19 March 2018 3:48:46.227 PM NMS_TEST FORTRAN90 version Test the NMS library. TEST001: ALNGAM evaluates the log of the Gamma function. GAMMA_VALUES returns some exact values. X Exact F ALNGAM(X) 0.0100 4.59948 4.59948 0.1000 2.25271 2.25271 0.2000 1.52406 1.52406 0.4000 0.796678 0.796678 0.5000 0.572365 0.572365 0.6000 0.398234 0.398234 0.8000 0.152060 0.152060 1.0000 0.00000 0.00000 1.1000 -0.498724E-01 -0.498724E-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 -0.958077E-01 1.8000 -0.710839E-01 -0.710839E-01 1.9000 -0.389843E-01 -0.389843E-01 2.0000 0.00000 0.00000 3.0000 0.693147 0.693147 4.0000 1.79176 1.79176 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. BESSEL_I0_VALUES returns some exact values. 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. BESSEL_J0_VALUES returns some exact values. 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 0.300079 8.0000 0.171651 0.171651 9.0000 -0.903336E-01 -0.903336E-01 10.0000 -0.245936 -0.245936 11.0000 -0.171190 -0.171190 12.0000 0.476893E-01 0.476893E-01 13.0000 0.206926 0.206926 14.0000 0.171073 0.171073 15.0000 -0.142245E-01 -0.142245E-01 TEST004: BESJ evaluates the Bessel function. BESSEL_J1_VALUES returns some exact values. 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 -0.468282E-02 -0.468282E-02 8.0000 0.234636 0.234636 9.0000 0.245312 0.245312 10.0000 0.434727E-01 0.434727E-01 11.0000 -0.176785 -0.176785 12.0000 -0.223447 -0.223447 13.0000 -0.703181E-01 -0.703181E-01 14.0000 0.133375 0.133375 15.0000 0.205104 0.205104 TEST005: BESJ evaluates the Bessel function. BESSEL_JN_VALUES returns some exact values. 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 0.254630 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 0.261141 5 10.0000 -0.234062 -0.234062 5 50.0000 -0.814002E-01 -0.814002E-01 10 1.0000 0.263062E-09 0.263062E-09 10 2.0000 0.251539E-06 0.251539E-06 10 5.0000 0.146780E-02 0.146780E-02 10 10.0000 0.207486 0.207486 10 50.0000 -0.113848 -0.113848 20 1.0000 0.387350E-24 0.387350E-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: BP01 evaluates the Bernstein polynomials. BERNSTEIN_POLY_VALUES returns some exact values. N K X Exact B(N,K)(X) 0 0 0.2500 1.00000 1.00000 1 0 0.2500 0.750000 0.750000 1 1 0.2500 0.250000 0.250000 2 0 0.2500 0.562500 0.562500 2 1 0.2500 0.375000 0.375000 2 2 0.2500 0.625000E-01 0.625000E-01 3 0 0.2500 0.421875 0.421875 3 1 0.2500 0.421875 0.421875 3 2 0.2500 0.140625 0.140625 3 3 0.2500 0.156250E-01 0.156250E-01 4 0 0.2500 0.316406 0.316406 4 1 0.2500 0.421875 0.421875 4 2 0.2500 0.210938 0.210938 4 3 0.2500 0.468750E-01 0.468750E-01 4 4 0.2500 0.390625E-02 0.390625E-02 TEST007 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 -3.00000 2 -3.00000 -3.00000 3 -3.00000 -3.00000 4 -3.00000 -3.00000 5 -0.968750 -0.968750 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 -3.00000 2 -3.00000 -3.00000 3 -3.00000 -3.00000 4 -3.00000 -3.00000 5 -0.968750 -0.968750 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 0.354955 2 0.994216E-01 3 1.00000 4 1.00000 5 1.00000 TEST008 For real fast cosine transforms, 1D, COSTI