Thu Sep 13 15:56:54 2018 R8GE_TEST Python version: 3.6.5 Test the R8GE library. 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. 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. 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_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_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. R8GE_CG_TEST Python version: 3.6.5 R8GE_CG applies CG to an R8GE matrix. Number of variables N = 10 Norm of residual ||Ax-b|| = 1.72262e-14 Norm of error ||x1-x2|| = 1.84883e-14 R8GE_CG_TEST Normal end of execution. R8GE_CO_TEST Python version: 3.6.5 R8GE_CO estimates the condition number of an R8GE matrix. Matrix order N = 4 The L1 condition number is 10 The R8GE_CO estimate is 7 R8GE_CO_TEST: Normal end of execution. R8GE_DET_TEST Python version: 3.6.5 R8GE_DET computes the determinant of an R8GE matrix. R8GE_DET computes the determinant = 112 Exact determinant = 112 R8GE_DET_TEST: Normal end of execution. R8GE_DIF2_TEST Python version: 3.6.5 R8GE_DIF2 returns the second difference matrix. DIF2 matrix: Col: 0 1 2 3 Row 0 : 2 -1 0 0 1 : -1 2 -1 0 2 : 0 -1 2 -1 3 : 0 0 -1 2 4 : 0 0 0 -1 R8GE_DIF2_TEST: Normal end of execution. R8GE_DILU_TEST Python version: 3.6.5 R8GE_DILU returns the DILU factors of an R8GE matrix. Matrix rows M = 9 Matrix columns N = 9 Matrix A: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0 -1 2 : 0 -1 4 -1 0 3 : -1 0 -1 4 -1 4 : 0 -1 0 -1 4 5 : 0 0 -1 0 -1 6 : 0 0 0 -1 0 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 4 -1 0 -1 6 : -1 4 -1 0 7 : 0 -1 4 -1 8 : -1 0 -1 4 DILU factor: 0: 0.25 1: 0.266667 2: 0.267857 3: 0.287179 4: 0.290179 5: 0.290532 6: 0.292202 7: 0.292601 8: 0.292666 R8GE_DILU_TEST: Normal end of execution. R8GE_FA_TEST01 Python version: 3.6.5 R8GE_FA computes the LU factors of an R8GE matrix, R8GE_SL solves a factored R8GE system. Matrix order N = 10 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution: 0: 1 1: 1 2: 1 3: 1 4: 1 5: 1 6: 1 7: 1 8: 1 9: 1 Solution of transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8GE_FA_TEST01 Normal end of execution. R8GE_FA_TEST02 Python version: 3.6.5 R8GE_FA computes the LU factors of an R8GE system, R8GE_SL solves a factored R8GE system. Matrix order N = 5 The matrix: 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 The compressed LU factors: Col: 0 1 2 3 4 Row 0 : 0.956318 0.257578 0.449539 0.897504 0.840847 1 : -0.228395 0.522106 0.602062 -0.376149 -0.104858 2 : -0.867399 0.217324 0.614552 -0.510026 -0.507943 3 : -0.587352 0.20582 -0.231419 -0.391459 -0.511487 4 : -0.434277 -0.0139612 0.0803036 -0.610161 0.939815 The pivot vector P: 0 1 1 4 2 3 3 3 4 4 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 R8GE_FA_TEST02 Normal end of execution. R8GE_FS_TEST Python version: 3.6.5 R8GE_FS factors and solves a linear system involving an R8GE matrix. Matrix order N = 10 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8GE_FS_TEST Normal end of execution. R8GE_FSS_TEST Python version: 3.6.5 R8GE_FSS factors and solves multiple linear systems associated with an R8GE matrix. Matrix order N = 10 Solution: Col: 0 1 2 Row 0 : 1 1 1 1 : 1 2 2 2 : 1 3 3 3 : 1 4 1 4 : 1 5 2 5 : 1 6 3 6 : 1 7 1 7 : 1 8 2 8 : 1 9 3 9 : 1 10 1 R8GE_FSS_TEST: Normal end of execution. R8GE_HILBERT_TEST Python version: 3.6.5 R8GE_HILBERT returns the Hilbert matrix. Hilbert matrix: Col: 0 1 2 3 