Laxmi Kant Tiwari
CMSIS DSP Lib
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Diff: cmsis_dsp/MatrixFunctions/arm_mat_inverse_f32.c
- Revision:
- 1:fdd22bb7aa52
- Child:
- 2:da51fb522205
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/cmsis_dsp/MatrixFunctions/arm_mat_inverse_f32.c Wed Nov 28 12:30:09 2012 +0000
@@ -0,0 +1,668 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_mat_inverse_f32.c
+*
+* Description: Floating-point matrix inverse.
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Version 1.1.0 2012/02/15
+* Updated with more optimizations, bug fixes and minor API changes.
+*
+* 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
+ */