June 24 2002 1:08:25.254 PM LINPLUS_PRB Problems for LINPLUS. TEST01 C3_CR_FA factors a complex tridiagonal matrix; C3_CR_SL solves a factored system. Matrix order N = 10 Solution: 1 0.00000 0.00000 2 0.999990 10.0000 3 1.99999 20.0000 4 3.00000 30.0000 5 4.00000 40.0000 6 5.00000 50.0000 7 6.00000 60.0000 8 7.00000 70.0000 9 8.00000 80.0000 10 9.00000 90.0000 TEST014 For a complex tridiagonal matrix that can be factored with no pivoting, C3_NP_FA factors; C3_NP_SL solves a factored system. C3_NP_ML multiplies A*X when A has been factored. Matrix order N = 10 The tridiagonal matrix Columns: 1 1 2 2 3 3 Row --- 1 0.65544 0.11524 0.44848 0.43446 2 0.60056 0.76504 0.24082 0.52424 0.29170 0.13133 3 0.97340E-01 0.97478 0.43136 0.13788E-02 4 0.14299E-02 0.79398 Columns: 4 4 5 5 6 6 Row --- 3 0.52347 0.69430E-01 4 0.83368 0.72685 0.67663 0.95396 5 0.73201 0.94630 0.86577 0.63038 0.28915E-01 0.37587 6 0.78385E-01 0.74508 0.48883 0.18950 7 0.72147 0.89901 Columns: 7 7 8 8 9 9 Row --- 6 0.51778 0.61086 7 0.96813 0.61414 0.11078 0.84198E-01 8 0.82537 0.18356 0.83793 0.46562 0.11948 0.12562 9 0.54714 0.91573 0.98862E-01 0.73238 10 0.99132 0.18125 Columns: 10 10 Row --- 9 0.51097 0.53804 10 0.64181 0.93802E-02 The right hand side 1 -8.28913 16.5082 2 -20.1177 21.7806 3 -18.7316 38.0576 4 -93.8694 77.2808 5 -84.4927 83.4958 6 -84.4348 78.6326 7 -91.6749 130.286 8 -47.8474 141.704 9 -182.599 123.063 10 -1.91019 155.125 The solution 1 1.00000 10.0000 2 2.00000 20.0000 3 2.99999 30.0000 4 4.00001 40.0000 5 4.99999 50.0000 6 5.99998 60.0000 7 7.00002 70.0000 8 7.99999 80.0000 9 8.99997 90.0000 10 10.0000 100.000 The second right hand side 1 14.5399 11.3939 2 17.3656 24.0323 3 33.5947 25.8968 4 57.1625 107.314 5 65.1112 99.3534 6 60.3557 98.3337 7 109.553 115.659 8 129.423 74.9601 9 84.4674 203.352 10 151.675 32.5901 The second solution 1 10.0000 0.999999 2 20.0000 2.00000 3 30.0000 3.00000 4 40.0000 3.99999 5 50.0000 5.00000 6 60.0000 6.00001 7 70.0000 6.99999 8 80.0000 8.00000 9 90.0000 9.00000 10 100.000 9.99999 TEST015 For a complex tridiagonal matrix that can be factored with no pivoting, C3_NP_FA factors; C3_NP_SL solves a factored system. C3_NP_ML multiplies A*X when A has been factored. We will look at the TRANSPOSED linear system. Matrix order N = 10 The tridiagonal matrix Columns: 1 1 2 2 3 3 Row --- 1 0.30055 0.48797 0.45569 0.48210 2 0.68513 0.98349 0.38268 0.47338 0.99913E-01 0.18494 3 0.31229 0.16471 0.89617 0.54110E-02 4 0.89491 0.13390 Columns: 4 4 5 5 6 6 Row --- 3 0.24552 0.35135 4 0.61854 0.66863 0.95643 0.65828E-01 5 0.17531 0.63567 0.76188 0.48716 0.29170 0.92238 6 0.50773 0.10267E-01 0.31369 0.21305E-01 7 0.75221 0.29837 Columns: 7 7 8 8 9 9 Row --- 6 0.89575 0.66084 7 0.60497 0.47523 0.49202 0.19420 8 0.49352 0.24530 0.42229 0.25173 0.83261E-01 0.40095E-01 9 0.87767 0.78908 0.41217 0.24217 10 0.84389 0.14020 Columns: 10 10 Row --- 9 0.14181 0.19611 10 0.79882 0.55267 The right hand side B1 1 -22.8787 19.1630 2 -17.0720 23.5024 3 -2.74909 65.6011 4 -64.9818 47.7798 5 -16.9255 109.576 6 -59.6772 92.8894 7 -78.9831 144.829 8 -90.0283 157.690 9 -26.2078 132.047 10 -63.6522 99.9365 The solution to At * X1 = B1 1 0.999981 9.99999 2 2.00001 20.0000 3 3.00002 30.0000 4 3.99998 40.0000 5 5.00003 50.0000 6 6.00001 60.0000 7 6.99998 70.0000 8 8.00000 80.0001 9 9.00002 90.0000 10 9.99999 100.000 The second right hand side B2 1 14.2531 26.2203 2 19.6564 21.3879 3 63.7577 15.6850 4 33.9660 73.1564 5 104.054 38.2886 6 79.2328 76.8894 7 126.321 106.098 8 136.740 119.471 9 124.243 51.8368 10 85.3531 82.1812 Solution to At * X2 = B2 1 9.99997 1.00000 2 20.0000 2.00000 3 30.0000 3.00000 4 40.0000 4.00000 5 50.0000 4.99998 6 60.0000 6.00001 7 70.0000 6.99998 8 80.0000 8.00002 9 90.0000 9.00000 10 100.000 10.0000 TEST016 CCI_SL solves a complex circulant system. Matrix order N = 10 The circulant matrix: Columns 1 2 3 4 Row --- 1 0.962 0.960 0.285 0.113 0.715 0.127E-02 0.147E-01 0.606 2 0.679 0.682 0.962 0.960 0.285 0.113 0.715 0.127E-02 3 0.853 0.272 0.679 0.682 0.962 0.960 0.285 0.113 4 0.205 0.737 0.853 0.272 0.679 0.682 0.962 0.960 5 0.808 0.378 0.205 0.737 0.853 0.272 0.679 0.682 6 0.425 0.229 0.808 0.378 0.205 0.737 0.853 0.272 7 0.323 0.196 0.425 0.229 0.808 0.378 0.205 0.737 8 0.147E-01 0.606 0.323 0.196 0.425 0.229 0.808 0.378 9 0.715 0.127E-02 0.147E-01 0.606 0.323 0.196 0.425 0.229 10 0.285 0.113 0.715 0.127E-02 0.147E-01 0.606 0.323 0.196 Columns 5 6 7 8 Row --- 1 0.323 0.196 0.425 0.229 0.808 0.378 0.205 0.737 2 0.147E-01 0.606 0.323 0.196 0.425 0.229 0.808 0.378 3 0.715 0.127E-02 0.147E-01 0.606 0.323 0.196 0.425 0.229 4 0.285 0.113 0.715 0.127E-02 0.147E-01 0.606 0.323 0.196 5 0.962 0.960 0.285 0.113 0.715 0.127E-02 0.147E-01 0.606 6 0.679 0.682 0.962 0.960 0.285 0.113 0.715 0.127E-02 7 0.853 0.272 0.679 0.682 0.962 0.960 0.285 0.113 8 0.205 0.737 0.853 0.272 0.679 0.682 0.962 0.960 9 0.808 0.378 0.205 0.737 0.853 0.272 0.679 0.682 10 0.425 0.229 0.808 0.378 0.205 0.737 0.853 0.272 Columns 9 10 Row --- 1 0.853 0.272 0.679 0.682 2 0.205 0.737 0.853 0.272 3 0.808 0.378 0.205 0.737 4 0.425 0.229 0.808 0.378 5 0.323 0.196 0.425 0.229 6 0.147E-01 0.606 0.323 0.196 7 0.715 0.127E-02 0.147E-01 0.606 8 0.285 0.113 0.715 0.127E-02 9 0.962 0.960 0.285 0.113 10 0.679 0.682 0.962 0.960 Solution: 1 1.00003 10.0000 2 2.00001 20.0000 3 2.99998 30.0000 4 4.00001 40.0000 5 5.00001 50.0000 6 6.00003 60.0000 7 7.00000 70.0000 8 7.99996 80.0000 9 8.99999 90.0000 10 10.0000 100.000 Solution to transposed system: 1 0.999950 9.99999 2 1.99998 20.0000 3 3.00001 30.0000 4 4.00001 40.0000 5 5.00003 50.0000 6 5.99997 60.0000 7 7.00002 70.0000 8 8.00001 80.0000 9 9.00000 90.0000 10 10.0000 100.000 TEST017 CTO_SL solves a complex Toeplitz system. Matrix order N = 4 The Toeplitz matrix: Columns 1 2 3 4 Row --- 1 0.891 0.168 0.260E-01 0.447 0.905 0.982 0.516 0.718E-01 2 0.673 0.501 0.891 0.168 0.260E-01 0.447 0.905 0.982 3 0.502 0.150 0.673 0.501 0.891 0.168 0.260E-01 0.447 4 0.433 0.699 0.502 0.150 0.673 0.501 0.891 0.168 Desired solution: 1 1.00000 0.00000 2 -0.874228E-07 2.00000 3 -3.00000 -0.262268E-06 4 0.476995E-07 -4.00000 Right Hand Side: 1 -2.42922 -4.79218 2 4.18729 -2.67617 3 -1.38644 0.887358 4 -1.21322 -3.36344 Solution: 1 1.00000 0.00000 2 0.197440E-06 2.00000 3 -3.00000 0.238419E-06 4 0.635246E-06 -4.00000 Desired solution to transposed system: 1 1.00000 0.00000 2 -0.874228E-07 2.00000 3 -3.00000 -0.262268E-06 4 0.476995E-07 -4.00000 Right Hand Side of transposed system: 1 1.18247 -0.667143 2 -1.72883 -1.27985 3 -0.659069 -2.16100 4 -0.853753 -3.02268 Solution to transposed system: 1 1.00000 -0.834465E-06 2 0.00000 2.00000 3 -3.00000 -0.190735E-05 4 0.952870E-06 -4.00000 TEST02 S3_CR_FA factors a real tridiagonal matrix; S3_CR_SL solves a factored system. Matrix order N = 100 Demonstrate multiple system solution method. Solve linear system number 1 Solution: 1 0.00000 2 1.00000 3 2.00000 4 3.00000 5 4.00000 6 5.00000 7 6.00000 8 7.00000 ...... .............. 