arm_mat_inverse_f32.c
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| text/x-c
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CLexer
r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_mat_inverse_f32.c | ||||
* | ||||
* Description: Floating-point matrix inverse. | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | ||||
* | ||||
* Version 1.0.10 2011/7/15 | ||||
* Big Endian support added and Merged M0 and M3/M4 Source code. | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated. | ||||
* -------------------------------------------------------------------- */ | ||||
#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 till 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 *pInT3, *pInT4; /* 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 */ | ||||
#ifndef ARM_MATH_CM0 | ||||
/* 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 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, pSrc). | ||||
* Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst). | ||||
*----------------------------------------------------------------------------------------------------------------*/ | ||||
/* Working pointer for destination matrix */ | ||||
pInT2 = 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) | ||||
{ | ||||
*pInT2++ = 0.0f; | ||||
j--; | ||||
} | ||||
/* Writing all ones in the diagonal of the destination matrix */ | ||||
*pInT2++ = 1.0f; | ||||
/* Writing all zeroes in upper triangle of the destination matrix */ | ||||
j = rowCnt - 1u; | ||||
while(j > 0u) | ||||
{ | ||||
*pInT2++ = 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 */ | ||||
pInT3 = 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 */ | ||||
i = numRows - (l + 1u); | ||||
while(i > 0u) | ||||
{ | ||||
/* Update the input and destination pointers */ | ||||
pInT2 = pInT1 + (numCols * l); | ||||
pInT4 = pInT3 + (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 */ | ||||
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 = *pInT4; | ||||
*pInT4++ = *pInT3; | ||||
*pInT3++ = 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)) | ||||
{ | ||||
status = ARM_MATH_SINGULAR; | ||||
break; | ||||
} | ||||
/* 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 = *(pIn + (l * numCols)); | ||||
/* 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 */ | ||||
pInT2 = 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) | ||||
{ | ||||
*pInT2++ = 0.0f; | ||||
j--; | ||||
} | ||||
/* Writing all ones in the diagonal of the destination matrix */ | ||||
*pInT2++ = 1.0f; | ||||
/* Writing all zeroes in upper triangle of the destination matrix */ | ||||
j = rowCnt - 1u; | ||||
while(j > 0u) | ||||
{ | ||||
*pInT2++ = 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 */ | ||||
pInT3 = 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); | ||||
pInT4 = pInT3 + (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 = *pInT4; | ||||
*pInT4++ = *pInT3; | ||||
*pInT3++ = 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)) | ||||
{ | ||||
status = ARM_MATH_SINGULAR; | ||||
break; | ||||
} | ||||
/* 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 = *(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; | ||||
} | ||||
for (j = 0u; j < numCols; j++) | ||||
{ | ||||
/* Divide each element of the row of the destination matrix | ||||
* by the pivot element */ | ||||
*pInT2++ = *pInT2 / in; | ||||
} | ||||
/* 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; | ||||
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; | ||||
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 */ | ||||
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++); | ||||
} | ||||
/* 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 */ | ||||
*pInT2++ = *pInT2 - (in * *pPRT_pDst++); | ||||
} | ||||
} | ||||
/* Increment the temporary input pointer */ | ||||
pInT1 = pInT1 + l; | ||||
} | ||||
/* Increment the input pointer */ | ||||
pIn++; | ||||
/* Decrement the loop counter */ | ||||
loopCnt--; | ||||
/* Increment the index modifier */ | ||||
l++; | ||||
} | ||||
#endif /* #ifndef ARM_MATH_CM0 */ | ||||
/* Set status as ARM_MATH_SUCCESS */ | ||||
status = ARM_MATH_SUCCESS; | ||||
if((flag != 1u) && (in == 0.0f)) | ||||
{ | ||||
status = ARM_MATH_SINGULAR; | ||||
} | ||||
} | ||||
/* Return to application */ | ||||
return (status); | ||||
} | ||||
/** | ||||
* @} end of MatrixInv group | ||||
*/ | ||||