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Popular solver with an API (C, C++, Java, .Net, Python, Matlab and R). Free for academics. Excel Solver Function: A nonlinear solver adjusted to spreadsheets in which function evaluations are based on the recalculating cells. Basic version available as a standard add-on for Excel. GAMS: A high-level modeling system for mathematical optimization ...
Consider an example from the expression language found in Microsoft_excel. Excel can calculate a cell's value dynamically by typing an expression such as "=SUM(C5:C10)", which performs the arithmetic sum of those 6 cells. The expression language in Ignition functions similarly. It is used to define dynamic values for tags and component properties.
Given a current cell as a parameter; Mark the current cell as visited; While the current cell has any unvisited neighbour cells Choose one of the unvisited neighbours; Remove the wall between the current cell and the chosen cell; Invoke the routine recursively for the chosen cell; which is invoked once for any initial cell in the area.
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
Moreover, the final row and the final column give the marginal probability distribution for A and the marginal probability distribution for B respectively. For example, for A the first of these cells gives the sum of the probabilities for A being red, regardless of which possibility for B in the column above the cell occurs, as 2 / 3 .
For example, suppose P(L = red) = 0.2, P(L = yellow) = 0.1, and P(L = green) = 0.7. Multiplying each column in the conditional distribution by the probability of that column occurring results in the joint probability distribution of H and L, given in the central 2×3 block of entries. (Note that the cells in this 2×3 block add up to 1).
Relational databases are very well suited to flat data layouts, where relationships between data are only one or two levels deep. For example, an accounting database might need to look up all the line items for all the invoices for a given customer, a three-join query. Graph databases are aimed at datasets that contain many more links.
Hilbert matrix — example of a matrix which is extremely ill-conditioned (and thus difficult to handle) Wilkinson matrix — example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues; Convergent matrix — square matrix whose successive powers approach the zero matrix; Algorithms for matrix multiplication: