blender-archive/source/blender/python/mathutils/mathutils_Matrix.c

/*
 * ***** BEGIN GPL LICENSE BLOCK *****
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * Contributor(s): Michel Selten & Joseph Gilbert
 *
 * ***** END GPL LICENSE BLOCK *****
 */

/** \file blender/python/mathutils/mathutils_Matrix.c
 *  \ingroup pymathutils
 */


#include <Python.h>

#include "mathutils.h"

#include "BLI_math.h"
#include "BLI_utildefines.h"

#include "../generic/python_utildefines.h"

#ifndef MATH_STANDALONE
#  include "BLI_string.h"
#  include "BLI_dynstr.h"
#endif

typedef enum eMatrixAccess_t {
	MAT_ACCESS_ROW,
	MAT_ACCESS_COL
} eMatrixAccess_t;

static PyObject *Matrix_copy_notest(MatrixObject *self, const float *matrix);
static PyObject *Matrix_copy(MatrixObject *self);
static PyObject *Matrix_deepcopy(MatrixObject *self, PyObject *args);
static int Matrix_ass_slice(MatrixObject *self, int begin, int end, PyObject *value);
static PyObject *matrix__apply_to_copy(PyNoArgsFunction matrix_func, MatrixObject *self);
static PyObject *MatrixAccess_CreatePyObject(MatrixObject *matrix, const eMatrixAccess_t type);

static int matrix_row_vector_check(MatrixObject *mat, VectorObject *vec, int row)
{
	if ((vec->size != mat->num_col) || (row >= mat->num_row)) {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix(): "
		                "owner matrix has been resized since this row vector was created");
		return 0;
	}
	else {
		return 1;
	}
}

static int matrix_col_vector_check(MatrixObject *mat, VectorObject *vec, int col)
{
	if ((vec->size != mat->num_row) || (col >= mat->num_col)) {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix(): "
		                "owner matrix has been resized since this column vector was created");
		return 0;
	}
	else {
		return 1;
	}
}

/* ----------------------------------------------------------------------------
 * matrix row callbacks
 * this is so you can do matrix[i][j] = val OR matrix.row[i][j] = val */

unsigned char mathutils_matrix_row_cb_index = -1;

static int mathutils_matrix_row_check(BaseMathObject *bmo)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	return BaseMath_ReadCallback(self);
}

static int mathutils_matrix_row_get(BaseMathObject *bmo, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int col;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;
	if (!matrix_row_vector_check(self, (VectorObject *)bmo, row))
		return -1;

	for (col = 0; col < self->num_col; col++) {
		bmo->data[col] = MATRIX_ITEM(self, row, col);
	}

	return 0;
}

static int mathutils_matrix_row_set(BaseMathObject *bmo, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int col;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;
	if (!matrix_row_vector_check(self, (VectorObject *)bmo, row))
		return -1;

	for (col = 0; col < self->num_col; col++) {
		MATRIX_ITEM(self, row, col) = bmo->data[col];
	}

	(void)BaseMath_WriteCallback(self);
	return 0;
}

static int mathutils_matrix_row_get_index(BaseMathObject *bmo, int row, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;
	if (!matrix_row_vector_check(self, (VectorObject *)bmo, row))
		return -1;

	bmo->data[col] = MATRIX_ITEM(self, row, col);
	return 0;
}

static int mathutils_matrix_row_set_index(BaseMathObject *bmo, int row, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;
	if (!matrix_row_vector_check(self, (VectorObject *)bmo, row))
		return -1;

	MATRIX_ITEM(self, row, col) = bmo->data[col];

	(void)BaseMath_WriteCallback(self);
	return 0;
}

Mathutils_Callback mathutils_matrix_row_cb = {
	mathutils_matrix_row_check,
	mathutils_matrix_row_get,
	mathutils_matrix_row_set,
	mathutils_matrix_row_get_index,
	mathutils_matrix_row_set_index
};


/* ----------------------------------------------------------------------------
 * matrix row callbacks
 * this is so you can do matrix.col[i][j] = val */

unsigned char mathutils_matrix_col_cb_index = -1;

static int mathutils_matrix_col_check(BaseMathObject *bmo)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	return BaseMath_ReadCallback(self);
}

static int mathutils_matrix_col_get(BaseMathObject *bmo, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int num_row;
	int row;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;
	if (!matrix_col_vector_check(self, (VectorObject *)bmo, col))
		return -1;

	/* for 'translation' size will always be '3' even on 4x4 vec */
	num_row = min_ii(self->num_row, ((VectorObject *)bmo)->size);

	for (row = 0; row < num_row; row++) {
		bmo->data[row] = MATRIX_ITEM(self, row, col);
	}

	return 0;
}

static int mathutils_matrix_col_set(BaseMathObject *bmo, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int num_row;
	int row;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;
	if (!matrix_col_vector_check(self, (VectorObject *)bmo, col))
		return -1;

	/* for 'translation' size will always be '3' even on 4x4 vec */
	num_row = min_ii(self->num_row, ((VectorObject *)bmo)->size);

	for (row = 0; row < num_row; row++) {
		MATRIX_ITEM(self, row, col) = bmo->data[row];
	}

	(void)BaseMath_WriteCallback(self);
	return 0;
}

static int mathutils_matrix_col_get_index(BaseMathObject *bmo, int col, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;
	if (!matrix_col_vector_check(self, (VectorObject *)bmo, col))
		return -1;

	bmo->data[row] = MATRIX_ITEM(self, row, col);
	return 0;
}

static int mathutils_matrix_col_set_index(BaseMathObject *bmo, int col, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;
	if (!matrix_col_vector_check(self, (VectorObject *)bmo, col))
		return -1;

	MATRIX_ITEM(self, row, col) = bmo->data[row];

	(void)BaseMath_WriteCallback(self);
	return 0;
}

Mathutils_Callback mathutils_matrix_col_cb = {
	mathutils_matrix_col_check,
	mathutils_matrix_col_get,
	mathutils_matrix_col_set,
	mathutils_matrix_col_get_index,
	mathutils_matrix_col_set_index
};


/* ----------------------------------------------------------------------------
 * matrix row callbacks
 * this is so you can do matrix.translation = val
 * note, this is _exactly like matrix.col except the 4th component is always omitted */

unsigned char mathutils_matrix_translation_cb_index = -1;

static int mathutils_matrix_translation_check(BaseMathObject *bmo)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	return BaseMath_ReadCallback(self);
}

static int mathutils_matrix_translation_get(BaseMathObject *bmo, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int row;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;

	for (row = 0; row < 3; row++) {
		bmo->data[row] = MATRIX_ITEM(self, row, col);
	}

	return 0;
}

static int mathutils_matrix_translation_set(BaseMathObject *bmo, int col)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;
	int row;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	for (row = 0; row < 3; row++) {
		MATRIX_ITEM(self, row, col) = bmo->data[row];
	}

	(void)BaseMath_WriteCallback(self);
	return 0;
}

static int mathutils_matrix_translation_get_index(BaseMathObject *bmo, int col, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback(self) == -1)
		return -1;

	bmo->data[row] = MATRIX_ITEM(self, row, col);
	return 0;
}

static int mathutils_matrix_translation_set_index(BaseMathObject *bmo, int col, int row)
{
	MatrixObject *self = (MatrixObject *)bmo->cb_user;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	MATRIX_ITEM(self, row, col) = bmo->data[row];

	(void)BaseMath_WriteCallback(self);
	return 0;
}

Mathutils_Callback mathutils_matrix_translation_cb = {
	mathutils_matrix_translation_check,
	mathutils_matrix_translation_get,
	mathutils_matrix_translation_set,
	mathutils_matrix_translation_get_index,
	mathutils_matrix_translation_set_index
};


/* matrix column callbacks, this is so you can do matrix.translation = Vector()  */

/* ----------------------------------mathutils.Matrix() ----------------- */
/* mat is a 1D array of floats - row[0][0], row[0][1], row[1][0], etc. */
/* create a new matrix type */
static PyObject *Matrix_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
	if (kwds && PyDict_Size(kwds)) {
		PyErr_SetString(PyExc_TypeError,
		                "Matrix(): "
		                "takes no keyword args");
		return NULL;
	}

	switch (PyTuple_GET_SIZE(args)) {
		case 0:
			return Matrix_CreatePyObject(NULL, 4, 4, type);
		case 1:
		{
			PyObject *arg = PyTuple_GET_ITEM(args, 0);

			/* Input is now as a sequence of rows so length of sequence
			 * is the number of rows */
			/* -1 is an error, size checks will accunt for this */
			const unsigned short num_row = PySequence_Size(arg);

			if (num_row >= 2 && num_row <= 4) {
				PyObject *item = PySequence_GetItem(arg, 0);
				/* Since each item is a row, number of items is the
				 * same as the number of columns */
				const unsigned short num_col = PySequence_Size(item);
				Py_XDECREF(item);

				if (num_col >= 2 && num_col <= 4) {
					/* sane row & col size, new matrix and assign as slice  */
					PyObject *matrix = Matrix_CreatePyObject(NULL, num_col, num_row, type);
					if (Matrix_ass_slice((MatrixObject *)matrix, 0, INT_MAX, arg) == 0) {
						return matrix;
					}
					else { /* matrix ok, slice assignment not */
						Py_DECREF(matrix);
					}
				}
			}
			break;
		}
	}

	/* will overwrite error */
	PyErr_SetString(PyExc_TypeError,
	                "Matrix(): "
	                "expects no args or a single arg containing 2-4 numeric sequences");
	return NULL;
}

static PyObject *matrix__apply_to_copy(PyNoArgsFunction matrix_func, MatrixObject *self)
{
	PyObject *ret = Matrix_copy(self);
	if (ret) {
		PyObject *ret_dummy = matrix_func(ret);
		if (ret_dummy) {
			Py_DECREF(ret_dummy);
			return (PyObject *)ret;
		}
		else { /* error */
			Py_DECREF(ret);
			return NULL;
		}
	}
	else {
		/* copy may fail if the read callback errors out */
		return NULL;
	}
}

/* when a matrix is 4x4 size but initialized as a 3x3, re-assign values for 4x4 */
static void matrix_3x3_as_4x4(float mat[16])
{
	mat[10] = mat[8];
	mat[9] = mat[7];
	mat[8] = mat[6];
	mat[7] = 0.0f;
	mat[6] = mat[5];
	mat[5] = mat[4];
	mat[4] = mat[3];
	mat[3] = 0.0f;
}

