| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_mat_inverse_f32.c |
| * Description: Floating-point matrix inverse |
| * |
| * $Date: 27. January 2017 |
| * $Revision: V.1.5.1 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved. |
| * |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the License); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #include "arm_math.h" |
| |
| /** |
| * @ingroup groupMatrix |
| */ |
| |
| /** |
| * @defgroup MatrixInv Matrix Inverse |
| * |
| * 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. |
| * |
| * \par 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 |
| * <code>ARM_MATH_SINGULAR</code>. |
| * \image html MatrixInverse.gif "Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method" |
| */ |
| |
| /** |
| * @addtogroup MatrixInv |
| * @{ |
| */ |
| |
| /** |
| * @brief Floating-point matrix inverse. |
| * @param[in] *pSrc points to input matrix structure |
| * @param[out] *pDst points to output matrix structure |
| * @return The function returns |
| * <code>ARM_MATH_SIZE_MISMATCH</code> if the input matrix is not square or if the size |
| * of the output matrix does not match the size of the input matrix. |
| * If the input matrix is found to be singular (non-invertible), then the function returns |
| * <code>ARM_MATH_SINGULAR</code>. Otherwise, the function returns <code>ARM_MATH_SUCCESS</code>. |
| */ |
| |
| arm_status arm_mat_inverse_f32( |
| const arm_matrix_instance_f32 * pSrc, |
| arm_matrix_instance_f32 * pDst) |
| { |
| float32_t *pIn = pSrc->pData; /* input data matrix pointer */ |
| float32_t *pOut = pDst->pData; /* output data matrix pointer */ |
| float32_t *pInT1, *pInT2; /* Temporary input data matrix pointer */ |
| float32_t *pOutT1, *pOutT2; /* Temporary output data matrix pointer */ |
| float32_t *pPivotRowIn, *pPRT_in, *pPivotRowDst, *pPRT_pDst; /* Temporary input and output data matrix pointer */ |
| uint32_t numRows = pSrc->numRows; /* Number of rows in the matrix */ |
| uint32_t numCols = pSrc->numCols; /* Number of Cols in the matrix */ |
| |
| #if defined (ARM_MATH_DSP) |
| float32_t maxC; /* maximum value in the column */ |
| |
| /* Run the below code for Cortex-M4 and Cortex-M3 */ |
| |
| float32_t Xchg, in = 0.0f, in1; /* Temporary input values */ |
| uint32_t i, rowCnt, flag = 0U, j, loopCnt, k, l; /* loop counters */ |
| arm_status status; /* status of matrix inverse */ |
| |
| #ifdef ARM_MATH_MATRIX_CHECK |
| |
| |
| /* Check for matrix mismatch condition */ |
| if ((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols) |
| || (pSrc->numRows != pDst->numRows)) |
| { |
| /* Set status as ARM_MATH_SIZE_MISMATCH */ |
| status = ARM_MATH_SIZE_MISMATCH; |
| } |
| else |
| #endif /* #ifdef ARM_MATH_MATRIX_CHECK */ |
| |
| { |
| |
| /*-------------------------------------------------------------------------------------------------------------- |
| * Matrix Inverse can be solved using elementary row operations. |
| * |
| * Gauss-Jordan Method: |
| * |
| * 1. First combine the identity matrix and the input matrix separated by a bar to form an |
| * augmented matrix as follows: |
| * _ _ _ _ |
| * | a11 a12 | 1 0 | | X11 X12 | |
| * | | | = | | |
| * |_ a21 a22 | 0 1 _| |_ X21 X21 _| |
| * |
| * 2. In our implementation, pDst Matrix is used as identity matrix. |
| * |
| * 3. Begin with the first row. Let i = 1. |
| * |
| * 4. Check to see if the pivot for column i is the greatest of the column. |
| * The pivot is the element of the main diagonal that is on the current row. |
| * For instance, if working with row i, then the pivot element is aii. |
| * If the pivot is not the most significant of the columns, exchange that row with a row |
| * below it that does contain the most significant value in column i. If the most |
