[{"id":34099,"web_url":"https://patchwork.libcamera.org/comment/34099/","msgid":"<174617218287.1586992.12766708855039261289@ping.linuxembedded.co.uk>","date":"2025-05-02T07:49:42","subject":"Re: [PATCH v3 05/16] libcamera: matrix: Add inverse() function","submitter":{"id":4,"url":"https://patchwork.libcamera.org/api/people/4/","name":"Kieran Bingham","email":"kieran.bingham@ideasonboard.com"},"content":"Quoting Stefan Klug (2025-04-03 16:49:10)\n> For calculations in upcoming algorithm patches, the inverse of a matrix\n> is required. Add an implementation of the inverse() function for square\n> matrices.\n> \n> Signed-off-by: Stefan Klug \n> Signed-off-by: Laurent Pinchart \n> \n\nGiven there's a test structure added after this...\n\n\nReviewed-by: Kieran Bingham \n\nMaybe that should be just acked by as I'm not spending a lot of time to\nreview the Gaussian Ellimination here - but I trust you and\nLaurent and the results of some tests being added to the unit tests for\nit so I'm fine with it ;-)\n\n> ---\n> \n> Changes in v2:\n> - Replaced the implementation by a generic one provided by Laurent that\n> supports arbitrary square matrices instead of 2x2 and 3x3 only.\n> - Moved the implementation into the cpp file.\n> \n> Changes inv3:\n> - Added stack allocated scratchBuffers to matrixInvert so that no heap\n> allocations are necessary.\n> ---\n> include/libcamera/internal/matrix.h | 23 ++++\n> src/libcamera/matrix.cpp | 166 ++++++++++++++++++++++++++++\n> 2 files changed, 189 insertions(+)\n> \n> diff --git a/include/libcamera/internal/matrix.h b/include/libcamera/internal/matrix.h\n> index 6d40567af0a0..a07a47701336 100644\n> --- a/include/libcamera/internal/matrix.h\n> +++ b/include/libcamera/internal/matrix.h\n> @@ -19,6 +19,12 @@ namespace libcamera {\n> \n> LOG_DECLARE_CATEGORY(Matrix)\n> \n> +#ifndef __DOXYGEN__\n> +template\n> +bool matrixInvert(Span dataIn, Span dataOut, unsigned int dim,\n> + Span scratchBuffer, Span swapBuffer);\n> +#endif /* __DOXYGEN__ */\n> +\n> template\n> class Matrix\n> {\n> @@ -91,6 +97,23 @@ public:\n> return *this;\n> }\n> \n> + Matrix inverse(bool *ok = nullptr) const\n> + {\n> + static_assert(Rows == Cols, \"Matrix must be square\");\n> +\n> + Matrix inverse;\n> + std::array scratchBuffer;\n> + std::array swapBuffer;\n> + bool res = matrixInvert(Span(data_),\n> + Span(inverse.data_),\n> + Rows,\n> + Span(scratchBuffer),\n> + Span(swapBuffer));\n> + if (ok)\n> + *ok = res;\n> + return inverse;\n> + }\n> +\n> private:\n> /*\n> * \\todo The initializer is only necessary for the constructor to be\n> diff --git a/src/libcamera/matrix.cpp b/src/libcamera/matrix.cpp\n> index 49e2aa3b4f2c..68fc1b7bd5ac 100644\n> --- a/src/libcamera/matrix.cpp\n> +++ b/src/libcamera/matrix.cpp\n> @@ -7,6 +7,12 @@\n> \n> #include \"libcamera/internal/matrix.h\"\n> \n> +#include \n> +#include \n> +#include \n> +#include \n> +#include \n> +\n> #include \n> \n> /**\n> @@ -87,6 +93,20 @@ LOG_DEFINE_CATEGORY(Matrix)\n> * \\return Row \\a i from the matrix, as a Span\n> */\n> \n> +/**\n> + * \\fn Matrix::inverse(bool *ok) const\n> + * \\param[out] ok Indicate if the matrix was successfully inverted\n> + * \\brief Compute the inverse of the matrix\n> + *\n> + * This function computes the inverse of the matrix. It is only implemented for\n> + * matrices of float and double types. If \\a ok is provided it will be set to a\n> + * boolean value to indicate of the inversion was successful. This can be used\n> + * to check if the matrix is singular, in which case the function will return\n> + * an identity matrix.