[PATCH v3 05/16] libcamera: matrix: Add inverse() function
Paul Elder
paul.elder at ideasonboard.com
Wed May 7 18:41:53 CEST 2025
On Fri, May 02, 2025 at 08:49:42AM +0100, Kieran Bingham wrote:
> 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 ;-)
I went through and reviewed the Gaussian Elimination...
Reviewed-by: Paul Elder <paul.elder at ideasonboard.com>
>
> > ---
> >
> > 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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