Cholesky XLL Help

Function References

Excel Functions
Cholesky Add-In Function reference.

 

Available Functions

Excel® Add-Ins are still the most efficient and powerful way to incorporate algorithms into Excel®.

Loading the Add-In

To load this library you can either double click on the Xll. This will start Excel® if it wasn’t already running, and register the XLL. Once you quit Excel® the Add-In will be unloaded. 
To persist the Add-In so that it is available during future Excel® sessions, you must call the Add-In manager. Use the menu commands [Tools and then Add-Ins].  The name of the Add-In should appear in the list on the left hand side if you have already loaded the XLL in a previous session. If this is the case activate the add-in by clicking on the checkbox. If you cannot see the Add-In name displayed in the list, click on Browse to select the file.

Calling the Functions

As with any function available from Excel®, you can call the algorithms in this Add-In by typing = followed by the name of the function in a cell or range of cells.

A friendlier approach is to load the function via the Function Wizard. To access the function wizard from the menu commands call [Insert-and then Function]. You can also invoke the wizard from the Toolbar by clicking on the  symbol.

 

Cholesky

Description

The Cholesky Function computes the Cholesky coefficients of the input matrix.

 

Syntax

Cholesky(    Symmetric Pos. Def. Matrix to Decompose , 
Return Type, 
Activation Key
)

Arguments

Input Matrix:

Excel® range containing your original matrix. The matrix must be symmetric positive definite.

Return Type:

Code Description 

0 (Default) Lower Cholesky Matrix.
1 Upper Cholesky Matrix.
2 Lower Cholesky Inverse.
3 Upper Cholesky Inverse. 

Activation Key

Activation control. Either 0 (IDLE) or 1 (ACTIVE). This key is due to the Automatic recalculation
feature in Excel® which sends an empty matrix when using the function wizard or DDE hotlinks. 

 

Return Type

The function returns either an upper or lower triangular matrix or range of coefficients (or inverse coefficients). 
You must therefore select a range as an output field in order to display results.

If you have already typed the function in a single cell, you can easily expand the result by following this sequence:

 

1)     Select the cell where you entered the function.

2)     Press shift + right or down arrow, extending the cell will the arrow keys (or mouse). The formula must be in the upper left hand corner.

3)     Once you have selected the whole range to display, hit the F2 key {edit} and then press simultaneously on: Shift + Ctrl + Enter.

 

Validation

If P is a symmetric positive definite matrix C is the Cholesky decomposition of P, and C’ is the Transpose of C., you can then confirm the results by simply multiplying the resulting matrix by its transpose

 

P=C*C^T

 

Further details regarding the application of Cholesky factorization are available in the application section.