3, 3, 1 1.00, 0.20, 0.30, 1.10 0.30, 1.00, 0.10, 2.20 1.14, -2.78, 0.31, -4.73 Unused information follows. Appendix B's TestCase for MUse.exe: Linear Depencence Example vsn 0.50 ~Page 21: 4 equations, 3 unknowns, 1 output... [A:Y] The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- 3, 3, 4 0.30, 1.00, 0.10, 2.20, 0.0, 1.0, 0.0 1.00, 0.20, 0.30, 1.10, 1.0, 0.0, 0.0 0.10, 0.20, 1.00, -0.50, 0.0, 0.0, 1.0 Unused information follows. Appendix A's TestCase for M1stUse.exe Example vsn 0.50 ~Page 3: 3 equations, 3 unknowns, 4 outputs... [A:Y] Opening example - but rows 1 & 2 are interchanged (including I) to show row swapping. - Row swapping restores the original example and the solution proceeds. The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- Test datasets for: M1stUse.bas/.exe version 0.50 2011.09.09 Jeff Setterholm (A simple matrix solver for kEquations=nUnknowns.) and: MUse.bas /.exe version 0.50 (An OverWriting matrix solver.) ^Both these programs relate to Hat.pdf version 0.50 Only the top dataset is read and used. Note: Trailing commas will cause data misreads. The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y (-or-) =Z -------------------------------------------------------------- 3, 3, 4 1.00, 0.20, 0.30, 1.10, 1.0, 0.0, 0.0 0.30, 1.00, 0.10, 2.20, 0.0, 1.0, 0.0 0.10, 0.20, 1.00, -0.50, 0.0, 0.0, 1.0 Unused information follows. Example vsn 0.50 ~Page 3: 3 equations, 3 unknowns, 4 outputs... [A:Y] Opening example The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- 3, 3, 4 1.00, 0.20, 0.30, 1.10, 1.0, 0.0, 0.0 0.30, 1.00, 0.10, 2.20, 0.0, 1.0, 0.0 1.14, -2.78, 0.31, -4.73, 0.0, 0.0, 1.0 Unused information follows. Example vsn 0.50 ~Page 21: 3 equations, 3 unknowns, 4 outputs... [A:Y] Linear Depencence (including I) The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- 3, 3, 1 1.00, 0.20, 0.30, 1.10 0.30, 1.00, 0.10, 2.20 0.10, 0.20, 1.00, -0.50 Unused information follows. Example vsn 0.50 ~Page 3: 3 equations, 3 unknowns, 1 outputs... [A:Y] Opening example - for the OverWriter (not including I) The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- 12, 12, 1 1., 1. , 1. , 0.20, 0.20, 0.20, 0.30, 0.30, 0.30 , 0.06, 0.06, 0.06 , 1.1 1., 0.3, 0.09, 1. , 0.3 , 0.09, 0.1 , 0.03, 0.009, 0.1 , 0.03, 0.009, 2.2 1., 0.1, 0.01, 0.2 , 0.02, 0.002, 1. , 0.1 , 0.01 , 0.2 , 0.02, 0.002,-0.5 1., -1. , 1. , 0.3 , -0.3 , 0.3 , 0.2 , -0.2 , 0.2 , 0.06, -0.06, 0.06 ,-0.6 1., 0.5, 0.25, -1. , -0.5 , -0.25, -0.3 , -0.15, -0.075, 0.3 , 0.15, 0.075,-1.2 1., -1. , 1. , 0. , 0. , 0. , 2. , -2. , 2. , 0. , 0. , 0. ,-3.0 1., -1. , 1. , 0.5 , -0.5 , 0.5 , -2. , 2. , -2. ,-1. , 1. , -1. , 2.0 1., -1. , 1. , 0.5 , -0.5 , 0.5 , 2. , -2. , 2. , 1. , -1. , 1. ,-2.0 1., 1. , 1. , -0.5 , -0.5 , -0.5 , -2. , -2. , -2. , 1. , 1. , 1. , 2.0 1., 0. , 0. , 0.5 , 0. , 0. , -2. , 0. , 0. ,-1. , 0. , 0. , 3.0 1., 1. , 1. , -0.5 , -0.5 , -0.5 , 2. , 2. , 2. ,-1. , -1. , -1. ,-2.0 1., 1. , 1. , 0.5 , 0.5 , 0.5 , -2. , -2. , -2. ,-1. , -1. , -1. , 4.0 Unused information follows. X(1)^1 X(2)^1 X(3)^1 Y X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3: Y ^0^0^0 ^1^0^0 ^2^0^0 ^0^1^0 ^1^1^0 ^2^1^0 ^0^0^1 ^1^0^1 ^2^0^1 ^0^1^1 ^1^1^1 ^2^1^1 Example vsn 0.50 ~Page 12: 12 of the 27 equations, 12 unknowns, 1 outputs... [A:Y] These are some of the polynomial partial derivatives and outputs of a testcase polynomial. The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Y -------------------------------------------------------------- 5 3 1 1.0, 0.2, 0.3, 1.1 0.3, 1.0, 0.1, 2.2 0.1, 0.2, 1.0, -0.5 -1.0, 0.3, 0.2, -0.6 0.5, -1.0, -0.3, -1.2 Unused information follows. Example vsn 