Row 0 : 1 0.5 0.333333 0.25 1 : 0.5 0.333333 0.25 0.2 2 : 0.333333 0.25 0.2 0.166667 3 : 0.25 0.2 0.166667 0.142857 4 : 0.2 0.166667 0.142857 0.125 R8GE_HILBERT_TEST: Normal end of execution. R8GE_HILBERT_INVERSE_TEST Python version: 3.6.5 R8GE_HILBERT_INVERSE computes the inverse of the Hilbert matrix, stored as an R8GE matrix. Matrix order N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 1 0.5 0.333333 0.25 1 : 0.5 0.333333 0.25 0.2 2 : 0.333333 0.25 0.2 0.166667 3 : 0.25 0.2 0.166667 0.142857 Inverse matrix B: Col: 0 1 2 3 Row 0 : 16 -120 240 -140 1 : -120 1200 -2700 1680 2 : 240 -2700 6480 -4200 3 : -140 1680 -4200 2800 Product A * B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 -5.68434e-14 3 : 0 0 0 1 R8GE_HILBERT_INVERSE_TEST: Normal end of execution. R8GE_HOUSE_AXH_TEST Python version: 3.6.5 R8GE_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 R8GE_HOUSE_AXH_TEST Normal end of execution. R8GE_HOUSE_FORM_TEST Python version: 3.6.5 R8GE_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 R8GE_HOUSE_FORM_TEST Normal end of execution. R8GE_IDENTITY_TEST Python version: 3.6.5 R8GE_IDENTITY returns the identity matrix. Identity matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 R8GE_IDENTITY_TEST: Normal end of execution. R8GE_ILU_TEST Python version: 3.6.5 R8GE_ILU returns the ILU factors of an R8GE matrix. Matrix rows M = 9 Matrix columns N = 9 Matrix A: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0 -1 2 : 0 -1 4 -1 0 3 : -1 0 -1 4 -1 4 : 0 -1 0 -1 4 5 : 0 0 -1 0 -1 6 : 0 0 0 -1 0 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 4 -1 0 -1 6 : -1 4 -1 0 7 : 0 -1 4 -1 8 : -1 0 -1 4 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : -0.25 1 0 0 0 2 : 0 -0.266667 1 0 0 3 : -0.25 0 -0.267857 1 0 4 : 0 -0.266667 0 -0.287179 1 5 : 0 0 -0.267857 0 -0.290179 6 : 0 0 0 -0.287179 0 7 : 0 0 0 0 -0.290179 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 5 : 1 0 0 0 6 : -0.290532 1 0 0 7 : 0 -0.292202 1 0 8 : -0.290532 0 -0.292601 1 Factor U: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : 0 3.75 -1 0 -1 2 : 0 0 3.73333 -1 0 3 : 0 0 0 3.48214 -1 4 : 0 0 0 0 3.44615 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0 -1 0 0 4 : -1 0 -1 0 5 : 3.44196 -1 0 -1 6 : 0 3.42229 -1 0 7 : 0 0 3.41762 -1 8 : 0 0 0 3.41687 Product L*U: Col: 0 1 2 3 4 Row 0 : 4 -1 0 -1 0 1 : -1 4 -1 0.25 -1 2 : 0 -1 4 -1 0.266667 3 : -1 0.25 -1 4 -1 4 : 0 -1 0.266667 -1 4 5 : 0 0 -1 0.267857 -1 6 : 0 0 0 -1 0.287179 7 : 0 0 0 0 -1 8 : 0 0 0 0 0 Col: 5 6 7 8 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : -1 0 0 0 3 : 0.267857 -1 0 0 4 : -1 0.287179 -1 0 5 : 4 -1 0.290179 -1 6 : -1 4 -1 0.290532 7 : 0.290179 -1 4 -1 8 : -1 0.290532 -1 4 R8GE_ILU_TEST: Normal end of execution. R8GE_INDICATOR_TEST Python version: 3.6.5 R8GE_INDICATOR returns the indicator matrix. 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 R8GE_INDICATOR_TEST: Normal end of execution. R8GE_INVERSE_TEST Python version: 3.6.5 R8GE_INVERSE computes the inverse of an R8GE matrix. Matrix order N = 4 Matrix A: Col: 0 1 2 3 Row 0 : 5 3 3 3 1 : 3 5 3 3 2 : 3 3 5 3 3 : 3 3 3 5 Inverse matrix B: Col: 0 1 2 3 Row 0 : 0.392857 -0.107143 -0.107143 -0.107143 1 : -0.107143 0.392857 -0.107143 -0.107143 2 : -0.107143 -0.107143 0.392857 -0.107143 3 : -0.107143 -0.107143 -0.107143 0.392857 Product matrix: Col: 0 1 2 3 Row 0 : 1 -1.11022e-16 