SVD
Advanced Analysis Library Only
AnalysisLibErrType SVD (void *inputMatrix, ssize_t numberOfRows, ssize_t numberOfColumns, void *uMatrix, double singularValuesVector[], void *vMatrix);
Purpose
 |
Note The function has been superseded by SVDEx. |
Calculates the singular value decomposition (SVD) factorization of the real 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 = USVT
| where | uMatrix is an orthogonal matrix of dimensions n-by-min(n, m) |
| vMatrix 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) | |
| n is number of rows | |
| m is the number of columns |
The diagonal elements of singularValuesVector are called the singular values of inputMatrix and are arranged in descending order. The columns of the output matrices UMatrix and VMatrix are the corresponding singular vectors.
The SVD 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 * | The input matrix to decompose. The input matrix can be either square or rectangular. |
| numberOfRows | ssize_t | The number of rows in inputMatrix. |
| numberOfColumns | ssize_t | The number of columns in inputMatrix. |
| Output | ||
| Name | Type | Description |
| uMatrix | void * | The result orthogonal matrix U that SVD factorization generates, whose size is n*min(n,m). |
| singularValuesVector | double [] | Array that contains the singular values of inputMatrix, in descending order. |
| vMatrix | void * | The result orthogonal matrix V that matrix SVD factorization generates, whose size if m*min(n,m). |
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