initializes the transforms, COST does a forward or backward transform The number of data items is N = 4096 First 10 data values: 1 0.15441427E-01 2 0.52405601 3 0.80930069 4 0.91671028 5 0.14975941 6 0.64746253E-02 7 0.81902779 8 0.40008638 9 0.25180872 10 0.14908369 First 10 FFT coefficients: 1 4069.0552 2 -33.627846 3 -.62210966 4 -27.807589 5 42.418429 6 -59.688277 7 4.2655459 8 -60.497355 9 -12.161034 10 -54.211112 First 10 retrieved data values: 1 0.15441427E-01 2 0.52405601 3 0.80930069 4 0.91671028 5 0.14975941 6 0.64746253E-02 7 0.81902779 8 0.40008638 9 0.25180872 10 0.14908369 TEST009 DNOR, normal random number generator. Number of normal values to compute is 10000 Number of bins is 32 Histogram for DNOR: number in bin 1,...,32 (-infinity,-3],(-3,-2.8],...,(2.8,3],(3,infinity) (values are slightly computer dependent) 14 8 8 43 60 93 118 182 233 333 477 535 639 703 764 753 769 769 637 674 529 449 354 293 194 118 107 59 38 26 12 9 TEST010 DNOR generates random normal numbers. ISEED = 305 RSEED = 305.000 0.335785 0.230143 1.02517 -0.508283 -0.184653 TEST011 DDRIV1 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 -0.00003 1.00000 0.00000 -0.00000 -0.00003 2.09440 0.86601 -0.50002 0.86603 -0.50000 -0.00002 -0.00002 2.61799 0.49998 -0.86603 0.50000 -0.86603 -0.00002 -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 0.50001 -0.86603 0.50000 0.00004 0.00001 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 TEST012 DDRIV2 is an ODE solver. DDRIV2 results t, y(1), y(2), ms 0.00000 10.00000 0.00000 1 0.10000 9.87534 -2.20270 2 0.20000 9.59906 -3.19245 2 0.30000 9.25464 -3.63713 2 0.40000 8.87961 -3.83688 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 5.69997 -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 TEST013 DNSQE, nonlinear equation system solver. Initial solution estimate X0: 2.00000 3.00000 Function value F(X0): -22.0000 10.0000 DNSQE solution estimate X: 2.00000 1.00000 Function value F(X): 0.126467E-07 0.280377E-07 TEST014 DQRLS 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 -3.020000 4.491429 -0.728571 Residuals 0.257143 -0.748571 0.702857 -0.188571 -0.022857 TEST015 DSVDC computes the singular value decomposition. Computed singular values: 0.1059E+08 64.77 0.3462E-03 Computed polynomial coefficients: -0.1671E-02 -1.617 0.8710E-03 Model True Year Population Population Error 1900 71.90 75.99 4.09 1910 88.92 91.97 3.05 1920 106.11 105.71 -0.40 1930 123.47 122.78 -0.69 1940 141.00 131.67 -9.34 1950 158.71 150.70 -8.02 1960 176.60 179.32 2.72 1970 194.66 203.24 8.58 1980 212.891 RMS error is 16.0966 TEST016 DGEFS 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 DGEFS results: Estimated number of accurate digits = 14 Solution: 0.000000 -1.000000 1.000000 TEST017: ERROR_F evaluates the Error function. ERF_VALUES returns some exact values. X Exact F ERROR_F(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 TEST018: ERROR_FC evaluates the Complementary Error function. ERF_VALUES returns some exact values. X Exact F ERROR_FC(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 