/*-----------------------CLASS-METHODS----------------------------*/

/* mat is a 1D array of floats - row[0][0], row[0][1], row[1][0], etc. */
PyDoc_STRVAR(C_Matrix_Identity_doc,
".. classmethod:: Identity(size)\n"
"\n"
"   Create an identity matrix.\n"
"\n"
"   :arg size: The size of the identity matrix to construct [2, 4].\n"
"   :type size: int\n"
"   :return: A new identity matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_Identity(PyObject *cls, PyObject *args)
{
	int matSize;

	if (!PyArg_ParseTuple(args, "i:Matrix.Identity", &matSize)) {
		return NULL;
	}

	if (matSize < 2 || matSize > 4) {
		PyErr_SetString(PyExc_RuntimeError,
		                "Matrix.Identity(): "
		                "size must be between 2 and 4");
		return NULL;
	}

	return Matrix_CreatePyObject(NULL, matSize, matSize, (PyTypeObject *)cls);
}

PyDoc_STRVAR(C_Matrix_Rotation_doc,
".. classmethod:: Rotation(angle, size, axis)\n"
"\n"
"   Create a matrix representing a rotation.\n"
"\n"
"   :arg angle: The angle of rotation desired, in radians.\n"
"   :type angle: float\n"
"   :arg size: The size of the rotation matrix to construct [2, 4].\n"
"   :type size: int\n"
"   :arg axis: a string in ['X', 'Y', 'Z'] or a 3D Vector Object\n"
"      (optional when size is 2).\n"
"   :type axis: string or :class:`Vector`\n"
"   :return: A new rotation matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_Rotation(PyObject *cls, PyObject *args)
{
	PyObject *vec = NULL;
	const char *axis = NULL;
	int matSize;
	double angle; /* use double because of precision problems at high values */
	float mat[16] = {0.0f, 0.0f, 0.0f, 0.0f,
		             0.0f, 0.0f, 0.0f, 0.0f,
		             0.0f, 0.0f, 0.0f, 0.0f,
		             0.0f, 0.0f, 0.0f, 1.0f};

	if (!PyArg_ParseTuple(args, "di|O:Matrix.Rotation", &angle, &matSize, &vec)) {
		return NULL;
	}

	if (vec && PyUnicode_Check(vec)) {
		axis = _PyUnicode_AsString((PyObject *)vec);
		if (axis == NULL || axis[0] == '\0' || axis[1] != '\0' || axis[0] < 'X' || axis[0] > 'Z') {
			PyErr_SetString(PyExc_ValueError,
			                "Matrix.Rotation(): "
			                "3rd argument axis value must be a 3D vector "
			                "or a string in 'X', 'Y', 'Z'");
			return NULL;
		}
		else {
			/* use the string */
			vec = NULL;
		}
	}

	angle = angle_wrap_rad(angle);

	if (matSize != 2 && matSize != 3 && matSize != 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.Rotation(): "
		                "can only return a 2x2 3x3 or 4x4 matrix");
		return NULL;
	}
	if (matSize == 2 && (vec != NULL)) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.Rotation(): "
		                "cannot create a 2x2 rotation matrix around arbitrary axis");
		return NULL;
	}
	if ((matSize == 3 || matSize == 4) && (axis == NULL) && (vec == NULL)) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.Rotation(): "
		                "axis of rotation for 3d and 4d matrices is required");
		return NULL;
	}

	/* check for valid vector/axis above */
	if (vec) {
		float tvec[3];

		if (mathutils_array_parse(tvec, 3, 3, vec, "Matrix.Rotation(angle, size, axis), invalid 'axis' arg") == -1)
			return NULL;

		axis_angle_to_mat3((float (*)[3])mat, tvec, angle);
	}
	else if (matSize == 2) {
		angle_to_mat2((float (*)[2])mat, angle);

	}
	else {
		/* valid axis checked above */
		axis_angle_to_mat3_single((float (*)[3])mat, axis[0], angle);
	}

	if (matSize == 4) {
		matrix_3x3_as_4x4(mat);
	}
	/* pass to matrix creation */
	return Matrix_CreatePyObject(mat, matSize, matSize, (PyTypeObject *)cls);
}


PyDoc_STRVAR(C_Matrix_Translation_doc,
".. classmethod:: Translation(vector)\n"
"\n"
"   Create a matrix representing a translation.\n"
"\n"
"   :arg vector: The translation vector.\n"
"   :type vector: :class:`Vector`\n"
"   :return: An identity matrix with a translation.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_Translation(PyObject *cls, PyObject *value)
{
	float mat[4][4];

	unit_m4(mat);

	if (mathutils_array_parse(mat[3], 3, 4, value, "mathutils.Matrix.Translation(vector), invalid vector arg") == -1)
		return NULL;

	return Matrix_CreatePyObject(&mat[0][0], 4, 4, (PyTypeObject *)cls);
}
/* ----------------------------------mathutils.Matrix.Scale() ------------- */
/* mat is a 1D array of floats - row[0][0], row[0][1], row[1][0], etc. */
PyDoc_STRVAR(C_Matrix_Scale_doc,
".. classmethod:: Scale(factor, size, axis)\n"
"\n"
"   Create a matrix representing a scaling.\n"
"\n"
"   :arg factor: The factor of scaling to apply.\n"
"   :type factor: float\n"
"   :arg size: The size of the scale matrix to construct [2, 4].\n"
"   :type size: int\n"
"   :arg axis: Direction to influence scale. (optional).\n"
"   :type axis: :class:`Vector`\n"
"   :return: A new scale matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_Scale(PyObject *cls, PyObject *args)
{
	PyObject *vec = NULL;
	int vec_size;
	float tvec[3];
	float factor;
	int matSize;
	float mat[16] = {0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 1.0f};

	if (!PyArg_ParseTuple(args, "fi|O:Matrix.Scale", &factor, &matSize, &vec)) {
		return NULL;
	}
	if (matSize != 2 && matSize != 3 && matSize != 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.Scale(): "
		                "can only return a 2x2 3x3 or 4x4 matrix");
		return NULL;
	}
	if (vec) {
		vec_size = (matSize == 2 ? 2 : 3);
		if (mathutils_array_parse(tvec, vec_size, vec_size, vec,
		                          "Matrix.Scale(factor, size, axis), invalid 'axis' arg") == -1)
		{
			return NULL;
		}
	}
	if (vec == NULL) {  /* scaling along axis */
		if (matSize == 2) {
			mat[0] = factor;
			mat[3] = factor;
		}
		else {
			mat[0] = factor;
			mat[4] = factor;
			mat[8] = factor;
		}
	}
	else {
		/* scaling in arbitrary direction
		 * normalize arbitrary axis */
		float norm = 0.0f;
		int x;
		for (x = 0; x < vec_size; x++) {
			norm += tvec[x] * tvec[x];
		}
		norm = sqrtf(norm);
		for (x = 0; x < vec_size; x++) {
			tvec[x] /= norm;
		}
		if (matSize == 2) {
			mat[0] = 1 + ((factor - 1) * (tvec[0] * tvec[0]));
			mat[1] =     ((factor - 1) * (tvec[0] * tvec[1]));
			mat[2] =     ((factor - 1) * (tvec[0] * tvec[1]));
			mat[3] = 1 + ((factor - 1) * (tvec[1] * tvec[1]));
		}
		else {
			mat[0] = 1 + ((factor - 1) * (tvec[0] * tvec[0]));
			mat[1] =     ((factor - 1) * (tvec[0] * tvec[1]));
			mat[2] =     ((factor - 1) * (tvec[0] * tvec[2]));
			mat[3] =     ((factor - 1) * (tvec[0] * tvec[1]));
			mat[4] = 1 + ((factor - 1) * (tvec[1] * tvec[1]));
			mat[5] =     ((factor - 1) * (tvec[1] * tvec[2]));
			mat[6] =     ((factor - 1) * (tvec[0] * tvec[2]));
			mat[7] =     ((factor - 1) * (tvec[1] * tvec[2]));
			mat[8] = 1 + ((factor - 1) * (tvec[2] * tvec[2]));
		}
	}
	if (matSize == 4) {
		matrix_3x3_as_4x4(mat);
	}
	/* pass to matrix creation */
	return Matrix_CreatePyObject(mat, matSize, matSize, (PyTypeObject *)cls);
}
/* ----------------------------------mathutils.Matrix.OrthoProjection() --- */
/* mat is a 1D array of floats - row[0][0], row[0][1], row[1][0], etc. */
PyDoc_STRVAR(C_Matrix_OrthoProjection_doc,
".. classmethod:: OrthoProjection(axis, size)\n"
"\n"
"   Create a matrix to represent an orthographic projection.\n"
"\n"
"   :arg axis: Can be any of the following: ['X', 'Y', 'XY', 'XZ', 'YZ'],\n"
"      where a single axis is for a 2D matrix.\n"
"      Or a vector for an arbitrary axis\n"
"   :type axis: string or :class:`Vector`\n"
"   :arg size: The size of the projection matrix to construct [2, 4].\n"
"   :type size: int\n"
"   :return: A new projection matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_OrthoProjection(PyObject *cls, PyObject *args)
{
	PyObject *axis;

	int matSize, x;
	float norm = 0.0f;
	float mat[16] = {0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 1.0f};

	if (!PyArg_ParseTuple(args, "Oi:Matrix.OrthoProjection", &axis, &matSize)) {
		return NULL;
	}
	if (matSize != 2 && matSize != 3 && matSize != 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.OrthoProjection(): "
		                "can only return a 2x2 3x3 or 4x4 matrix");
		return NULL;
	}

	if (PyUnicode_Check(axis)) {  /* ortho projection onto cardinal plane */
		Py_ssize_t plane_len;
		const char *plane = _PyUnicode_AsStringAndSize(axis, &plane_len);
		if (matSize == 2) {
			if (plane_len == 1 && plane[0] == 'X') {
				mat[0] = 1.0f;
			}
			else if (plane_len == 1 && plane[0] == 'Y') {
				mat[3] = 1.0f;
			}
			else {
				PyErr_Format(PyExc_ValueError,
				             "Matrix.OrthoProjection(): "
				             "unknown plane, expected: X, Y, not '%.200s'",
				             plane);
				return NULL;
			}
		}
		else {
			if (plane_len == 2 && plane[0] == 'X' && plane[1] == 'Y') {
				mat[0] = 1.0f;
				mat[4] = 1.0f;
			}
			else if (plane_len == 2 && plane[0] == 'X' && plane[1] == 'Z') {
				mat[0] = 1.0f;
				mat[8] = 1.0f;
			}
			else if (plane_len == 2 && plane[0] == 'Y' && plane[1] == 'Z') {
				mat[4] = 1.0f;
				mat[8] = 1.0f;
			}
			else {
				PyErr_Format(PyExc_ValueError,
				             "Matrix.OrthoProjection(): "
				             "unknown plane, expected: XY, XZ, YZ, not '%.200s'",
				             plane);
				return NULL;
			}
		}
	}
	else {
		/* arbitrary plane */

		int vec_size = (matSize == 2 ? 2 : 3);
		float tvec[4];

		if (mathutils_array_parse(tvec, vec_size, vec_size, axis,
		                          "Matrix.OrthoProjection(axis, size), invalid 'axis' arg") == -1)
		{
			return NULL;
		}

		/* normalize arbitrary axis */
		for (x = 0; x < vec_size; x++) {
			norm += tvec[x] * tvec[x];
		}
		norm = sqrtf(norm);
		for (x = 0; x < vec_size; x++) {
			tvec[x] /= norm;
		}
		if (matSize == 2) {
			mat[0] = 1 - (tvec[0] * tvec[0]);
			mat[1] =   - (tvec[0] * tvec[1]);
			mat[2] =   - (tvec[0] * tvec[1]);
			mat[3] = 1 - (tvec[1] * tvec[1]);
		}
		else if (matSize > 2) {
			mat[0] = 1 - (tvec[0] * tvec[0]);
			mat[1] =   - (tvec[0] * tvec[1]);
			mat[2] =   - (tvec[0] * tvec[2]);
			mat[3] =   - (tvec[0] * tvec[1]);
			mat[4] = 1 - (tvec[1] * tvec[1]);
			mat[5] =   - (tvec[1] * tvec[2]);
			mat[6] =   - (tvec[0] * tvec[2]);
			mat[7] =   - (tvec[1] * tvec[2]);
			mat[8] = 1 - (tvec[2] * tvec[2]);
		}
	}
	if (matSize == 4) {
		matrix_3x3_as_4x4(mat);
	}
	/* pass to matrix creation */
	return Matrix_CreatePyObject(mat, matSize, matSize, (PyTypeObject *)cls);
}