\n> + *\n> + * \\return The inverse of the matrix\n> + */\n> +\n> /**\n> * \\fn Matrix::operator[](size_t i)\n> * \\copydoc Matrix::operator[](size_t i) const\n> @@ -142,6 +162,152 @@ LOG_DEFINE_CATEGORY(Matrix)\n> */\n> \n> #ifndef __DOXYGEN__\n> +template\n> +bool matrixInvert(Span dataIn, Span dataOut, unsigned int dim,\n> + Span scratchBuffer, Span swapBuffer)\n> +{\n> + /*\n> + * Convenience class to access matrix data, providing a row-major (i,j)\n> + * element accessor through the call operator, and the ability to swap\n> + * rows without modifying the backing storage.\n> + */\n> + class MatrixAccessor\n> + {\n> + public:\n> + MatrixAccessor(Span data, Span swapBuffer, unsigned int rows, unsigned int cols)\n> + : data_(data), swap_(swapBuffer), rows_(rows), cols_(cols)\n> + {\n> + ASSERT(swap_.size() == rows);\n> + std::iota(swap_.begin(), swap_.end(), T{ 0 });\n> + }\n> +\n> + T &operator()(unsigned int row, unsigned int col)\n> + {\n> + assert(row < rows_ && col < cols_);\n> + return data_[index(row, col)];\n> + }\n> +\n> + void swap(unsigned int a, unsigned int b)\n> + {\n> + assert(a < rows_ && a < cols_);\n> + std::swap(swap_[a], swap_[b]);\n> + }\n> +\n> + private:\n> + unsigned int index(unsigned int row, unsigned int col) const\n> + {\n> + return swap_[row] * cols_ + col;\n> + }\n> +\n> + Span data_;\n> + Span swap_;\n> + unsigned int rows_;\n> + unsigned int cols_;\n> + };\n> +\n> + /*\n> + * Matrix inversion using Gaussian elimination.\n> + *\n> + * Start by augmenting the original matrix with an identiy matrix of\n> + * the same size.\n> + */\n> + ASSERT(scratchBuffer.size() == dim * dim * 2);\n> + MatrixAccessor matrix(scratchBuffer, swapBuffer, dim, dim * 2);\n> +\n> + for (unsigned int i = 0; i < dim; ++i) {\n> + for (unsigned int j = 0; j < dim; ++j) {\n> + matrix(i, j) = dataIn[i * dim + j];\n> + matrix(i, j + dim) = T{ 0 };\n> + }\n> + matrix(i, i + dim) = T{ 1 };\n> + }\n> +\n> + /* Start by triangularizing the input . */\n> + for (unsigned int pivot = 0; pivot < dim; ++pivot) {\n> + /*\n> + * Locate the next pivot. To improve numerical stability, use\n> + * the row with the largest value in the pivot's column.\n> + */\n> + unsigned int row;\n> + T maxValue{ 0 };\n> +\n> + for (unsigned int i = pivot; i < dim; ++i) {\n> + T value = std::abs(matrix(i, pivot));\n> + if (maxValue < value) {\n> + maxValue = value;\n> + row = i;\n> + }\n> + }\n> +\n> + /*\n> + * If no pivot is found in the column, the matrix is not\n> + * invertible. Return an identity matrix.