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The Nial example of the inner product of two arrays can be implemented using the native matrix multiplication operator. If a is a row vector of size [1 n] and b is a corresponding column vector of size [n 1]. a * b; By contrast, the entrywise product is implemented as: a .* b;
VBA can, however, control one application from another using OLE Automation. For example, VBA can automatically create a Microsoft Word report from Microsoft Excel data that Excel collects automatically from polled sensors. VBA can use, but not create, ActiveX/COM DLLs, and later versions add support for class modules.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
The fields that would be created will be visible on the right hand side of the worksheet. By default, the pivot table layout design will appear below this list. Pivot Table fields are the building blocks of pivot tables. Each of the fields from the list can be dragged on to this layout, which has four options: Filters; Columns; Rows; Values
[Here = is Hooshmand's name for the linear approximation to the natural tetration function.] The proof is much the same as before; the recursion equation ensures that f ′ ( − 1 + ) = f ′ ( 0 + ) , {\displaystyle f^{\prime }(-1^{+})=f^{\prime }(0^{+}),} and then the convexity condition implies that f {\displaystyle f} is linear on (−1, 0) .
For example, multiple e-mail addresses in the "To" field in some e-mail clients have to be delimited by a semicolon. In Microsoft Excel , the semicolon is used as a list separator, especially in cases where the decimal separator is a comma, such as 0,32; 3,14; 4,50 , instead of 0.32, 3.14, 4.50 .
In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams).