Matrix Inverse

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f16 (const riscv_matrix_instance_f16 *pSrc, riscv_matrix_instance_f16 *pDst)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f32 (const riscv_matrix_instance_f32 *pSrc, riscv_matrix_instance_f32 *pDst)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f64 (const riscv_matrix_instance_f64 *pSrc, riscv_matrix_instance_f64 *pDst)

riscv_status riscv_mat_solve_lower_triangular_f16(const riscv_matrix_instance_f16 *lt, const riscv_matrix_instance_f16 *a, riscv_matrix_instance_f16 *dst)

riscv_status riscv_mat_solve_lower_triangular_f32(const riscv_matrix_instance_f32 *lt, const riscv_matrix_instance_f32 *a, riscv_matrix_instance_f32 *dst)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_solve_lower_triangular_f64 (const riscv_matrix_instance_f64 *lt, const riscv_matrix_instance_f64 *a, riscv_matrix_instance_f64 *dst)

riscv_status riscv_mat_solve_upper_triangular_f16(const riscv_matrix_instance_f16 *ut, const riscv_matrix_instance_f16 *a, riscv_matrix_instance_f16 *dst)

riscv_status riscv_mat_solve_upper_triangular_f32(const riscv_matrix_instance_f32 *ut, const riscv_matrix_instance_f32 *a, riscv_matrix_instance_f32 *dst)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_solve_upper_triangular_f64 (const riscv_matrix_instance_f64 *ut, const riscv_matrix_instance_f64 *a, riscv_matrix_instance_f64 *dst)

group MatrixInv

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 NMSIS DSP library only supports matrix inversion of floating-point matrices.

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

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 RISCV_MATH_SINGULAR.
Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method

Functions

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f16 (const riscv_matrix_instance_f16 *pSrc, riscv_matrix_instance_f16 *pDst)

Floating-point matrix inverse.

Parameters

pSrc – [in] points to input matrix structure. The source matrix is modified by the function.
pDst – [out] points to output matrix structure

Returns

execution status

RISCV_MATH_SUCCESS : Operation successful
RISCV_MATH_SIZE_MISMATCH : Matrix size check failed
RISCV_MATH_SINGULAR : Input matrix is found to be singular (non-invertible)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f32 (const riscv_matrix_instance_f32 *pSrc, riscv_matrix_instance_f32 *pDst)

Floating-point matrix inverse.

Parameters

pSrc – [in] points to input matrix structure. The source matrix is modified by the function.
pDst – [out] points to output matrix structure

Returns

execution status

RISCV_MATH_SUCCESS : Operation successful
RISCV_MATH_SIZE_MISMATCH : Matrix size check failed
RISCV_MATH_SINGULAR : Input matrix is found to be singular (non-invertible)

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_inverse_f64 (const riscv_matrix_instance_f64 *pSrc, riscv_matrix_instance_f64 *pDst)

Floating-point (64 bit) matrix inverse.

Floating-point matrix inverse.

Parameters

pSrc – [in] points to input matrix structure. The source matrix is modified by the function.
pDst – [out] points to output matrix structure

Returns

execution status

RISCV_MATH_SUCCESS : Operation successful
RISCV_MATH_SIZE_MISMATCH : Matrix size check failed
RISCV_MATH_SINGULAR : Input matrix is found to be singular (non-invertible)

riscv_status riscv_mat_solve_lower_triangular_f16(const riscv_matrix_instance_f16 *lt, const riscv_matrix_instance_f16 *a, riscv_matrix_instance_f16 *dst)

Solve LT . X = A where LT is a lower triangular matrix.

Parameters

lt – [in] The lower triangular matrix
a – [in] The matrix a
dst – [out] The solution X of LT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved.

riscv_status riscv_mat_solve_lower_triangular_f32(const riscv_matrix_instance_f32 *lt, const riscv_matrix_instance_f32 *a, riscv_matrix_instance_f32 *dst)

Solve LT . X = A where LT is a lower triangular matrix.

Parameters

lt – [in] The lower triangular matrix
a – [in] The matrix a
dst – [out] The solution X of LT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved. Notice: The instruction vfredusum may introduce errors. So, if we use the V-extension implementation, we have to accept the errors that may happen in this function.

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_solve_lower_triangular_f64 (const riscv_matrix_instance_f64 *lt, const riscv_matrix_instance_f64 *a, riscv_matrix_instance_f64 *dst)

Solve LT . X = A where LT is a lower triangular matrix.

Parameters

lt – [in] The lower triangular matrix
a – [in] The matrix a
dst – [out] The solution X of LT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved. Notice: The instruction vfredusum may introduce errors. So, if we use the V-extension implementation, we have to accept the errors that may happen in this function.

riscv_status riscv_mat_solve_upper_triangular_f16(const riscv_matrix_instance_f16 *ut, const riscv_matrix_instance_f16 *a, riscv_matrix_instance_f16 *dst)

Solve UT . X = A where UT is an upper triangular matrix.

Parameters

ut – [in] The upper triangular matrix
a – [in] The matrix a
dst – [out] The solution X of UT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved.

riscv_status riscv_mat_solve_upper_triangular_f32(const riscv_matrix_instance_f32 *ut, const riscv_matrix_instance_f32 *a, riscv_matrix_instance_f32 *dst)

Solve UT . X = A where UT is an upper triangular matrix.

Parameters

ut – [in] The upper triangular matrix
a – [in] The matrix a
dst – [out] The solution X of UT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved. Notice: The instruction vfredusum may introduce errors. So, if we use the V-extension implementation, we have to accept the errors that may happen in this function.

RISCV_DSP_ATTRIBUTE riscv_status riscv_mat_solve_upper_triangular_f64 (const riscv_matrix_instance_f64 *ut, const riscv_matrix_instance_f64 *a, riscv_matrix_instance_f64 *dst)

Solve UT . X = A where UT is an upper triangular matrix.

Parameters

ut – [in] The upper triangular matrix
a – [in] The matrix a
dst – [out] The solution X of UT . X = A

Returns

The function returns RISCV_MATH_SINGULAR, if the system can’t be solved. Notice: The instruction vfredusum may introduce errors. So, if we use the V-extension implementation, we have to accept the errors that may happen in this function.