PyDoc_STRVAR(C_Matrix_Shear_doc,
".. classmethod:: Shear(plane, size, factor)\n"
"\n"
"   Create a matrix to represent an shear transformation.\n"
"\n"
"   :arg plane: Can be any of the following: ['X', 'Y', 'XY', 'XZ', 'YZ'],\n"
"      where a single axis is for a 2D matrix only.\n"
"   :type plane: string\n"
"   :arg size: The size of the shear matrix to construct [2, 4].\n"
"   :type size: int\n"
"   :arg factor: The factor of shear to apply. For a 3 or 4 *size* matrix\n"
"      pass a pair of floats corresponding with the *plane* axis.\n"
"   :type factor: float or float pair\n"
"   :return: A new shear matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *C_Matrix_Shear(PyObject *cls, PyObject *args)
{
	int matSize;
	const char *plane;
	PyObject *fac;
	float mat[16] = {0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 0.0f,
	                 0.0f, 0.0f, 0.0f, 1.0f};

	if (!PyArg_ParseTuple(args, "siO:Matrix.Shear", &plane, &matSize, &fac)) {
		return NULL;
	}
	if (matSize != 2 && matSize != 3 && matSize != 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.Shear(): "
		                "can only return a 2x2 3x3 or 4x4 matrix");
		return NULL;
	}

	if (matSize == 2) {
		float const factor = PyFloat_AsDouble(fac);

		if (factor == -1.0f && PyErr_Occurred()) {
			PyErr_SetString(PyExc_TypeError,
			                "Matrix.Shear(): "
			                "the factor to be a float");
			return NULL;
		}

		/* unit */
		mat[0] = 1.0f;
		mat[3] = 1.0f;

		if (STREQ(plane, "X")) {
			mat[2] = factor;
		}
		else if (STREQ(plane, "Y")) {
			mat[1] = factor;
		}
		else {
			PyErr_SetString(PyExc_ValueError,
			                "Matrix.Shear(): "
			                "expected: X, Y or wrong matrix size for shearing plane");
			return NULL;
		}
	}
	else {
		/* 3 or 4, apply as 3x3, resize later if needed */
		float factor[2];

		if (mathutils_array_parse(factor, 2, 2, fac, "Matrix.Shear()") == -1) {
			return NULL;
		}

		/* unit */
		mat[0] = 1.0f;
		mat[4] = 1.0f;
		mat[8] = 1.0f;

		if (STREQ(plane, "XY")) {
			mat[6] = factor[0];
			mat[7] = factor[1];
		}
		else if (STREQ(plane, "XZ")) {
			mat[3] = factor[0];
			mat[5] = factor[1];
		}
		else if (STREQ(plane, "YZ")) {
			mat[1] = factor[0];
			mat[2] = factor[1];
		}
		else {
			PyErr_SetString(PyExc_ValueError,
			                "Matrix.Shear(): "
			                "expected: X, Y, XY, XZ, YZ");
			return NULL;
		}
	}

	if (matSize == 4) {
		matrix_3x3_as_4x4(mat);
	}
	/* pass to matrix creation */
	return Matrix_CreatePyObject(mat, matSize, matSize, (PyTypeObject *)cls);
}

void matrix_as_3x3(float mat[3][3], MatrixObject *self)
{
	copy_v3_v3(mat[0], MATRIX_COL_PTR(self, 0));
	copy_v3_v3(mat[1], MATRIX_COL_PTR(self, 1));
	copy_v3_v3(mat[2], MATRIX_COL_PTR(self, 2));
}

static void matrix_copy(MatrixObject *mat_dst, const MatrixObject *mat_src)
{
	BLI_assert((mat_dst->num_col == mat_src->num_col) &&
	           (mat_dst->num_row == mat_src->num_row));
	BLI_assert(mat_dst != mat_src);

	memcpy(mat_dst->matrix, mat_src->matrix, sizeof(float) * (mat_dst->num_col * mat_dst->num_row));
}

/* transposes memory layout, rol/col's don't have to match */
static void matrix_transpose_internal(float mat_dst_fl[], const MatrixObject *mat_src)
{
	unsigned short col, row;
	unsigned int i = 0;

	for (row = 0; row < mat_src->num_row; row++) {
		for (col = 0; col < mat_src->num_col; col++) {
			mat_dst_fl[i++] = MATRIX_ITEM(mat_src, row, col);
		}
	}
}

/* assumes rowsize == colsize is checked and the read callback has run */
static float matrix_determinant_internal(const MatrixObject *self)
{
	if (self->num_col == 2) {
		return determinant_m2(MATRIX_ITEM(self, 0, 0), MATRIX_ITEM(self, 0, 1),
		                      MATRIX_ITEM(self, 1, 0), MATRIX_ITEM(self, 1, 1));
	}
	else if (self->num_col == 3) {
		return determinant_m3(MATRIX_ITEM(self, 0, 0), MATRIX_ITEM(self, 0, 1), MATRIX_ITEM(self, 0, 2),
		                      MATRIX_ITEM(self, 1, 0), MATRIX_ITEM(self, 1, 1), MATRIX_ITEM(self, 1, 2),
		                      MATRIX_ITEM(self, 2, 0), MATRIX_ITEM(self, 2, 1), MATRIX_ITEM(self, 2, 2));
	}
	else {
		return determinant_m4((float (*)[4])self->matrix);
	}
}

static void adjoint_matrix_n(float *mat_dst, const float *mat_src, const unsigned short dim)
{
	/* calculate the classical adjoint */
	switch (dim) {
		case 2:
		{
			adjoint_m2_m2((float (*)[2])mat_dst, (float (*)[2])mat_src);
			break;
		}
		case 3:
		{
			adjoint_m3_m3((float (*)[3])mat_dst, (float (*)[3])mat_src);
			break;
		}
		case 4:
		{
			adjoint_m4_m4((float (*)[4])mat_dst, (float (*)[4])mat_src);
			break;
		}
		default:
			BLI_assert(0);
	}
}

static void matrix_invert_with_det_n_internal(float *mat_dst, const float *mat_src, const float det, const unsigned short dim)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];
	unsigned short i, j, k;

	BLI_assert(det != 0.0f);

	adjoint_matrix_n(mat, mat_src, dim);

	/* divide by determinant & set values */
	k = 0;
	for (i = 0; i < dim; i++) {  /* num_col */
		for (j = 0; j < dim; j++) {  /* num_row */
			mat_dst[MATRIX_ITEM_INDEX_NUMROW(dim, j, i)] = mat[k++] / det;
		}
	}
}

/**
 * \param r_mat can be from ``self->matrix`` or not.
 */
static bool matrix_invert_internal(const MatrixObject *self, float *r_mat)
{
	float det;
	BLI_assert(self->num_col == self->num_row);
	det = matrix_determinant_internal(self);

	if (det != 0.0f) {
		matrix_invert_with_det_n_internal(r_mat, self->matrix, det, self->num_col);
		return true;
	}
	else {
		return false;
	}
}

/**
 * Similar to ``matrix_invert_internal`` but should never error.
 * \param r_mat can be from ``self->matrix`` or not.
 */
static void matrix_invert_safe_internal(const MatrixObject *self, float *r_mat)
{
	float det;
	float *in_mat = self->matrix;
	BLI_assert(self->num_col == self->num_row);
	det = matrix_determinant_internal(self);

	if (det == 0.0f) {
		const float eps = PSEUDOINVERSE_EPSILON;

		/* We will copy self->matrix into r_mat (if needed), and modify it in place to add diagonal epsilon. */
		in_mat = r_mat;

		switch (self->num_col) {
			case 2:
			{
				float (*mat)[2] = (float (*)[2])in_mat;

				if (in_mat != self->matrix) {
					copy_m2_m2(mat, (float (*)[2])self->matrix);
				}
				mat[0][0] += eps;
				mat[1][1] += eps;

				if (UNLIKELY((det = determinant_m2(mat[0][0], mat[0][1], mat[1][0], mat[1][1])) == 0.0f)) {
					unit_m2(mat);
					det = 1.0f;
				}
				break;
			}
			case 3:
			{
				float (*mat)[3] = (float (*)[3])in_mat;

				if (in_mat != self->matrix) {
					copy_m3_m3(mat, (float (*)[3])self->matrix);
				}
				mat[0][0] += eps;
				mat[1][1] += eps;
				mat[2][2] += eps;

				if (UNLIKELY((det = determinant_m3_array(mat)) == 0.0f)) {
					unit_m3(mat);
					det = 1.0f;
				}
				break;
			}
			case 4:
			{
				float (*mat)[4] = (float (*)[4])in_mat;

				if (in_mat != self->matrix) {
					copy_m4_m4(mat, (float (*)[4])self->matrix);
				}
				mat[0][0] += eps;
				mat[1][1] += eps;
				mat[2][2] += eps;
				mat[3][3] += eps;

				if (UNLIKELY(det = determinant_m4(mat)) == 0.0f) {
					unit_m4(mat);
					det = 1.0f;
				}
				break;
			}
			default:
				BLI_assert(0);
		}
	}

	matrix_invert_with_det_n_internal(r_mat, in_mat, det, self->num_col);
}


/*-----------------------------METHODS----------------------------*/
PyDoc_STRVAR(Matrix_to_quaternion_doc,
".. method:: to_quaternion()\n"
"\n"
"   Return a quaternion representation of the rotation matrix.\n"
"\n"
"   :return: Quaternion representation of the rotation matrix.\n"
"   :rtype: :class:`Quaternion`\n"
);
static PyObject *Matrix_to_quaternion(MatrixObject *self)
{
	float quat[4];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/* must be 3-4 cols, 3-4 rows, square matrix */
	if ((self->num_row < 3) || (self->num_col < 3) || (self->num_row != self->num_col)) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.to_quat(): "
		                "inappropriate matrix size - expects 3x3 or 4x4 matrix");
		return NULL;
	}
	if (self->num_row == 3) {
		mat3_to_quat(quat, (float (*)[3])self->matrix);
	}
	else {
		mat4_to_quat(quat, (float (*)[4])self->matrix);
	}

	return Quaternion_CreatePyObject(quat, NULL);
}

/*---------------------------matrix.toEuler() --------------------*/
PyDoc_STRVAR(Matrix_to_euler_doc,
".. method:: to_euler(order, euler_compat)\n"
"\n"
"   Return an Euler representation of the rotation matrix\n"
"   (3x3 or 4x4 matrix only).\n"
"\n"
"   :arg order: Optional rotation order argument in\n"
"      ['XYZ', 'XZY', 'YXZ', 'YZX', 'ZXY', 'ZYX'].\n"
"   :type order: string\n"
"   :arg euler_compat: Optional euler argument the new euler will be made\n"
"      compatible with (no axis flipping between them).\n"
"      Useful for converting a series of matrices to animation curves.\n"
"   :type euler_compat: :class:`Euler`\n"
"   :return: Euler representation of the matrix.\n"
"   :rtype: :class:`Euler`\n"
);
static PyObject *Matrix_to_euler(MatrixObject *self, PyObject *args)
{
	const char *order_str = NULL;
	short order = EULER_ORDER_XYZ;
	float eul[3], eul_compatf[3];
	EulerObject *eul_compat = NULL;