| * significant value of the column is zero, then an inverse to that matrix does not exist. |
| * The most significant value of the column is the absolute maximum. |
| * |
| * 5. Divide every element of row i by the pivot. |
| * |
| * 6. For every row below and row i, replace that row with the sum of that row and |
| * a multiple of row i so that each new element in column i below row i is zero. |
| * |
| * 7. Move to the next row and column and repeat steps 2 through 5 until you have zeros |
| * for every element below and above the main diagonal. |
| * |
| * 8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc). |
| * Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst). |
| *----------------------------------------------------------------------------------------------------------------*/ |
| |
| /* Working pointer for destination matrix */ |
| pOutT1 = pOut; |
| |
| /* Loop over the number of rows */ |
| rowCnt = numRows; |
| |
| /* Making the destination matrix as identity matrix */ |
| while (rowCnt > 0U) |
| { |
| /* Writing all zeroes in lower triangle of the destination matrix */ |
| j = numRows - rowCnt; |
| while (j > 0U) |
| { |
| *pOutT1++ = 0.0f; |
| j--; |
| } |
| |
| /* Writing all ones in the diagonal of the destination matrix */ |
| *pOutT1++ = 1.0f; |
| |
| /* Writing all zeroes in upper triangle of the destination matrix */ |
| j = rowCnt - 1U; |
| while (j > 0U) |
| { |
| *pOutT1++ = 0.0f; |
| j--; |
| } |
| |
| /* Decrement the loop counter */ |
| rowCnt--; |
| } |
| |
| /* Loop over the number of columns of the input matrix. |
| All the elements in each column are processed by the row operations */ |
| loopCnt = numCols; |
| |
| /* Index modifier to navigate through the columns */ |
| l = 0U; |
| |
| while (loopCnt > 0U) |
| { |
| /* Check if the pivot element is zero.. |
| * If it is zero then interchange the row with non zero row below. |
| * If there is no non zero element to replace in the rows below, |
| * then the matrix is Singular. */ |
| |
| /* Working pointer for the input matrix that points |
| * to the pivot element of the particular row */ |
| pInT1 = pIn + (l * numCols); |
| |
| /* Working pointer for the destination matrix that points |
| * to the pivot element of the particular row */ |
| pOutT1 = pOut + (l * numCols); |
| |
| /* Temporary variable to hold the pivot value */ |
| in = *pInT1; |
| |
| /* Grab the most significant value from column l */ |
| maxC = 0; |
| for (i = l; i < numRows; i++) |
| { |
| maxC = *pInT1 > 0 ? (*pInT1 > maxC ? *pInT1 : maxC) : (-*pInT1 > maxC ? -*pInT1 : maxC); |
| pInT1 += numCols; |
| } |
| |
| /* Update the status if the matrix is singular */ |
| if (maxC == 0.0f) |
| { |
| return ARM_MATH_SINGULAR; |
| } |
| |
| /* Restore pInT1 */ |
| pInT1 = pIn; |
| |
| /* Destination pointer modifier */ |
| k = 1U; |
| |
| /* Check if the pivot element is the most significant of the column */ |
| if ( (in > 0.0f ? in : -in) != maxC) |
| { |
| /* Loop over the number rows present below */ |
| i = numRows - (l + 1U); |
| |
| while (i > 0U) |
| { |
| /* Update the input and destination pointers */ |
| pInT2 = pInT1 + (numCols * l); |
| pOutT2 = pOutT1 + (numCols * k); |
| |
| /* Look for the most significant element to |
| * replace in the rows below */ |
| if ((*pInT2 > 0.0f ? *pInT2: -*pInT2) == maxC) |
| { |
| /* Loop over number of columns |
| * to the right of the pilot element */ |
| j = numCols - l; |
| |
| while (j > 0U) |
| { |
| /* Exchange the row elements of the input matrix */ |
| Xchg = *pInT2; |
| *pInT2++ = *pInT1; |
| *pInT1++ = Xchg; |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| /* Loop over number of columns of the destination matrix */ |
| j = numCols; |
| |
| while (j > 0U) |
| { |
| /* Exchange the row elements of the destination matrix */ |
| Xchg = *pOutT2; |