\n> + */\n> + if (maxValue == 0) {\n> + std::fill(dataOut.begin(), dataOut.end(), T{ 0 });\n> + for (unsigned int i = 0; i < dim; ++i)\n> + dataOut[i * dim + i] = T{ 1 };\n> + return false;\n> + }\n> +\n> + /* Swap rows to bring the pivot in the right location. */\n> + matrix.swap(pivot, row);\n> +\n> + /* Process all rows below the pivot to zero the pivot column. */\n> + const T pivotValue = matrix(pivot, pivot);\n> +\n> + for (unsigned int i = pivot + 1; i < dim; ++i) {\n> + const T factor = matrix(i, pivot) / pivotValue;\n> +\n> + /*\n> + * We know the element in the pivot column will be 0,\n> + * hardcode it instead of computing it.\n> + */\n> + matrix(i, pivot) = T{ 0 };\n> +\n> + for (unsigned int j = pivot + 1; j < dim * 2; ++j)\n> + matrix(i, j) -= matrix(pivot, j) * factor;\n> + }\n> + }\n> +\n> + /*\n> + * Then diagonalize the input, walking the diagonal backwards. There's\n> + * no need to update the input matrix, as all the values we would write\n> + * in the top-right triangle aren't used in further calculations (and\n> + * would all by definition be zero).\n> + */\n> + for (unsigned int pivot = dim - 1; pivot > 0; --pivot) {\n> + const T pivotValue = matrix(pivot, pivot);\n> +\n> + for (unsigned int i = 0; i < pivot; ++i) {\n> + const T factor = matrix(i, pivot) / pivotValue;\n> +\n> + for (unsigned int j = dim; j < dim * 2; ++j)\n> + matrix(i, j) -= matrix(pivot, j) * factor;\n> + }\n> + }\n> +\n> + /*\n> + * Finally, normalize the diagonal and store the result in the output\n> + * data.\n> + */\n> + for (unsigned int i = 0; i < dim; ++i) {\n> + const T factor = matrix(i, i);\n> +\n> + for (unsigned int j = 0; j < dim; ++j)\n> + dataOut[i * dim + j] = matrix(i, j + dim) / factor;\n> + }\n> +\n> + return true;\n> +}\n> +\n> +template bool matrixInvert(Span dataIn, Span dataOut,\n> + unsigned int dim, Span scratchBuffer,\n> + Span swapBuffer);\n> +template bool matrixInvert(Span data, Span dataOut,\n> + unsigned int dim, Span scratchBuffer,\n> + Span swapBuffer);\n> +\n> /*\n> * The YAML data shall be a list of numerical values. Its size shall be equal\n> * to the product of the number of rows and columns of the matrix (Rows x\n> -- \n> 2.43.0\n>","headers":{"Return-Path":"","X-Original-To":"parsemail@patchwork.libcamera.org","Delivered-To":"parsemail@patchwork.libcamera.org","Received":["from lancelot.ideasonboard.com (lancelot.ideasonboard.com\n\t[92.243.16.209])\n\tby patchwork.libcamera.org (Postfix) with ESMTPS id 52416C327D\n\tfor ;\n\tFri, 2 May 2025 07:49:48 +0000 (UTC)","from lancelot.ideasonboard.com (localhost [IPv6:::1])\n\tby lancelot.ideasonboard.com (Postfix) with ESMTP id 9F99168AD8;\n\tFri, 2 May 2025 09:49:47 +0200 (CEST)","from perceval.ideasonboard.com (perceval.ideasonboard.com\n\t[213.167.242.64])\n\tby lancelot.ideasonboard.com (Postfix) with ESMTPS id 39DBA68ACB\n\tfor ;\n\tFri, 2 May 2025 09:49:46 +0200 (CEST)","from pendragon.ideasonboard.com\n\t(cpc89244-aztw30-2-0-cust6594.18-1.cable.virginm.net [86.31.185.195])\n\tby perceval.ideasonboard.com (Postfix) with ESMTPSA id 57BF5353;\n\tFri, 2 May 2025 09:49:38 +0200 (CEST)"],"Authentication-Results":"lancelot.ideasonboard.com; dkim=pass (1024-bit key;\n\tunprotected) header.d=ideasonboard.com