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| arm_status | arm_mat_inverse_f16 (const arm_matrix_instance_f16 *pSrc, arm_matrix_instance_f16 *pDst) |
| | Floating-point matrix inverse.
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| arm_status | arm_mat_inverse_f32 (const arm_matrix_instance_f32 *pSrc, arm_matrix_instance_f32 *pDst) |
| | Floating-point matrix inverse.
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| arm_status | arm_mat_inverse_f64 (const arm_matrix_instance_f64 *pSrc, arm_matrix_instance_f64 *pDst) |
| | Floating-point (64 bit) matrix inverse.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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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
\[
\begin{pmatrix}
a_{1,1} & a_{1,2} & a_{1,3} & | & 1 & 0 & 0\\
a_{2,1} & a_{2,2} & a_{2,3} & | & 0 & 1 & 0\\
a_{3,1} & a_{3,2} & a_{3,3} & | & 0 & 0 & 1\\
\end{pmatrix}
\rightarrow
\begin{pmatrix}
1 & 0 & 0 & | & x_{1,1} & x_{2,1} & x_{3,1} \\
0 & 1 & 0 & | & x_{1,2} & x_{2,2} & x_{3,2} \\
0 & 0 & 1 & | & x_{1,3} & x_{2,3} & x_{3,3} \\
\end{pmatrix}
\]
◆ arm_mat_inverse_f16()
Floating-point matrix inverse.
- Parameters
-
| [in] | pSrc | points to input matrix structure. The source matrix is modified by the function. |
| [out] | pDst | points to output matrix structure |
- Returns
- execution status
◆ arm_mat_inverse_f32()
Floating-point matrix inverse.
- Parameters
-
| [in] | pSrc | points to input matrix structure. The source matrix is modified by the function. |
| [out] | pDst | points to output matrix structure |
- Returns
- execution status
◆ arm_mat_inverse_f64()
Floating-point (64 bit) matrix inverse.
Floating-point matrix inverse.
- Parameters
-
| [in] | pSrc | points to input matrix structure. The source matrix is modified by the function. |
| [out] | pDst | points to output matrix structure |
- Returns
- execution status
◆ arm_mat_solve_lower_triangular_f16()
Solve LT . X = A where LT is a lower triangular matrix.
- Parameters
-
| [in] | lt | The lower triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The 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()
Solve LT . X = A where LT is a lower triangular matrix.
- Parameters
-
| [in] | lt | The lower triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The 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()
Solve LT . X = A where LT is a lower triangular matrix.
- Parameters
-
| [in] | lt | The lower triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The 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()
Solve UT . X = A where UT is an upper triangular matrix.
- Parameters
-
| [in] | ut | The upper triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The 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()
Solve UT . X = A where UT is an upper triangular matrix.
- Parameters
-
| [in] | ut | The upper triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The 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()
Solve UT . X = A where UT is an upper triangular matrix.
- Parameters
-
| [in] | ut | The upper triangular matrix |
| [in] | a | The matrix a |
| [out] | dst | The solution X of UT . X = A |
- Returns
- The function returns ARM_MATH_SINGULAR, if the system can't be solved.