	float mat[3][3];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if (!PyArg_ParseTuple(args, "|sO!:to_euler", &order_str, &euler_Type, &eul_compat))
		return NULL;

	if (eul_compat) {
		if (BaseMath_ReadCallback(eul_compat) == -1)
			return NULL;

		copy_v3_v3(eul_compatf, eul_compat->eul);
	}

	/*must be 3-4 cols, 3-4 rows, square matrix */
	if (self->num_row == 3 && self->num_col == 3) {
		copy_m3_m3(mat, (float (*)[3])self->matrix);
	}
	else if (self->num_row == 4 && self->num_col == 4) {
		copy_m3_m4(mat, (float (*)[4])self->matrix);
	}
	else {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.to_euler(): "
		                "inappropriate matrix size - expects 3x3 or 4x4 matrix");
		return NULL;
	}

	if (order_str) {
		order = euler_order_from_string(order_str, "Matrix.to_euler()");

		if (order == -1)
			return NULL;
	}

	normalize_m3(mat);

	if (eul_compat) {
		if (order == 1) mat3_normalized_to_compatible_eul(eul, eul_compatf, mat);
		else            mat3_normalized_to_compatible_eulO(eul, eul_compatf, order, mat);
	}
	else {
		if (order == 1) mat3_normalized_to_eul(eul, mat);
		else            mat3_normalized_to_eulO(eul, order, mat);
	}

	return Euler_CreatePyObject(eul, order, NULL);
}

PyDoc_STRVAR(Matrix_resize_4x4_doc,
".. method:: resize_4x4()\n"
"\n"
"   Resize the matrix to 4x4.\n"
);
static PyObject *Matrix_resize_4x4(MatrixObject *self)
{
	float mat[4][4];
	int col;

	if (self->flag & BASE_MATH_FLAG_IS_WRAP) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.resize_4x4(): "
		                "cannot resize wrapped data - make a copy and resize that");
		return NULL;
	}
	if (self->cb_user) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.resize_4x4(): "
		                "cannot resize owned data - make a copy and resize that");
		return NULL;
	}

	self->matrix = PyMem_Realloc(self->matrix, (sizeof(float) * (MATRIX_MAX_DIM * MATRIX_MAX_DIM)));
	if (self->matrix == NULL) {
		PyErr_SetString(PyExc_MemoryError,
		                "Matrix.resize_4x4(): "
		                "problem allocating pointer space");
		return NULL;
	}

	unit_m4(mat);

	for (col = 0; col < self->num_col; col++) {
		memcpy(mat[col], MATRIX_COL_PTR(self, col), self->num_row * sizeof(float));
	}

	copy_m4_m4((float (*)[4])self->matrix, (float (*)[4])mat);

	self->num_col = 4;
	self->num_row = 4;

	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_to_4x4_doc,
".. method:: to_4x4()\n"
"\n"
"   Return a 4x4 copy of this matrix.\n"
"\n"
"   :return: a new matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_to_4x4(MatrixObject *self)
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if (self->num_row == 4 && self->num_col == 4) {
		return Matrix_CreatePyObject(self->matrix, 4, 4, Py_TYPE(self));
	}
	else if (self->num_row == 3 && self->num_col == 3) {
		float mat[4][4];
		copy_m4_m3(mat, (float (*)[3])self->matrix);
		return Matrix_CreatePyObject((float *)mat, 4, 4, Py_TYPE(self));
	}
	/* TODO, 2x2 matrix */

	PyErr_SetString(PyExc_ValueError,
	                "Matrix.to_4x4(): "
	                "inappropriate matrix size");
	return NULL;
}

PyDoc_STRVAR(Matrix_to_3x3_doc,
".. method:: to_3x3()\n"
"\n"
"   Return a 3x3 copy of this matrix.\n"
"\n"
"   :return: a new matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_to_3x3(MatrixObject *self)
{
	float mat[3][3];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if ((self->num_row < 3) || (self->num_col < 3)) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.to_3x3(): inappropriate matrix size");
		return NULL;
	}

	matrix_as_3x3(mat, self);

	return Matrix_CreatePyObject((float *)mat, 3, 3, Py_TYPE(self));
}

PyDoc_STRVAR(Matrix_to_translation_doc,
".. method:: to_translation()\n"
"\n"
"   Return the translation part of a 4 row matrix.\n"
"\n"
"   :return: Return the translation of a matrix.\n"
"   :rtype: :class:`Vector`\n"
);
static PyObject *Matrix_to_translation(MatrixObject *self)
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if ((self->num_row < 3) || self->num_col < 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.to_translation(): "
		                "inappropriate matrix size");
		return NULL;
	}

	return Vector_CreatePyObject(MATRIX_COL_PTR(self, 3), 3, NULL);
}

PyDoc_STRVAR(Matrix_to_scale_doc,
".. method:: to_scale()\n"
"\n"
"   Return the scale part of a 3x3 or 4x4 matrix.\n"
"\n"
"   :return: Return the scale of a matrix.\n"
"   :rtype: :class:`Vector`\n"
"\n"
"   .. note:: This method does not return a negative scale on any axis because it is not possible to obtain this data from the matrix alone.\n"
);
static PyObject *Matrix_to_scale(MatrixObject *self)
{
	float rot[3][3];
	float mat[3][3];
	float size[3];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 3-4 cols, 3-4 rows, square matrix */
	if ((self->num_row < 3) || (self->num_col < 3)) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.to_scale(): "
		                "inappropriate matrix size, 3x3 minimum size");
		return NULL;
	}

	matrix_as_3x3(mat, self);

	/* compatible mat4_to_loc_rot_size */
	mat3_to_rot_size(rot, size, mat);

	return Vector_CreatePyObject(size, 3, NULL);
}

/*---------------------------matrix.invert() ---------------------*/

/* re-usable checks for invert */
static bool matrix_invert_is_compat(const MatrixObject *self)
{
	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.invert(ed): "
		                "only square matrices are supported");
		return false;
	}
	else {
		return true;
	}
}

static bool matrix_invert_args_check(const MatrixObject *self, PyObject *args, bool check_type)
{
	switch (PyTuple_GET_SIZE(args)) {
		case 0:
			return true;
		case 1:
			if (check_type) {
				const MatrixObject *fallback = (MatrixObject *)PyTuple_GET_ITEM(args, 0);
				if (!MatrixObject_Check(fallback)) {
					PyErr_SetString(PyExc_TypeError,
					                "Matrix.invert: "
					                "expects a matrix argument or nothing");
					return false;
				}

				if ((self->num_col != fallback->num_col) ||
				    (self->num_row != fallback->num_row))
				{
					PyErr_SetString(PyExc_TypeError,
					                "Matrix.invert: "
					                "matrix argument has different dimensions");
					return false;
				}
			}

			return true;
		default:
			PyErr_SetString(PyExc_ValueError,
			                "Matrix.invert(ed): "
			                "takes at most one argument");
			return false;
	}
}

static void matrix_invert_raise_degenerate(void)
{
	PyErr_SetString(PyExc_ValueError,
	                "Matrix.invert(ed): "
	                "matrix does not have an inverse");
}

PyDoc_STRVAR(Matrix_invert_doc,
".. method:: invert(fallback=None)\n"
"\n"
"   Set the matrix to its inverse.\n"
"\n"
"   :arg fallback: Set the matrix to this value when the inverse cannot be calculated\n"
"      (instead of raising a :exc:`ValueError` exception).\n"
"   :type fallback: :class:`Matrix`\n"
"\n"
"   .. seealso:: `Inverse matrix <https://en.wikipedia.org/wiki/Inverse_matrix>` on Wikipedia.\n"
);
static PyObject *Matrix_invert(MatrixObject *self, PyObject *args)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (matrix_invert_is_compat(self) == false) {
		return NULL;
	}

	if (matrix_invert_args_check(self, args, true) == false) {
		return NULL;
	}

	if (matrix_invert_internal(self, self->matrix)) {
		/* pass */
	}
	else {
		if (PyTuple_GET_SIZE(args) == 1) {
			MatrixObject *fallback = (MatrixObject *)PyTuple_GET_ITEM(args, 0);

			if (BaseMath_ReadCallback(fallback) == -1)
				return NULL;

			if (self != fallback) {
				matrix_copy(self, fallback);
			}
		}
		else {
			matrix_invert_raise_degenerate();
			return NULL;
		}
	}

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_inverted_doc,
".. method:: inverted(fallback=None)\n"
"\n"
"   Return an inverted copy of the matrix.\n"
"\n"
"   :arg fallback: return this when the inverse can't be calculated\n"
"      (instead of raising a :exc:`ValueError`).\n"
"   :type fallback: any\n"
"   :return: the inverted matrix or fallback when given.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_inverted(MatrixObject *self, PyObject *args)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if (matrix_invert_args_check(self, args, false) == false) {
		return NULL;
	}

	if (matrix_invert_is_compat(self) == false) {
		return NULL;
	}

	if (matrix_invert_internal(self, mat)) {
		/* pass */
	}
	else {
		if (PyTuple_GET_SIZE(args) == 1) {
			PyObject *fallback = PyTuple_GET_ITEM(args, 0);
			Py_INCREF(fallback);
			return fallback;
		}
		else {
			matrix_invert_raise_degenerate();
			return NULL;
		}
	}

	return Matrix_copy_notest(self, mat);
}

static PyObject *Matrix_inverted_noargs(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (matrix_invert_is_compat(self) == false) {
		return NULL;
	}

	if (matrix_invert_internal(self, self->matrix)) {
		/* pass */
	}
	else {
		matrix_invert_raise_degenerate();
		return NULL;
	}

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_invert_safe_doc,
".. method:: invert_safe()\n"
"\n"
"   Set the matrix to its inverse, will never error.\n"
"   If degenerated (e.g. zero scale on an axis), add some epsilon to its diagonal, to get an invertible one.\n"
"   If tweaked matrix is still degenerated, set to the identity matrix instead.\n"
"\n"
"   .. seealso:: `Inverse Matrix <https://en.wikipedia.org/wiki/Inverse_matrix>` on Wikipedia.\n"
);
static PyObject *Matrix_invert_safe(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (matrix_invert_is_compat(self) == false) {
		return NULL;
	}

	matrix_invert_safe_internal(self, self->matrix);

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_inverted_safe_doc,
".. method:: inverted_safe()\n"
"\n"
"   Return an inverted copy of the matrix, will never error.\n"
"   If degenerated (e.g. zero scale on an axis), add some epsilon to its diagonal, to get an invertible one.\n"
"   If tweaked matrix is still degenerated, return the identity matrix instead.\n"
"\n"
"   :return: the inverted matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_inverted_safe(MatrixObject *self)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if (matrix_invert_is_compat(self) == false) {
		return NULL;
	}

	matrix_invert_safe_internal(self, mat);

	return Matrix_copy_notest(self, mat);
}

/*---------------------------matrix.adjugate() ---------------------*/
PyDoc_STRVAR(Matrix_adjugate_doc,
".. method:: adjugate()\n"
"\n"
"   Set the matrix to its adjugate.\n"
"\n"
"   .. note:: When the matrix cannot be adjugated a :exc:`ValueError` exception is raised.\n"
"\n"
"   .. seealso:: `Adjugate matrix <https://en.wikipedia.org/wiki/Adjugate_matrix>` on Wikipedia.\n"
);
static PyObject *Matrix_adjugate(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.adjugate(d): "
		                "only square matrices are supported");
		return NULL;
	}