100 99.0000 Solve linear system number 2 Solution: 1 0.00000 2 1.00000 3 1.00000 4 1.00000 5 1.00000 6 1.00000 7 1.00000 8 1.00000 ...... .............. 100 1.00000 TEST03 For a real tridiagonal matrix, using CYCLIC REDUCTION, S3_CR_FA factors; S3_CR_SL solves. Matrix order N = 100 The matrix is NOT symmetric. The solution: 1 0.00000 2 1.00000 3 2.00000 4 3.00000 5 4.00000 6 5.00000 7 6.00000 8 7.00000 ...... .............. 100 99.0000 TEST035 For a real tridiagonal system, S3_GS_SL solves a linear system using Gauss-Seidel iteration Matrix order N = 100 Iterations per call = è Solution after call 1 1 0.252679 2 0.506519 3 0.762101 4 1.02001 5 1.28081 6 1.54510 7 1.81345 8 2.08644 ...... .............. 100 99.1981 Solution after call 2 1 0.698130 2 1.39684 3 2.09641 4 2.79714 5 3.49930 6 4.20319 7 4.90908 8 5.61725 ...... .............. 100 99.7104 Solution after call 3 1 0.884923 2 1.77007 3 2.65555 4 3.54147 5 4.42794 6 5.31508 7 6.20299 8 7.09178 ...... .............. 100 99.8903 TEST04 For a real tridiagonal system, S3_JAC_SL solves a linear system using Jacobi iteration Matrix order N = 100 Iterations per call = 1000 Solution after call 1 1 0.310821E-01 2 0.621642E-01 3 0.943947E-01 4 0.126625 5 0.161175 6 0.195725 7 0.233812 8 0.271898 ...... .............. 100 98.4523 Solution after call 2 1 0.281638 2 0.563275 3 0.847221 4 1.13117 5 1.41973 6 1.70829 7 2.00376 8 2.29924 ...... .............. 100 99.1981 Solution after call 3 1 0.537777 2 1.07555 3 1.61505 4 2.15455 5 2.69748 6 3.24041 7 3.78847 8 4.33653 ...... .............. 100 99.5256 TEST05 For a tridiagonal matrix that can be factored with no pivoting, S3_NP_FA factors, S3_NP_DET computes the determinant. Matrix order N = 10 S3_NP_DET computes determinant = ************** SGE_DET computes determinant = ************** TEST06 For a tridiagonal matrix that can be factored with no pivoting, S3_NP_FA factors; S3_NP_SL solves a factored system. Matrix order N = 10 The tridiagonal matrix: Columns 1 2 3 4 5 Row --- 1 0.547935 0.494041 2 0.464935E-01 0.434889 0.367038 3 0.237491 0.193369E-01 0.883149 4 0.425952 0.164065 0.495752 5 0.844916 0.415886 6 0.664514 Columns 6 7 8 9 10 Row --- 5 0.390289 6 0.674648E-01 0.565481 7 0.650399E-01 0.664771 0.631935 8 0.490064 0.247878 0.170251 9 0.603570 0.911471 0.911576 10 0.713699 0.257960 Solution: 1 0.999999 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution to tranposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST07 S3_NP_FS factors and solves a tridiagonal linear system. Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00001 10 10.0000 TEST08 S3_NP_ML computes A*x or transpose(A)*X where A has been factored by S3_FA. Matrix order N = 10 A*x and PLU*x 1 1.18728 1.18728 2 1.97021 1.97021 3 2.94667 2.94667 4 7.07635 7.07635 5 8.56143 8.56143 6 9.25837 9.25837 7 9.34199 9.34199 8 16.1734 16.1734 9 16.4916 16.4916 10 10.6062 10.6062 AT*x and (PLU)T*x 1 2.29152 2.29152 2 3.68971 3.68971 3 2.75719 2.75719 4 3.86470 3.86470 5 6.91464 6.91464 6 13.6470 13.6470 7 8.79119 8.79119 8 13.3351 13.3351 9 11.4474 11.4474 10 3.45941 3.45941 TEST09 S3P_DET, determinant of a tridiagonal periodic matrix. Matrix order N = 12 The periodic tridiagonal matrix: Columns 1 2 3 4 5 Row --- 1 0.140242 0.888269 2 0.734177 0.145495 0.965451 3 0.875337 0.367189 0.588735 4 0.249400 0.633611 0.627418 5 0.176154 0.713544 6 0.940828 7 8 9 10 11 12 0.337509 Columns 6 7 8 9 10 Row --- 5 0.730669E-01 6 0.363208E-01 0.322424 7 0.230905E-01 0.820735 0.217401 8 0.528680 0.935541 0.243603 9 0.190629 0.851823 0.354009 10 0.322071 0.735168 11 0.482486 Columns 11 12 Row --- 1 0.977014 2 3 4 5 6 7 8 9 10 0.943273 11 0.723477 0.727489 12 0.340666 0.923113 S3P_DET computes the determinant = ************** SGE_DET computes the determinant = -0.571921E-03 TEST10 S3P_FA factors a tridiagonal periodic system. S3P_SL solves a tridiagonal periodic system. Matrix order N = 10 Solution: 1 1.00000 2 1.99999 3 3.00003 4 4.00000 5 4.99997 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution to transposed system: 1 0.999985 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST11 S3P_ML computes A*x or transpose(A)*X where A has been factored by S3P_FA. Matrix order N = 10 A*x and PLU*x 1 2.67549 2.67549 2 1.43258 1.43258 3 2.97612 2.97612 4 0.727111 0.727111 5 7.81378 7.81378 6 7.28956 7.28956 7 11.0420 11.0420 8 16.5769 16.5769 9 10.4882 10.4882 10 4.87704 4.87704 A'*x and (PLU)'*x 1 10.9545 10.9545 2 1.50949 1.50949 3 5.40824 5.40824 4 7.27909 7.27909 5 6.59423 6.59423 6 5.75809 5.75810 7 9.00470 9.00470 8 14.6477 14.6477 9 19.3210 19.3210 10 6.59658 6.59658 TEST12 S5_FS factors and solves a pentadiagonal linear system. The pentadiagonal matrix: Columns: 1 2 3 4 5 Row --- 1 0.564340 0.125060 0.291772 2 0.954191 0.749572 0.664448 0.470268 3 0.580737 0.989861 0.182555 0.663216 0.381190 4 0.280614 0.644419E-01 0.621476 0.666908 5 0.177276 0.798151 0.972051 6 0.247537 0.843783 7 0.568066 Columns: 6 7 8 9 10 Row --- 4 0.726989 5 0.607643 0.921891 6 0.275323 0.671644 0.708229 7 0.404011 0.115305 0.671408 0.874959 8 0.548615 0.429066E-01 0.621239 0.582721 0.528172 9 0.693001 0.533893 0.995916 0.909532 10 0.675860 0.331886 0.854729 Solution: 1 0.999984 2 2.00002 3 3.00002 4 3.99997 5 5.00002 6 6.00000 7 7.00000 8 7.99999 9 9.00000 10 10.0000 TEST13 For a border banded matrix: SBB_FA factors; SBB_PRINT prints; SBB_RANDOM randomizes; SBB_SL solves. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The border-banded matrix: Columns 1 2 3 4 5 Row --- 1 0.408754 0.724315 0. 0. 0. 2 0.109515E-01 0.870894 0.286291E-01 0. 0. 3 0. 0.753648 0.210879 0.704260E-01 0. 4 0. 0. 0.563301 0.166037 0.987900 5 0. 0. 0. 0.838246E-01 0.134790 6 0. 0. 0. 0. 0.648769 7 0. 0. 0. 0. 0. 8 0. 0. 0. 0. 0. 9 0.825004 0.826982 0.772446 0.259039 0.104236 10 0.568382 0.651338E-01 0.121165 0.527966 0.111489 Columns 6 7 8 9 10 Row --- 1 0. 0. 0. 0.834314 0.222069 2 0. 0. 0. 0.816760 0.628228 3 0. 0. 0. 0.313409 0.521807 4 0. 0. 0. 0.210687 0.779972 5 0.490939E-01 0. 0. 0.635361 0.254593 6 0.216777E-01 0.298966 0. 0.249638E-01 0.436634 7 0.649485 0.284380 0.622942 0.380245 0.992483 8 0. 0.209510 0.667988 0.552804 0.916441 9 0.753510 0.124053 0.474793 0.141351 0.749284 10 0.615266 0.320959 0.411114 0.285134 0.350336 Solution: 1 1.00002 2 1.99999 3 2.99999 4 4.00000 5 4.99998 6 5.99999 7 7.00000 8 7.99997 9 8.99999 10 10.0000 TEST14 For a border banded matrix: SBB_FA factors; SBB_SL solves. Matrix order N = 10 Matrix suborder N1 = 0 Matrix suborder N2 = 10 Lower bandwidth ML = 0 Upper bandwidth MU = 0 Solution: 1 1.00001 2 2.00000 3 3.00001 4 3.99999 5 4.99999 6 6.00001 7 7.00000 8 8.00000 9 9.00000 10 9.99999 TEST15 For a border banded matrix: SBB_FA factors; SBB_SL solves. Matrix order N = 10 Matrix suborder N1 = 10 Matrix suborder N2 = 0 Lower bandwidth ML = 1 Upper bandwidth MU = 1 Solution: 1 1.00000 2 2.00000 3 3.00001 4 4.00000 5 4.99999 6 6.00001 7 6.99998 8 7.99999 9 9.00001 10 10.0000 TEST155 For a real block Toeplitz matrix, SBTO_MXV computes A * x. SBTO_VXM computes x * A. The block Toeplitz matrix: Columns 1 2 3 4 5 Row --- 1 1. 2. 3. 4. 5. 2 5. 5. 6. 6. 7. 3 7. 8. 1. 2. 3. 4 8. 8. 5. 5. 6. 5 9. 0. 7. 8. 1. 6 9. 9. 8. 8. 5. Columns 6 Row --- 1 6. 2 7. 3 4. 4 6. 5 2. 6 5. The vector x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 The product A*x: 1 91.0000 2 134.000 3 73.0000 4 125.000 5 79.0000 6 138.000 The product x*A: 1 163.000 2 122.000 3 121.000 4 130.000 5 87.0000 6 96.0000 TEST16 For a compact band matrix, no pivoting: SCB_NP_FA factors; SCB_DET computes the determinant; Matrix order N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The compact band matrix: Columns 1 2 3 4 5 Row --- 1 0.314138 0.487556 0.727541 0.599850 2 0.650477 0.418810 0.392122 0.159583 0.767562 3 0.876320 0.220968E-01 0.779277 0.903026 0.842189 4 0.231190 0.339380 0.371314E-01 0.212334 5 0.127917 0.733332 0.325925E-01 6 0.124133 0.842686 7 0.437422 Columns 6 7 8 9 10 Row --- 3 0.530611 4 0.474504 0.987577 5 0.569505 0.511039 0.529016 6 0.243226 0.990363 0.696260 0.791834 7 0.709678 0.676725 0.796761 0.852166 0.132382 8 0.916995 0.201607 0.547454 0.886204 0.744484 9 0.214591 0.903054 0.314261 0.700824 10 0.476745E-01 0.908018 0.898925 SCB_DET computes the determinant = 0.152181E-01 SGE_DET computes the determinant = 0.152181E-01 TEST17 For a compact band matrix, no pivoting: SCB_NP_FA factors; SCB_NP_SL solves. Matrix order N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 1 0.999992 2 2.00001 3 3.00002 4 4.00000 5 4.99995 6 6.00002 7 7.00001 8 7.99995 9 9.00001 10 10.0000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST18 For a compact band matrix: SCB_ML computes A*x or transpose(A)*X where A has been factored by SCB_FA. Matrix order N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 A*x and PLU*x 1 3.09885 3.09885 2 4.05659 4.05659 3 5.57715 5.57715 4 14.9551 14.9551 5 11.5780 11.5780 6 17.2397 17.2397 7 8.52654 8.52655 8 20.0739 20.0739 9 14.2794 14.2794 10 10.1582 10.1582 AT*x and (PLU)T*x 1 1.69584 1.69584 2 2.70629 2.01056 3 2.19014 4.91182 4 5.52235 -3.75338 5 8.91854 6.34609 6 12.7654 8.40835 7 14.1331 8.79909 8 9.11458 6.32768 9 6.49748 1.77845 10 12.7668 12.7668 TEST19 For a compressed border banded matrix: SCBB_RANDOM randomly generates; SCBB_PRINT prints; SCBB_FA factors (no pivoting); SCBB_SL solves. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The compact border-banded matrix: Columns 1 2 3 4 5 Row --- 1 0.604394 0.510456 0.547699 0. 0. 2 0.888652 0.359231 0.906733 0.894937 0. 3 0. 0.547699 0.493391 0.127922 0.354565 4 0. 0. 0.894937 0.586994 0.945861 5 0. 0. 0. 0.354565 0.994076 6 0. 0. 0. 0. 0.561201 7 0. 0. 0. 0. 0. 8 0. 0. 0. 0. 0. 9 0.337175 0.633549 0.438971 0.589748 0.823429E-01 10 0.764489 0.759128 0.476620 0.414899 0.762115 Columns 6 7 8 9 10 Row --- 1 0. 0. 0. 0.657134 0.950258 2 0. 0. 0. 0.511954 0.906634 3 0. 0. 0. 0.295704 0.309768 4 0.561201 0. 0. 0.458391 0.760847 5 0.658614 0.712293 0. 0.528505 0.937868 6 0.584723E-01 0.534667E-01 0.938548 0.304243 0.547393 7 0.712293 0.443632 0.662052 0.933269E-01 0.182992 8 0. 0.938548 0.839883 0.406531 0.624211 9 0.779365 0.585232 0.864088 0.755395 0.557645 10 0.603717 0.832838 0.916007 0.434729 0.472194 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST195 SCI_EVAL finds the eigenvalues of a real circulant system. Matrix order N = 5 The circulant matrix: Columns 1 2 3 4 5 Row --- 1 0.470883 0.316207 0.213902 0.443643 0.186042 2 0.186042 0.470883 0.316207 0.213902 0.443643 3 0.443643 0.186042 0.470883 0.316207 0.213902 4 0.213902 0.443643 0.186042 0.470883 0.316207 5 0.316207 0.213902 0.443643 0.186042 0.470883 The eigenvalues: 1 0.941215E-01 0.112443E-01 2 0.941215E-01 -0.112444E-01 3 0.267748 0.295006 4 0.267748 -0.295006 5 1.63068 0.00000 TEST20 SCI_SL solves a circulant system. Matrix order N = 10 The circulant matrix: Columns 1 2 3 4 5 Row --- 1 0.726424 0.344013 0.486966 0.103315 0.986786 2 0.792192 0.726424 0.344013 0.486966 0.103315 3 0.177089 0.792192 0.726424 0.344013 0.486966 4 0.268256 0.177089 0.792192 0.726424 0.344013 5 0.143698 0.268256 0.177089 0.792192 0.726424 6 0.663994 0.143698 0.268256 0.177089 0.792192 7 0.986786 0.663994 0.143698 0.268256 0.177089 8 0.103315 0.986786 0.663994 0.143698 0.268256 9 0.486966 0.103315 0.986786 0.663994 0.143698 10 0.344013 0.486966 0.103315 0.986786 0.663994 Columns 6 7 8 9 10 Row --- 1 0.663994 0.143698 0.268256 0.177089 0.792192 2 0.986786 0.663994 0.143698 0.268256 0.177089 3 0.103315 0.986786 0.663994 0.143698 0.268256 4 0.486966 0.103315 0.986786 0.663994 0.143698 5 0.344013 