0.338949E-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 0.720957E-02 0.720957E-02 2.0000 0.467773E-02 0.467773E-02 TEST019 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 0.353857E+00 0.184303E+00 -0.152911E-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 TEST020 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 0.525809E-16 2 0.175654 0.430229E-16 3 0.972947E-01 0.392149E-16 4 0.501320E-01 0.245576E-16 5 0.285903E-01 0.140370E-16 6 0.149957E-01 0.110187E-16 7 0.105194E-01 0.124872E-16 8 0.383778E-02 0.375994E-17 Trigonometric polynomial order n= 16 X Interpolant Runge Error -1.00000 0.384615E-01 0.384615E-01 -0.346945E-16 -0.900000 0.459554E-01 0.470588E-01 -0.110339E-02 -0.800000 0.606974E-01 0.588235E-01 0.187385E-02 -0.700000 0.732069E-01 0.754717E-01 -0.226483E-02 -0.600000 0.101743 0.100000 0.174329E-02 -0.500000 0.137931 0.137931 -0.111022E-15 -0.400000 0.197306 0.200000 -0.269380E-02 -0.300000 0.312976 0.307692 0.528322E-02 -0.200000 0.494078 0.500000 -0.592182E-02 -0.100000 0.802987 0.800000 0.298694E-02 0.00000 1.00000 1.00000 0.222045E-15 0.100000 0.802987 0.800000 0.298694E-02 0.200000 0.494078 0.500000 -0.592182E-02 0.300000 0.312976 0.307692 0.528322E-02 0.400000 0.197306 0.200000 -0.269380E-02 0.500000 0.137931 0.137931 -0.555112E-16 0.600000 0.101743 0.100000 0.174329E-02 0.700000 0.732069E-01 0.754717E-01 -0.226483E-02 0.800000 0.606974E-01 0.588235E-01 0.187385E-02 0.900000 0.459554E-01 0.470588E-01 -0.110339E-02 1.00000 0.384615E-01 0.384615E-01 -0.346945E-16 EZFFTF results N = 17 AZERO = 0.274581 j dfta(j) dftb(j) 1 0.344243 0.564034E-16 2 0.175520 0.439250E-16 3 0.969903E-01 0.246525E-16 4 0.496442E-01 0.224021E-16 5 0.275968E-01 0.228443E-16 6 0.132331E-01 0.121986E-16 7 0.709946E-02 0.485929E-17 8 0.141325E-02 -0.286819E-18 Trigonometric polynomial order n= 17 X Interpolant Runge Error -1.00000 0.384615E-01 0.384615E-01 -0.145717E-15 -0.900000 0.464565E-01 0.470588E-01 -0.602328E-03 -0.800000 0.596512E-01 0.588235E-01 0.827626E-03 -0.700000 0.744720E-01 0.754717E-01 -0.999687E-03 -0.600000 0.101106 0.100000 0.110565E-02 -0.500000 0.136885 0.137931 -0.104587E-02 -0.400000 0.200632 0.200000 0.632300E-03 -0.300000 0.308171 0.307692 0.478911E-03 -0.200000 0.497123 0.500000 -0.287691E-02 -0.100000 0.806918 0.800000 0.691821E-02 0.00000 0.990320 1.00000 -0.967973E-02 0.100000 0.806918 0.800000 0.691821E-02 0.200000 0.497123 0.500000 -0.287691E-02 0.300000 0.308171 0.307692 0.478911E-03 0.400000 0.200632 0.200000 0.632300E-03 0.500000 0.136885 0.137931 -0.104587E-02 0.600000 0.101106 0.100000 0.110565E-02 0.700000 0.744720E-01 0.754717E-01 -0.999687E-03 0.800000 0.596512E-01 0.588235E-01 0.827626E-03 0.900000 0.464565E-01 0.470588E-01 -0.602328E-03 1.00000 0.384615E-01 0.384615E-01 -0.145717E-15 TEST021 FMIN, function minimizer. Find a minimizer of F(X) = X^3 - 2 * X - 5. The initial interval is [A,B]: A = 0.100000 F(A) = -5.19900 F'(A) = -1.97000 B = 0.900000 F(B) = -6.07100 F'(B) = 0.430000 The final interval [A,B] and minimizer X*: A = 0.816497 F(A) = -6.08866 F'(A) = -0.230429E-06 B = 0.816497 F(B) = -6.08866 