	/* calculate the classical adjoint */
	if (self->num_col <= 4) {
		adjoint_matrix_n(self->matrix, self->matrix, self->num_col);
	}
	else {
		PyErr_Format(PyExc_ValueError,
		             "Matrix adjugate(d): size (%d) unsupported",
		             (int)self->num_col);
		return NULL;
	}


	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_adjugated_doc,
".. method:: adjugated()\n"
"\n"
"   Return an adjugated copy of the matrix.\n"
"\n"
"   :return: the adjugated matrix.\n"
"   :rtype: :class:`Matrix`\n"
"\n"
"   .. note:: When the matrix cant be adjugated a :exc:`ValueError` exception is raised.\n"
);
static PyObject *Matrix_adjugated(MatrixObject *self)
{
	return matrix__apply_to_copy((PyNoArgsFunction)Matrix_adjugate, self);
}

PyDoc_STRVAR(Matrix_rotate_doc,
".. method:: rotate(other)\n"
"\n"
"   Rotates the matrix by another mathutils value.\n"
"\n"
"   :arg other: rotation component of mathutils value\n"
"   :type other: :class:`Euler`, :class:`Quaternion` or :class:`Matrix`\n"
"\n"
"   .. note:: If any of the columns are not unit length this may not have desired results.\n"
);
static PyObject *Matrix_rotate(MatrixObject *self, PyObject *value)
{
	float self_rmat[3][3], other_rmat[3][3], rmat[3][3];

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (mathutils_any_to_rotmat(other_rmat, value, "matrix.rotate(value)") == -1)
		return NULL;

	if (self->num_row != 3 || self->num_col != 3) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.rotate(): "
		                "must have 3x3 dimensions");
		return NULL;
	}

	matrix_as_3x3(self_rmat, self);
	mul_m3_m3m3(rmat, other_rmat, self_rmat);

	copy_m3_m3((float (*)[3])(self->matrix), rmat);

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

/*---------------------------matrix.decompose() ---------------------*/
PyDoc_STRVAR(Matrix_decompose_doc,
".. method:: decompose()\n"
"\n"
"   Return the translation, rotation and scale components of this matrix.\n"
"\n"
"   :return: trans, rot, scale triple.\n"
"   :rtype: (:class:`Vector`, :class:`Quaternion`, :class:`Vector`)"
);
static PyObject *Matrix_decompose(MatrixObject *self)
{
	PyObject *ret;
	float loc[3];
	float rot[3][3];
	float quat[4];
	float size[3];

	if (self->num_row != 4 || self->num_col != 4) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.decompose(): "
		                "inappropriate matrix size - expects 4x4 matrix");
		return NULL;
	}

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	mat4_to_loc_rot_size(loc, rot, size, (float (*)[4])self->matrix);
	mat3_to_quat(quat, rot);

	ret = PyTuple_New(3);
	PyTuple_SET_ITEMS(ret,
	        Vector_CreatePyObject(loc, 3, NULL),
	        Quaternion_CreatePyObject(quat, NULL),
	        Vector_CreatePyObject(size, 3, NULL));
	return ret;
}



PyDoc_STRVAR(Matrix_lerp_doc,
".. function:: lerp(other, factor)\n"
"\n"
"   Returns the interpolation of two matrices.\n"
"\n"
"   :arg other: value to interpolate with.\n"
"   :type other: :class:`Matrix`\n"
"   :arg factor: The interpolation value in [0.0, 1.0].\n"
"   :type factor: float\n"
"   :return: The interpolated matrix.\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_lerp(MatrixObject *self, PyObject *args)
{
	MatrixObject *mat2 = NULL;
	float fac, mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];

	if (!PyArg_ParseTuple(args, "O!f:lerp", &matrix_Type, &mat2, &fac))
		return NULL;

	if (self->num_col != mat2->num_col || self->num_row != mat2->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.lerp(): "
		                "expects both matrix objects of the same dimensions");
		return NULL;
	}

	if (BaseMath_ReadCallback(self) == -1 || BaseMath_ReadCallback(mat2) == -1)
		return NULL;

	/* TODO, different sized matrix */
	if (self->num_col == 4 && self->num_row == 4) {
		interp_m4_m4m4((float (*)[4])mat, (float (*)[4])self->matrix, (float (*)[4])mat2->matrix, fac);
	}
	else if (self->num_col == 3 && self->num_row == 3) {
		interp_m3_m3m3((float (*)[3])mat, (float (*)[3])self->matrix, (float (*)[3])mat2->matrix, fac);
	}
	else {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.lerp(): "
		                "only 3x3 and 4x4 matrices supported");
		return NULL;
	}

	return Matrix_CreatePyObject(mat, self->num_col, self->num_row, Py_TYPE(self));
}

/*---------------------------matrix.determinant() ----------------*/
PyDoc_STRVAR(Matrix_determinant_doc,
".. method:: determinant()\n"
"\n"
"   Return the determinant of a matrix.\n"
"\n"
"   :return: Return the determinant of a matrix.\n"
"   :rtype: float\n"
"\n"
"   .. seealso:: `Determinant <https://en.wikipedia.org/wiki/Determinant>` on Wikipedia.\n"
);
static PyObject *Matrix_determinant(MatrixObject *self)
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.determinant(): "
		                "only square matrices are supported");
		return NULL;
	}

	return PyFloat_FromDouble((double)matrix_determinant_internal(self));
}
/*---------------------------matrix.transpose() ------------------*/
PyDoc_STRVAR(Matrix_transpose_doc,
".. method:: transpose()\n"
"\n"
"   Set the matrix to its transpose.\n"
"\n"
"   .. seealso:: `Transpose <https://en.wikipedia.org/wiki/Transpose>` on Wikipedia.\n"
);
static PyObject *Matrix_transpose(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.transpose(d): "
		                "only square matrices are supported");
		return NULL;
	}

	if (self->num_col == 2) {
		const float t = MATRIX_ITEM(self, 1, 0);
		MATRIX_ITEM(self, 1, 0) = MATRIX_ITEM(self, 0, 1);
		MATRIX_ITEM(self, 0, 1) = t;
	}
	else if (self->num_col == 3) {
		transpose_m3((float (*)[3])self->matrix);
	}
	else {
		transpose_m4((float (*)[4])self->matrix);
	}

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_transposed_doc,
".. method:: transposed()\n"
"\n"
"   Return a new, transposed matrix.\n"
"\n"
"   :return: a transposed matrix\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_transposed(MatrixObject *self)
{
	return matrix__apply_to_copy((PyNoArgsFunction)Matrix_transpose, self);
}

/*---------------------------matrix.normalize() ------------------*/
PyDoc_STRVAR(Matrix_normalize_doc,
".. method:: normalize()\n"
"\n"
"   Normalize each of the matrix columns.\n"
);
static PyObject *Matrix_normalize(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.normalize(): "
		                "only square matrices are supported");
		return NULL;
	}

	if (self->num_col == 3) {
		normalize_m3((float (*)[3])self->matrix);
	}
	else if (self->num_col == 4) {
		normalize_m4((float (*)[4])self->matrix);
	}
	else {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.normalize(): "
		                "can only use a 3x3 or 4x4 matrix");
	}

	(void)BaseMath_WriteCallback(self);
	Py_RETURN_NONE;
}

PyDoc_STRVAR(Matrix_normalized_doc,
".. method:: normalized()\n"
"\n"
"   Return a column normalized matrix\n"
"\n"
"   :return: a column normalized matrix\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_normalized(MatrixObject *self)
{
	return matrix__apply_to_copy((PyNoArgsFunction)Matrix_normalize, self);
}

/*---------------------------matrix.zero() -----------------------*/
PyDoc_STRVAR(Matrix_zero_doc,
".. method:: zero()\n"
"\n"
"   Set all the matrix values to zero.\n"
"\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_zero(MatrixObject *self)
{
	if (BaseMath_Prepare_ForWrite(self) == -1)
		return NULL;

	copy_vn_fl(self->matrix, self->num_col * self->num_row, 0.0f);

	if (BaseMath_WriteCallback(self) == -1)
		return NULL;

	Py_RETURN_NONE;

}
/*---------------------------matrix.identity(() ------------------*/
static void matrix_identity_internal(MatrixObject *self)
{
	BLI_assert((self->num_col == self->num_row) && (self->num_row <= 4));

	if (self->num_col == 2) {
		unit_m2((float (*)[2])self->matrix);
	}
	else if (self->num_col == 3) {
		unit_m3((float (*)[3])self->matrix);
	}
	else {
		unit_m4((float (*)[4])self->matrix);
	}
}

PyDoc_STRVAR(Matrix_identity_doc,
".. method:: identity()\n"
"\n"
"   Set the matrix to the identity matrix.\n"
"\n"
"   .. note:: An object with a location and rotation of zero, and a scale of one\n"
"      will have an identity matrix.\n"
"\n"
"   .. seealso:: `Identity matrix <https://en.wikipedia.org/wiki/Identity_matrix>` on Wikipedia.\n"
);
static PyObject *Matrix_identity(MatrixObject *self)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (self->num_col != self->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix.identity(): "
		                "only square matrices are supported");
		return NULL;
	}

	matrix_identity_internal(self);

	if (BaseMath_WriteCallback(self) == -1)
		return NULL;

	Py_RETURN_NONE;
}

/*---------------------------Matrix.copy() ------------------*/

static PyObject *Matrix_copy_notest(MatrixObject *self, const float *matrix)
{
	return Matrix_CreatePyObject((float *)matrix, self->num_col, self->num_row, Py_TYPE(self));
}

PyDoc_STRVAR(Matrix_copy_doc,
".. method:: copy()\n"
"\n"
"   Returns a copy of this matrix.\n"
"\n"
"   :return: an instance of itself\n"
"   :rtype: :class:`Matrix`\n"
);
static PyObject *Matrix_copy(MatrixObject *self)
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	return Matrix_copy_notest(self, self->matrix);
}
static PyObject *Matrix_deepcopy(MatrixObject *self, PyObject *args)
{
	if (!mathutils_deepcopy_args_check(args))
		return NULL;
	return Matrix_copy(self);
}

/*----------------------------print object (internal)-------------*/
/* print the object to screen */
static PyObject *Matrix_repr(MatrixObject *self)
{
	int col, row;
	PyObject *rows[MATRIX_MAX_DIM] = {NULL};

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	for (row = 0; row < self->num_row; row++) {
		rows[row] = PyTuple_New(self->num_col);
		for (col = 0; col < self->num_col; col++) {
			PyTuple_SET_ITEM(rows[row], col, PyFloat_FromDouble(MATRIX_ITEM(self, row, col)));
		}
	}
	switch (self->num_row) {
		case 2: return PyUnicode_FromFormat("Matrix((%R,\n"
		                                    "        %R))", rows[0], rows[1]);

		case 3: return PyUnicode_FromFormat("Matrix((%R,\n"
		                                    "        %R,\n"
		                                    "        %R))", rows[0], rows[1], rows[2]);

		case 4: return PyUnicode_FromFormat("Matrix((%R,\n"
		                                    "        %R,\n"
		                                    "        %R,\n"
		                                    "        %R))", rows[0], rows[1], rows[2], rows[3]);
	}