0 0 1 : 3.33067e-16 1 0 0 2 : 4.44089e-16 -1.11022e-16 1 2.22045e-16 3 : 4.44089e-16 -1.11022e-16 0 1 R8GE_ML_TEST Python version: 3.6.5 R8GE_ML computes A*x or A'*X where A has been factored by R8GE_FA. Matrix order N = 10 A*x and PLU*x 0: 32.6597 32.6597 1: 30.7617 30.7617 2: 20.173 20.173 3: 24.1126 24.1126 4: 30.7597 30.7597 5: 32.7342 32.7342 6: 28.0252 28.0252 7: 28.3091 28.3091 8: 28.7501 28.7501 9: 17.3141 17.3141 A'*x and (PLU)'*x 0: 29.518 29.518 1: 34.2533 34.2533 2: 29.9813 29.9813 3: 25.9818 25.9818 4: 28.7133 28.7133 5: 28.373 28.373 6: 33.4872 33.4872 7: 26.6124 26.6124 8: 24.8414 24.8414 9: 26.539 26.539 R8GE_ML_TEST Normal end of execution. R8GE_MM_TEST Python version: 3.6.5 R8GE_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 R8GE_MM_TEST Normal end of execution. R8GE_MTM_TEST Python version: 3.6.5 R8GE_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 R8GE_MTM_TEST Normal end of execution. R8GE_MTV_TEST Python version: 3.6.5 R8GE_MTV computes a matrix product b=A'*x for an R8GE matrix. The matrix A: 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 The vector x: 0: 1 1: 2 2: 3 The vector b=A'*x: 0: 146 1: 152 2: 158 3: 164 4: 170 The matrix A: 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 4 : 51 52 53 54 55 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A'*x: 0: 565 1: 580 2: 595 3: 610 4: 625 The matrix A: Col: 0 1 2 Row 0 : 11 12 13 1 : 21 22 23 2 : 31 32 33 3 : 41 42 43 4 : 51 52 53 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A'*x: 0: 565 1: 580 2: 595 R8GE_MTV_TEST Normal end of execution. R8GE_MU_TEST Python version: 3.6.5 R8GE_MU computes A*x or A'*X where A has been factored by R8GE_TRF. Matrix rows M = 5 Matrix columns N = 3 A*x and PLU*x 0: 0.535837 0.535837 1: 2.82009 2.82009 2: 2.25334 2.25334 3: 2.91337 2.91337 4: 4.0751 4.0751 A'*x and (PLU)'*x 0: 3.29537 3.29537 1: 4.24167 4.24167 2: 6.82191 6.82191 Matrix is 3 by 5 A*x and PLU*x 0: 5.9938 5.9938 1: 8.7752 8.7752 2: 5.78077 5.78077 A'*x and (PLU)'*x 0: 1.84787 1.84787 1: 2.65991 2.65991 2: 3.22133 3.22133 3: 4.06077 4.06077 4: 3.50791 3.50791 R8GE_MU_TEST: Normal end of execution. R8GE_MV_TEST Python version: 3.6.5 R8GE_MV computes a matrix product b=A*x for an R8GE matrix. The 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 The vector X: 0: 1 1: 2 2: 3 3: 4 4: 5 The vector b=A*x: 0: 130 1: 230 2: 330 3: 430 R8GE_MV_TEST Normal end of execution. R8GE_ORTH_RANDOM_TEST Python version: 3.6.5 R8GE_ORTH_RANDOM computes a random orthogonal matrix. ORTH_RANDOM matrix: Col: 0 1 2 3 4 Row 0 : -0.559743 -0.371903 -0.0337166 0.68224 0.285986 1 : 0.188708 -0.906112 0.0432361 -0.368531 0.0752686 2 : -0.404357 -0.0795868 -0.732356 -0.200174 -0.503733 3 : -0.423174 0.184571 -0.114406 -0.542494 0.692437 4 : 0.555425 0.0157436 -0.668999 0.253702 0.423476 R8GE_ORTH_RANDOM_TEST: Normal end of execution. R8GE_PDS_RANDOM_TEST Python version: 3.6.5 R8GE_PDS_RANDOM computes the PDS_RANDOM matrix. PDS_RANDOM matrix: Col: 0 1 2 3 4 Row 0 : 0.497055 0.1657 -0.0383139 -0.136355 0.0927247 1 : 0.1657 0.873143 0.0517221 -0.0475388 -0.0540219 2 : -0.0383139 0.0517221 0.614563 0.00896361 0.239044 3 : -0.136355 -0.0475388 0.00896361 0.446983 0.0594034 4 : 0.0927247 -0.0540219 0.239044 0.0594034 0.549504 R8GE_PDS_RANDOM_TEST Normal end of execution. R8GE_PLU_TEST Python version: 3.6.5 R8GE_PLU returns the PLU factors of an R8GE