CxConditionNumber
Advanced Analysis Library Only
AnalysisLibErrType CxConditionNumber (void *inputMatrix, ssize_t numberOfRows, ssize_t numberOfColumns, int normType, double *conditionNumber);
Purpose
Calculates the condition number of a complex input matrix. The normType parameter indicates what type of norm to use to calculate the condition number. The input matrix can be either square or rectangular when normType is 2-norm.
The following formula defines the condition number c of a matrix A:
is the p-norm of the matrix A
The normType value defines the p-norm behavior. For a 2-norm normType, c is the ratio of the largest singular value of A to the smallest singular value of A.
The condition number of a matrix indicates how near to singular the matrix is. A matrix with a large condition number is nearly singular, and a matrix with a condition number close to one is far from singular. The condition number of a matrix is always greater than or equal to one, and it can help assess the accuracy of a solution to a linear system of equations and matrix inversion.
Parameters
| Input | |||||||||||||||||
| Name | Type | Description | |||||||||||||||
| inputMatrix | void * | Input complex, square matrix. If normType is 2-norm, the matrix can be square or rectangular; otherwise, it must be square. This matrix must be an array of ComplexNum. The following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum; |
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| numberOfRows | ssize_t | Number of rows in inputMatrix. | |||||||||||||||
| numberOfColumns | ssize_t | The number of columns in inputMatrix. | |||||||||||||||
| normType | int | Type of p-norm function to use to calculate the condition number. The following table shows valid norm type values.
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| Output | |||||||||||||||||
| Name | Type | Description | |||||||||||||||
| conditionNumber | double | Complex condition number of the matrix. | |||||||||||||||
Return Value
| Name | Type | Description |
| status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants. |
Additional Information
Library: Advanced Analysis Library
Include file: analysis.h
LabWindows/CVI compatibility: LabWindows/CVI 5.0 and later