header.i=@ideasonboard.com\n\theader.b=\"klb1vlqb\"; dkim-atps=neutral","DKIM-Signature":"v=1; a=rsa-sha256; c=relaxed/simple; d=ideasonboard.com;\n\ts=mail; t=1746172178;\n\tbh=AekfZ2XSj2hZz5/27FMz54wc+/YEZ9YlY8YKCeE9VSY=;\n\th=In-Reply-To:References:Subject:From:Cc:To:Date:From;\n\tb=klb1vlqbhVkvDjT8Tpk7zXivAg9JZ8LvROWpwhCqEFrwllqoPAYCQEvJdUaM4Dgr2\n\ttLVdPkQNSZVqOlMGON39kIA8uTYRrfA0Pox5pCkOOr4fRXHyXxG8HzcQqOKip84MPy\n\tqKku3ArxZfSM60eaE5vthA3LMnlzvXZKI+0Q2PV8=","Content-Type":"text/plain; charset=\"utf-8\"","MIME-Version":"1.0","Content-Transfer-Encoding":"quoted-printable","In-Reply-To":"<20250403154925.382973-6-stefan.klug@ideasonboard.com>","References":"<20250403154925.382973-1-stefan.klug@ideasonboard.com>\n\t<20250403154925.382973-6-stefan.klug@ideasonboard.com>","Subject":"Re: [PATCH v3 05/16] libcamera: matrix: Add inverse() function","From":"Kieran Bingham ","Cc":"Stefan Klug ,\n\tLaurent Pinchart ","To":"Stefan Klug ,\n\tlibcamera-devel@lists.libcamera.org","Date":"Fri, 02 May 2025 08:49:42 +0100","Message-ID":"<174617218287.1586992.12766708855039261289@ping.linuxembedded.co.uk>","User-Agent":"alot/0.10","X-BeenThere":"libcamera-devel@lists.libcamera.org","X-Mailman-Version":"2.1.29","Precedence":"list","List-Id":"","List-Unsubscribe":",\n\t","List-Archive":"","List-Post":"","List-Help":"","List-Subscribe":",\n\t","Errors-To":"libcamera-devel-bounces@lists.libcamera.org","Sender":"\"libcamera-devel\" "}},{"id":34142,"web_url":"https://patchwork.libcamera.org/comment/34142/","msgid":"","date":"2025-05-07T16:41:53","subject":"Re: [PATCH v3 05/16] libcamera: matrix: Add inverse() function","submitter":{"id":17,"url":"https://patchwork.libcamera.org/api/people/17/","name":"Paul Elder","email":"paul.elder@ideasonboard.com"},"content":"On Fri, May 02, 2025 at 08:49:42AM +0100, Kieran Bingham wrote:\n> Quoting Stefan Klug (2025-04-03 16:49:10)\n> > For calculations in upcoming algorithm patches, the inverse of a matrix\n> > is required. Add an implementation of the inverse() function for square\n> > matrices.\n> > \n> > Signed-off-by: Stefan Klug \n> > Signed-off-by: Laurent Pinchart \n> > \n> \n> Given there's a test structure added after this...\n> \n> \n> Reviewed-by: Kieran Bingham \n> \n> Maybe that should be just acked by as I'm not spending a lot of time to\n> review the Gaussian Ellimination here - but I trust you and\n> Laurent and the results of some tests being added to the unit tests for\n> it so I'm fine with it ;-)\n\nI went through and reviewed the Gaussian Elimination...\n\nReviewed-by: Paul Elder \n\n> \n> > ---\n> > \n> > Changes in v2:\n> > - Replaced the implementation by a generic one provided by Laurent that\n> > supports arbitrary square matrices instead of 2x2 and 3x3 only.\n> > - Moved the implementation into the cpp file.\n> > \n> > Changes inv3:\n> > - Added stack allocated scratchBuffers to matrixInvert so that no heap\n> > allocations are necessary.