CxSVD
Advanced Analysis Library Only
AnalysisLibErrType CxSVD (void *inputMatrix, ssize_t numberOfRows, ssize_t numberOfColumns, void *uOrthogonalMatrix, NIComplexNumber singularValuesVector[], void *vOrthogonalMatrix);
Purpose
 |
Note The function has been superseded by CxSVDEx. |
Calculates the Singular Value Decomposition (SVD) factorization of the complex input matrix. The input matrix can be square or rectangular.
The following formula defines the SVD factorization of an n-by-m matrix A:
A = USVH
| where | uOrthogonalMatrix is an orthogonal matrix of dimensions n-by-min(n, m) |
| vOrthogonalMatrix is an orthogonal matrix of dimensions m-by-min(n, m) | |
| singularValuesVector is a diagonal matrix of dimensions min(n, m)-by-min(n, m) | |
| numberOfRows is the number of rows | |
| numberOfColumns is the number of columns |
VH represents the complex conjugate transpose of V. The diagonal elements of S are called the singular values of A and are arranged in descending order. CxSVD stores the diagonal elements of S in the output array.
The Singular Value Decomposition is an eigenvalue-like decomposition for rectangular matrices. You can use it to calculate the condition number of a matrix or to solve linear, least square problems. SVD is useful for ill-conditioned or rank-deficient problems because it can detect small singular values.
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. |
| Output | ||
| Name | Type | Description |
| uOrthogonalMatrix | void * | The numberOfRows-by-numberOfColumns orthogonal matrix that SVD factorization generates. The following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum; |
| singularValuesVector | NIComplexNumber [] | Array that contains the singular values of inputMatrix, in descending order. SThe following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum; |
| vOrthogonalMatrix | void * | The numberOfColumns-by-numberOfColumns orthogonal matrix that SVD factorization generates. The following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum; |
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