	Py_FatalError("Matrix(): invalid row size!");
	return NULL;
}

#ifndef MATH_STANDALONE
static PyObject *Matrix_str(MatrixObject *self)
{
	DynStr *ds;

	int maxsize[MATRIX_MAX_DIM];
	int row, col;

	char dummy_buf[64];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	ds = BLI_dynstr_new();

	/* First determine the maximum width for each column */
	for (col = 0; col < self->num_col; col++) {
		maxsize[col] = 0;
		for (row = 0; row < self->num_row; row++) {
			int size = BLI_snprintf(dummy_buf, sizeof(dummy_buf), "%.4f", MATRIX_ITEM(self, row, col));
			maxsize[col] = max_ii(maxsize[col], size);
		}
	}

	/* Now write the unicode string to be printed */
	BLI_dynstr_appendf(ds, "<Matrix %dx%d (", self->num_row, self->num_col);
	for (row = 0; row < self->num_row; row++) {
		for (col = 0; col < self->num_col; col++) {
			BLI_dynstr_appendf(ds, col ? ", %*.4f" : "%*.4f", maxsize[col], MATRIX_ITEM(self, row, col));
		}
		BLI_dynstr_append(ds, row + 1 != self->num_row ? ")\n            (" : ")");
	}
	BLI_dynstr_append(ds, ">");

	return mathutils_dynstr_to_py(ds); /* frees ds */
}
#endif

static PyObject *Matrix_richcmpr(PyObject *a, PyObject *b, int op)
{
	PyObject *res;
	int ok = -1; /* zero is true */

	if (MatrixObject_Check(a) && MatrixObject_Check(b)) {
		MatrixObject *matA = (MatrixObject *)a;
		MatrixObject *matB = (MatrixObject *)b;

		if (BaseMath_ReadCallback(matA) == -1 || BaseMath_ReadCallback(matB) == -1)
			return NULL;

		ok = ((matA->num_row == matB->num_row) &&
		      (matA->num_col == matB->num_col) &&
		      EXPP_VectorsAreEqual(matA->matrix, matB->matrix, (matA->num_col * matA->num_row), 1)
		      ) ? 0 : -1;
	}

	switch (op) {
		case Py_NE:
			ok = !ok;
			ATTR_FALLTHROUGH;
		case Py_EQ:
			res = ok ? Py_False : Py_True;
			break;

		case Py_LT:
		case Py_LE:
		case Py_GT:
		case Py_GE:
			res = Py_NotImplemented;
			break;
		default:
			PyErr_BadArgument();
			return NULL;
	}

	return Py_INCREF_RET(res);
}

static Py_hash_t Matrix_hash(MatrixObject *self)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];

	if (BaseMath_ReadCallback(self) == -1)
		return -1;

	if (BaseMathObject_Prepare_ForHash(self) == -1)
		return -1;

	matrix_transpose_internal(mat, self);

	return mathutils_array_hash(mat, self->num_row * self->num_col);
}

/*---------------------SEQUENCE PROTOCOLS------------------------
 * ----------------------------len(object)------------------------
 * sequence length */
static int Matrix_len(MatrixObject *self)
{
	return self->num_row;
}
/*----------------------------object[]---------------------------
 * sequence accessor (get)
 * the wrapped vector gives direct access to the matrix data */
static PyObject *Matrix_item_row(MatrixObject *self, int row)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (row < 0 || row >= self->num_row) {
		PyErr_SetString(PyExc_IndexError,
		                "matrix[attribute]: "
		                "array index out of range");
		return NULL;
	}
	return Vector_CreatePyObject_cb((PyObject *)self, self->num_col, mathutils_matrix_row_cb_index, row);
}
/* same but column access */
static PyObject *Matrix_item_col(MatrixObject *self, int col)
{
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return NULL;

	if (col < 0 || col >= self->num_col) {
		PyErr_SetString(PyExc_IndexError,
		                "matrix[attribute]: "
		                "array index out of range");
		return NULL;
	}
	return Vector_CreatePyObject_cb((PyObject *)self, self->num_row, mathutils_matrix_col_cb_index, col);
}

/*----------------------------object[]-------------------------
 * sequence accessor (set) */

static int Matrix_ass_item_row(MatrixObject *self, int row, PyObject *value)
{
	int col;
	float vec[MATRIX_MAX_DIM];
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	if (row >= self->num_row || row < 0) {
		PyErr_SetString(PyExc_IndexError,
		                "matrix[attribute] = x: bad row");
		return -1;
	}

	if (mathutils_array_parse(vec, self->num_col, self->num_col, value, "matrix[i] = value assignment") == -1) {
		return -1;
	}

	/* Since we are assigning a row we cannot memcpy */
	for (col = 0; col < self->num_col; col++) {
		MATRIX_ITEM(self, row, col) = vec[col];
	}

	(void)BaseMath_WriteCallback(self);
	return 0;
}
static int Matrix_ass_item_col(MatrixObject *self, int col, PyObject *value)
{
	int row;
	float vec[MATRIX_MAX_DIM];
	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	if (col >= self->num_col || col < 0) {
		PyErr_SetString(PyExc_IndexError,
		                "matrix[attribute] = x: bad col");
		return -1;
	}

	if (mathutils_array_parse(vec, self->num_row, self->num_row, value, "matrix[i] = value assignment") == -1) {
		return -1;
	}

	/* Since we are assigning a row we cannot memcpy */
	for (row = 0; row < self->num_row; row++) {
		MATRIX_ITEM(self, row, col) = vec[row];
	}

	(void)BaseMath_WriteCallback(self);
	return 0;
}


/*----------------------------object[z:y]------------------------
 * sequence slice (get)*/
static PyObject *Matrix_slice(MatrixObject *self, int begin, int end)
{

	PyObject *tuple;
	int count;

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	CLAMP(begin, 0, self->num_row);
	CLAMP(end, 0, self->num_row);
	begin = MIN2(begin, end);

	tuple = PyTuple_New(end - begin);
	for (count = begin; count < end; count++) {
		PyTuple_SET_ITEM(tuple, count - begin,
		                 Vector_CreatePyObject_cb((PyObject *)self, self->num_col, mathutils_matrix_row_cb_index, count));
	}

	return tuple;
}
/*----------------------------object[z:y]------------------------
 * sequence slice (set)*/
static int Matrix_ass_slice(MatrixObject *self, int begin, int end, PyObject *value)
{
	PyObject *value_fast;

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	CLAMP(begin, 0, self->num_row);
	CLAMP(end, 0, self->num_row);
	begin = MIN2(begin, end);

	/* non list/tuple cases */
	if (!(value_fast = PySequence_Fast(value, "matrix[begin:end] = value"))) {
		/* PySequence_Fast sets the error */
		return -1;
	}
	else {
		PyObject **value_fast_items = PySequence_Fast_ITEMS(value_fast);
		const int size = end - begin;
		int row, col;
		float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];
		float vec[4];

		if (PySequence_Fast_GET_SIZE(value_fast) != size) {
			Py_DECREF(value_fast);
			PyErr_SetString(PyExc_ValueError,
			                "matrix[begin:end] = []: "
			                "size mismatch in slice assignment");
			return -1;
		}

		memcpy(mat, self->matrix, self->num_col * self->num_row * sizeof(float));

		/* parse sub items */
		for (row = begin; row < end; row++) {
			/* parse each sub sequence */
			PyObject *item = value_fast_items[row - begin];

			if (mathutils_array_parse(vec, self->num_col, self->num_col, item,
			                          "matrix[begin:end] = value assignment") == -1)
			{
				Py_DECREF(value_fast);
				return -1;
			}

			for (col = 0; col < self->num_col; col++) {
				mat[col * self->num_row + row] = vec[col];
			}
		}

		Py_DECREF(value_fast);

		/*parsed well - now set in matrix*/
		memcpy(self->matrix, mat, self->num_col * self->num_row * sizeof(float));

		(void)BaseMath_WriteCallback(self);
		return 0;
	}
}
/*------------------------NUMERIC PROTOCOLS----------------------
 *------------------------obj + obj------------------------------*/
static PyObject *Matrix_add(PyObject *m1, PyObject *m2)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];
	MatrixObject *mat1 = NULL, *mat2 = NULL;

	mat1 = (MatrixObject *)m1;
	mat2 = (MatrixObject *)m2;

	if (!MatrixObject_Check(m1) || !MatrixObject_Check(m2)) {
		PyErr_Format(PyExc_TypeError,
		             "Matrix addition: (%s + %s) "
		             "invalid type for this operation",
		             Py_TYPE(m1)->tp_name, Py_TYPE(m2)->tp_name);
		return NULL;
	}

	if (BaseMath_ReadCallback(mat1) == -1 || BaseMath_ReadCallback(mat2) == -1)
		return NULL;

	if (mat1->num_col != mat2->num_col || mat1->num_row != mat2->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix addition: "
		                "matrices must have the same dimensions for this operation");
		return NULL;
	}

	add_vn_vnvn(mat, mat1->matrix, mat2->matrix, mat1->num_col * mat1->num_row);

	return Matrix_CreatePyObject(mat, mat1->num_col, mat1->num_row, Py_TYPE(mat1));
}
/*------------------------obj - obj------------------------------
 * subtraction */
static PyObject *Matrix_sub(PyObject *m1, PyObject *m2)
{
	float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];
	MatrixObject *mat1 = NULL, *mat2 = NULL;

	mat1 = (MatrixObject *)m1;
	mat2 = (MatrixObject *)m2;

	if (!MatrixObject_Check(m1) || !MatrixObject_Check(m2)) {
		PyErr_Format(PyExc_TypeError,
		             "Matrix subtraction: (%s - %s) "
		             "invalid type for this operation",
		             Py_TYPE(m1)->tp_name, Py_TYPE(m2)->tp_name);
		return NULL;
	}

	if (BaseMath_ReadCallback(mat1) == -1 || BaseMath_ReadCallback(mat2) == -1)
		return NULL;

	if (mat1->num_col != mat2->num_col || mat1->num_row != mat2->num_row) {
		PyErr_SetString(PyExc_ValueError,
		                "Matrix addition: "
		                "matrices must have the same dimensions for this operation");
		return NULL;
	}

	sub_vn_vnvn(mat, mat1->matrix, mat2->matrix, mat1->num_col * mat1->num_row);

	return Matrix_CreatePyObject(mat, mat1->num_col, mat1->num_row, Py_TYPE(mat1));
}
/*------------------------obj * obj------------------------------
 * multiplication */
static PyObject *matrix_mul_float(MatrixObject *mat, const float scalar)
{
	float tmat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];
	mul_vn_vn_fl(tmat, mat->matrix, mat->num_col * mat->num_row, scalar);
	return Matrix_CreatePyObject(tmat, mat->num_col, mat->num_row, Py_TYPE(mat));
}

static PyObject *Matrix_mul(PyObject *m1, PyObject *m2)
{
	float scalar;
	int vec_size;