F'(B) = 0.215378E-06 X* = 0.816497 F(X*) = -6.08866 F'(X*) = -0.752548E-08 TEST022 FMIN_RC, function minimizer with reverse communication. Find a minimizer of F(X) = X^3 - 2 * X - 5. The initial interval is [A,B]: A = 0.100000 F(A) = -5.19900 F'(A) = -1.97000 B = 0.900000 F(B) = -6.07100 F'(B) = 0.430000 The final interval [A,B] and minimizer X*: A = 0.816497 F(A) = -6.08866 F'(A) = -0.752548E-08 B = 0.816497 F(B) = -6.08866 F'(B) = 0.111684E-06 X* = 0.816497 F(X*) = -6.08866 F'(X*) = 0.111684E-06 TEST023 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= -0.515785E-06 TEST024: GAMMA evaluates the Gamma function. GAMMA_VALUES returns some exact values. X Exact F GAMMA(X) -0.2000 -3.54491 -5.82115 -0.0100 -100.587 -100.587 0.0100 99.4326 99.4326 0.1000 9.51351 9.51351 0.2000 4.59084 4.59084 0.4000 2.21816 2.21816 0.5000 1.77245 1.77245 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 3.0000 2.00000 2.00000 4.0000 6.00000 6.00000 10.0000 362880. 362880. 20.0000 0.121645E+18 0.121645E+18 30.0000 0.884176E+31 0.884176E+31 TEST025 PCHEZ carries out piecewise cubic spline or Hermite interpolation. PCHEV evaluates the interpolant. -1.0000 0.038462 0.038462 0.00000 -0.9900 0.039212 0.039181 -0.308918E-04 -0.9800 0.039984 0.039935 -0.485212E-04 -0.9700 0.040779 0.040724 -0.552114E-04 -0.9600 0.041597 0.041544 -0.533257E-04 -0.9500 0.042440 0.042395 -0.452705E-04 -0.9400 0.043309 0.043275 -0.334976E-04 -0.9300 0.044204 0.044183 -0.205064E-04 -0.9200 0.045126 0.045118 -0.884751E-05 -0.9100 0.046078 0.046077 -0.112499E-05 -0.9000 0.047059 0.047059 0.00000 -0.8900 0.048071 0.048069 -0.228500E-05 -0.8800 0.049116 0.049113 -0.310310E-05 -0.8700 0.050195 0.050192 -0.267772E-05 -0.8600 0.051308 0.051307 -0.130444E-05 -0.8500 0.052459 0.052460 0.644554E-06 -0.8400 0.053648 0.053651 0.271564E-05 -0.8300 0.054877 0.054882 0.436864E-05 -0.8200 0.056148 0.056153 0.497128E-05 -0.8100 0.057463 0.057467 0.379328E-05 -0.8000 0.058824 0.058824 0.00000 -0.7900 0.060232 0.060228 -0.399457E-05 -0.7800 0.061690 0.061685 -0.536439E-05 -0.7700 0.063201 0.063197 -0.450436E-05 -0.7600 0.064767 0.064765 -0.194428E-05 -0.7500 0.066390 0.066392 0.164206E-05 -0.7400 0.068074 0.068079 0.542702E-05 -0.7300 0.069820 0.069829 0.841856E-05 -0.7200 0.071633 0.071643 0.944880E-05 -0.7100 0.073516 0.073523 0.716174E-05 -0.7000 0.075472 0.075472 0.00000 -0.6900 0.077504 0.077497 -0.742334E-05 -0.6800 0.079618 0.079608 -0.974780E-05 -0.6700 0.081816 0.081809 -0.775770E-05 -0.6600 0.084104 0.084102 -0.250322E-05 -0.6500 0.086486 0.086491 0.468003E-05 -0.6400 0.088968 0.088980 0.121500E-04 -0.6300 0.091554 0.091572 0.179354E-04 -0.6200 0.094251 0.094270 0.197110E-04 -0.6100 0.097064 0.097079 0.147709E-04 -0.6000 0.100000 0.100000 0.00000 -0.5900 0.103066 0.103051 -0.148073E-04 -0.5800 0.106270 0.106251 -0.185423E-04 -0.5700 0.109619 0.109606 -0.130638E-04 -0.5600 0.113122 0.113121 -0.780745E-06 -0.5500 0.116788 0.116804 0.153042E-04 -0.5400 0.120627 0.120659 0.315492E-04 -0.5300 0.124649 0.124693 0.436227E-04 -0.5200 0.128866 0.128912 0.464503E-04 -0.5100 0.133289 0.133323 