06 October 2025 6:33:38.646 PM r8ut_test(): Fortran90 version: Test r8ut(). R8GE_TO_R8UT_TEST R8GE_TO_R8UT converts an R8GE matrix to R8UT format. The random R8GE matrix: Col: 1 2 3 4 Row --- 1 0.522371 0.690521 0.194620 0.938203 2 0.965402 0.133151E-01 0.706768 0.376779 3 0.806618 0.182090 0.706528 0.687039 4 0.530517 0.834228 0.891047 0.144045 5 0.893859E-01 0.596928 0.658365 0.540423 The R8UT matrix Col: 1 2 3 4 Row --- 1 0.522371 0.690521 0.194620 0.938203 2 0.133151E-01 0.706768 0.376779 3 0.706528 0.687039 4 0.144045 5 R8UT_DET_TEST R8UT_DET computes the determinant of an R8UT matrix. The matrix A: Col: 1 2 3 4 5 Row --- 1 0.174638 0.857901 0.449588E-01 0.862897 0.787504 2 0.537101 0.387137 0.649404 0.958842 3 0.356574 0.316115 0.528092 4 0.964241 0.718352 5 0.505357 Determinant is 0.162978E-01 R8UT_INDICATOR_TEST R8UT_INDICATOR sets up an indicator matrix. Matrix rows M = 5 Matrix columns N = 4 The R8UT indicator matrix: Col: 1 2 3 4 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 22.0000 23.0000 24.0000 3 33.0000 34.0000 4 44.0000 5 R8UT_INVERSE_TEST R8UT_INVERSE computes the inverse of an R8UT matrix. The matrix A: Col: 1 2 3 4 5 Row --- 1 0.971062 0.329616 0.844118 0.630200 0.942916 2 0.779657 0.928033 0.172275 0.121893 3 0.542611 0.210094 0.680213 4 0.716007E-01 0.225487 5 0.709089 The inverse matrix B: Col: 1 2 3 4 5 Row --- 1 1.02980 -0.435369 -0.857404 -5.50052 1.27709 2 1.28262 -2.19367 3.35075 0.818334 3 1.84294 -5.40765 -0.482829E-01 4 13.9663 -4.44124 5 1.41026 The product C = A * B: Col: 1 2 3 4 5 Row --- 1 1.00000 0.00000 0.00000 0.00000 0.222045E-15 2 1.00000 -0.222045E-15 0.00000 -0.277556E-16 3 1.00000 0.00000 0.00000 4 1.00000 0.00000 5 1.00000 R8UT_MM_TEST R8UT_MM computes C = A * B for R8UT matrices. The matrix A: Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 1.00000 1.00000 1.00000 3 1.00000 1.00000 1.00000 4 1.00000 1.00000 5 1.00000 The product C = A * A Col: 1 2 3 4 5 Row --- 1 1.00000 2.00000 3.00000 4.00000 5.00000 2 1.00000 2.00000 3.00000 4.00000 3 1.00000 2.00000 3.00000 4 1.00000 2.00000 5 1.00000 R8UT_MTM_TEST R8UT_MTM computes C = A' * B for R8UT matrices. The matrix A: Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 1.00000 1.00000 1.00000 3 1.00000 1.00000 1.00000 4 1.00000 1.00000 5 1.00000 The product C = A' * A Col: 1 2 3 4 5 Row --- 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 2.00000 2.00000 2.00000 2.00000 3 1.00000 2.00000 3.00000 3.00000 3.00000 4 1.00000 2.00000 3.00000 4.00000 4.00000 5 1.00000 2.00000 3.00000 4.00000 5.00000 R8UT_MTV_TEST R8UT_MTV computes A'*x for an R8UT matrix. The matrix A: Col: 1 2 3 4 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 22.0000 23.0000 24.0000 3 33.0000 34.0000 4 44.0000 5 The vector x 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 b = A'*x: 1 11.0000 2 56.0000 3 158.000 4 340.000 R8UT_MV_TEST R8UT_MV computes A*x for an R8UT matrix. The matrix A: Col: 1 2 3 4 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 22.0000 23.0000 24.0000 3 33.0000 34.0000 4 44.0000 5 The vector x 1 1.00000 2 2.00000 3 3.00000 4 4.00000 b = A*x: 1 130.000 2 209.000 3 235.000 4 176.000 5 0.00000 R8UT_PRINT_TEST R8UT_PRINT prints an R8UT matrix. Matrix rows M = 6 Matrix columns N = 4 The R8UT matrix: Col: 1 2 3 4 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 22.0000 23.0000 24.0000 3 33.0000 34.0000 4 44.0000 5 6 R8UT_PRINT_SOME_TEST R8UT_PRINT_SOME prints some of an R8UT matrix. Matrix rows M = 4 Matrix columns N = 6 Some of the matrix: Col: 4 5 6 Row --- 1 14.0000 15.0000 16.0000 2 24.0000 25.0000 26.0000 3 34.0000 35.0000 36.0000 R8UT_RANDOM_TEST R8UT_RANDOM randomizes an R8UT matrix. Matrix order M, N = 5 4 The matrix: Col: 1 2 3 4 Row --- 1 0.829074 0.755521E-01 0.630452 0.965045 2 0.502099 0.462503E-01 0.915424 3 0.539293 0.423865 4 0.411295 5 R8UT_SL_TEST R8UT_SL solves A*x=b for an upper triangular A. Matrix order N = 5 The upper triangular matrix: Col: 1 2 3 4 5 Row --- 1 1.00000 2.00000 3.00000 4.00000 5.00000 2 2.00000 3.00000 4.00000 5.00000 3 3.00000 4.00000 5.00000 4 4.00000 5.00000 5 5.00000 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 R8UT_SLT_TEST R8UT_SLT solves A'*x=b for an upper triangular A. Matrix order N = 5 The upper triangular matrix: Col: 1 2 3 4 5 Row --- 1 1.00000 2.00000 3.00000 4.00000 5.00000 2 2.00000 3.00000 4.00000 5.00000 3 3.00000 4.00000 5.00000 4 4.00000 5.00000 5 5.00000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 R8UT_TO_R8GE_TEST R8UT_TO_R8GE converts an R8UT matrix to R8GE format. The random R8UT matrix: Col: 1 2 3 4 Row --- 1 0.305063 0.931226 0.324197 0.608972 2 0.599088 0.520562 0.706147 3 0.641052 0.569294 4 0.353693 5 The R8GE matrix Col: 1 2 3 4 Row --- 1 0.305063 0.931226 0.324197 0.608972 2 0.00000 0.599088 0.520562 0.706147 3 0.00000 0.00000 0.641052 0.569294 4 0.00000 0.00000 0.00000 0.353693 5 0.00000 0.00000 0.00000 0.00000 R8UT_ZEROS_TEST R8UT_ZEROS zeros out a matrix in R8UT format. Matrix order M, N = 5 4 The matrix: Col: 1 2 3 4 Row --- 1 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 4 0.00000 5 R8UT_TEST Normal end of execution. 06 October 2025 6:33:38.647 PM