	MatrixObject *mat1 = NULL, *mat2 = NULL;

	if (MatrixObject_Check(m1)) {
		mat1 = (MatrixObject *)m1;
		if (BaseMath_ReadCallback(mat1) == -1)
			return NULL;
	}
	if (MatrixObject_Check(m2)) {
		mat2 = (MatrixObject *)m2;
		if (BaseMath_ReadCallback(mat2) == -1)
			return NULL;
	}

	if (mat1 && mat2) {
		/* MATRIX * MATRIX */
		float mat[MATRIX_MAX_DIM * MATRIX_MAX_DIM];

		int col, row, item;

		if (mat1->num_col != mat2->num_row) {
			PyErr_SetString(PyExc_ValueError,
			                "matrix1 * matrix2: matrix1 number of columns "
			                "and the matrix2 number of rows must be the same");
			return NULL;
		}

		for (col = 0; col < mat2->num_col; col++) {
			for (row = 0; row < mat1->num_row; row++) {
				double dot = 0.0f;
				for (item = 0; item < mat1->num_col; item++) {
					dot += (double)(MATRIX_ITEM(mat1, row, item) * MATRIX_ITEM(mat2, item, col));
				}
				mat[(col * mat1->num_row) + row] = (float)dot;
			}
		}

		return Matrix_CreatePyObject(mat, mat2->num_col, mat1->num_row, Py_TYPE(mat1));
	}
	else if (mat2) {
		/*FLOAT/INT * MATRIX */
		if (((scalar = PyFloat_AsDouble(m1)) == -1.0f && PyErr_Occurred()) == 0) {
			return matrix_mul_float(mat2, scalar);
		}
	}
	else if (mat1) {
		/* MATRIX * VECTOR */
		if (VectorObject_Check(m2)) {
			VectorObject *vec2 = (VectorObject *)m2;
			float tvec[MATRIX_MAX_DIM];
			if (BaseMath_ReadCallback(vec2) == -1)
				return NULL;
			if (column_vector_multiplication(tvec, vec2, mat1) == -1) {
				return NULL;
			}

			if (mat1->num_col == 4 && vec2->size == 3) {
				vec_size = 3;
			}
			else {
				vec_size = mat1->num_row;
			}

			return Vector_CreatePyObject(tvec, vec_size, Py_TYPE(m2));
		}
		/*FLOAT/INT * MATRIX */
		else if (((scalar = PyFloat_AsDouble(m2)) == -1.0f && PyErr_Occurred()) == 0) {
			return matrix_mul_float(mat1, scalar);
		}
	}
	else {
		BLI_assert(!"internal error");
	}

	PyErr_Format(PyExc_TypeError,
	             "Matrix multiplication: "
	             "not supported between '%.200s' and '%.200s' types",
	             Py_TYPE(m1)->tp_name, Py_TYPE(m2)->tp_name);
	return NULL;
}

/*-----------------PROTOCOL DECLARATIONS--------------------------*/
static PySequenceMethods Matrix_SeqMethods = {
	(lenfunc) Matrix_len,                       /* sq_length */
	(binaryfunc) NULL,                          /* sq_concat */
	(ssizeargfunc) NULL,                        /* sq_repeat */
	(ssizeargfunc) Matrix_item_row,             /* sq_item */
	(ssizessizeargfunc) NULL,                   /* sq_slice, deprecated */
	(ssizeobjargproc) Matrix_ass_item_row,      /* sq_ass_item */
	(ssizessizeobjargproc) NULL,                /* sq_ass_slice, deprecated */
	(objobjproc) NULL,                          /* sq_contains */
	(binaryfunc) NULL,                          /* sq_inplace_concat */
	(ssizeargfunc) NULL,                        /* sq_inplace_repeat */
};


static PyObject *Matrix_subscript(MatrixObject *self, PyObject *item)
{
	if (PyIndex_Check(item)) {
		Py_ssize_t i;
		i = PyNumber_AsSsize_t(item, PyExc_IndexError);
		if (i == -1 && PyErr_Occurred())
			return NULL;
		if (i < 0)
			i += self->num_row;
		return Matrix_item_row(self, i);
	}
	else if (PySlice_Check(item)) {
		Py_ssize_t start, stop, step, slicelength;

		if (PySlice_GetIndicesEx(item, self->num_row, &start, &stop, &step, &slicelength) < 0)
			return NULL;

		if (slicelength <= 0) {
			return PyTuple_New(0);
		}
		else if (step == 1) {
			return Matrix_slice(self, start, stop);
		}
		else {
			PyErr_SetString(PyExc_IndexError,
			                "slice steps not supported with matrices");
			return NULL;
		}
	}
	else {
		PyErr_Format(PyExc_TypeError,
		             "matrix indices must be integers, not %.200s",
		             Py_TYPE(item)->tp_name);
		return NULL;
	}
}

static int Matrix_ass_subscript(MatrixObject *self, PyObject *item, PyObject *value)
{
	if (PyIndex_Check(item)) {
		Py_ssize_t i = PyNumber_AsSsize_t(item, PyExc_IndexError);
		if (i == -1 && PyErr_Occurred())
			return -1;
		if (i < 0)
			i += self->num_row;
		return Matrix_ass_item_row(self, i, value);
	}
	else if (PySlice_Check(item)) {
		Py_ssize_t start, stop, step, slicelength;

		if (PySlice_GetIndicesEx(item, self->num_row, &start, &stop, &step, &slicelength) < 0)
			return -1;

		if (step == 1)
			return Matrix_ass_slice(self, start, stop, value);
		else {
			PyErr_SetString(PyExc_IndexError,
			                "slice steps not supported with matrices");
			return -1;
		}
	}
	else {
		PyErr_Format(PyExc_TypeError,
		             "matrix indices must be integers, not %.200s",
		             Py_TYPE(item)->tp_name);
		return -1;
	}
}

static PyMappingMethods Matrix_AsMapping = {
	(lenfunc)Matrix_len,
	(binaryfunc)Matrix_subscript,
	(objobjargproc)Matrix_ass_subscript
};


static PyNumberMethods Matrix_NumMethods = {
	(binaryfunc)    Matrix_add,     /*nb_add*/
	(binaryfunc)    Matrix_sub,     /*nb_subtract*/
	(binaryfunc)    Matrix_mul,     /*nb_multiply*/
	NULL,                               /*nb_remainder*/
	NULL,                               /*nb_divmod*/
	NULL,                               /*nb_power*/
	(unaryfunc)     0,      /*nb_negative*/
	(unaryfunc)     0,      /*tp_positive*/
	(unaryfunc)     0,      /*tp_absolute*/
	(inquiry)   0,      /*tp_bool*/
	(unaryfunc) Matrix_inverted_noargs,        /*nb_invert*/
	NULL,                   /*nb_lshift*/
	(binaryfunc)0,      /*nb_rshift*/
	NULL,                   /*nb_and*/
	NULL,                   /*nb_xor*/
	NULL,                   /*nb_or*/
	NULL,                   /*nb_int*/
	NULL,                   /*nb_reserved*/
	NULL,                   /*nb_float*/
	NULL,                   /* nb_inplace_add */
	NULL,                   /* nb_inplace_subtract */
	NULL,                   /* nb_inplace_multiply */
	NULL,                   /* nb_inplace_remainder */
	NULL,                   /* nb_inplace_power */
	NULL,                   /* nb_inplace_lshift */
	NULL,                   /* nb_inplace_rshift */
	NULL,                   /* nb_inplace_and */
	NULL,                   /* nb_inplace_xor */
	NULL,                   /* nb_inplace_or */
	NULL,                   /* nb_floor_divide */
	NULL,                   /* nb_true_divide */
	NULL,                   /* nb_inplace_floor_divide */
	NULL,                   /* nb_inplace_true_divide */
	NULL,                   /* nb_index */
};

PyDoc_STRVAR(Matrix_translation_doc,
"The translation component of the matrix.\n\n:type: Vector"
);
static PyObject *Matrix_translation_get(MatrixObject *self, void *UNUSED(closure))
{
	PyObject *ret;

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 4x4 square matrix*/
	if (self->num_row != 4 || self->num_col != 4) {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.translation: "
		                "inappropriate matrix size, must be 4x4");
		return NULL;
	}

	ret = (PyObject *)Vector_CreatePyObject_cb((PyObject *)self, 3, mathutils_matrix_translation_cb_index, 3);

	return ret;
}

static int Matrix_translation_set(MatrixObject *self, PyObject *value, void *UNUSED(closure))
{
	float tvec[3];

	if (BaseMath_ReadCallback_ForWrite(self) == -1)
		return -1;

	/*must be 4x4 square matrix*/
	if (self->num_row != 4 || self->num_col != 4) {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.translation: "
		                "inappropriate matrix size, must be 4x4");
		return -1;
	}

	if ((mathutils_array_parse(tvec, 3, 3, value, "Matrix.translation")) == -1) {
		return -1;
	}

	copy_v3_v3(((float (*)[4])self->matrix)[3], tvec);

	(void)BaseMath_WriteCallback(self);

	return 0;
}

PyDoc_STRVAR(Matrix_row_doc,
"Access the matix by rows (default), (read-only).\n\n:type: Matrix Access"
);
static PyObject *Matrix_row_get(MatrixObject *self, void *UNUSED(closure))
{
	return MatrixAccess_CreatePyObject(self, MAT_ACCESS_ROW);
}

PyDoc_STRVAR(Matrix_col_doc,
"Access the matix by colums, 3x3 and 4x4 only, (read-only).\n\n:type: Matrix Access"
);
static PyObject *Matrix_col_get(MatrixObject *self, void *UNUSED(closure))
{
	return MatrixAccess_CreatePyObject(self, MAT_ACCESS_COL);
}

PyDoc_STRVAR(Matrix_median_scale_doc,
"The average scale applied to each axis (read-only).\n\n:type: float"
);
static PyObject *Matrix_median_scale_get(MatrixObject *self, void *UNUSED(closure))
{
	float mat[3][3];

	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 3-4 cols, 3-4 rows, square matrix*/
	if ((self->num_row < 3) || (self->num_col < 3)) {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.median_scale: "
		                "inappropriate matrix size, 3x3 minimum");
		return NULL;
	}

	matrix_as_3x3(mat, self);

	return PyFloat_FromDouble(mat3_to_scale(mat));
}

PyDoc_STRVAR(Matrix_is_negative_doc,
"True if this matrix results in a negative scale, 3x3 and 4x4 only, (read-only).\n\n:type: bool"
);
static PyObject *Matrix_is_negative_get(MatrixObject *self, void *UNUSED(closure))
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 3-4 cols, 3-4 rows, square matrix*/
	if (self->num_row == 4 && self->num_col == 4)
		return PyBool_FromLong(is_negative_m4((float (*)[4])self->matrix));
	else if (self->num_row == 3 && self->num_col == 3)
		return PyBool_FromLong(is_negative_m3((float (*)[3])self->matrix));
	else {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.is_negative: "
		                "inappropriate matrix size - expects 3x3 or 4x4 matrix");
		return NULL;
	}
}

PyDoc_STRVAR(Matrix_is_orthogonal_doc,
"True if this matrix is orthogonal, 3x3 and 4x4 only, (read-only).\n\n:type: bool"
);
static PyObject *Matrix_is_orthogonal_get(MatrixObject *self, void *UNUSED(closure))
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 3-4 cols, 3-4 rows, square matrix*/
	if (self->num_row == 4 && self->num_col == 4)
		return PyBool_FromLong(is_orthonormal_m4((float (*)[4])self->matrix));
	else if (self->num_row == 3 && self->num_col == 3)
		return PyBool_FromLong(is_orthonormal_m3((float (*)[3])self->matrix));
	else {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.is_orthogonal: "
		                "inappropriate matrix size - expects 3x3 or 4x4 matrix");
		return NULL;
	}
}

