[PATCH v3 05/16] libcamera: matrix: Add inverse() function
Kieran Bingham
kieran.bingham at ideasonboard.com
Fri May 2 09:49:42 CEST 2025
Quoting Stefan Klug (2025-04-03 16:49:10)
> For calculations in upcoming algorithm patches, the inverse of a matrix
> is required. Add an implementation of the inverse() function for square
> matrices.
>
> Signed-off-by: Stefan Klug <stefan.klug at ideasonboard.com>
> Signed-off-by: Laurent Pinchart <laurent.pinchart at ideasonboard.com>
>
Given there's a test structure added after this...
Reviewed-by: Kieran Bingham <kieran.bingham at ideasonboard.com>
Maybe that should be just acked by as I'm not spending a lot of time to
review the Gaussian Ellimination here - but I trust you and
Laurent and the results of some tests being added to the unit tests for
it so I'm fine with it ;-)
> ---
>
> Changes in v2:
> - Replaced the implementation by a generic one provided by Laurent that
> supports arbitrary square matrices instead of 2x2 and 3x3 only.
> - Moved the implementation into the cpp file.
>
> Changes inv3:
> - Added stack allocated scratchBuffers to matrixInvert so that no heap
> allocations are necessary.
> ---
> include/libcamera/internal/matrix.h | 23 ++++
> src/libcamera/matrix.cpp | 166 ++++++++++++++++++++++++++++
> 2 files changed, 189 insertions(+)
>
> diff --git a/include/libcamera/internal/matrix.h b/include/libcamera/internal/matrix.h
> index 6d40567af0a0..a07a47701336 100644
> --- a/include/libcamera/internal/matrix.h
> +++ b/include/libcamera/internal/matrix.h
> @@ -19,6 +19,12 @@ namespace libcamera {
>
> LOG_DECLARE_CATEGORY(Matrix)
>
> +#ifndef __DOXYGEN__
> +template<typename T>
> +bool matrixInvert(Span<const T> dataIn, Span<T> dataOut, unsigned int dim,
> + Span<T> scratchBuffer, Span<unsigned int> swapBuffer);
> +#endif /* __DOXYGEN__ */
> +
> template<typename T, unsigned int Rows, unsigned int Cols>
> class Matrix
> {
> @@ -91,6 +97,23 @@ public:
> return *this;
> }
>
> + Matrix<T, Rows, Cols> inverse(bool *ok = nullptr) const
> + {
> + static_assert(Rows == Cols, "Matrix must be square");
> +
> + Matrix<T, Rows, Cols> inverse;
> + std::array<T, Rows * Cols * 2> scratchBuffer;
> + std::array<unsigned int, Rows> swapBuffer;
> + bool res = matrixInvert(Span<const T>(data_),
> + Span<T>(inverse.data_),
> + Rows,
> + Span<T>(scratchBuffer),
> + Span<unsigned int>(swapBuffer));
> + if (ok)
> + *ok = res;
> + return inverse;
> + }
> +
> private:
> /*
> * \todo The initializer is only necessary for the constructor to be
> diff --git a/src/libcamera/matrix.cpp b/src/libcamera/matrix.cpp
> index 49e2aa3b4f2c..68fc1b7bd5ac 100644
> --- a/src/libcamera/matrix.cpp
> +++ b/src/libcamera/matrix.cpp
> @@ -7,6 +7,12 @@
>
> #include "libcamera/internal/matrix.h"
>
> +#include <algorithm>
> +#include <assert.h>
> +#include <cmath>
> +#include <numeric>
> +#include <vector>
> +
> #include <libcamera/base/log.h>
>
> /**
> @@ -87,6 +93,20 @@ LOG_DEFINE_CATEGORY(Matrix)
> * \return Row \a i from the matrix, as a Span
> */
>
> +/**
> + * \fn Matrix::inverse(bool *ok) const
> + * \param[out] ok Indicate if the matrix was successfully inverted
> + * \brief Compute the inverse of the matrix
> + *
> + * This function computes the inverse of the matrix. It is only implemented for
> + * matrices of float and double types. If \a ok is provided it will be set to a
> + * boolean value to indicate of the inversion was successful. This can be used
> + * to check if the matrix is singular, in which case the function will return
> + * an identity matrix.
> + *
> + * \return The inverse of the matrix
> + */
> +
> /**
> * \fn Matrix::operator[](size_t i)
> * \copydoc Matrix::operator[](size_t i) const
> @@ -142,6 +162,152 @@ LOG_DEFINE_CATEGORY(Matrix)
> */
>
> #ifndef __DOXYGEN__
> +template<typename T>
> +bool matrixInvert(Span<const T> dataIn, Span<T> dataOut, unsigned int dim,
> + Span<T> scratchBuffer, Span<unsigned int> swapBuffer)
> +{
> + /*
> + * Convenience class to access matrix data, providing a row-major (i,j)
> + * element accessor through the call operator, and the ability to swap
> + * rows without modifying the backing storage.