| *pOutT2++ = *pOutT1; |
| *pOutT1++ = Xchg; |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| /* Flag to indicate whether exchange is done or not */ |
| flag = 1U; |
| |
| /* Break after exchange is done */ |
| break; |
| } |
| |
| /* Update the destination pointer modifier */ |
| k++; |
| |
| /* Decrement the loop counter */ |
| i--; |
| } |
| } |
| |
| /* Update the status if the matrix is singular */ |
| if ((flag != 1U) && (in == 0.0f)) |
| { |
| return ARM_MATH_SINGULAR; |
| } |
| |
| /* Points to the pivot row of input and destination matrices */ |
| pPivotRowIn = pIn + (l * numCols); |
| pPivotRowDst = pOut + (l * numCols); |
| |
| /* Temporary pointers to the pivot row pointers */ |
| pInT1 = pPivotRowIn; |
| pInT2 = pPivotRowDst; |
| |
| /* Pivot element of the row */ |
| in = *pPivotRowIn; |
| |
| /* Loop over number of columns |
| * to the right of the pilot element */ |
| j = (numCols - l); |
| |
| while (j > 0U) |
| { |
| /* Divide each element of the row of the input matrix |
| * by the pivot element */ |
| in1 = *pInT1; |
| *pInT1++ = in1 / in; |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| /* Loop over number of columns of the destination matrix */ |
| j = numCols; |
| |
| while (j > 0U) |
| { |
| /* Divide each element of the row of the destination matrix |
| * by the pivot element */ |
| in1 = *pInT2; |
| *pInT2++ = in1 / in; |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| /* Replace the rows with the sum of that row and a multiple of row i |
| * so that each new element in column i above row i is zero.*/ |
| |
| /* Temporary pointers for input and destination matrices */ |
| pInT1 = pIn; |
| pInT2 = pOut; |
| |
| /* index used to check for pivot element */ |
| i = 0U; |
| |
| /* Loop over number of rows */ |
| /* to be replaced by the sum of that row and a multiple of row i */ |
| k = numRows; |
| |
| while (k > 0U) |
| { |
| /* Check for the pivot element */ |
| if (i == l) |
| { |
| /* If the processing element is the pivot element, |
| only the columns to the right are to be processed */ |
| pInT1 += numCols - l; |
| |
| pInT2 += numCols; |
| } |
| else |
| { |
| /* Element of the reference row */ |
| in = *pInT1; |
| |
| /* Working pointers for input and destination pivot rows */ |
| pPRT_in = pPivotRowIn; |
| pPRT_pDst = pPivotRowDst; |
| |
| /* Loop over the number of columns to the right of the pivot element, |
| to replace the elements in the input matrix */ |
| j = (numCols - l); |
| |
| while (j > 0U) |
| { |
| /* Replace the element by the sum of that row |
| and a multiple of the reference row */ |
| in1 = *pInT1; |
| *pInT1++ = in1 - (in * *pPRT_in++); |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| /* Loop over the number of columns to |
| replace the elements in the destination matrix */ |
| j = numCols; |
| |
| while (j > 0U) |
| { |
| /* Replace the element by the sum of that row |
| and a multiple of the reference row */ |
| in1 = *pInT2; |
| *pInT2++ = in1 - (in * *pPRT_pDst++); |
| |
| /* Decrement the loop counter */ |
| j--; |
| } |
| |
| } |
| |
| /* Increment the temporary input pointer */ |
| pInT1 = pInT1 + l; |
| |
| /* Decrement the loop counter */ |
| k--; |
| |
| /* Increment the pivot index */ |
| i++; |
| } |
| |
| /* Increment the input pointer */ |
| pIn++; |
| |
| /* Decrement the loop counter */ |
| loopCnt--; |
| |
| /* Increment the index modifier */ |
| l++; |
| } |
| |
| |
| #else |
| |
| /* Run the below code for Cortex-M0 */ |
| |
| float32_t Xchg, in = 0.0f; /* Temporary input values */ |
| uint32_t i, rowCnt, flag = 0U, j, loopCnt, k, l; /* loop counters */ |
| arm_status status; /* status of matrix inverse */ |
| |
| #ifdef ARM_MATH_MATRIX_CHECK |
| |
| /* Check for matrix mismatch condition */ |
| if ((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols) |