0.486966 0.103315 0.986786 0.663994 6 0.726424 0.344013 0.486966 0.103315 0.986786 7 0.792192 0.726424 0.344013 0.486966 0.103315 8 0.177089 0.792192 0.726424 0.344013 0.486966 9 0.268256 0.177089 0.792192 0.726424 0.344013 10 0.143698 0.268256 0.177089 0.792192 0.726424 Solution: 1 0.999998 2 2.00000 3 3.00002 4 4.00000 5 5.00002 6 6.00001 7 7.00001 8 7.99999 9 8.99999 10 9.99999 Solution to transposed system: 1 0.999958 2 1.99994 3 2.99996 4 3.99999 5 5.00001 6 6.00004 7 7.00005 8 8.00001 9 9.00000 10 9.99999 TEST21 SGB_DET, determinant of a banded matrix. Number of rows M = 10 Number of columns N = 10 Lower bandwidth ML = 3 Upper bandwidth MU = 2 SGB_DET computes the determinant = 0.574560E-02 SGE_DET computes the determinant = 0.574560E-02 TEST22 SGB_FA factor routine for general band matrices. SGB_SL solve routine for general band matrices. Number of matrix rows M = 10 Number of matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 1 0.999997 2 2.00000 3 3.00000 4 4.00000 5 4.99999 6 6.00001 7 7.00000 8 7.99999 9 9.00000 10 10.0000 Solution to transposed system: 1 0.999997 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00001 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST23 SGB_FA factors a general band matrix, using LINPACK conventions; SGB_TRF factors a general band matrix, using LAPACK conventions; Number of matrix rows M = 5 Number of matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The SGB_FA factors: Columns 1 2 3 4 5 Row --- 1 0.201988 0.800479 2 -0.422570 0.705506 0.906128 3 -0.157091 0.426309 0.961861 4 -0.108656 0.653438 0.766400 5 0.392726 0.297574 The SGB_TRF factors: Columns 1 2 3 4 5 Row --- 1 0.688811 0.302418E-01 2 0.731302 0.963273 0.924525 3 0.444631 -1.05926 -0.400732 4 -0.407889 0.598702 0.168568 5 0.711171 0.730610 TEST24 SGB_ML computes A*x or transpose(A)*X where A has been factored by SGB_FA. Number of matrix rows M = 10 Number of matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 A*x and PLU*x 1 3.17783 3.17783 2 1.84873 1.84873 3 6.59191 6.59191 4 5.57806 5.57806 5 11.7901 11.7901 6 14.6465 14.6465 7 15.5023 15.5023 8 18.0975 18.0975 9 21.5347 21.5347 10 8.27976 8.27976 AT*x and (PLU)T*x 1 1.90221 1.90221 2 4.64099 4.64099 3 4.20149 4.20149 4 6.27936 6.27936 5 9.38684 9.38684 6 10.3847 10.3847 7 15.5571 15.5571 8 8.66226 8.66226 9 14.2809 14.2809 10 13.8155 13.8155 TEST25 SGB_PRINT prints out a banded matrix. The banded matrix: Columns 1 2 3 4 5 Row --- 1 11. 12. 2 21. 22. 23. 3 31. 32. 33. 34. 4 41. 42. 43. 44. 45. 5 52. 53. 54. 55. 6 63. 64. 65. 7 74. 75. 8 85. Columns 6 7 8 9 10 Row --- 5 56. 6 66. 67. 7 76. 77. 78. 8 86. 87. 88. 89. 9 96. 97. 98. 99. 100. 10 107. 108. 109. 110. TEST26 SGB_SCAN counts zero/nonzero entries in a general band matrix. Number of matrix rows M = 10 Number of matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Nonzero entries = 23 Zero entries = 20 TEST27 SGB_TRF factor routine for general band matrices. SGB_TRS solve routine for general band matrices. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00002 4 3.99999 5 5.00000 6 6.00001 7 7.00001 8 7.99999 9 8.99999 10 10.0000 TEST28 For a general diagonal matrix: SGD_MXV computes A * x; SGD_PRINT prints it; SGD_RANDOM randomly generates one; SGD_VXM computes Transpose(A)*x; Matrix order N = 10 Number of diagonals NDIAG = 4 The raw matrix: Columns: 1 2 3 4 Row --- 1 0. 0.216156 0.165168 0.592076E-01 2 0. 0.281276 0.777777 0. 3 0.995522 0.936727 0.949023E-01 0. 4 0.176741E-01 0.368152 0.814226 0. 5 0.964781 0.596212 0.506129 0. 6 0.455688 0.112824 0.765837E-01 0. 7 0.286367 0.506449 0.647277 0. 8 0.561390 0.467043 0.125407 0. 9 0.182310 0.594211 0.287689 0. 10 0.543801 0.835059 0. 0. The general diagonal matrix: Columns 1 2 3 4 5 Row --- 1 0.216156 0.165168 0. 0. 0. 2 0. 0.281276 0.777777 0. 0. 3 0.995522 0. 0.936727 0.949023E-01 0. 4 0. 0.176741E-01 0. 0.368152 0.814226 5 0. 0. 0.964781 0. 0.596212 6 0. 0. 0. 0.455688 0. 7 0. 0. 0. 0. 0.286367 8 0. 0. 0. 0. 0. 9 0. 0. 0. 0. 0. 10 0. 0. 0. 0. 0. Columns 6 7 8 9 10 Row --- 1 0. 0. 0. 0. 0.592076E-01 2 0. 0. 0. 0. 0. 3 0. 0. 0. 0. 0. 4 0. 0. 0. 0. 0. 5 0.506129 0. 0. 0. 0. 6 0.112824 0.765837E-01 0. 0. 0. 7 0. 0.506449 0.647277 0. 0. 8 0.561390 0. 0.467043 0.125407 0. 9 0. 0.182310 0. 0.594211 0.287689 10 0. 0. 0.543801 0. 0.835059 A * x: 1 1.13857 2 2.89588 3 4.18531 4 5.57909 5 8.91218 6 3.03578 7 10.1552 8 8.23335 9 9.50096 10 12.7010 Transpose ( A ) * x: 1 3.20272 2 0.798417 3 9.18964 4 4.49144 5 8.24253 6 7.69871 7 5.64543 8 13.7053 9 6.35116 10 10.9990 TEST29 SGE_DET, determinant of a general matrix. Matrix order N = 4 SGE_DET computes the determinant = 112.000 True determinant = 112.000 TEST295 SGE_DILU returns the DILU factors of a matrix. Matrix A: Columns: 1 2 3 4 5 Row --- 1 4. -1. 0. -1. 0. 2 -1. 4. -1. 0. -1. 3 0. -1. 4. -1. 0. 4 -1. 0. -1. 4. -1. 5 0. -1. 0. -1. 4. 6 0. 0. -1. 0. -1. 7 0. 0. 0. -1. 0. 8 0. 0. 0. 0. -1. 9 0. 0. 0. 0. 0. Columns: 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 -1. 0. 0. 0. 4 0. -1. 0. 0. 5 -1. 0. -1. 0. 6 4. -1. 0. -1. 7 -1. 4. -1. 0. 8 0. -1. 4. -1. 9 -1. 0. -1. 4. DILU factor: 1 0.250000 2 0.266667 3 0.267857 4 0.287179 5 0.290179 6 0.290532 7 0.292202 8 0.292601 9 0.292666 TEST30 SGE_FA factors a general linear system, SGE_SL solves a factored system. Matrix order N = 10 Solution: 1 0.999967 2 1.99999 3 3.00000 4 3.99996 5 4.99995 6 6.00007 7 7.00003 8 7.99997 9 9.00005 10 10.0000 Solution: 1 0.999987 2 0.999996 3 1.00000 4 0.999983 5 0.999978 6 1.00003 7 1.00001 8 0.999992 9 1.00002 10 1.00001 Solution of transposed system: 1 0.999997 2 1.99999 3 2.99999 4 3.99999 5 5.00002 6 6.00003 7 7.00000 8 7.99998 9 9.00000 10 9.99999 TEST31 SGE_FA factors a general linear system, SGE_SL solves a factored system. Matrix order N = 10 Solution: 1 1.00001 2 2.00000 3 2.99999 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 9.99999 TEST315 SGE_ILU returns the ILU factors of a matrix. Matrix A: Columns: 1 2 3 4 5 Row --- 1 4. -1. 0. -1. 0. 2 -1. 4. -1. 0. -1. 3 0. -1. 4. -1. 0. 4 -1. 0. -1. 4. -1. 5 0. -1. 0. -1. 4. 6 0. 0. -1. 0. -1. 7 0. 0. 0. -1. 0. 8 0. 0. 0. 0. -1. 9 0. 0. 0. 0. 0. Columns: 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 -1. 