/* ----------------------------------------------------------------------
* 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
*/