0.341559E-04 -0.5000 0.137931 0.137931 0.00000 -0.4900 0.142806 0.142774 -0.318942E-04 -0.4800 0.147929 0.147893 -0.356766E-04 -0.4700 0.153315 0.153298 -0.170057E-04 -0.4600 0.158983 0.159000 0.172978E-04 -0.4500 0.164948 0.165008 0.591638E-04 -0.4400 0.171233 0.171332 0.991804E-04 -0.4300 0.177857 0.177983 0.126497E-03 -0.4200 0.184843 0.184972 0.128722E-03 -0.4100 0.192215 0.192307 0.918191E-04 -0.4000 0.200000 0.200000 0.00000 -0.3900 0.208225 0.208152 -0.733518E-04 -0.3800 0.216920 0.216862 -0.578857E-04 -0.3700 0.226116 0.226140 0.231136E-04 -0.3600 0.235849 0.235993 0.144198E-03 -0.3500 0.246154 0.246432 0.277675E-03 -0.3400 0.257069 0.257463 0.393550E-03 -0.3300 0.268637 0.269096 0.459492E-03 -0.3200 0.280899 0.281340 0.440847E-03 -0.3100 0.293902 0.294202 0.300698E-03 -0.3000 0.307692 0.307692 0.00000 -0.2900 0.322321 0.322151 -0.169729E-03 -0.2800 0.337838 0.337865 0.270537E-04 -0.2700 0.354296 0.354761 0.465165E-03 -0.2600 0.371747 0.372766 0.101906E-02 -0.2500 0.390244 0.391808 0.156376E-02 -0.2400 0.409836 0.411812 0.197606E-02 -0.2300 0.430571 0.432707 0.213613E-02 -0.2200 0.452489 0.454418 0.192946E-02 -0.2100 0.475624 0.476874 0.124936E-02 -0.2000 0.500000 0.500000 0.00000 -0.1900 0.525624 0.525224 -0.399804E-03 -0.1800 0.552486 0.553520 0.103381E-02 -0.1700 0.580552 0.584133 0.358160E-02 -0.1600 0.609756 0.616310 0.655390E-02 -0.1500 0.640000 0.649297 0.929687E-02 -0.1400 0.671141 0.682340 0.111991E-01 -0.1300 0.702988 0.714686 0.116979E-01 -0.1200 0.735294 0.745580 0.102859E-01 -0.1100 0.767754 0.774269 0.651506E-02 -0.1000 0.800000 0.800000 0.00000 -0.0900 0.831601 0.825040 -0.656083E-02 -0.0800 0.862069 0.851520 -0.105490E-01 -0.0700 0.890869 0.878480 -0.123886E-01 -0.0600 0.917431 0.904960 -0.124712E-01 -0.0500 0.941176 0.930000 -0.111765E-01 -0.0400 0.961538 0.952640 -0.889846E-02 -0.0300 0.977995 0.971920 -0.607511E-02 -0.0200 0.990099 0.986880 -0.321901E-02 -0.0100 0.997506 0.996560 -0.946234E-03 0.0000 1.000000 1.000000 0.00000 TEST026 PCHEZ carries out piecewise cubic spline or Hermite interpolation. PCHQA integrates the interpolant. PCHQA estimates the integral from A to B. A = 0.00000 B = 1.00000 Integral estimate = 0.274679 Return code IERR = 0 TEST0265 PCHIM carries out piecewise cubic Hermite interpolation. PCHFE evaluates the interpolant. -1.0000 0.038462 0.038462 0.00000 -0.9900 0.039212 0.039181 -0.308918E-04 -0.9800 0.039984 0.039935 -0.485212E-04 -0.9700 0.040779 0.040724 -0.552114E-04 -0.9600 0.041597 0.041544 -0.533257E-04 -0.9500 0.042440 0.042395 -0.452705E-04 -0.9400 0.043309 0.043275 -0.334976E-04 -0.9300 0.044204 0.044183 -0.205064E-04 -0.9200 0.045126 0.045118 -0.884751E-05 -0.9100 0.046078 0.046077 -0.112499E-05 -0.9000 0.047059 0.047059 0.00000 -0.8900 0.048071 0.048069 -0.228500E-05 -0.8800 0.049116 0.049113 -0.310310E-05 -0.8700 0.050195 0.050192 -0.267772E-05 -0.8600 0.051308 0.051307 -0.130444E-05 -0.8500 0.052459 0.052460 0.644554E-06 -0.8400 0.053648 0.053651 0.271564E-05 -0.8300 0.054877 0.054882 0.436864E-05 -0.8200 0.056148 0.056153 0.497128E-05 -0.8100 0.057463 0.057467 0.379328E-05 -0.8000 