CxMatrixRank
Advanced Analysis Library Only
AnalysisLibErrType CxMatrixRank (void *inputMatrix, ssize_t numberOfRows, ssize_t numberOfColumns, double tolerance, ssize_t *rank);
Purpose
Calculates the rank of the complex input matrix. The input matrix can be square or rectangular.
The maximum number of linearly independent rows or columns of the matrix defines the rank of a matrix. The rank is always less than or equal to the minimum of the number of rows and columns of the matrix. If the rank equals this minimum value, the matrix is a full-rank matrix. Otherwise, it is a rank-deficient matrix.
The rank of a matrix can be calculated in a number of ways. CxMatrixRank first calculates the singular values of the input matrix and then calculates the rank as the number of singular values of the input matrix that are larger than the input tolerance.
You must specify the input tolerance as a positive number close to machine precision. If the matrix in your application is a full-rank matrix, any small value of tolerance gives the same rank. If the matrix in your application is a rank-deficient matrix, different values of tolerance can result in different values of rank.
Parameters
| Input | ||
| Name | Type | Description |
| inputMatrix | void * | Input complex matrix. This matrix must be an array of ComplexNum. The following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum; |
| numberOfRows | ssize_t | The number of rows in inputMatrix. |
| numberOfColumns | ssize_t | The number of columns in inputMatrix. |
| tolerance | double | Tolerance value. Matrix rank is the number of singular values in the input matrix that are larger than the tolerance. Set tolerance close to eps, which is the smallest possible double-precision, floating-point number. |
| Output | ||
| Name | Type | Description |
| rank | ssize_t | The rank of inputMatrix. |
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