12 September 2021 12:15:15.066 PM minpack_test(): FORTRAN90 version Test minpack(). CHKDER_TEST 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: 1 0.50000000 2 0.50000000 3 0.50000000 4 0.50000000 5 0.50000000 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 gradient component error estimates: > 0.5, the component is probably correct. < 0.5, the 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: 1 0.50000000 2 0.50000000 3 0.50000000 4 0.50000000 5 0.50000000 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 gradient component error estimates: > 0.5, the component is probably correct. < 0.5, the component is probably incorrect. 1 0.354955 2 0.994216E-01 3 1.00000 4 1.00000 5 1.00000 HYBRD1_TEST HYBRD1 solves a nonlinear system of equations. Initial X: 1 3.0000000 2 0.0000000 Initial F(X): 1 -13.000000 2 11.000000 Returned value of INFO = 1 Final X: 1 1.0000000 2 1.0000000 Final F(X): 1 -0.96195052E-10 2 -0.12353851E-09 HYBRJ1_TEST HYBRJ1 solves a nonlinear system of equations. Initial X: 1 3.0000000 2 0.0000000 F(X): 1 -13.000000 2 11.000000 Returned value of INFO = 1 X: 1 1.0000000 2 1.0000000 F(X): 1 -0.96195052E-10 2 -0.12353851E-09 LMDER1_TEST LMDER1 minimizes M functions in N variables. Initial X: 1 0.0000000 2 5.0000000 F(X): 1 3.0000000 2 -6.0000000 3 -23.000000 4 -35.000000 Returned value of INFO = 3 X: 1 6.5500000 2 -12.500000 F(X): 1 -1.4000000 2 2.7000000 3 -1.2000000 4 -0.10000000 LMDER1_2_TEST LMDER1 minimizes M functions in N variables. Initial X: 1 0.0000000 2 5.0000000 3 1.3000000 F(X): 1 1.0000000 2 -0.68855587 3 -7.1441624 4 -18.685669 5 -35.483585 6 -57.646904 7 -85.252351 8 -118.35736 9 -157.00681 10 -201.23688 Returned value of INFO = 2 X: 1 1.0000000 2 3.0000000 3 2.0000000 F(X): 1 0.13233858E-12 2 0.33750780E-13 3 0.23803182E-12 4 0.85975671E-12 5 0.19895197E-11 6 0.36948222E-11 7 0.60822458E-11 8 0.90381036E-11 9 0.12818191E-10 10 0.17280399E-10 LMDIF1_TEST LMDIF1 minimizes M functions in N variables. Initial X: 1 0.0000000 2 5.0000000 F(X): 1 3.0000000 2 -6.0000000 3 -23.000000 4 -35.000000 Returned value of INFO = 3 X: 1 6.5500000 2 -12.500000 F(X): 1 -1.4000000 2 2.7000000 3 -1.2000000 4 -0.10000000 LMDIF1_2_TEST LMDIF1 minimizes M functions in N variables. X: 1 0.0000000 2 5.0000000 3 1.3000000 F(X): 1 1.0000000 2 -0.68855587 3 -7.1441624 4 -18.685669 5 -35.483585 6 -57.646904 7 -85.252351 8 -118.35736 9 -157.00681 10 -201.23688 Returned value of INFO = 2 X: 1 1.0000000 2 3.0000000 3 2.0000000 F(X): 1 0.18918200E-12 2 0.42632564E-13 3 0.26290081E-12 4 0.99475983E-12 5 0.23732127E-11 6 0.44337867E-11 7 0.72759576E-11 8 0.10970780E-10 9 0.15546675E-10 10 0.21032065E-10 LMSTR1_TEST LMSTR1 minimizes M functions in N variables. Initial X: 1 0.0000000 2 5.0000000 F(X): 1 3.0000000 2 -6.0000000 3 -23.000000 4 -35.000000 Returned value of INFO = 2 X: 1 6.5500000 2 -12.500000 F(X): 1 -1.4000000 2 2.7000000 3 -1.2000000 4 -0.10000000 LMSTR1_2_TEST LMSTR1 minimizes M functions in N variables. Initial X: 1 0.0000000 2 5.0000000 3 1.3000000 F(X): 1 1.0000000 2 -0.68855587 3 -7.1441624 4 -18.685669 5 -35.483585 6 -57.646904 7 -85.252351 8 -118.35736 9 -157.00681 10 -201.23688 Returned value of INFO = 2 X: 1 1.0000000 2 3.0000000 3 2.0000000 F(X): 1 0.13322676E-12 2 0.33750780E-13 3 0.24158453E-12 4 0.85975671E-12 5 0.19895197E-11 6 0.36948222E-11 7 0.60822458E-11 8 0.90381036E-11 9 0.12818191E-10 10 0.17280399E-10 QFORM_TEST: QFORM constructs the Q factor explicitly after the use of QRFAC. Matrix A: Col 1 2 3 4 5 Row 1: 0.462074 0.415158 0.262718 0.671100 0.773599 2: 0.830328 0.767792E-01 0.582900 0.994973E-01 0.315562 3: 0.160589E-01 0.205475 0.202428 0.697111 0.687451 4: 0.897170 0.794856 0.515605 0.176087E-01 0.998439 5: 0.560022 0.933144 0.895927 0.256553 0.407669E-01 Col 6 7 Row 1: 0.706296 0.433363 2: 0.972696 0.619621 3: 0.991735 0.467871 4: 0.885219 0.831423 5: 0.901412 0.968743 Matrix R: Col 1 2 3 4 5 Row 1: -1.42188 -1.05113 -1.10626 -0.396222 -1.08948 2: 0. 0.786223 0.354171 0.338844 0.220185 3: 0. 0. -0.411174 -0.136249 0.499956 4: 0. 0. 0. 0.849705 0.729268 5: 0. 0. 0. 0. 0.389771 Col 6 7 Row 1: -1.72232 -1.41411 2: 0.389282 0.511370 3: -0.423455 -0.293971 4: 0.749612 0.197934 5: 0.406828 0.183233 Matrix Q: Col 1 2 3 4 5 Row 1: -0.324973 0.935727E-01 0.315989 0.651621 -0.600980 2: -0.583963 -0.683067 -0.434875 0.474522E-01 0.322155E-01 3: -0.112941E-01 0.246245 -0.249824 0.676893 0.647024 4: -0.630973 0.167408 0.587839 -0.246003 0.409605 5: -0.393859 0.660304 -0.550516 -0.233316 -0.226648 Matrix A2 = Q * R: Col 1 2 3 4 5 Row 1: 0.462074 0.415158 0.262718 0.671100 0.773599 2: 0.830328 0.767792E-01 0.582900 0.994973E-01 0.315562 3: 0.160589E-01 0.205475 0.202428 0.697111 0.687451 4: 0.897170 0.794856 0.515605 0.176087E-01 0.998439 5: 0.560022 0.933144 0.895927 0.256553 0.407669E-01 Col 6 7 Row 1: 0.706296 0.433363 2: 0.972696 0.619621 3: 0.991735 0.467871 4: 0.885219 0.831423 5: 0.901412 0.968743 minpack_test(): Normal end of execution. 12 September 2021 12:15:15.067 PM