\n> > ---\n> > include/libcamera/internal/matrix.h | 23 ++++\n> > src/libcamera/matrix.cpp | 166 ++++++++++++++++++++++++++++\n> > 2 files changed, 189 insertions(+)\n> > \n> > diff --git a/include/libcamera/internal/matrix.h b/include/libcamera/internal/matrix.h\n> > index 6d40567af0a0..a07a47701336 100644\n> > --- a/include/libcamera/internal/matrix.h\n> > +++ b/include/libcamera/internal/matrix.h\n> > @@ -19,6 +19,12 @@ namespace libcamera {\n> > \n> > LOG_DECLARE_CATEGORY(Matrix)\n> > \n> > +#ifndef __DOXYGEN__\n> > +template\n> > +bool matrixInvert(Span dataIn, Span dataOut, unsigned int dim,\n> > + Span scratchBuffer, Span swapBuffer);\n> > +#endif /* __DOXYGEN__ */\n> > +\n> > template\n> > class Matrix\n> > {\n> > @@ -91,6 +97,23 @@ public:\n> > return *this;\n> > }\n> > \n> > + Matrix inverse(bool *ok = nullptr) const\n> > + {\n> > + static_assert(Rows == Cols, \"Matrix must be square\");\n> > +\n> > + Matrix inverse;\n> > + std::array scratchBuffer;\n> > + std::array swapBuffer;\n> > + bool res = matrixInvert(Span(data_),\n> > + Span(inverse.data_),\n> > + Rows,\n> > + Span(scratchBuffer),\n> > + Span(swapBuffer));\n> > + if (ok)\n> > + *ok = res;\n> > + return inverse;\n> > + }\n> > +\n> > private:\n> > /*\n> > * \\todo The initializer is only necessary for the constructor to be\n> > diff --git a/src/libcamera/matrix.cpp b/src/libcamera/matrix.cpp\n> > index 49e2aa3b4f2c..68fc1b7bd5ac 100644\n> > --- a/src/libcamera/matrix.cpp\n> > +++ b/src/libcamera/matrix.cpp\n> > @@ -7,6 +7,12 @@\n> > \n> > #include \"libcamera/internal/matrix.h\"\n> > \n> > +#include \n> > +#include \n> > +#include \n> > +#include \n> > +#include \n> > +\n> > #include \n> > \n> > /**\n> > @@ -87,6 +93,20 @@ LOG_DEFINE_CATEGORY(Matrix)\n> > * \\return Row \\a i from the matrix, as a Span\n> > */\n> > \n> > +/**\n> > + * \\fn Matrix::inverse(bool *ok) const\n> > + * \\param[out] ok Indicate if the matrix was successfully inverted\n> > + * \\brief Compute the inverse of the matrix\n> > + *\n> > + * This function computes the inverse of the matrix. It is only implemented for\n> > + * matrices of float and double types. If \\a ok is provided it will be set to a\n> > + * boolean value to indicate of the inversion was successful. This can be used\n> > + * to check if the matrix is singular, in which case the function will return\n> > + * an identity matrix.\n> > + *\n> > + * \\return The inverse of the matrix\n> > + */\n> > +\n> > /**\n> > * \\fn Matrix::operator[](size_t i)\n> > * \\copydoc Matrix::operator[](size_t i) const\n> > @@ -142,6 +162,152 @@ LOG_DEFINE_CATEGORY(Matrix)\n> > */\n> > \n> > #ifndef __DOXYGEN__\n> > +template\n> > +bool matrixInvert(Span dataIn, Span dataOut, unsigned int dim,\n> > + Span scratchBuffer, Span swapBuffer)\n> > +{\n> > + /*\n> > + * Convenience class to access matrix data, providing a row-major (i,j)\n> > + * element accessor through the call operator, and the ability to swap\n> > + * rows without modifying the backing storage.\n> > + */\n> > + class MatrixAccessor\n> > + {\n> > + public:\n> > + MatrixAccessor(Span data, Span swapBuffer, unsigned int rows, unsigned int cols)\n> > + : data_(data), swap_(swapBuffer), rows_(rows), cols_(cols)\n> > + {\n> > + ASSERT(swap_.size() == rows);\n> > + std::iota(swap_.begin(), swap_.end(), T{ 0 });\n> > + }\n> > +\n> > + T &operator()(unsigned int row, unsigned int col)\n> > + {\n> > + assert(row < rows_ && col < cols_);\n> > + return data_[index(row, col)];\n> > + }\n> > +\n> > + void swap(unsigned int a, unsigned int b)\n> > + {\n> > + assert(a < rows_ && a < cols_);\n> > + std::swap(swap_[a], swap_[b]);\n> > + }\n> > +\n> > + private:\n> > + unsigned int index(unsigned int row, unsigned int col) const\n> > + {\n> > + return swap_[row] * cols_ + col;\n> > + }\n> > +\n> > + Span data_;\n> > + Span swap_;\n> > + unsigned int rows_;\n> > + unsigned int cols_;\n> > + };\n> > +\n> > + /*\n> > + * Matrix inversion using Gaussian elimination.