matrix. Matrix rows M = 5 Matrix columns N = 4 Matrix A: 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 Factor P: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 1 1 : 1 0 0 0 0 2 : 0 0 0 1 0 3 : 0 0 1 0 0 4 : 0 1 0 0 0 Factor L: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0.434277 1 0 0 0 2 : 0.587352 -0.20582 1 0 0 3 : 0.867399 -0.217324 0.231419 1 0 4 : 0.228395 0.0139612 -0.0803036 0.610161 1 Factor U: Col: 0 1 2 3 Row 0 : 0.956318 0.257578 0.449539 0.897504 1 : 0 0.522106 0.602062 -0.376149 2 : 0 0 0.614552 -0.510026 3 : 0 0 0 -0.391459 4 : 0 0 0 0 Product P*L*U: 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 R8GE_PLU_TEST: Normal end of execution. R8GE_POLY_TEST Python version: 3.6.5 R8GE_POLY computes the characteristic polynomial of an R8GE matrix. Matrix order N = 12 I, P(I), True P(I) 0: 1 1 1: -23 -23 2: 231 231 3: -1330 -1330 4: 4845 4845 5: -11628 -11628 6: 18564 18564 7: -19448 -19448 ...... .............. .............. 12: 1 1 R8GE_POLY_TEST: Normal end of execution. R8GE_PRINT_TEST Python version: 3.6.5 R8GE_PRINT prints an R8GE matrix. Here is an R8GE: 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 R8GE_PRINT_TEST: Normal end of execution. R8GE_PRINT_SOME_TEST Python version: 3.6.5 R8GE_PRINT_SOME prints some of an R8GE matrix. Rows 0:2, Cols 3:5: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8GE_PRINT_SOME_TEST: Normal end of execution. R8GE_RANDOM_TEST Python version: 3.6.5 R8GE_RANDOM computes a random R8GE. 0 <= X <= 1 Initial seed is 123456789 Random R8GE: 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 R8GE_RANDOM_TEST: Normal end of execution. R8GE_RANDOM_AB_TEST Python version: 3.6.5 R8GE_RANDOM_AB computes a random R8GE. -1 <= X <= 5 Initial seed is 123456789 Random R8GE: 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 R8GE_RANDOM_AB_TEST: Normal end of execution. R8GE_RES_TEST Python version: 3.6.5 R8GE_RES computes b-A*x, where A is an R8GE matrix. We check three cases, MN. Residual A*x-b: 0: 0 1: -4.44089e-16 2: 0 Residual A*x-b: 0: 8.88178e-16 1: 8.88178e-16 2: -2.22045e-16 3: 2.08167e-17 4: 4.44089e-16 Residual A*x-b: 0: -8.32667e-17 1: -2.22045e-16 2: 2.22045e-16 3: 0 4: 0 R8GE_RES_TEST: Normal end of execution. R8GE_SL_TEST Python version: 3.6.5 R8GE_SL solves a linear system A*x=b that was factored by R8GE_FA. Matrix order N = 10 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution: 0: 1 1: 1 2: 1 3: 1 4: 1 5: 1 6: 1 7: 1 8: 1 9: 1 Solution of transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8GE_SL_TEST: Normal end of execution. R8GE_SL_IT_TEST Python version: 3.6.5 R8GE_SL_IT applies one step of iterative refinement to a R8GE_SL solution. Matrix order N = 6 i, x, b-A*x 0: 0.166667 1.13687e-13 1: 0.142857 -9.09495e-13 2: 0.125 1.45519e-11 3: 0.111111 -5.82077e-11 4: 0.1 0 5: 0.0909091 -1.45519e-11 Iterative refinement step 1 I, DX: 0 -1.24677e-11 1 -1.03287e-11 2 -8.79936e-12 3 -7.66042e-12 4 -6.78115e-12 5 -6.08241e-12 i, x, b-A*x 0: 0.166667 -5.68434e-14 1: 0.142857 1.81899e-12 2: 0.125 -2.91038e-11 3: 0.111111 2.91038e-11 4: 0.1 0 5: 0.0909091 7.27596e-12 Iterative refinement step 2 I, DX: 0 -3.60008e-13 1 1.62139e-13 2 3.75167e-13 3 4.65078e-13 4 4.99681e-13 5 5.07613e-13 i, x, b-A*x 0: 0.166667 -1.7053e-13 1: 0.142857 9.09495e-13 2: 0.125 -1.45519e-11 3: 0.111111 8.73115e-11 4: 0.1 -2.91038e-11 5: 0.0909091 3.63798e-11 