reactor shielding problem Monte Carlo simulation using the UNI code for uniform random numbers. Reactor Shielding Problem Tallies: % absorbed, energy, std dev: 50.0000 0.258131E-01 0.263628E-01 % reflected, energy, sd: 30.0000 0.457862 0.336214 % transmitted, energy, sd: 10.0000 0.191756 0.00000 NMS_PRB Normal end of execution.