| || (pSrc->numRows != pDst->numRows)) |
| { |
| /* Set status as ARM_MATH_SIZE_MISMATCH */ |
| status = ARM_MATH_SIZE_MISMATCH; |
| } |
| else |
| #endif /* #ifdef ARM_MATH_MATRIX_CHECK */ |
| { |
| |
| /*-------------------------------------------------------------------------------------------------------------- |
| * Matrix Inverse can be solved using elementary row operations. |
| * |
| * Gauss-Jordan Method: |
| * |
| * 1. First combine the identity matrix and the input matrix separated by a bar to form an |
| * augmented matrix as follows: |
| * _ _ _ _ _ _ _ _ |
| * | | a11 a12 | | | 1 0 | | | X11 X12 | |
| * | | | | | | | = | | |
| * |_ |_ a21 a22 _| | |_0 1 _| _| |_ X21 X21 _| |
| * |
| * 2. In our implementation, pDst Matrix is used as identity matrix. |
| * |
| * 3. Begin with the first row. Let i = 1. |
| * |
| * 4. Check to see if the pivot for row i is zero. |
| * The pivot is the element of the main diagonal that is on the current row. |
| * For instance, if working with row i, then the pivot element is aii. |
| * If the pivot is zero, exchange that row with a row below it that does not |
| * contain a zero in column i. If this is not possible, then an inverse |
| * to that matrix does not exist. |
| * |
| * 5. Divide every element of row i by the pivot. |
| * |
| * 6. For every row below and row i, replace that row with the sum of that row and |
| * a multiple of row i so that each new element in column i below row i is zero. |
| * |
| * 7. Move to the next row and column and repeat steps 2 through 5 until you have zeros |
| * for every element below and above the main diagonal. |
| * |
| * 8. Now an identical matrix is formed to the left of the bar(input matrix, src). |
| * Therefore, the matrix to the right of the bar is our solution(dst matrix, dst). |
| *----------------------------------------------------------------------------------------------------------------*/ |
| |
| /* Working pointer for destination matrix */ |
| pOutT1 = pOut; |
| |
| /* Loop over the number of rows */ |
| rowCnt = numRows; |
| |
| /* Making the destination matrix as identity matrix */ |
| while (rowCnt > 0U) |
| { |
| /* Writing all zeroes in lower triangle of the destination matrix */ |
| j = numRows - rowCnt; |
| while (j > 0U) |
| { |
| *pOutT1++ = 0.0f; |
| j--; |
| } |
| |
| /* Writing all ones in the diagonal of the destination matrix */ |
| *pOutT1++ = 1.0f; |
| |
| /* Writing all zeroes in upper triangle of the destination matrix */ |
| j = rowCnt - 1U; |
| while (j > 0U) |
| { |
| *pOutT1++ = 0.0f; |
| j--; |
| } |
| |
| /* Decrement the loop counter */ |
| rowCnt--; |
| } |
| |
| /* Loop over the number of columns of the input matrix. |
| All the elements in each column are processed by the row operations */ |
| loopCnt = numCols; |
| |
| /* Index modifier to navigate through the columns */ |
| l = 0U; |
| //for(loopCnt = 0U; loopCnt < numCols; loopCnt++) |
| while (loopCnt > 0U) |
| { |
| /* Check if the pivot element is zero.. |
| * If it is zero then interchange the row with non zero row below. |
| * If there is no non zero element to replace in the rows below, |
| * then the matrix is Singular. */ |
| |
| /* Working pointer for the input matrix that points |
| * to the pivot element of the particular row */ |
| pInT1 = pIn + (l * numCols); |
| |
| /* Working pointer for the destination matrix that points |
| * to the pivot element of the particular row */ |
| pOutT1 = pOut + (l * numCols); |
| |
| /* Temporary variable to hold the pivot value */ |
| in = *pInT1; |
| |
| /* Destination pointer modifier */ |
| k = 1U; |
| |
| /* Check if the pivot element is zero */ |
| if (*pInT1 == 0.0f) |
| { |
| /* Loop over the number rows present below */ |
| for (i = (l + 1U); i < numRows; i++) |
| { |