0. 0. 0. 4 0. -1. 0. 0. 5 -1. 0. -1. 0. 6 4. -1. 0. -1. 7 -1. 4. -1. 0. 8 0. -1. 4. -1. 9 -1. 0. -1. 4. Factor L: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 -0.250000 1. 0. 0. 0. 3 0. -0.266667 1. 0. 0. 4 -0.250000 0. -0.267857 1. 0. 5 0. -0.266667 0. -0.287179 1. 6 0. 0. -0.267857 0. -0.290179 7 0. 0. 0. -0.287179 0. 8 0. 0. 0. 0. -0.290179 9 0. 0. 0. 0. 0. Columns: 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 0. 0. 0. 0. 4 0. 0. 0. 0. 5 0. 0. 0. 0. 6 1. 0. 0. 0. 7 -0.290532 1. 0. 0. 8 0. -0.292202 1. 0. 9 -0.290532 0. -0.292601 1. Factor U: Columns: 1 2 3 4 5 Row --- 1 4. -1. 0. -1. 0. 2 0. 3.75000 -1. 0. -1. 3 0. 0. 3.73333 -1. 0. 4 0. 0. 0. 3.48214 -1. 5 0. 0. 0. 0. 3.44615 6 0. 0. 0. 0. 0. 7 0. 0. 0. 0. 0. 8 0. 0. 0. 0. 0. 9 0. 0. 0. 0. 0. Columns: 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 -1. 0. 0. 0. 4 0. -1. 0. 0. 5 -1. 0. -1. 0. 6 3.44196 -1. 0. -1. 7 0. 3.42229 -1. 0. 8 0. 0. 3.41762 -1. 9 0. 0. 0. 3.41687 Product L*U: Columns: 1 2 3 4 5 Row --- 1 4. -1. 0. -1. 0. 2 -1. 4. -1. 0.250000 -1. 3 0. -1. 4. -1. 0.266667 4 -1. 0.250000 -1. 4. -1. 5 0. -1. 0.266667 -1.00000 4. 6 0. 0. -1. 0.267857 -1. 7 0. 0. 0. -1.00000 0.287179 8 0. 0. 0. 0. -1. 9 0. 0. 0. 0. 0. Columns: 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 -1. 0. 0. 0. 4 0.267857 -1. 0. 0. 5 -1. 0.287179 -1. 0. 6 4. -1. 0.290179 -1. 7 -1.00000 4. -1. 0.290532 8 0.290179 -1.00000 4. -1. 9 -1.00000 0.290532 -1.00000 4. TEST32 SGE_NP_FA factors without pivoting, SGE_NP_SL solves factored systems. Matrix order N = 10 Solution: 1 0.999994 2 1.00000 3 0.999994 4 1.00000 5 1.00001 6 0.999994 7 1.00000 8 1.00001 9 0.999990 10 0.999998 Solution: 1 1.00011 2 1.99995 3 2.99984 4 4.00015 5 4.99987 6 6.00004 7 6.99999 8 7.99990 9 9.00008 10 10.0001 Solution of transposed system: 1 1.00001 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 6.99999 8 7.99999 9 9.00000 10 10.0000 TEST33 SGE_NP_FA factors without pivoting, SGE_NP_INVERSE computes the inverse. Matrix order N = 5 The random matrix: Columns: 1 2 3 4 5 Row --- 1 0.492595 0.650271 0.303988 0.511411 0.546867 2 0.640254 0.576645E-01 0.918776E-02 0.967537 0.596762 3 0.922788 0.990675 0.115231 0.508842 0.161350 4 0.409880 0.466365 0.274118E-01 0.376470 0.851108 5 0.339987E-01 0.534251E-01 0.694971 0.382278 0.628576 The inverse matrix: Columns: 1 2 3 4 5 Row --- 1 -8.95009 0.166394 4.51607 2.51455 3.06469 2 5.47563 -0.637616 -1.86437 -1.21894 -2.02947 3 -2.21526 -0.376882 1.45145 -0.197537 2.18000 4 6.55328 1.08841 -2.95795 -2.72713 -2.28285 5 -1.51752 -0.200049 0.108357 1.84454 0.575703 The product: Columns: 1 2 3 4 5 Row --- 1 1.00000 0.126660E-06 -0.204891E-06 -0.238419E-06 -0.238419E-06 2 0.298023E-06 1. 0.245869E-06 0.119209E-06 0.387430E-06 3 0.759959E-06 0.298023E-06 1.00000 -0.476837E-06 0.290573E-06 4 0.476837E-06 0.745058E-07 -0.745058E-08 1.00000 0.298023E-07 5 0.953674E-06 0.178814E-06 -0.499189E-06 -0.357628E-06 1.00000 TEST34 SGE_FS, full storage factor/solve routine. Matrix order N = 10 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 4.99999 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST35 SGE_INVERSE inverts a general matrix. Matrix order N = 4 Matrix A: Columns: 1 2 3 4 Row --- 1 5. 3. 3. 3. 2 3. 5. 3. 3. 3 3. 3. 5. 3. 4 3. 3. 3. 5. Inverse matrix B: Columns: 1 2 3 4 Row --- 1 0.392857 -0.107143 -0.107143 -0.107143 2 -0.107143 0.392857 -0.107143 -0.107143 3 -0.107143 -0.107143 0.392857 -0.107143 4 -0.107143 -0.107143 -0.107143 0.392857 Product matrix: Columns: 1 2 3 4 Row --- 1 1.00000 -0.119209E-06 -0.894070E-07 0. 2 0. 1.00000 -0.894070E-07 0. 3 0. -0.119209E-06 1.00000 0. 4 0. -0.119209E-06 -0.596046E-07 1.00000 TEST36 SGE_ML computes A*x or transpose(A)*X where A has been factored by SGE_FA. Matrix order N = 10 A*x and PLU*x 1 28.2937 28.2937 2 32.8897 32.8897 3 35.3017 35.3017 4 15.2610 15.2610 5 28.6160 28.6160 6 15.8071 15.8071 7 34.3913 34.3913 8 17.1339 17.1339 9 28.6791 28.6791 10 32.0760 32.0760 AT*x and (PLU)T*x 1 21.8309 21.8309 2 32.7550 32.7550 3 28.5676 28.5676 4 29.1572 29.1572 5 37.3431 37.3431 6 22.7747 22.7747 7 26.6796 26.6796 8 40.7069 40.7069 9 37.5629 37.5629 10 38.3178 38.3178 TEST37 SGE_NP_ML computes A*x or transpose(A)*X where A has been factored by SGE_NP_FA. Matrix order N = 10 A*x and PLU*x 1 21.6261 21.6261 2 36.1456 36.1456 3 28.6101 28.6101 4 33.6444 33.6444 5 19.2142 19.2142 6 42.0514 42.0514 7 28.0165 28.0165 8 37.9122 37.9122 9 27.1883 27.1883 10 33.6648 33.6648 AT*x and (PLU)T*x 1 31.7059 31.7059 2 26.6360 26.6360 3 27.5727 27.5727 4 18.9174 18.9174 5 11.5327 11.5326 6 38.0655 38.0654 7 19.1284 19.1284 8 35.8778 35.8780 9 29.0268 29.0268 10 21.6100 21.6100 TEST38 SGE_MU computes A*x or transpose(A)*X where A has been factored by SGE_TRF. Number of matrix rows M = 5 Number of matrix columns N = 3 A*x and PLU*x 1 0.875230 0.875230 2 4.06876 4.06876 3 4.69510 4.69510 4 4.40203 4.40203 5 2.58267 2.58267 AT*x and (PLU)T*x 1 6.45673 6.45673 2 8.96912 8.96912 3 11.9134 11.9134 Matrix is 3 by 5 A*x and PLU*x 1 8.10047 8.10047 2 6.97578 6.97578 3 7.88901 7.88901 AT*x and (PLU)T*x 1 3.94960 3.94960 2 4.57232 4.57232 3 3.86422 3.86422 4 4.25344 4.25344 5 1.81920 1.81920 TEST385 SGE_PLU returns the PLU factors of a matrix. Matrix A: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. Factor P: Columns: 1 2 3 Row --- 1 0. 1. 0. 2 0. 0. 1. 3 1. 0. 0. Factor L: Columns: 1 2 3 Row --- 1 1. 0. 0. 2 0.111111 1. 0. 3 0.555556 0.500000 1. Factor U: Columns: 1 2 3 4 Row --- 1 9. 10. 11. 12. 2 0. 0.888889 1.77778 2.66667 3 0. 0. -0.596046E-07 0.476837E-06 Product P*L*U: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. Matrix A: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. 4 13. 14. 15. 16. Factor P: Columns: 1 2 3 4 Row --- 1 0. 1. 0. 0. 2 0. 0. 0. 1. 3 0. 0. 1. 0. 4 1. 0. 0. 0. Factor L: Columns: 1 2 3 4 Row --- 1 1. 0. 0. 0. 2 0.769231E-01 1. 0. 0. 3 0.692308 0.333333 1. 0. 4 0.384615 0.666667 -0.133333 1. Factor U: Columns: 1 2 3 4 Row --- 1 13. 14. 15. 16. 2 0. 0.923077 1.84615 2.76923 3 0. 0. 0.894070E-06 0.178814E-05 4 0. 0. 0. 0. Product P*L*U: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. 4 13. 14. 15. 