Wed Oct 8 08:24:58 2025 linpack_d_test(): python version: 3.10.12 numpy version: 1.26.4 Test linpack_d(). dgeco_test() dgeco() computes the condition number of a matrix stored in general format. The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgeco() factors and analyzes the matrix The reciprocal condition number RCOND: 0.024644549763033173 dgedet_test() dgedet() computes the determinant of a matrix stored in general format, after it has been factored by dgefa(). The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgefa() factors the matrix dgedet() computes the determinant: The determinant DET: 26.999999999999993 dgefa_test() dgefa() computes pivot vector and LU factors of a matrix stored in general format. The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgefa() factors the matrix The matrix ALU: [[ 7. 8. 0. ] [-0.57142857 0.85714286 3. ] [-0.14285714 -0.5 4.5 ]] The pivot vector IPVT: [2 2 2] dgeinv_test() dgeinv() computes inverse of a matrix stored in general format, which has been factored by dgefa(). The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgefa() factors the matrix dgeinv() computes the inverse matrix The inverse matrix AINV: [[-1.77777778 0.88888889 -0.11111111] [ 1.55555556 -0.77777778 0.22222222] [-0.11111111 0.22222222 -0.11111111]] The product A * AINV: [[ 1.00000000e+00 5.55111512e-17 -4.16333634e-17] [ 5.55111512e-17 1.00000000e+00 -8.32667268e-17] [ 1.77635684e-15 -8.88178420e-16 1.00000000e+00]] dgesl_test() dgesl() solves a linear system involving a matrix stored in general format, after dgefa() has computed the LU factorization; The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgefa() factors the matrix The right hand side B [14. 32. 23.] dgesl() solves the linear system. Computed solution X (should be (1,2,3)) [1. 2. 3.] dgeslt_test(): dgeslt() solves a transposed linear system involving a matrix stored in general format, after dgefa() has computed the LU factorization; The number of equations is N = 3 The matrix A: [[1. 2. 3.] [4. 5. 6.] [7. 8. 0.]] dgefa() factors the matrix The right hand side B [30. 36. 15.] dgeslt() solves the linear system. Computed solution X (should be (1,2,3)) [1. 2. 3.] dpofa_test(): dpofa() computes the LU factors of a positive definite symmetric matrix, Matrix A: [[ 2. -1. 0. 0. 0.] [-1. 2. -1. 0. 0.] [ 0. -1. 2. -1. 0.] [ 0. 0. -1. 2. -1.] [ 0. 0. 0. -1. 2.]] Call DPOFA to factor the matrix. Upper triangular factor U: [[ 1.41421356 -0.70710678 0. 0. 0. ] [ 0. 1.22474487 -0.81649658 0. 0. ] [ 0. 0. 1.15470054 -0.8660254 0. ] [ 0. 0. 0. 1.11803399 -0.89442719] [ 0. 0. 0. 0. 1.09544512]] Product Ut * U: [[ 2. -1. 0. 0. 0.] [-1. 2. -1. 0. 0.] [ 0. -1. 2. -1. 0.] [ 0. 0. -1. 2. -1.] [ 0. 0. 0. -1. 2.]] dqrdc_test(): dqrdc() computes the QR decomposition of a rectangular matrix, but does not return Q and R explicitly. Show how Q and R can be recovered using DQRSL. The original matrix A: [[1. 1. 0.] [1. 0. 1.] [0. 1. 