\n> > + *\n> > + * Start by augmenting the original matrix with an identiy matrix of\n> > + * the same size.\n> > + */\n> > + ASSERT(scratchBuffer.size() == dim * dim * 2);\n> > + MatrixAccessor matrix(scratchBuffer, swapBuffer, dim, dim * 2);\n> > +\n> > + for (unsigned int i = 0; i < dim; ++i) {\n> > + for (unsigned int j = 0; j < dim; ++j) {\n> > + matrix(i, j) = dataIn[i * dim + j];\n> > + matrix(i, j + dim) = T{ 0 };\n> > + }\n> > + matrix(i, i + dim) = T{ 1 };\n> > + }\n> > +\n> > + /* Start by triangularizing the input . */\n> > + for (unsigned int pivot = 0; pivot < dim; ++pivot) {\n> > + /*\n> > + * Locate the next pivot. To improve numerical stability, use\n> > + * the row with the largest value in the pivot's column.\n> > + */\n> > + unsigned int row;\n> > + T maxValue{ 0 };\n> > +\n> > + for (unsigned int i = pivot; i < dim; ++i) {\n> > + T value = std::abs(matrix(i, pivot));\n> > + if (maxValue < value) {\n> > + maxValue = value;\n> > + row = i;\n> > + }\n> > + }\n> > +\n> > + /*\n> > + * If no pivot is found in the column, the matrix is not\n> > + * invertible. Return an identity matrix.\n> > + */\n> > + if (maxValue == 0) {\n> > + std::fill(dataOut.begin(), dataOut.end(), T{ 0 });\n> > + for (unsigned int i = 0; i < dim; ++i)\n> > + dataOut[i * dim + i] = T{ 1 };\n> > + return false;\n> > + }\n> > +\n> > + /* Swap rows to bring the pivot in the right location. */\n> > + matrix.swap(pivot, row);\n> > +\n> > + /* Process all rows below the pivot to zero the pivot column. */\n> > + const T pivotValue = matrix(pivot, pivot);\n> > +\n> > + for (unsigned int i = pivot + 1; i < dim; ++i) {\n> > + const T factor = matrix(i, pivot) / pivotValue;\n> > +\n> > + /*\n> > + * We know the element in the pivot column will be 0,\n> > + * hardcode it instead of computing it.\n> > + */\n> > + matrix(i, pivot) = T{ 0 };\n> > +\n> > + for (unsigned int j = pivot + 1; j < dim * 2; ++j)\n> > + matrix(i, j) -= matrix(pivot, j) * factor;\n> > + }\n> > + }\n> > +\n> > + /*\n> > + * Then diagonalize the input, walking the diagonal backwards. There's\n> > + * no need to update the input matrix, as all the values we would write\n> > + * in the top-right triangle aren't used in further calculations (and\n> > + * would all by definition be zero).\n> > + */\n> > + for (unsigned int pivot = dim - 1; pivot > 0; --pivot) {\n> > + const T pivotValue = matrix(pivot, pivot);\n> > +\n> > + for (unsigned int i = 0; i < pivot; ++i) {\n> > + const T factor = matrix(i, pivot) / pivotValue;\n> > +\n> > + for (unsigned int j = dim; j < dim * 2; ++j)\n> > + matrix(i, j) -= matrix(pivot, j) * factor;\n> > + }\n> > + }\n> > +\n> > + /*\n> > + * Finally, normalize the diagonal and store the result in the output\n> > + * data.