0.50 ~Page 6: 5 equations, 3 unknowns, 1 outputs... [B:Z] More equations than unknowns The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Z -------------------------------------------------------------- 27, 3, 1 1.0 , 0.2 , 0.3 , 1.1 0.3 , 1.0 , 0.1 , 2.2 0.1 , 0.2 , 1.0 , -0.5 -1.0 , 0.3 , 0.2 , -0.6 0.5 , -1.0 , -0.3 , -1.19 -1.00, 0.00, 2.00, -3.00 -1.00, 0.50, -2.00, 2.00 -1.00, 0.50, 0.00, 0.00 -1.00, 0.50, 2.00, -2.00 0.00, -0.50, -2.00, 1.00 0.00, -0.50, 0.00, -1.00 0.00, -0.50, 2.00, -3.00 0.00, 0.00, -2.00, 2.00 0.00, 0.00, 0.00, 0.00 0.00, 0.00, 2.00, -2.00 0.00, 0.50, -2.00, 3.00 0.00, 0.50, 0.00, 1.00 0.00, 0.50, 2.00, -1.00 1.00, -0.50, -2.00, 2.00 1.00, -0.50, 0.00, 0.00 1.00, -0.50, 2.00, -2.00 1.00, 0.00, -2.00, 3.00 1.00, 0.00, 0.00, 1.00 1.00, 0.00, 2.00, -1.00 1.00, 0.50, -2.00, 4.00 1.00, 0.50, 0.00, 2.00 1.00, 0.50, 2.00, 0.00 Unused information follows. X(1) X(2) X(3) Y Example vsn 0.50 ~Page 11: 27 equations, 3 unknowns, 1 outputs... [B:Z] equations>unknowns; dataset with Y(5) noise. The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Z ------------------------------------------------------------------------------------------ 27, 12, 1 1. , 1. , 1. , 0.20, 0.20, 0.20 , 0.30, 0.30, 0.30 , 0.06, 0.06, 0.06 , 1.1 1. , 0.3 , 0.09, 1. , 0.3 , 0.09 , 0.1 , 0.03, 0.009, 0.1 , 0.03, 0.009, 2.2 1. , 0.1 , 0.01, 0.2 , 0.02, 0.002, 1. , 0.1 , 0.01 , 0.2 , 0.02, 0.002,-0.5 1. , -1. , 1. , 0.3 , -0.3 , 0.3 , 0.2 , -0.2 , 0.2 , 0.06, -0.06, 0.06 ,-0.6 1. , 0.5 , 0.25, -1. , -0.5 , -0.25 ,-0.3 , -0.15, -0.075, 0.3 , 0.15, 0.075,-1.19 1. , -1. , 1. , 0. , 0. , 0. , 2. , -2. , 2. , 0. , 0. , 0. ,-3.0 1. , -1. , 1. , 0.5 , -0.5 , 0.5 ,-2. , 2. , -2. ,-1. , 1. , -1. , 2.0 1. , -1. , 1. , 0.5 , -0.5 , 0.5 , 0. , 0. , 0. , 0. , 0. , 0. , 0.0 1. , -1. , 1. , 0.5 , -0.5 , 0.5 , 2. , -2. , 2. , 1. , -1. , 1. ,-2.0 1. , 0. , 0. , -0.5 , 0. , 0. ,-2. , 0. , 0. , 1. , 0. , 0. , 1.0 1. , 0. , 0. , -0.5 , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,-1.0 1. , 0. , 0. , -0.5 , 0. , 0. , 2. , 0. , 0. ,-1. , 0. , 0. ,-3.0 1. , 0. , 0. , 0. , 0. , 0. ,-2. , 0. , 0. , 0. , 0. , 0. , 2.0 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.0 1. , 0. , 0. , 0. , 0. , 0. , 2. , 0. , 0. , 0. , 0. , 0. ,-2.0 1. , 0. , 0. , 0.5 , 0. , 0. ,-2. , 0. , 0. ,-1. , 0. , 0. , 3.0 1. , 0. , 0. , 0.5 , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1.0 1. , 0. , 0. , 0.5 , 0. , 0. , 2. , 0. , 0. , 1. , 0. , 0. ,-1.0 1. , 1. , 1. , -0.5 , -0.5 , -0.5 ,-2. , -2. , -2. , 1. , 1. , 1. , 2.0 1. , 1. , 1. , -0.5 , -0.5 , -0.5 , 0. , 0. , 0. , 0. , 0. , 0. , 0.0 1. , 1. , 1. , -0.5 , -0.5 , -0.5 , 2. , 2. , 2. ,-1. , -1. , -1. ,-2.0 1. , 1. , 1. , 0. , 0. , 0. ,-2. , -2. , -2. , 0. , 0. , 0. , 3.0 1. , 1. , 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1.0 1. , 1. , 1. , 0. , 0. , 0. , 2. , 2. , 2. , 0. , 0. , 0. ,-1.0 1. , 1. , 1. , 0.5 , 0.5 , 0.5 ,-2. , -2. , -2. ,-1. , -1. , -1. , 4.0 1. , 1. , 1. , 0.5 , 0.5 , 0.5 , 0. , 0. , 0. , 0. , 0. , 0. , 2.0 1. , 1. , 1. , 0.5 , 0.5 , 0.5 , 2. , 2. , 2. , 1. , 1. , 1. , 0.0 Unused information follows. X(1)^1 X(2)^1 X(3)^1 Z These are exactly the same as the input data columns. X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3 X1X2X3: Z ^0^0^0 ^1^0^0 ^2^0^0 ^0^1^0 ^1^1^0 ^2^1^0 ^0^0^1 ^1^0^1 ^2^0^1 ^0^1^1 ^1^1^1 ^2^1^1 Example vsn 0.50 ~Page 12: 27 equations, 12 unknowns, 1 outputs... [C:Z] These are the polynomial partial derivatives and output. Dataset Y(5) has noise. The testcase polynomial is: 1.0*X(1) + 2.0*X(2) - 1.0*X(3) = Z ------------------------------------------------------------------------------------------