1.]] Decompose the matrix. The packed matrix A which describes Q and R: [[-1.41421356 -0.70710678 -0.70710678] [ 0.70710678 1.22474487 0.40824829] [ 0. -0.81649658 1.15470054]] The QRAUX vector, containing some additional information defining Q: [1.70710678 1.57735027 0. ] The R factor: [[-1.41421356 -0.70710678 -0.70710678] [ 0. 1.22474487 0.40824829] [ 0. 0. 1.15470054]] The Q factor: [[-0.70710678 0.40824829 -0.57735027] [-0.70710678 -0.40824829 0.57735027] [ 0. 0.81649658 0.57735027]] The product Q * R: [[ 1.00000000e+00 1.00000000e+00 -8.79548322e-17] [ 1.00000000e+00 -6.78135690e-17 1.00000000e+00] [ 0.00000000e+00 1.00000000e+00 1.00000000e+00]] dqrsl_test(): dqrsl() solves a rectangular linear system A*x=b in the least squares sense after A has been factored by DQRDC. The matrix A: [[ 1. 1. 1.] [ 1. 2. 4.] [ 1. 3. 9.] [ 1. 4. 16.] [ 1. 5. 25.]] Decompose the matrix. X X(expected): -3.02 -3.02 4.49143 4.49143 -0.728571 -0.728571 drotg_test(): drotg() generates a real Givens rotation ( C S ) * ( A ) = ( R ) ( -S C ) ( B ) ( 0 ) A = 0.478628 B = 0.743914 C = 0.541076 S = 0.840974 R = 0.884587 Z = 1.84817 C*A+S*B = 0.884587 -S*A+C*B = 0 A = 0.770897 B = 0.724496 C = 0.728697 S = 0.684836 R = 1.05791 Z = 0.684836 C*A+S*B = 1.05791 -S*A+C*B = -1.11022e-16 A = 0.990596 B = 0.685868 C = 0.822165 S = 0.56925 R = 1.20486 Z = 0.56925 C*A+S*B = 1.20486 -S*A+C*B = 0 A = 0.0406485 B = 0.432578 C = 0.0935559 S = 0.995614 R = 0.434484 Z = 10.6888 C*A+S*B = 0.434484 -S*A+C*B = 0 A = 0.686081 B = 0.859973 C = 0.623643 S = 0.78171 R = 1.10012 Z = 1.60348 C*A+S*B = 1.10012 -S*A+C*B = 0 dsvdc_test(): dsvdc() computes the singular value decomposition for an MxN matrix A in general storage. A = U * S * V' Matrix rows M = 6 Matrix columns N = 4 The matrix A: [[0.9825534 0.0882425 0.25673196 0.9832903 ] [0.83381316 0.67235694 0.07905347 0.22531269] [0.93813307 0.31541779 0.63475568 0.99785734] [0.39569993 0.52068569 0.16455037 0.34453659] [0.00440325 0.15677663 0.48420754 0.883464 ] [0.72854331 0.96857459 0.79689154 0.61125688]] Decompose the matrix. Singular values: [2.84389866 0.97035341 0.75987796 0.26901712 0. 0. 0. ] Left singular vectors U: [[-0.45781585 0.35939141 0.5708186 0.12066523 -0.25849164 -0.50401444] [-0.3236936 -0.55366459 0.32257238 0.33637055 0.60859986 0.03295606] [-0.53219811 0.25883391 0.12042728 -0.47056907 0.11438448 0.63304691] [-0.24752732 -0.23715137 -0.0766715 0.54618427 -0.63156902 0.4235732 ] [-0.27116053 0.52888715 -0.53408779 0.48177456 0.35637731 -0.04887811] [-0.51729535 -0.40166648 -0.5142783 -0.34703822 -0.15433811 -0.40290399]] Right singular vectors V: [[-0.59601763 -0.25748794 0.70463554 -0.28627209] [-0.38620782 -0.70954966 -0.41655634 0.41696956] [-0.37455547 0.1131316 -0.56924923 -0.72309388] [-0.5960828 0.64609634 -0.07697332 0.47044651]] Product U * S * V should equal A: [[0.9825534 0.0882425 0.25673196 0.9832903 ] [0.83381316 0.67235694 0.07905347 0.22531269] [0.93813307 0.31541779 0.63475568 0.99785734] [0.39569993 0.52068569 0.16455037 0.34453659] [0.00440325 0.15677663 0.48420754 0.883464 ] [0.72854331 0.96857459 0.79689154 0.61125688]] linpack_d_test(): Normal end of execution. Wed Oct 8 08:24:58 2025