0.058824 0.058824 0.00000 -0.7900 0.060232 0.060228 -0.399457E-05 -0.7800 0.061690 0.061685 -0.536439E-05 -0.7700 0.063201 0.063197 -0.450436E-05 -0.7600 0.064767 0.064765 -0.194428E-05 -0.7500 0.066390 0.066392 0.164206E-05 -0.7400 0.068074 0.068079 0.542702E-05 -0.7300 0.069820 0.069829 0.841856E-05 -0.7200 0.071633 0.071643 0.944880E-05 -0.7100 0.073516 0.073523 0.716174E-05 -0.7000 0.075472 0.075472 0.00000 -0.6900 0.077504 0.077497 -0.742334E-05 -0.6800 0.079618 0.079608 -0.974780E-05 -0.6700 0.081816 0.081809 -0.775770E-05 -0.6600 0.084104 0.084102 -0.250322E-05 -0.6500 0.086486 0.086491 0.468003E-05 -0.6400 0.088968 0.088980 0.121500E-04 -0.6300 0.091554 0.091572 0.179354E-04 -0.6200 0.094251 0.094270 0.197110E-04 -0.6100 0.097064 0.097079 0.147709E-04 -0.6000 0.100000 0.100000 0.00000 -0.5900 0.103066 0.103051 -0.148073E-04 -0.5800 0.106270 0.106251 -0.185423E-04 -0.5700 0.109619 0.109606 -0.130638E-04 -0.5600 0.113122 0.113121 -0.780745E-06 -0.5500 0.116788 0.116804 0.153042E-04 -0.5400 0.120627 0.120659 0.315492E-04 -0.5300 0.124649 0.124693 0.436227E-04 -0.5200 0.128866 0.128912 0.464503E-04 -0.5100 0.133289 0.133323 0.341559E-04 -0.5000 0.137931 0.137931 0.00000 -0.4900 0.142806 0.142774 -0.318942E-04 -0.4800 0.147929 0.147893 -0.356766E-04 -0.4700 0.153315 0.153298 -0.170057E-04 -0.4600 0.158983 0.159000 0.172978E-04 -0.4500 0.164948 0.165008 0.591638E-04 -0.4400 0.171233 0.171332 0.991804E-04 -0.4300 0.177857 0.177983 0.126497E-03 -0.4200 0.184843 0.184972 0.128722E-03 -0.4100 0.192215 0.192307 0.918191E-04 -0.4000 0.200000 0.200000 0.00000 -0.3900 0.208225 0.208152 -0.733518E-04 -0.3800 0.216920 0.216862 -0.578857E-04 -0.3700 0.226116 0.226140 0.231136E-04 -0.3600 0.235849 0.235993 0.144198E-03 -0.3500 0.246154 0.246432 0.277675E-03 -0.3400 0.257069 0.257463 0.393550E-03 -0.3300 0.268637 0.269096 0.459492E-03 -0.3200 0.280899 0.281340 0.440847E-03 -0.3100 0.293902 0.294202 0.300698E-03 -0.3000 0.307692 0.307692 0.00000 -0.2900 0.322321 0.322151 -0.169729E-03 -0.2800 0.337838 0.337865 0.270537E-04 -0.2700 0.354296 0.354761 0.465165E-03 -0.2600 0.371747 0.372766 0.101906E-02 -0.2500 0.390244 0.391808 0.156376E-02 -0.2400 0.409836 0.411812 0.197606E-02 -0.2300 0.430571 0.432707 0.213613E-02 -0.2200 0.452489 0.454418 0.192946E-02 -0.2100 0.475624 0.476874 0.124936E-02 -0.2000 0.500000 0.500000 0.00000 -0.1900 0.525624 0.525224 -0.399804E-03 -0.1800 0.552486 0.553520 0.103381E-02 -0.1700 0.580552 0.584133 0.358160E-02 -0.1600 0.609756 0.616310 0.655390E-02 -0.1500 0.640000 0.649297 0.929687E-02 -0.1400 0.671141 0.682340 0.111991E-01 -0.1300 0.702988 0.714686 0.116979E-01 -0.1200 0.735294 0.745580 0.102859E-01 -0.1100 0.767754 0.774269 0.651506E-02 -0.1000 0.800000 0.800000 0.00000 -0.0900 0.831601 0.825040 -0.656083E-02 -0.0800 0.862069 0.851520 -0.105490E-01 -0.0700 0.890869 0.878480 -0.123886E-01 -0.0600 0.917431 0.904960 -0.124712E-01 -0.0500 0.941176 0.930000 -0.111765E-01 -0.0400 0.961538 0.952640 -0.889846E-02 -0.0300 0.977995 0.971920 -0.607511E-02 -0.0200 0.990099 0.986880 -0.321901E-02 -0.0100 0.997506 0.996560 -0.946234E-03 