CMSIS-DSP  
CMSIS DSP Software Library
Functions
Matrix Inverse
Matrix Functions

Functions

arm_status arm_mat_inverse_f16 (const arm_matrix_instance_f16 *pSrc, arm_matrix_instance_f16 *pDst)
 Floating-point matrix inverse. More...
 
arm_status arm_mat_inverse_f32 (const arm_matrix_instance_f32 *pSrc, arm_matrix_instance_f32 *pDst)
 Floating-point matrix inverse. More...
 
arm_status arm_mat_inverse_f64 (const arm_matrix_instance_f64 *pSrc, arm_matrix_instance_f64 *pDst)
 Floating-point (64 bit) matrix inverse. More...
 
arm_status arm_mat_solve_lower_triangular_f16 (const arm_matrix_instance_f16 *lt, const arm_matrix_instance_f16 *a, arm_matrix_instance_f16 *dst)
 Solve LT . X = A where LT is a lower triangular matrix. More...
 
arm_status arm_mat_solve_lower_triangular_f32 (const arm_matrix_instance_f32 *lt, const arm_matrix_instance_f32 *a, arm_matrix_instance_f32 *dst)
 Solve LT . X = A where LT is a lower triangular matrix. More...
 
arm_status arm_mat_solve_lower_triangular_f64 (const arm_matrix_instance_f64 *lt, const arm_matrix_instance_f64 *a, arm_matrix_instance_f64 *dst)
 Solve LT . X = A where LT is a lower triangular matrix. More...
 
arm_status arm_mat_solve_upper_triangular_f16 (const arm_matrix_instance_f16 *ut, const arm_matrix_instance_f16 *a, arm_matrix_instance_f16 *dst)
 Solve UT . X = A where UT is an upper triangular matrix. More...
 
arm_status arm_mat_solve_upper_triangular_f32 (const arm_matrix_instance_f32 *ut, const arm_matrix_instance_f32 *a, arm_matrix_instance_f32 *dst)
 Solve UT . X = A where UT is an upper triangular matrix. More...
 
arm_status arm_mat_solve_upper_triangular_f64 (const arm_matrix_instance_f64 *ut, const arm_matrix_instance_f64 *a, arm_matrix_instance_f64 *dst)
 Solve UT . X = A where UT is an upper triangular matrix. More...
 

Description

Computes the inverse of a matrix.

The inverse is defined only if the input matrix is square and non-singular (the determinant is non-zero). The function checks that the input and output matrices are square and of the same size.

Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix inversion of floating-point matrices.

Algorithm
The Gauss-Jordan method is used to find the inverse. The algorithm performs a sequence of elementary row-operations until it reduces the input matrix to an identity matrix. Applying the same sequence of elementary row-operations to an identity matrix yields the inverse matrix. If the input matrix is singular, then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method

\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} & | & 1 & 0 & 0\\ a_{2,1} & a_{2,2} & a_{2,3} & | & 0 & 1 & 0\\ a_{3,1} & a_{3,2} & a_{3,3} & | & 0 & 0 & 1\\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 0 & 0 & | & x_{1,1} & x_{2,1} & x_{3,1} \\ 0 & 1 & 0 & | & x_{1,2} & x_{2,2} & x_{3,2} \\ 0 & 0 & 1 & | & x_{1,3} & x_{2,3} & x_{3,3} \\ \end{pmatrix} \]

Function Documentation

◆ arm_mat_inverse_f16()

arm_status arm_mat_inverse_f16 ( const arm_matrix_instance_f16 *  pSrc,
arm_matrix_instance_f16 *  pDst 
)
Parameters
[in]pSrcpoints to input matrix structure. The source matrix is modified by the function.
[out]pDstpoints to output matrix structure
Returns
execution status

◆ arm_mat_inverse_f32()

arm_status arm_mat_inverse_f32 ( const arm_matrix_instance_f32 *  pSrc,
arm_matrix_instance_f32 *  pDst 
)
Parameters
[in]pSrcpoints to input matrix structure. The source matrix is modified by the function.
[out]pDstpoints to output matrix structure
Returns
execution status

◆ arm_mat_inverse_f64()

arm_status arm_mat_inverse_f64 ( const arm_matrix_instance_f64 *  pSrc,
arm_matrix_instance_f64 *  pDst 
)

Floating-point matrix inverse.

Parameters
[in]pSrcpoints to input matrix structure. The source matrix is modified by the function.
[out]pDstpoints to output matrix structure
Returns
execution status

◆ arm_mat_solve_lower_triangular_f16()

arm_status arm_mat_solve_lower_triangular_f16 ( const arm_matrix_instance_f16 *  lt,
const arm_matrix_instance_f16 *  a,
arm_matrix_instance_f16 *  dst 
)
Parameters
[in]ltThe lower triangular matrix
[in]aThe matrix a
[out]dstThe solution X of LT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.

◆ arm_mat_solve_lower_triangular_f32()

arm_status arm_mat_solve_lower_triangular_f32 ( const arm_matrix_instance_f32 *  lt,
const arm_matrix_instance_f32 *  a,
arm_matrix_instance_f32 *  dst 
)
Parameters
[in]ltThe lower triangular matrix
[in]aThe matrix a
[out]dstThe solution X of LT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.

◆ arm_mat_solve_lower_triangular_f64()

arm_status arm_mat_solve_lower_triangular_f64 ( const arm_matrix_instance_f64 *  lt,
const arm_matrix_instance_f64 *  a,
arm_matrix_instance_f64 *  dst 
)
Parameters
[in]ltThe lower triangular matrix
[in]aThe matrix a
[out]dstThe solution X of LT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.

◆ arm_mat_solve_upper_triangular_f16()

arm_status arm_mat_solve_upper_triangular_f16 ( const arm_matrix_instance_f16 *  ut,
const arm_matrix_instance_f16 *  a,
arm_matrix_instance_f16 *  dst 
)
Parameters
[in]utThe upper triangular matrix
[in]aThe matrix a
[out]dstThe solution X of UT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.

◆ arm_mat_solve_upper_triangular_f32()

arm_status arm_mat_solve_upper_triangular_f32 ( const arm_matrix_instance_f32 *  ut,
const arm_matrix_instance_f32 *  a,
arm_matrix_instance_f32 *  dst 
)
Parameters
[in]utThe upper triangular matrix
[in]aThe matrix a
[out]dstThe solution X of UT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.

◆ arm_mat_solve_upper_triangular_f64()

arm_status arm_mat_solve_upper_triangular_f64 ( const arm_matrix_instance_f64 *  ut,
const arm_matrix_instance_f64 *  a,
arm_matrix_instance_f64 *  dst 
)
Parameters
[in]utThe upper triangular matrix
[in]aThe matrix a
[out]dstThe solution X of UT . X = A
Returns
The function returns ARM_MATH_SINGULAR, if the system can't be solved.