Iterative refinement step 3 I, DX: 0 1.7504e-11 1 1.43887e-11 2 1.22018e-11 3 1.05912e-11 4 9.35679e-12 5 8.38066e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 0 2: 0.125 -2.18279e-11 3: 0.111111 0 4: 0.1 0 5: 0.0909091 -1.45519e-11 Iterative refinement step 4 I, DX: 0 -9.70128e-12 1 -7.53581e-12 2 -6.18456e-12 3 -5.25486e-12 4 -4.57346e-12 5 -4.05139e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 1.81899e-12 2: 0.125 2.91038e-11 3: 0.111111 0 4: 0.1 -8.73115e-11 5: 0.0909091 0 Iterative refinement step 5 I, DX: 0 -6.85153e-12 1 -6.66963e-12 2 -6.19756e-12 3 -5.6995e-12 4 -5.24042e-12 5 -4.83331e-12 i, x, b-A*x 0: 0.166667 0 1: 0.142857 0 2: 0.125 0 3: 0.111111 0 4: 0.1 5.82077e-11 5: 0.0909091 7.27596e-12 R8GE_SL_IT_TEST: Normal end of execution. R8GE_TO_R8VEC_TEST Python version: 3.6.5 R8GE_TO_R8VEC converts an R8GE matrix to an R8VEC vector. R8GE matrix: Col: 0 1 2 Row 0 : 11 12 13 1 : 21 22 23 2 : 31 32 33 3 : 41 42 43 Corresponding R8VEC vector: 0: 11 1: 21 2: 31 3: 41 4: 12 5: 22 6: 32 7: 42 8: 13 9: 23 10: 33 11: 43 R8GE_TO_R8VEC_TEST: Normal end of execution. R8GE_TRANSPOSE_TEST Python version: 3.6.5 R8GE_TRANSPOSE makes a transposed copy of an R8GE matrix. Indicator 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 B = A': 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 R8GE_TRANSPOSE_TEST: Normal end of execution. R8GE_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8GE_TRANSPOSE_PRINT prints the transpose of an R8GE matrix. Here is an R8GE matrix, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 R8GE_TRANSPOSE_PRINT_TEST: Normal end of execution. R8GE_TRANSPOSE_PRINT_SOME_TEST Python version: 3.6.5 R8GE_TRANSPOSE_PRINT_SOME prints some of an R8GE matrix, transposed. R8GE matrix, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 R8GE_TRANSPOSE_PRINT_SOME_TEST: Normal end of execution. R8GE_TRF_TEST Python version: 3.6.5 R8GE_TRF computes the LU factors of an R8GE matrix, so that R8GE_TRS can solve the factored system. Number of matrix rows M = 5 Number of matrix columns N = 5 Solution: 0: 0 1: 0 2: 0 3: 0 4: 5 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 R8GE_TRF_TEST: Normal end of execution. R8GE_TRS_TEST Python version: 3.6.5 R8GE_TRS solves a linear system that has been factored by R8GE_TRF. Number of matrix rows M = 5 Number of matrix columns N = 5 Solution: 0: 0 1: 0 2: 0 3: 0 4: 5 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 R8GE_TRS_TEST: Normal end of execution. R8GE_ZEROS_TEST Python version: 3.6.5 R8GE_ZEROS zeros out space for a general matrix. Matrix order M, N = 5, 4 Matrix A: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 R8GE_ZEROS_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_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_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_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_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_TO_R8GE_TEST Python version: 3.6.5 R8VEC_TO_R8GE converts an R8VEC vector to an R8GE matrix. The R8VEC vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 10: 11 11: 12 Corresponding R8GE matrix: Col: 0 1 2 Row 0 : 1 5 9 1 : 2 6 10 2 : 3 7 11 3 : 4 8 12 R8VEC_TO_R8GE_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. 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. R8GE_TEST: Normal end of execution. Thu Sep 13 15:56:54 2018