15 December 2024 5:45:13.098 PM rref2_test(): Fortran90 version Test rref(), which analyzes matrices using the reduced row echelon form (RREF) is_rref_test(): is_rref() reports if a matrix is in reduced row echelon format. Matrix A0: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 0.00000 9.00000 4.00000 2: 0.00000 0.00000 1.00000 0.00000 8.00000 3: 0.00000 0.00000 0.00000 0.00000 0.00000 4: 0.00000 0.00000 0.00000 1.00000 0.00000 is_rref(A0) = F Matrix A1: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 0.00000 9.00000 4.00000 2: 0.00000 0.00000 0.00000 1.00000 0.00000 3: 0.00000 0.00000 1.00000 0.00000 8.00000 4: 0.00000 0.00000 0.00000 1.00000 0.00000 is_rref(A1) = F Matrix A2: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 0.00000 9.00000 4.00000 2: 0.00000 1.00000 0.00000 2.00000 8.00000 3: 0.00000 0.00000 3.00000 0.00000 0.00000 4: 0.00000 0.00000 0.00000 0.00000 0.00000 is_rref(A2) = F Matrix A3: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 3.00000 9.00000 4.00000 2: 0.00000 1.00000 0.00000 2.00000 8.00000 3: 0.00000 0.00000 1.00000 0.00000 0.00000 4: 0.00000 0.00000 0.00000 0.00000 0.00000 is_rref(A3) = F Matrix A4: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 3.00000 0.00000 4.00000 2: 0.00000 1.00000 2.00000 0.00000 8.00000 3: 0.00000 0.00000 0.00000 1.00000 0.00000 4: 0.00000 0.00000 0.00000 0.00000 0.00000 is_rref(A4) = T rref_compute_test(): rref_compute() is a user-written code to compute the reduced row echelon form (RREF) of a matrix. Matrix A: Col 1 2 3 4 5 Row 1: 1.00000 3.00000 0.00000 2.00000 6.00000 2: -2.00000 -6.00000 0.00000 -2.00000 -8.00000 3: 3.00000 9.00000 0.00000 0.00000 6.00000 4: -1.00000 -3.00000 0.00000 1.00000 0.00000 Col 6 7 Row 1: 3.00000 1.00000 2: 3.00000 1.00000 3: 6.00000 2.00000 4: 9.00000 3.00000 rref_compute(A): Col 1 2 3 4 5 Row 1: 1.00000 3.00000 0.00000 0.00000 2.00000 2: 0.00000 0.00000 0.00000 1.00000 2.00000 3: 0.00000 0.00000 0.00000 0.00000 0.00000 4: 0.00000 0.00000 0.00000 0.00000 0.00000 Col 6 7 Row 1: 0.00000 0.00000 2: 0.00000 0.277556E-16 3: 1.00000 0.333333 4: 0.00000 0.00000 Column indices 1: 1 2: 4 3: 6 4: 0 5: 0 6: 0 7: 0 rref_columns_test(): rref_columns() uses the reduced row echelon form (RREF) of a matrix to find the linearly independent columns. Matrix A: Col 1 2 3 4 Row 1: 1.00000 2.00000 3.00000 1.00000 2: 2.00000 4.00000 9.00000 3.00000 3: 3.00000 6.00000 0.00000 0.00000 4: 4.00000 8.00000 0.00000 2.00000 5: 5.00000 10.0000 6.00000 6.00000 6: 6.00000 12.0000 6.00000 3.00000 7: 7.00000 14.0000 2.00000 1.00000 Number of independent columns is 3 Independent column indices 1: 1 2: 3 3: 4 Independent columns: Col 1 2 3 Row 1: 1.00000 3.00000 1.00000 2: 2.00000 9.00000 3.00000 3: 3.00000 0.00000 0.00000 4: 4.00000 0.00000 2.00000 5: 5.00000 6.00000 6.00000 6: 6.00000 6.00000 3.00000 7: 7.00000 2.00000 1.00000 rref_determinant_test(): rref_determinant() uses the reduced row echelon form of a square matrix to compute the determinant. matrix A: Col 1 2 3 4 Row 1: 5.00000 7.00000 6.00000 5.00000 2: 7.00000 10.0000 8.00000 7.00000 3: 6.00000 8.00000 10.0000 9.00000 4: 5.00000 7.00000 9.00000 10.0000 Estimated determinant of A = 1.00000 rref_inverse_test(): rref_inverse() uses the reduced row echelon form of a square matrix to compute its inverse. matrix A: Col 1 2 3 4 Row 1: 5.00000 7.00000 6.00000 5.00000 2: 7.00000 10.0000 8.00000 7.00000 3: 6.00000 8.00000 10.0000 9.00000 4: 5.00000 7.00000 9.00000 10.0000 Estimated inverse A_inv: Col 1 2 3 4 Row 1: 68.0000 -41.0000 -17.0000 10.0000 2: -41.0000 25.0000 10.0000 -6.00000 3: -17.0000 10.0000 5.00000 -3.00000 4: 10.0000 -6.00000 -3.00000 2.00000 Product A_inv * A: Col 1 2 3 4 Row 1: 1.00000 0.00000 -0.284217E-13 0.568434E-13 2: 0.00000 1.00000 0.284217E-13 0.00000 3: -0.142109E-13 -0.284217E-13 1.00000 -0.710543E-14 4: 0.710543E-14 0.213163E-13 0.710543E-14 1.00000 rref_rank_test(): rref_rank() uses the reduced row echelon form of a matrix to estimate its rank. matrix A: Col 1 2 3 4 5 Row 1: 1.00000 3.00000 0.00000 2.00000 6.00000 2: -2.00000 -6.00000 0.00000 -2.00000 -8.00000 3: 3.00000 9.00000 0.00000 0.00000 6.00000 4: -1.00000 -3.00000 0.00000 1.00000 0.00000 Col 6 7 Row 1: 3.00000 1.00000 2: 3.00000 1.00000 3: 6.00000 2.00000 4: 9.00000 3.00000 A has rank 3 rref_solve_test(): rref_solve() uses the reduced row echelon form of a square matrix to solve a linear system. matrix A: Col 1 2 3 4 Row 1: 5.00000 7.00000 6.00000 5.00000 2: 7.00000 10.0000 8.00000 7.00000 3: 6.00000 8.00000 10.0000 9.00000 4: 5.00000 7.00000 9.00000 10.0000 Right hand side b: Col 1 Row 1: 57.0000 2: 79.0000 3: 88.0000 4: 86.0000 Estimated solution: Col 1 Row 1: 1.00000 2: 2.00000 3: 3.00000 4: 4.00000 Product A * x: Col 1 Row 1: 57.0000 2: 79.0000 3: 88.0000 4: 86.0000 rref2_test(): Normal end of execution. 15 December 2024 5:45:13.099 PM