16. Matrix A: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. 4 13. 14. 15. 16. 5 17. 18. 19. 20. Factor P: Columns: 1 2 3 4 5 Row --- 1 0. 1. 0. 0. 0. 2 0. 0. 0. 0. 1. 3 0. 0. 0. 1. 0. 4 0. 0. 1. 0. 0. 5 1. 0. 0. 0. 0. Factor L: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 0.588235E-01 1. 0. 0. 0. 3 0.764706 0.250000 1. 0. 0. 4 0.529412 0.499999 0.588235E-01 1. 0. 5 0.294118 0.750000 -0.352941 0.117647 1. Factor U: Columns: 1 2 3 4 Row --- 1 17. 18. 19. 20. 2 0. 0.941176 1.88235 2.82353 3 0. 0. -0.101328E-05 -0.101328E-05 4 0. 0. 0. 0.101328E-05 5 0. 0. 0. 0. Product P*L*U: Columns: 1 2 3 4 Row --- 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. 4 13. 14. 15. 16. 5 17. 18. 19. 20. TEST39 SGE_POLY computes the characteristic polynomial of a matrix. Matrix order N = 12 I, P(I), True P(I) 1 1.00000 1.00000 2 -23.0000 -23.0000 3 231.000 231.000 4 -1330.00 -1330.00 5 4845.00 4845.00 6 -11628.0 -11628.0 7 18564.0 18564.0 8 -19448.0 -19448.0 ...... .............. .............. 13 1.00000 1.00000 TEST40 SGE_SL_IT applies one step of iterative refinement to an SGE_SL solution. i, x, b-A*x 1 0.168862 -0.152588E-04 2 0.144724 -0.488281E-03 3 0.126627 -0.781250E-02 4 0.112555 0.00000 5 0.101298 0.156250E-01 6 0.920880E-01 0.781250E-02 Iterative refinement step 1 i, dx 1 0.159237E-02 2 0.162138E-02 3 0.154055E-02 4 0.143671E-02 5 0.133401E-02 6 0.123945E-02 i, x, b-A*x 1 0.170454 -0.305176E-04 2 0.146345 0.195312E-02 3 0.128168 0.00000 4 0.113991 0.468750E-01 5 0.102632 -0.781250E-01 6 0.933274E-01 0.117187E-01 Iterative refinement step 2 i, dx 1 -0.103658E-02 2 -0.136094E-02 3 -0.142706E-02 4 -0.140346E-02 5 -0.134728E-02 6 -0.128069E-02 i, x, b-A*x 1 0.169417 -0.152588E-04 2 0.144984 0.00000 3 0.126741 -0.781250E-02 4 0.112588 -0.312500E-01 5 0.101285 0.00000 6 0.920467E-01 0.00000 Iterative refinement step 3 i, dx 1 -0.105421E-01 2 -0.830428E-02 3 -0.685740E-02 4 -0.584246E-02 5 -0.509034E-02 6 -0.451034E-02 i, x, b-A*x 1 0.158875 0.152588E-04 2 0.136680 0.146484E-02 3 0.119883 -0.781250E-02 4 0.106746 0.468750E-01 5 0.961942E-01 0.156250E-01 6 0.875364E-01 -0.390625E-02 Iterative refinement step 4 i, dx 1 0.124753E-01 2 0.100819E-01 3 0.846798E-02 4 0.730144E-02 5 0.641798E-02 6 0.572545E-02 i, x, b-A*x 1 0.171351 -0.610352E-04 2 0.146762 -0.146484E-02 3 0.128351 0.390625E-02 4 0.114047 0.156250E-01 5 0.102612 -0.156250E-01 6 0.932619E-01 0.234375E-01 Iterative refinement step 5 i, dx 1 0.525933E-02 2 0.438018E-02 3 0.374291E-02 4 0.326726E-02 5 0.289954E-02 6 0.260683E-02 i, x, b-A*x 1 0.176610 0.00000 2 0.151142 0.146484E-02 3 0.132094 -0.390625E-02 4 0.117314 -0.156250E-01 5 0.105512 -0.625000E-01 6 0.958687E-01 -0.234375E-01 TEST41 SGE_TRF factors a general linear system, SGE_TRS solves a factored system. Number of matrix rows M = 5 Number of matrix columns N = 5 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 TEST42 Using the LAPACK general matrix format, SGE_NP_TRF factors without pivoting, SGE_NP_TRS solves factored systems. SGE_NP_TRM computes A*X for factored A. Matrix dimensions: M = 10 N = 10 Solution: 1 1.00000 2 1.00000 3 0.999998 4 0.999998 5 0.999997 6 1.00000 7 1.00000 8 1.00000 9 0.999999 10 1.00000 Solution: 1 0.999990 2 2.00005 3 2.99999 4 3.99998 5 4.99996 6 6.00001 7 7.00001 8 8.00002 9 8.99999 10 10.0000 Solution of transposed system: 1 1.00000 2 2.00004 3 2.99993 4 3.99993 5 5.00010 6 6.00000 7 7.00002 8 7.99999 9 8.99996 10 10.0000 TEST43 For a lower triangular matrix, SLT_SL solves systems; Matrix order N = 10 The lower triangular matrix: Columns 1 2 3 4 5 Row --- 1 1. 2 1. 2. 3 1. 2. 3. 4 1. 2. 3. 4. 5 1. 2. 3. 4. 5. 6 1. 2. 3. 4. 5. 7 1. 2. 3. 4. 5. 8 1. 2. 3. 4. 5. 9 1. 2. 3. 4. 5. 10 1. 2. 3. 4. 5. Columns 6 7 8 9 10 Row --- 6 6. 7 6. 7. 8 6. 7. 8. 9 6. 7. 8. 9. 10 6. 7. 8. 9. 10. Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST44 For a lower triangular matrix, SLT_INVERSE computes the inverse. SLT_DET computes the inverse. Matrix order N = 5 Matrix A: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 1. 2. 0. 0. 0. 3 1. 2. 3. 0. 0. 4 1. 2. 3. 4. 0. 5 1. 2. 3. 4. 5. Determinant is 120.000 Inverse matrix B: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 -0.500000 0.500000 0. 0. 0. 3 0. -0.333333 0.333333 0. 0. 4 0. 0. -0.250000 0.250000 0. 5 0. 0. 0. -0.200000 0.200000 Product A * B: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 0. 1. 0. 0. 0. 3 0. 0. 1. 0. 0. 4 0. 0. 0. 1. 0. 5 0. 0. 0. 0. 1. TEST45 SPB_CG applies the conjugate gradient method to a symmetric positive definite banded linear system. Matrix order N = 50 Upper bandwidth MU = 1 The symmetric banded matrix: Columns 1 2 3 4 5 Row --- 1 2. -1. 2 -1. 2. -1. 3 -1. 2. -1. 4 -1. 2. -1. 5 -1. 2. 6 -1. Columns 6 7 8 9 10 Row --- 5 -1. 6 2. -1. 7 -1. 2. -1. 8 -1. 2. -1. 9 -1. 2. -1. 10 -1. 2. Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00001 7 7.00000 8 8.00001 ...... .............. 50 50.0000 Maximum residual= 0.267029E-04 TEST46 SPB_DET, determinant of a positive definite symmetric banded matrix. Matrix order N = 10 Upper bandwidth MU = 3 SPB_DET computes the determinant = 34611.6 SGE_DET computes the determinant = 34611.6 TEST47 SPB_FA factors a banded positive definite symmetric linear system. SPB_SL solves a banded positive definite symmetric linear system. Matrix order N = 50 Upper bandwidth MU = 1 Solution: 1 1.00001 2 2.00002 3 3.00003 4 4.00005 5 5.00006 6 6.00007 7 7.00008 8 8.00010 ...... .............. 50 50.0000 TEST48 SPB_ML computes A*x where A has been factored by SPB_FA. Matrix order N = 10 Upper bandwidth MU = 3 A*x and PLU*x 1 2.79333 2.79333 2 11.2003 11.2003 3 25.0808 25.0808 4 34.4641 34.4641 5 28.7485 28.7485 6 39.5478 39.5478 7 37.1436 37.1436 8 63.4684 63.4684 9 51.1794 51.1794 10 55.1691 55.1691 TEST49 SPB_SOR, SOR routine for iterative solution of A*x=b. Matrix order N = 50 Upper bandwidth MU = 1 SOR iteration. Relaxation factor OMEGA = 0.250000 Iterations taken= 5081 Solution: 1 0.162362E-02 2 0.673113E-01 3 0.132723 4 0.197592 5 0.261650 6 0.324636 7 0.386290 8 0.446361 ...... .............. 50 0.162354E-02 Maximum error = 0.998974E-04 SOR iteration. Relaxation factor OMEGA = 0.750000 Iterations taken= 1694 Solution: 1 0.162050E-02 2 0.673051E-01 3 0.132714 4 0.197579 5 0.261635 6 0.324618 7 0.386269 8 0.446337 ...... .............. 