Shareware Super Platinum 8

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Text File | 1988-06-13 | 16.9 KB | 533 lines

6. MATRICES and A SET OF LINEAR EQUATIONS This feature of the program allows the user to solve a set of linear equations with up to 70 unknown, to invert a square matrix and to multiply two matrices. Each matrix can be up to the size of 70x70. NOTE: To invert a matrix or to solve a set or linear equations, this program uses the Lotus INVERT command. Therefore any matrix that can't be inverted by LOTUS 1-2-3, can't be inverted by this program. Integration Differentiation Curve_fit Root_find Matrices Help Integration of functions and data [ESC] - Previous menu Press <M> to get the next menu: Invert_square_matrix Multiply_matrices Linear_equations_solver 6.1 <I>nvert_square_matrix Press <I> to get the next menu: Retrieve Edit Clear Invert Data_save Help 6.1A <R>etrieve Retrieve a spreadsheet matrix file (*.WK1), the matrix file includes the matrix as a square range starting at the A1 cell: Press <R> to get the next prompt: Input the file name - MATRIX Type the file name and press ENTER to get the next screen: ____________________________________________________________________________ Retrieve Edit Clear Invert Data_save Help Retrieve a spreadsheet which include a matrix (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 1 1 8 9 1 2 2 7 10 2 3 3 6 3 7 4 4 5 4 5 5 6 7 8 9 10 11 12 13 14 ____________________________________________________________________________ The program combines the matrix file and puts it at the upper corner at the cell GA1. 6.1B <E>dit Press <E> to get into the EDIT mode. The program is now in the Lotus EDIT mode. Type the numbers in the cells. Use the cursor keys to move through the cells, press the ENTER key only after you have finished inserting the numbers or if you don't want to change anything. The ENTER key is used ONLY to finish the EDIT mode and to get back to the menu. **** WARNING **** Since the program is now in the EDIT mode the Lotus keys are operative, however the user is strongly advised to use ONLY the UP, PGUP, DOWN and PGDN keys to scroll between the lines, the program doesn't allow scrolling to the sides by hiding all the columns except the current column. Trying to unhide the columns MAY destroy the program code. For example: if by mistake you have pressed the "/" key press ESC to get back to the READY mode and then press F2 to enter EDIT mode or just continue to type or press ENTER key to exit. 6.1C <I>nvert Press <I> to get the next screen: ____________________________________________________________________________ Retrieve Edit Clear Invert Data_save Help Retrieve a spreadsheet which include a matrix (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 160 0.1064814815 -0.2314814815 -0.412037037 0.6481481481 161 0.4814814815 -0.4814814815 -0.037037037 0.1481481481 162 -0.2916666667 0.4166666667 0.0416666667 -0.1666666667 163 -0.3333333333 0.3333333333 0.3333333333 -0.3333333333 164 165 166 167 168 169 170 171 171 173 ____________________________________________________________________________ The square matrix (4x4) is the inversion of the matrix at GA1. The program stores the inverted matrix starting in the cell GA160. 6.2 <M>ultiply_matrices Press <M> to get the next menu: Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Multiply Data_save Help 6.2A <R>etrieve Retrieve a spreadsheet matrix file (*.WK1), the matrix file includes the two matrices the first matrix starts at the A1 cell and the second matrix starts at the A80 cell. Press <R> to get the next prompt: Input the file name - MATRIX Type the file name and press ENTER to get the next screen: ____________________________________________________________________________ Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Multiply Data_save Help Retrieve a spreadsheet which includes the two matrices (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 1 1 8 9 1 2 2 7 10 2 3 3 6 3 7 4 4 5 4 5 5 6 7 8 9 10 11 12 13 14 ____________________________________________________________________________ The program combines the matrix file and puts it at the upper corner at the cell GA1 so that the second matrix is in the GA1 cell. To see or to edit the two matrices use the following options: <1>st_matrix_edit Press <1> to get the next screen and to enter the EDIT mode for the first matrix. ____________________________________________________________________________ GA1: 1 EDIT 1 A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 1 1 8 9 1 2 2 7 10 2 3 3 6 3 7 4 4 5 4 5 5 6 7 8 9 10 11 12 13 14 ____________________________________________________________________________ The program is now in the Lotus EDIT mode. Type the numbers in the cells. Use the cursor keys to move through the cells, press the ENTER key only after you have finished inserting the numbers or if you don't want to change anything. The ENTER key is used ONLY to finish the EDIT mode and to get back to the menu. **** WARNING **** Since the program is now in the EDIT mode the Lotus keys are operative, however the user is strongly advised to use ONLY the UP, PGUP, DOWN and PGDN keys to scroll