0.0000 1.000000 1.000000 0.00000 TEST027 Q1DA, quadrature routine. Q1DA results: a, b, eps, r, e, kf, iflag 0.0000 1.0000 0.0010 0.41406752E-01 0.23020055E-10 30 0 TEST029 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 0.116516E-04 Error tolerance 0.100000E-03 Integral estimate 0.147020E-01 Error estimate 0.450554E-06 TEST030 QAGI estimates an integral on a semi-infinite interval. Estimated integral = 0.702603 (Correct value) = 0.702600 Estimated error = 0.640152E-05 Function evaluations = 1005 Return code IER = 0 TEST031 QK15 estimates an integral using Gauss-Kronrod integration. QK15 estimate of ERF(1) 2 / sqrt ( PI ) * result, abserr 0.842701 0.829141E-14 TEST032 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 The first 10 data values: 1.09209 4.78159 4.14755 2.80848 2.07654 0.330594 1.28789 0.549784 0.219145 3.16983 Compute the sine coefficients from data. The first 10 sine coefficients: 12951.9 -32.8224 4365.25 199.779 2762.57 -221.224 2034.66 -255.913 1440.02 107.481 Retrieve data from coeficients. The first 10 data values: 1.09209 4.78159 4.14755 2.80848 2.07654 0.330594 1.28789 0.549784 0.219145 3.16983 TEST033 For real fast sine transforms, 1D, SINTI initializes the transforms, SINT does a forward or backward transform The number of data items is N = 4096 First 10 data values: 1 0.15441427E-01 2 0.52405601 3 0.80930069 4 0.91671028 5 0.14975941 6 0.64746253E-02 7 0.81902779 8 0.40008638 9 0.25180872 10 0.14908369 Fist 10 FFT coefficients: 1 2588.2399 2 -2.0756900 3 839.85207 4 15.346176 5 546.38180 6 -12.656401 7 389.17756 8 -36.347893 9 281.15262 10 -76.269816 First 10 retrieved data values: 1 0.15441427E-01 2 0.52405601 3 0.80930069 4 0.91671028 5 0.14975941 6 0.64746253E-02 7 0.81902779 8 0.40008638 9 0.25180872 10 0.14908369 TEST034 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*) = 91.0000 x* = 20.0000 -20.6053 TEST035 UNCMIN carries out unconstrained minimization of a scalar function of several variables. optdrv shift from forward to central differences in iteration 71 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. Return code = 1 f(x*) = 1.00000 x* = 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 TEST0355 UNCMIN carries out unconstrained minimization of a scalar function of several variables. 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. Return code = 1 f(x*) = 0.225448E-11 x* = 1 -0.000000 -0.000001 2 -3.000001 0.000000 3 -4.000000 3.000000 4 0.000001 3.999999 0.00000 3.00000 5.00000 4.00000 3.00000 0.00000 3.16228 5.00000 5.00000 3.16228 0.00000 4.12311 4.00000 5.00000 4.12311 0.00000 TEST036 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 TEST037 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 -0.152911E-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 TEST038 For complex fast Fourier transforms, 1D, ZFFTI initializes the transforms, ZFFTF does a forward transforms; ZFFTB does a backward transforms. The number of data items is N = 4096 The original data: 1 -0.122847 -0.187108E-01 2 0.779210 -0.449592 3 0.386667 0.157388E-01 4 -0.732450 0.531549 5 0.297286 