\n> > + */\n> > + for (unsigned int i = 0; i < dim; ++i) {\n> > + const T factor = matrix(i, i);\n> > +\n> > + for (unsigned int j = 0; j < dim; ++j)\n> > + dataOut[i * dim + j] = matrix(i, j + dim) / factor;\n> > + }\n> > +\n> > + return true;\n> > +}\n> > +\n> > +template bool matrixInvert(Span dataIn, Span dataOut,\n> > + unsigned int dim, Span scratchBuffer,\n> > + Span swapBuffer);\n> > +template bool matrixInvert(Span data, Span dataOut,\n> > + unsigned int dim, Span scratchBuffer,\n> > + Span swapBuffer);\n> > +\n> > /*\n> > * The YAML data shall be a list of numerical values. Its size shall be equal\n> > * to the product of the number of rows and columns of the matrix (Rows x\n> > -- \n> > 2.43.0\n> >","headers":{"Return-Path":"","X-Original-To":"parsemail@patchwork.libcamera.org","Delivered-To":"parsemail@patchwork.libcamera.org","Received":["from lancelot.ideasonboard.com (lancelot.ideasonboard.com\n\t[92.243.16.209])\n\tby patchwork.libcamera.org (Postfix) with ESMTPS id 94BABC3226\n\tfor ;\n\tWed, 7 May 2025 16:41:59 +0000 (UTC)","from lancelot.ideasonboard.com (localhost [IPv6:::1])\n\tby lancelot.ideasonboard.com (Postfix) with ESMTP id BFED168B31;\n\tWed, 7 May 2025 18:41:58 +0200 (CEST)","from perceval.ideasonboard.com (perceval.ideasonboard.com\n\t[IPv6:2001:4b98:dc2:55:216:3eff:fef7:d647])\n\tby lancelot.ideasonboard.com (Postfix) with ESMTPS id 8BE5168AD8\n\tfor ;\n\tWed, 7 May 2025 18:41:57 +0200 (CEST)","from pyrite.rasen.tech (unknown\n\t[IPv6:2001:861:3a80:3300:4f2f:8c2c:b3ef:17d4])\n\tby perceval.ideasonboard.com (Postfix) with ESMTPSA id C49806D5;\n\tWed, 7 May 2025 18:41:45 +0200 (CEST)"],"Authentication-Results":"lancelot.ideasonboard.com; dkim=pass (1024-bit key;\n\tunprotected) header.d=ideasonboard.com header.i=@ideasonboard.com\n\theader.b=\"V4uD75o9\"; dkim-atps=neutral","DKIM-Signature":"v=1; a=rsa-sha256; c=relaxed/simple; d=ideasonboard.com;\n\ts=mail; t=1746636105;\n\tbh=Bh8kZi7nmJX/j0a6Eoi5rsKs5xKs7xUbjWlniFNpK2Y=;\n\th=Date:From:To:Cc:Subject:References:In-Reply-To:From;\n\tb=V4uD75o9f+J4FfjzkbSEQJ5DWHG2bcVMiYLJw5RQj8wtO3IjiPG2M66SIHKwgCeks\n\tOd/mM7GZe2s1BaFDT8BagqX1z5Vtpn2nU+TD4bqn5vH3Kpqa6koU+1lTLdrXyay9Cp\n\t7DCNdWXLT5XaG9xGy5x5Gm1b/qKev5+QLg1eoIBo=","Date":"Wed, 7 May 2025 18:41:53 +0200","From":"Paul Elder ","To":"Kieran Bingham ","Cc":"Stefan Klug ,\n\tlibcamera-devel@lists.libcamera.org,\n\tLaurent Pinchart ","Subject":"Re: [PATCH v3 05/16] libcamera: matrix: Add inverse() function","Message-ID":"","References":"<20250403154925.382973-1-stefan.klug@ideasonboard.com>\n\t<20250403154925.382973-6-stefan.klug@ideasonboard.com>\n\t<174617218287.1586992.12766708855039261289@ping.linuxembedded.co.uk>","MIME-Version":"1.0","Content-Type":"text/plain; charset=us-ascii","Content-Disposition":"inline","In-Reply-To":"<174617218287.1586992.12766708855039261289@ping.linuxembedded.co.uk>","X-BeenThere":"libcamera-devel@lists.libcamera.org","X-Mailman-Version":"2.1.29","Precedence":"list","List-Id":"","List-Unsubscribe":",\n\t","List-Archive":"","List-Post":"","List-Help":"","List-Subscribe":",\n\t","Errors-To":"libcamera-devel-bounces@lists.libcamera.org","Sender":"\"libcamera-devel\" "}}]