| /* Update the input and destination pointers */ |
| pInT2 = pInT1 + (numCols * l); |
| pOutT2 = pOutT1 + (numCols * k); |
| |
| /* Check if there is a non zero pivot element to |
| * replace in the rows below */ |
| if (*pInT2 != 0.0f) |
| { |
| /* Loop over number of columns |
| * to the right of the pilot element */ |
| for (j = 0U; j < (numCols - l); j++) |
| { |
| /* Exchange the row elements of the input matrix */ |
| Xchg = *pInT2; |
| *pInT2++ = *pInT1; |
| *pInT1++ = Xchg; |
| } |
| |
| for (j = 0U; j < numCols; j++) |
| { |
| Xchg = *pOutT2; |
| *pOutT2++ = *pOutT1; |
| *pOutT1++ = Xchg; |
| } |
| |
| /* Flag to indicate whether exchange is done or not */ |
| flag = 1U; |
| |
| /* Break after exchange is done */ |
| break; |
| } |
| |
| /* Update the destination pointer modifier */ |
| k++; |
| } |
| } |
| |
| /* Update the status if the matrix is singular */ |
| if ((flag != 1U) && (in == 0.0f)) |
| { |
| return ARM_MATH_SINGULAR; |
| } |
| |
| /* Points to the pivot row of input and destination matrices */ |
| pPivotRowIn = pIn + (l * numCols); |
| pPivotRowDst = pOut + (l * numCols); |
| |
| /* Temporary pointers to the pivot row pointers */ |
| pInT1 = pPivotRowIn; |
| pOutT1 = pPivotRowDst; |
| |
| /* Pivot element of the row */ |
| in = *(pIn + (l * numCols)); |
| |
| /* Loop over number of columns |
| * to the right of the pilot element */ |
| for (j = 0U; j < (numCols - l); j++) |
| { |
| /* Divide each element of the row of the input matrix |
| * by the pivot element */ |
| *pInT1 = *pInT1 / in; |
| pInT1++; |
| } |
| for (j = 0U; j < numCols; j++) |
| { |
| /* Divide each element of the row of the destination matrix |
| * by the pivot element */ |
| *pOutT1 = *pOutT1 / in; |
| pOutT1++; |
| } |
| |
| /* Replace the rows with the sum of that row and a multiple of row i |
| * so that each new element in column i above row i is zero.*/ |
| |
| /* Temporary pointers for input and destination matrices */ |
| pInT1 = pIn; |
| pOutT1 = pOut; |
| |
| for (i = 0U; i < numRows; i++) |
| { |
| /* Check for the pivot element */ |
| if (i == l) |
| { |
| /* If the processing element is the pivot element, |
| only the columns to the right are to be processed */ |
| pInT1 += numCols - l; |
| pOutT1 += numCols; |
| } |
| else |
| { |
| /* Element of the reference row */ |
| in = *pInT1; |
| |
| /* Working pointers for input and destination pivot rows */ |
| pPRT_in = pPivotRowIn; |
| pPRT_pDst = pPivotRowDst; |
| |
| /* Loop over the number of columns to the right of the pivot element, |
| to replace the elements in the input matrix */ |
| for (j = 0U; j < (numCols - l); j++) |
| { |
| /* Replace the element by the sum of that row |
| and a multiple of the reference row */ |
| *pInT1 = *pInT1 - (in * *pPRT_in++); |
| pInT1++; |
| } |
| /* Loop over the number of columns to |
| replace the elements in the destination matrix */ |
| for (j = 0U; j < numCols; j++) |
| { |
| /* Replace the element by the sum of that row |
| and a multiple of the reference row */ |
| *pOutT1 = *pOutT1 - (in * *pPRT_pDst++); |
| pOutT1++; |
| } |
| |
| } |
| /* Increment the temporary input pointer */ |
| pInT1 = pInT1 + l; |
| } |
| /* Increment the input pointer */ |
| pIn++; |
| |
| /* Decrement the loop counter */ |
| loopCnt--; |
| /* Increment the index modifier */ |
| l++; |
| } |
| |
| |
| #endif /* #if defined (ARM_MATH_DSP) */ |
| |
| /* Set status as ARM_MATH_SUCCESS */ |
| status = ARM_MATH_SUCCESS; |
| |
| if ((flag != 1U) && (in == 0.0f)) |
| { |
| pIn = pSrc->pData; |
| for (i = 0; i < numRows * numCols; i++) |
| { |
| if (pIn[i] != 0.0f) |
| break; |
| } |
| |
| if (i == numRows * numCols) |
| status = ARM_MATH_SINGULAR; |
| } |
| } |
| /* Return to application */ |
| return (status); |
| } |
| |
| /** |
| * @} end of MatrixInv group |
| */ |