50 0.162038E-02 Maximum error = 0.998974E-04 SOR iteration. Relaxation factor OMEGA = 1.00000 Iterations taken= 1271 Solution: 1 0.161791E-02 2 0.673000E-01 3 0.132706 4 0.197569 5 0.261622 6 0.324602 7 0.386252 8 0.446318 ...... .............. 50 0.161780E-02 Maximum error = 0.997782E-04 TEST50 SPO_FA factors a positive definite symmetric linear system, SPO_SL solves a factored system. Matrix order N = 10 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution: 1 1.00000 2 1.00000 3 1.00000 4 1.00000 5 1.00000 6 1.00000 7 1.00000 8 1.00000 9 1.00000 10 1.00000 TEST51 For a symmetric positive definite matrix factored by SPO_FA, SPO_DET computes the determinant; SPO_INVERSE computes the inverse. Matrix order N = 4 Matrix A: Columns: 1 2 3 4 Row --- 1 1. 1. 1. 1. 2 1. 2. 2. 2. 3 1. 2. 3. 3. 4 1. 2. 3. 4. Matrix determinant = 0.00000 Inverse matrix B: Columns: 1 2 3 4 Row --- 1 2. -1. 0. 0. 2 -1. 2. -1. 0. 3 0. -1. 2. -1. 4 0. 0. -1. 1. Product A * B: Columns: 1 2 3 4 Row --- 1 1. 0. 0. 0. 2 0. 1. 0. 0. 3 0. 0. 1. 0. 4 0. 0. 0. 1. TEST52 SPO_RANDOM, compute a random positive definite symmetric matrix. Matrix order N = 5 Random matrix: Columns: 1 2 3 4 5 Row --- 1 0.758086 0.224175 0.553176 0.235559 0.596919 2 0.224175 0.816912E-01 0.192228 0.126475 0.187260 3 0.553176 0.192228 0.472750 0.343692 0.509933 4 0.235559 0.126475 0.343692 1.50559 0.766137 5 0.596919 0.187260 0.509933 0.766137 1.29184 TEST53 SPP_RANDOM, compute a random positive definite symmetric packed matrix. Matrix order N = 5 The matrix: Columns 1 2 3 4 5 Row --- 1 0.946615 0.223949 0.169217 0.825210 0.926767 2 0.223949 0.893779 0.317697 0.497187 0.653316 3 0.169217 0.317697 0.987634 1.01670 1.09378 4 0.825210 0.497187 1.01670 2.32813 1.90942 5 0.926767 0.653316 1.09378 1.90942 1.95462 TEST54 SSD_CG applies the conjugate gradient method to a symmetric positive definite linear system stored by diagonals. Matrix order N = 100 Number of diagonals is 3 First 10 rows and columns of matrix. Columns 1 2 3 4 5 Row --- 1 4. -1. 0. 0. 0. 2 -1. 4. -1. 0. 0. 3 0. -1. 4. -1. 0. 4 0. 0. -1. 4. -1. 5 0. 0. 0. -1. 4. 6 0. 0. 0. 0. -1. 7 0. 0. 0. 0. 0. 8 0. 0. 0. 0. 0. 9 0. 0. 0. 0. 0. 10 0. 0. 0. 0. 0. Columns 6 7 8 9 10 Row --- 1 0. 0. 0. 0. 0. 2 0. 0. 0. 0. 0. 3 0. 0. 0. 0. 0. 4 0. 0. 0. 0. 0. 5 -1. 0. 0. 0. 0. 6 4. -1. 0. 0. 0. 7 -1. 4. -1. 0. 0. 8 0. -1. 4. -1. 0. 9 0. 0. -1. 4. -1. 10 0. 0. 0. -1. 4. Right hand side: 1 11.0000 2 20.0000 3 30.0000 4 40.0000 5 50.0000 6 60.0000 7 70.0000 8 80.0000 ...... .............. 100 231.000 Solution: 1 11.0000 2 21.0000 3 31.0000 4 41.0000 5 51.0000 6 61.0000 7 71.0000 8 81.0000 ...... .............. 100 110.000 Maximum residual= 0.122070E-03 Second attempt at solution: 1 11.0000 2 21.0000 3 31.0000 4 41.0000 5 51.0000 6 61.0000 7 71.0000 8 81.0000 ...... .............. 100 110.000 Maximum residual of second attempt = 0.534058E-04 TEST55 SSD_CG is used for linear equation solving in a demonstration of inverse iteration to compute eigenvalues and eigenvectors of a symmetric matrix stored by diagonals. Problem size is N = 100 Here are 25 of the smallest eigenvalues: I, J, eigenvalue(I,J): 1 1 0.162028 1 2 0.398507 1 3 0.771293 1 4 1.25018 1 5 1.79638 2 1 0.398507 2 2 0.634986 2 3 1.00777 2 4 1.48666 2 5 2.03286 3 1 0.771293 3 2 1.00777 3 3 1.38056 3 4 1.85945 3 5 2.40565 4 1 1.25018 4 2 1.48666 4 3 1.85945 4 4 2.33834 4 5 2.88454 5 1 1.79638 5 2 2.03286 5 3 2.40565 5 4 2.88454 5 5 3.43074 Lambda estimate = 0.162028 Converged on step 7 Lambda estimate = 0.771293 Converged on step 12 Lambda estimate = 0.398507 Converged on step 15 TEST56 SSM_ML computes A*x or transpose(A)*X where A is a Sherman Morrison matrix. Matrix order N = 7 The Sherman Morrison matrix: Columns 1 2 3 4 5 Row --- 1 0.420924 -0.277337 -0.401781 0.705796 0.270696 2 0.389784 -0.288670 0.233968 0.642462 -0.117843 3 0.252322 -0.753706 -0.132495 0.629817 -0.874783E-01 4 -0.122694 0.173565 0.289940 0.670582 -0.585663 5 0.259004E-01 0.298426 0.863106 0.688640 0.521042 6 0.326325 0.639637 0.558834 0.471208 0.217879 7 0.169213 0.874234 0.422415 0.155185 0.652121 Columns 6 7 Row --- 1 0.700820 0.320001 2 0.770354 -0.313693 3 0.867143 0.574451E-01 4 0.502030 0.483857 5 0.962014 0.375082 6 0.863680 -0.354653E-01 7 0.312927 0.364124E-01 A*x and PLU*x 1 9.28250 9.28250 2 4.92126 4.92126 3 6.03427 6.03427 4 7.24745 7.24745 5 16.9695 16.9695 6 11.1902 11.1902 7 9.19872 9.19872 The Sherman Morrison matrix: Columns 1 2 3 4 5 Row --- 1 0.364611 0.619597 0.287252 0.455768 -0.440349 2 0.193003E-01 0.445292 0.625684 0.811382E-01 0.351922 3 0.878362 0.723768 0.307121 0.448907 -0.201755 4 0.515975 0.943601 0.243520 0.130696 -0.637470 5 0.227297 0.627635 0.146554 0.162921 -0.845665 6 -0.980805E-01 0.350175 0.219744 0.261872 -0.676903 7 0.729852 0.165155 0.698048 0.945763 0.121049 Columns 6 7 Row --- 1 -0.406017 0.211329 2 0.805299 0.698932 3 -0.253231 0.241507 4 -0.424342 0.225808 5 -0.243097 -0.288595E-01 6 -0.347330 0.648106 7 -0.109705E-01 0.268074 AT*x and (PLU)T*x 1 10.7592 10.7592 2 13.8512 13.8512 3 10.3716 10.3716 4 11.4937 11.4937 5 -10.3341 -10.3341 6 -4.62874 -4.62874 7 8.85780 8.85780 TEST57 SSM_SL implements the Sherman-Morrison method for solving a perturbed linear system. Matrix order N = 5 The Sherman-Morrison matrix A: Columns 1 2 3 4 5 Row --- 1 0.699371 0.287762 0.673236 -0.979821E-01 0.428345 2 0.653847 0.813927 -0.171062E-01 0.225030 -0.122497 3 -0.311688 0.278760 0.701471 -0.336604 0.924411E-02 4 0.734393 0.490164 0.383919 -0.690483E-01 0.659348 5 -0.848510E-01 0.883767E-01 0.618079E-01 0.641447 -0.428481 The right hand side vector B: 1 3.58532 2 5.15444 3 4.58815 4 2.27331 5 0.706075 Solution to At * X = B: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 The Sherman-Morrison matrix A: Columns 1 2 3 4 5 Row --- 1 0.385151 0.682435 0.275681 -0.159987 0.316059 2 0.341936 0.331304 0.228077 0.322618 0.140832 3 0.370792 0.514184 0.411348 0.346669 0.529075 4 -0.345796 0.468907E-01 0.129630 0.281891 0.213644 5 -0.137688 0.468484 0.131920E-01 0.277516 0.127024 The right hand side vector B: 1 3.51741 2 3.68341 3 6.66526 4 2.33266 5 2.58404 Solution to A * X = B: 1 0.999998 2 2.00000 3 3.00001 4 4.00000 5 5.00000 TEST58 For a symmetric skyline storage matrix, SSS_MXV computes A*x, SSS_PRINT prints it. Matrix order N = 9 Number of nonzero entries stored is 18 Diagonal storage indices: 1 1 2 3 3 4 4 6 5 11 6 12 7 13 8 16 9 18 The symmetric skyline storage matrix: Columns 1 2 3 4 5 Row --- 1 11. 