between the lines, the program doesn't allow scrolling to the sides by hiding all the columns except the current column. Trying to unhide the columns MAY destroy the program code. For example: if by mistake you have pressed the "/" key press ESC to get back to the READY mode and then press F2 to enter EDIT mode or just continue to type or press ENTER key to exit. <2>nd_matrix_edit Press <2> to get the next screen and to enter the EDIT mode for the second matrix. ____________________________________________________________________________ GA80: 1 EDIT 1 A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 80 1 5 81 2 5 82 3 4 83 4 0 84 85 86 87 88 89 90 91 92 93 ____________________________________________________________________________ In this case the second matrix is a 4x2 matrix therefore the multiplication of a 4x4 matrix by 4x2 matrix is a 4x2 matrix. The program stores the second matrix at the GA80 cell. <M>ultiply Press <M> to get the resulted matrix and the next screen: ____________________________________________________________________________ Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Multiply Data_save Help Retrieve a spreadsheet which includes the two matrices (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 240 48 81 241 54 85 242 52 57 243 46 61 244 245 246 247 248 249 250 251 252 253 ____________________________________________________________________________ The program prints the result of the multiplication at the GA240 cell. 6.3 <L>inear_equations_solver A set of linear equations can be written in matrix notation, for example let's look on a set of four linear equations with the 4 unknown W, X, Y and Z. W+8X+ 9Y+ Z=47 2W+7X+10Y+2Z=57 3W+6X+ 3Y+7Z=43 4W+5X+ 4Y+5Z=44 can be rewritten in matrix language as: | 1 8 9 Z | | W | | 47 | | 2 7 10 2 |.| X | = | 57 | | 3 6 3 7 | | Y | | 43 | | 4 5 4 5 | | Z | | 44 | The 4X4 matrix is called the 1st_matrix and the 4x1 matrix (vector) is called the 2nd_matrix. Press <L> to get the next menu: Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Solve Data_save Help 6.3A <R>etrieve Retrieve a spreadsheet matrix file (*.WK1), the matrix file includes the two matrices the first matrix starts at the A1 cell and the second matrix starts at the A80 cell. Press <R> to get the next prompt: Input the file name - LINEAR Type the file name and press ENTER to get the next screen: ____________________________________________________________________________ Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Solve Data_save Help Retrieve a spreadsheet which includes the two matrices (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 1 1 8 9 1 2 2 7 10 2 3 3 6 3 7 4 4 5 4 5 5 6 7 8 9 10 11 12 13 14 ____________________________________________________________________________ The program combines the matrix file and puts it at the upper corner at the cell GA1 so that the second matrix is in the GA1 cell. To see or to edit the two matrices use the following options: <1>st_matrix_edit Press <1> to get the next screen and to enter the EDIT mode for the first matrix. ____________________________________________________________________________ GA1: 1 EDIT 1 A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 1 1 8 9 1 2 2 7 10 2 3 3 6 3 7 4 4 5 4 5 5 6 7 8 9 10 11 12 13 14 ____________________________________________________________________________ The program is now in the Lotus EDIT mode. Type the numbers in the cells. Use the cursor keys to move through the cells, press the ENTER key only after you have finished inserting the numbers or if you dont want to change anything. The ENTER key is used ONLY to finish the EDIT mode and to get back to the menu. **** WARNING **** Since the program is now in the EDIT mode the Lotus keys are operative, however the user is strongly advised to use ONLY the UP, PGUP, DOWN and PGDN keys to scroll between the lines, the program doesn't allow scrolling to the sides by hiding all the columns except the current column. Trying to unhide the columns MAY destroy the program code. For example: if by mistake you have pressed the "/" key press ESC to get back to the READY mode and then press F2 to enter EDIT mode or just continue to type or press ENTER key to exit. <2>nd_matrix_edit Press <2> to get the next screen and to enter the EDIT mode for the second matrix. ____________________________________________________________________________ GA80: 1 EDIT 1 A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 80 47 81 57 82 43 83 44 84 85 86 87 88 89 90 91 92 93 ____________________________________________________________________________ <S>olve Press <s> to get the resulted matrix (solution) and the next screen: ____________________________________________________________________________ Retrieve 1st_matrix_edit 2nd_matrix_edit Clear Solve Data_save Help Retrieve a spreadsheet which includes the two matrices (see help) A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== GA GB GC GD GE 240 4 241 3 242 2 243 1 244 245 246 247 248 249 250 251 252 253 ____________________________________________________________________________ The program prints the result of the multiplication at the GA240 cell.