> + */
> + class MatrixAccessor
> + {
> + public:
> + MatrixAccessor(Span<T> data, Span<unsigned int> swapBuffer, unsigned int rows, unsigned int cols)
> + : data_(data), swap_(swapBuffer), rows_(rows), cols_(cols)
> + {
> + ASSERT(swap_.size() == rows);
> + std::iota(swap_.begin(), swap_.end(), T{ 0 });
> + }
> +
> + T &operator()(unsigned int row, unsigned int col)
> + {
> + assert(row < rows_ && col < cols_);
> + return data_[index(row, col)];
> + }
> +
> + void swap(unsigned int a, unsigned int b)
> + {
> + assert(a < rows_ && a < cols_);
> + std::swap(swap_[a], swap_[b]);
> + }
> +
> + private:
> + unsigned int index(unsigned int row, unsigned int col) const
> + {
> + return swap_[row] * cols_ + col;
> + }
> +
> + Span<T> data_;
> + Span<unsigned int> swap_;
> + unsigned int rows_;
> + unsigned int cols_;
> + };
> +
> + /*
> + * Matrix inversion using Gaussian elimination.
> + *
> + * Start by augmenting the original matrix with an identiy matrix of
> + * the same size.
> + */
> + ASSERT(scratchBuffer.size() == dim * dim * 2);
> + MatrixAccessor matrix(scratchBuffer, swapBuffer, dim, dim * 2);
> +
> + for (unsigned int i = 0; i < dim; ++i) {
> + for (unsigned int j = 0; j < dim; ++j) {
> + matrix(i, j) = dataIn[i * dim + j];
> + matrix(i, j + dim) = T{ 0 };
> + }
> + matrix(i, i + dim) = T{ 1 };
> + }
> +
> + /* Start by triangularizing the input . */
> + for (unsigned int pivot = 0; pivot < dim; ++pivot) {
> + /*
> + * Locate the next pivot. To improve numerical stability, use
> + * the row with the largest value in the pivot's column.
> + */
> + unsigned int row;
> + T maxValue{ 0 };
> +
> + for (unsigned int i = pivot; i < dim; ++i) {
> + T value = std::abs(matrix(i, pivot));
> + if (maxValue < value) {
> + maxValue = value;
> + row = i;
> + }
> + }
> +
> + /*
> + * If no pivot is found in the column, the matrix is not
> + * invertible. Return an identity matrix.
> + */
> + if (maxValue == 0) {
> + std::fill(dataOut.begin(), dataOut.end(), T{ 0 });
> + for (unsigned int i = 0; i < dim; ++i)
> + dataOut[i * dim + i] = T{ 1 };
> + return false;
> + }
> +
> + /* Swap rows to bring the pivot in the right location. */
> + matrix.swap(pivot, row);
> +
> + /* Process all rows below the pivot to zero the pivot column. */
> + const T pivotValue = matrix(pivot, pivot);
> +
> + for (unsigned int i = pivot + 1; i < dim; ++i) {
> + const T factor = matrix(i, pivot) / pivotValue;
> +
> + /*
> + * We know the element in the pivot column will be 0,
> + * hardcode it instead of computing it.
> + */
> + matrix(i, pivot) = T{ 0 };
> +
> + for (unsigned int j = pivot + 1; j < dim * 2; ++j)
> + matrix(i, j) -= matrix(pivot, j) * factor;
> + }
> + }
> +
> + /*
> + * Then diagonalize the input, walking the diagonal backwards. There's
> + * no need to update the input matrix, as all the values we would write
> + * in the top-right triangle aren't used in further calculations (and
> + * would all by definition be zero).
> + */
> + for (unsigned int pivot = dim - 1; pivot > 0; --pivot) {
> + const T pivotValue = matrix(pivot, pivot);
> +
> + for (unsigned int i = 0; i < pivot; ++i) {
> + const T factor = matrix(i, pivot) / pivotValue;
> +
> + for (unsigned int j = dim; j < dim * 2; ++j)
> + matrix(i, j) -= matrix(pivot, j) * factor;
> + }
> + }
> +
> + /*
> + * Finally, normalize the diagonal and store the result in the output
> + * data.
> + */
> + for (unsigned int i = 0; i < dim; ++i) {
> + const T factor = matrix(i, i);
> +
> + for (unsigned int j = 0; j < dim; ++j)
> + dataOut[i * dim + j] = matrix(i, j + dim) / factor;
> + }
> +
> + return true;
> +}
> +
> +template bool matrixInvert<float>(Span<const float> dataIn, Span<float> dataOut,
> + unsigned int dim, Span<float> scratchBuffer,
> + Span<unsigned int> swapBuffer);
> +template bool matrixInvert<double>(Span<const double> data, Span<double> dataOut,
> + unsigned int dim, Span<double> scratchBuffer,
> + Span<unsigned int> swapBuffer);
> +
> /*
> * The YAML data shall be a list of numerical values. Its size shall be equal
> * to the product of the number of rows and columns of the matrix (Rows x
> --
> 2.43.0
>
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