12. 0. 0. 15. 2 12. 22. 0. 0. 25. 3 0. 0. 33. 34. 35. 4 0. 0. 34. 44. 45. 5 15. 25. 35. 45. 55. 6 0. 0. 0. 0. 0. 7 0. 0. 0. 0. 0. 8 0. 0. 0. 0. 0. 9 0. 0. 0. 0. 0. Columns 6 7 8 9 Row --- 1 0. 0. 0. 0. 2 0. 0. 0. 0. 3 0. 0. 0. 0. 4 0. 0. 0. 0. 5 0. 0. 0. 0. 6 66. 0. 68. 0. 7 0. 77. 78. 0. 8 68. 78. 88. 89. 9 0. 0. 89. 99. SSS_MXV verse SGE_MXV 1 110.000 110.000 2 181.000 181.000 3 410.000 410.000 4 503.000 503.000 5 625.000 625.000 6 940.000 940.000 7 1163.00 1163.00 8 2459.00 2459.00 9 1603.00 1603.00 TEST583 SSTO_INVERSE computes the inverse of a positive definite symmetric Toeplitz matrix. Matrix order N = 3 The symmetric Toeplitz matrix A: Columns 1 2 3 Row --- 1 4. 2. 0.800000 2 2. 4. 2. 3 0.800000 2. 4. The inverse matrix B: Columns: 1 2 3 Row --- 1 0.334821 -0.178571 0.223214E-01 2 -0.178571 0.428571 -0.178571 3 0.223214E-01 -0.178571 0.334821 The product C = A * B: Columns: 1 2 3 Row --- 1 1.00000 0. 0.298023E-07 2 0.484288E-07 1. 0.596046E-07 3 0.372529E-07 0. 1. TEST585 SSTO_YW_SL solves the Yule-Walker equations for a symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix: Columns 1 2 3 Row --- 1 1. 0.500000 0.200000 2 0.500000 1. 0.500000 3 0.200000 0.500000 1. The right hand side, B: 1 -0.500000 2 -0.200000 3 -0.100000 The computed solution, X: 1 -0.535714 2 0.857143E-01 3 -0.357143E-01 The product A*X: 1 -0.500000 2 -0.200000 3 -0.100000 TEST587 SSTO_SL solves a positive definite symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix A: Columns 1 2 3 Row --- 1 1. 0.500000 0.200000 2 0.500000 1. 0.500000 3 0.200000 0.500000 1. The right hand side vector B: 1 4.00000 2 -1.00000 3 3.00000 The solution X: 1 6.33929 2 -6.71429 3 5.08929 The product vector B = A * X: 1 4.00000 2 -1.00000 3 3.00000 TEST59 STO_SL solves a Toeplitz system. Matrix order N = 10 The Toeplitz matrix: Columns 1 2 3 4 5 Row --- 1 0.451460 0.940819 0.201591 0.322692 0.766519 2 0.277386 0.451460 0.940819 0.201591 0.322692 3 0.733922 0.277386 0.451460 0.940819 0.201591 4 0.730327 0.733922 0.277386 0.451460 0.940819 5 0.657482 0.730327 0.733922 0.277386 0.451460 6 0.460238 0.657482 0.730327 0.733922 0.277386 7 0.610805E-01 0.460238 0.657482 0.730327 0.733922 8 0.272989 0.610805E-01 0.460238 0.657482 0.730327 9 0.743464 0.272989 0.610805E-01 0.460238 0.657482 10 0.501001 0.743464 0.272989 0.610805E-01 0.460238 Columns 6 7 8 9 10 Row --- 1 0.129292E-01 0.252812 0.406411 0.802702 0.742687 2 0.766519 0.129292E-01 0.252812 0.406411 0.802702 3 0.322692 0.766519 0.129292E-01 0.252812 0.406411 4 0.201591 0.322692 0.766519 0.129292E-01 0.252812 5 0.940819 0.201591 0.322692 0.766519 0.129292E-01 6 0.451460 0.940819 0.201591 0.322692 0.766519 7 0.277386 0.451460 0.940819 0.201591 0.322692 8 0.733922 0.277386 0.451460 0.940819 0.201591 9 0.730327 0.733922 0.277386 0.451460 0.940819 10 0.657482 0.730327 0.733922 0.277386 0.451460 Solution: 1 1.00000 2 1.99994 3 3.00000 4 4.00000 5 5.00000 6 5.99994 7 6.99994 8 8.00000 9 8.99994 10 10.0000 Solution to transposed system: 1 0.999969 2 2.00008 3 2.99998 4 4.00006 5 4.99994 6 6.00003 7 6.99995 8 8.00005 9 8.99997 10 10.0000 TEST60 For an upper triangular matrix, SUT_SL solves systems; Matrix order N = 10 The upper triangular matrix: Columns 1 2 3 4 5 Row --- 1 1. 2. 3. 4. 5. 2 2. 3. 4. 5. 3 3. 4. 5. 4 4. 5. 5 5. Columns 6 7 8 9 10 Row --- 1 6. 7. 8. 9. 10. 2 6. 7. 8. 9. 10. 3 6. 7. 8. 9. 10. 4 6. 7. 8. 9. 10. 5 6. 7. 8. 9. 10. 6 6. 7. 8. 9. 10. 7 7. 8. 9. 10. 8 8. 9. 10. 9 9. 10. 10 10. Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 TEST61 For an upper triangular matrix, SUT_INVERSE computes the inverse. SUT_DET computes the determinant. Matrix order N = 5 The matrix A: Columns 1 2 3 4 5 Row --- 1 1. 2. 3. 4. 5. 2 2. 3. 4. 5. 3 3. 4. 5. 4 4. 5. 5 5. Determinant is 120.000 The inverse matrix B: Columns 1 2 3 4 5 Row --- 1 1. -1. 0. 0. 0. 2 0.500000 -0.500000 0. 0. 3 0.333333 -0.333333 0. 4 0.250000 -0.250000 5 0.200000 The product A * B: Columns: 1 2 3 4 5 Row --- 1 1. 0. 0. 0. 0. 2 0. 1. 0. 0. 0. 3 0. 0. 1. 0. 0. 4 0. 0. 0. 1. 0. 5 0. 0. 0. 0. 1. TEST62 SVM_DET, determinant of a Vandermonde matrix. Matrix order N = 10 The Vandermonde matrix: Columns 1 2 3 4 5 Row --- 1 1. 1. 1. 1. 1. 2 0.405690 0.265358 0.275345 0.658904 0.578222 3 0.164585 0.704146E-01 0.758151E-01 0.434154 0.334341 4 0.667704E-01 0.186851E-01 0.208753E-01 0.286066 0.193324 5 0.270881E-01 0.495822E-02 0.574792E-02 0.188490 0.111784 6 0.109894E-01 0.131570E-02 0.158266E-02 0.124197 0.646360E-01 7 0.445829E-02 0.349131E-03 0.435779E-03 0.818337E-01 0.373740E-01 8 0.180868E-02 0.926446E-04 0.119990E-03 0.539205E-01 0.216105E-01 9 0.733765E-03 0.245839E-04 0.330386E-04 0.355284E-01 0.124957E-01 10 0.297681E-03 0.652354E-05 0.909703E-05 0.234098E-01 0.722528E-02 Columns 6 7 8 9 10 Row --- 1 1. 1. 1. 1. 1. 2 0.676979 0.385482 0.885614E-01 0.239508 0.874079 3 0.458300 0.148596 0.784312E-02 0.573641E-01 0.764014 4 0.310260 0.572811E-01 0.694598E-03 0.137392E-01 0.667809 5 0.210039 0.220808E-01 0.615146E-04 0.329064E-02 0.583718 6 0.142192 0.851176E-02 0.544782E-05 0.788134E-03 0.510216 7 0.962610E-01 0.328113E-02 0.482467E-06 0.188764E-03 0.445969 8 0.651667E-01 0.126481E-02 0.427279E-07 0.452106E-04 0.389812 9 0.441165E-01 0.487563E-03 0.378405E-08 0.108283E-04 0.340727 10 0.298659E-01 0.187947E-03 0.335121E-09 0.259346E-05 0.297822 SVM_DET computes the determinant = -0.170190E-30 SGE_DET computes the determinant = -0.171277E-30 TEST63 SVM_SL solves a Vandermonde system. Matrix order N = 10 Solution: 1 -157746. 2 3210.23 3 15868.2 4 0.144393E+07 5 3321.50 6 -0.129814E+07 7 13.8477 8 7.99805 9 -10399.1 10 -8.96740 Solution to transposed system: 1 141.707 2 -4753.94 3 46387.7 4 -226062. 5 652100. 6 -0.118956E+07 7 0.139372E+07 8 -0.102053E+07 9 426298. 10 -77694.1 LINPLUS_PRB Normal end of execution.