0.404264 6 0.289634 -0.752138 7 0.171588 0.682045 8 0.564249 0.401782 9 0.158831 0.390522 10 0.503769 -0.474654 The FFT coefficients: 1 -3.19144 -6.95364 2 11.0252 70.0894 3 -4.03462 -22.8225 4 32.0891 19.3522 5 -52.6949 6.47382 6 5.38100 82.0159 7 50.8479 8.09551 8 4.40469 -4.14458 9 -29.1171 0.138864 10 6.81949 21.5753 The retrieved data: 1 -0.122847 -0.187108E-01 2 0.779210 -0.449592 3 0.386667 0.157388E-01 4 -0.732450 0.531549 5 0.297286 0.404264 6 0.289634 -0.752138 7 0.171588 0.682045 8 0.564249 0.401782 9 0.158831 0.390522 10 0.503769 -0.474654 TEST039 For Fourier transforms of complex data, ZFFTI initializes, ZFFTF forward transforms data, ZFFTB backward transforms coefficient. Autocorrelation by the complex FFT method. 0.100000E+01 0.606740E+00 0.353857E+00 0.184303E+00 -0.152911E-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 TEST040 For two dimensional complex data: ZFFTF_2D computes the forward FFT transform; ZFFTB_2D computes the backward FFT transform. Maximum error in ZFFT2D calculation: 0.182995E-15 TEST041 ZFFTI initializes the complex FFT routines. ZFFTF does a forward Fourier transform on complex data. Results for N = 16 czero= 0.549222 0.00000 j output from ZFFTF, scaled coeffs 1 -0.275492E+01 -0.832667E-16 0.344365E+00 0.525809E-16 2 0.140523E+01 0.555112E-16 0.175654E+00 0.499617E-16 3 -0.778358E+00 0.277556E-16 0.972947E-01 0.322761E-16 4 0.401056E+00 0.000000E+00 0.501320E-01 0.245576E-16 5 -0.228722E+00 -0.832667E-16 0.285903E-01 0.279148E-16 6 0.119966E+00 -0.555112E-16 0.149957E-01 0.407980E-17 7 -0.841548E-01 0.832667E-16 0.105194E-01 -0.139060E-17 8 0.614044E-01 0.000000E+00 0.767555E-02 0.751987E-17 9 -0.841548E-01 0.277556E-16 0.105194E-01 0.812480E-17 10 0.119966E+00 -0.555112E-16 0.149957E-01 0.114256E-16 11 -0.228722E+00 0.277556E-16 0.285903E-01 0.136618E-15 12 0.401056E+00 0.000000E+00 0.501320E-01 0.736727E-16 13 -0.778358E+00 0.138778E-15 0.972947E-01 -0.208110E-15 14 0.140523E+01 0.555112E-16 0.175654E+00 0.308099E-15 15 -0.275492E+01 -0.138778E-15 0.344365E+00 0.187337E-14 Results for N = 17 czero= 0.549161 0.00000 j output from ZFFTF, scaled coeffs 1 -0.292606E+01 0.121089E-15 0.344243E+00 0.279118E-16 2 0.149192E+01 -0.794799E-17 0.175520E+00 0.420549E-16 3 -0.824417E+00 -0.933397E-16 0.969903E-01 0.466148E-16 4 0.421975E+00 0.162906E-16 0.496442E-01 0.262352E-16 5 -0.234573E+00 0.505423E-16 0.275968E-01 0.109520E-16 6 0.112482E+00 -0.210383E-16 0.132331E-01 0.724846E-17 7 -0.603455E-01 -0.104273E-16 0.709946E-02 0.731278E-17 8 0.120126E-01 0.142069E-16 0.141325E-02 0.305599E-17 9 0.120126E-01 -0.142069E-16 -0.141325E-02 0.113745E-18 10 -0.603455E-01 0.104273E-16 -0.709946E-02 -0.746759E-17 11 0.112482E+00 0.210383E-16 -0.132331E-01 -0.673151E-16 12 -0.234573E+00 -0.505423E-16 -0.275968E-01 -0.465018E-16 13 0.421975E+00 -0.162906E-16 -0.496442E-01 0.992525E-16 14 -0.824417E+00 0.933397E-16 -0.969903E-01 -0.155309E-15 15 0.149192E+01 0.794799E-17 -0.175520E+00 -0.946931E-15 16 -0.292606E+01 -0.121089E-15 -0.344243E+00 -0.688767E-15 NMS_TEST Normal end of execution. 19 March 2018 3:48:46.242 PM