PyDoc_STRVAR(Matrix_is_orthogonal_axis_vectors_doc,
"True if this matrix has got orthogonal axis vectors, 3x3 and 4x4 only, (read-only).\n\n:type: bool"
);
static PyObject *Matrix_is_orthogonal_axis_vectors_get(MatrixObject *self, void *UNUSED(closure))
{
	if (BaseMath_ReadCallback(self) == -1)
		return NULL;

	/*must be 3-4 cols, 3-4 rows, square matrix*/
	if (self->num_row == 4 && self->num_col == 4)
		return PyBool_FromLong(is_orthogonal_m4((float (*)[4])self->matrix));
	else if (self->num_row == 3 && self->num_col == 3)
		return PyBool_FromLong(is_orthogonal_m3((float (*)[3])self->matrix));
	else {
		PyErr_SetString(PyExc_AttributeError,
		                "Matrix.is_orthogonal_axis_vectors: "
		                "inappropriate matrix size - expects 3x3 or 4x4 matrix");
		return NULL;
	}
}

/*****************************************************************************/
/* Python attributes get/set structure:                                      */
/*****************************************************************************/
static PyGetSetDef Matrix_getseters[] = {
	{(char *)"median_scale", (getter)Matrix_median_scale_get, (setter)NULL, Matrix_median_scale_doc, NULL},
	{(char *)"translation", (getter)Matrix_translation_get, (setter)Matrix_translation_set, Matrix_translation_doc, NULL},
	{(char *)"row", (getter)Matrix_row_get, (setter)NULL, Matrix_row_doc, NULL},
	{(char *)"col", (getter)Matrix_col_get, (setter)NULL, Matrix_col_doc, NULL},
	{(char *)"is_negative", (getter)Matrix_is_negative_get, (setter)NULL, Matrix_is_negative_doc, NULL},
	{(char *)"is_orthogonal", (getter)Matrix_is_orthogonal_get, (setter)NULL, Matrix_is_orthogonal_doc, NULL},
	{(char *)"is_orthogonal_axis_vectors", (getter)Matrix_is_orthogonal_axis_vectors_get, (setter)NULL, Matrix_is_orthogonal_axis_vectors_doc, NULL},
	{(char *)"is_wrapped", (getter)BaseMathObject_is_wrapped_get, (setter)NULL, BaseMathObject_is_wrapped_doc, NULL},
	{(char *)"is_frozen",  (getter)BaseMathObject_is_frozen_get,  (setter)NULL, BaseMathObject_is_frozen_doc, NULL},
	{(char *)"owner", (getter)BaseMathObject_owner_get, (setter)NULL, BaseMathObject_owner_doc, NULL},
	{NULL, NULL, NULL, NULL, NULL}  /* Sentinel */
};

/*-----------------------METHOD DEFINITIONS ----------------------*/
static struct PyMethodDef Matrix_methods[] = {
	/* derived values */
	{"determinant", (PyCFunction) Matrix_determinant, METH_NOARGS, Matrix_determinant_doc},
	{"decompose", (PyCFunction) Matrix_decompose, METH_NOARGS, Matrix_decompose_doc},

	/* in place only */
	{"zero", (PyCFunction) Matrix_zero, METH_NOARGS, Matrix_zero_doc},
	{"identity", (PyCFunction) Matrix_identity, METH_NOARGS, Matrix_identity_doc},

	/* operate on original or copy */
	{"transpose", (PyCFunction) Matrix_transpose, METH_NOARGS, Matrix_transpose_doc},
	{"transposed", (PyCFunction) Matrix_transposed, METH_NOARGS, Matrix_transposed_doc},
	{"normalize", (PyCFunction) Matrix_normalize, METH_NOARGS, Matrix_normalize_doc},
	{"normalized", (PyCFunction) Matrix_normalized, METH_NOARGS, Matrix_normalized_doc},
	{"invert", (PyCFunction) Matrix_invert, METH_VARARGS, Matrix_invert_doc},
	{"inverted", (PyCFunction) Matrix_inverted, METH_VARARGS, Matrix_inverted_doc},
	{"invert_safe", (PyCFunction) Matrix_invert_safe, METH_NOARGS, Matrix_invert_safe_doc},
	{"inverted_safe", (PyCFunction) Matrix_inverted_safe, METH_NOARGS, Matrix_inverted_safe_doc},
	{"adjugate", (PyCFunction) Matrix_adjugate, METH_NOARGS, Matrix_adjugate_doc},
	{"adjugated", (PyCFunction) Matrix_adjugated, METH_NOARGS, Matrix_adjugated_doc},
	{"to_3x3", (PyCFunction) Matrix_to_3x3, METH_NOARGS, Matrix_to_3x3_doc},
	/* TODO. {"resize_3x3", (PyCFunction) Matrix_resize3x3, METH_NOARGS, Matrix_resize3x3_doc}, */
	{"to_4x4", (PyCFunction) Matrix_to_4x4, METH_NOARGS, Matrix_to_4x4_doc},
	{"resize_4x4", (PyCFunction) Matrix_resize_4x4, METH_NOARGS, Matrix_resize_4x4_doc},
	{"rotate", (PyCFunction) Matrix_rotate, METH_O, Matrix_rotate_doc},

	/* return converted representation */
	{"to_euler", (PyCFunction) Matrix_to_euler, METH_VARARGS, Matrix_to_euler_doc},
	{"to_quaternion", (PyCFunction) Matrix_to_quaternion, METH_NOARGS, Matrix_to_quaternion_doc},
	{"to_scale", (PyCFunction) Matrix_to_scale, METH_NOARGS, Matrix_to_scale_doc},
	{"to_translation", (PyCFunction) Matrix_to_translation, METH_NOARGS, Matrix_to_translation_doc},

	/* operation between 2 or more types  */
	{"lerp", (PyCFunction) Matrix_lerp, METH_VARARGS, Matrix_lerp_doc},
	{"copy", (PyCFunction) Matrix_copy, METH_NOARGS, Matrix_copy_doc},
	{"__copy__", (PyCFunction) Matrix_copy, METH_NOARGS, Matrix_copy_doc},
	{"__deepcopy__", (PyCFunction) Matrix_deepcopy, METH_VARARGS, Matrix_copy_doc},

	/* base-math methods */
	{"freeze", (PyCFunction)BaseMathObject_freeze, METH_NOARGS, BaseMathObject_freeze_doc},

	/* class methods */
	{"Identity", (PyCFunction) C_Matrix_Identity, METH_VARARGS | METH_CLASS, C_Matrix_Identity_doc},
	{"Rotation", (PyCFunction) C_Matrix_Rotation, METH_VARARGS | METH_CLASS, C_Matrix_Rotation_doc},
	{"Scale", (PyCFunction) C_Matrix_Scale, METH_VARARGS | METH_CLASS, C_Matrix_Scale_doc},
	{"Shear", (PyCFunction) C_Matrix_Shear, METH_VARARGS | METH_CLASS, C_Matrix_Shear_doc},
	{"Translation", (PyCFunction) C_Matrix_Translation, METH_O | METH_CLASS, C_Matrix_Translation_doc},
	{"OrthoProjection", (PyCFunction) C_Matrix_OrthoProjection,  METH_VARARGS | METH_CLASS, C_Matrix_OrthoProjection_doc},
	{NULL, NULL, 0, NULL}
};

/*------------------PY_OBECT DEFINITION--------------------------*/
PyDoc_STRVAR(matrix_doc,
".. class:: Matrix([rows])\n"
"\n"
"   This object gives access to Matrices in Blender, supporting square and rectangular\n"
"   matrices from 2x2 up to 4x4.\n"
"\n"
"   :param rows: Sequence of rows.\n"
"      When ommitted, a 4x4 identity matrix is constructed.\n"
"   :type rows: 2d number sequence\n"
);
PyTypeObject matrix_Type = {
	PyVarObject_HEAD_INIT(NULL, 0)
	"Matrix",                           /*tp_name*/
	sizeof(MatrixObject),               /*tp_basicsize*/
	0,                                  /*tp_itemsize*/
	(destructor)BaseMathObject_dealloc, /*tp_dealloc*/
	NULL,                               /*tp_print*/
	NULL,                               /*tp_getattr*/
	NULL,                               /*tp_setattr*/
	NULL,                               /*tp_compare*/
	(reprfunc) Matrix_repr,             /*tp_repr*/
	&Matrix_NumMethods,                 /*tp_as_number*/
	&Matrix_SeqMethods,                 /*tp_as_sequence*/
	&Matrix_AsMapping,                  /*tp_as_mapping*/
	(hashfunc)Matrix_hash,              /*tp_hash*/
	NULL,                               /*tp_call*/
#ifndef MATH_STANDALONE
	(reprfunc) Matrix_str,              /*tp_str*/
#else
	NULL,                               /*tp_str*/
#endif
	NULL,                               /*tp_getattro*/
	NULL,                               /*tp_setattro*/
	NULL,                               /*tp_as_buffer*/
	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | Py_TPFLAGS_HAVE_GC, /*tp_flags*/
	matrix_doc,                         /*tp_doc*/
	(traverseproc)BaseMathObject_traverse,  /* tp_traverse */
	(inquiry)BaseMathObject_clear,      /*tp_clear*/
	(richcmpfunc)Matrix_richcmpr,       /*tp_richcompare*/
	0,                                  /*tp_weaklistoffset*/
	NULL,                               /*tp_iter*/
	NULL,                               /*tp_iternext*/
	Matrix_methods,                     /*tp_methods*/
	NULL,                               /*tp_members*/
	Matrix_getseters,                   /*tp_getset*/
	NULL,                               /*tp_base*/
	NULL,                               /*tp_dict*/
	NULL,                               /*tp_descr_get*/
	NULL,                               /*tp_descr_set*/
	0,                                  /*tp_dictoffset*/
	NULL,                               /*tp_init*/
	NULL,                               /*tp_alloc*/
	Matrix_new,                         /*tp_new*/
	NULL,                               /*tp_free*/
	NULL,                               /*tp_is_gc*/
	NULL,                               /*tp_bases*/
	NULL,                               /*tp_mro*/
	NULL,                               /*tp_cache*/
	NULL,                               /*tp_subclasses*/
	NULL,                               /*tp_weaklist*/
	NULL                                /*tp_del*/
};

PyObject *Matrix_CreatePyObject(
        const float *mat,
        const unsigned short num_col, const unsigned short num_row,
        PyTypeObject *base_type)
{
	MatrixObject *self;
	float *mat_alloc;

	/* matrix objects can be any 2-4row x 2-4col matrix */
	if (num_col < 2 || num_col > 4 || num_row < 2 || num_row > 4) {
		PyErr_SetString(PyExc_RuntimeError,
		                "Matrix(): "
		                "row and column sizes must be between 2 and 4");
		return NULL;
	}

	mat_alloc = PyMem_Malloc(num_col * num_row * sizeof(float));
	if (UNLIKELY(mat_alloc == NULL)) {
		PyErr_SetString(PyExc_MemoryError,
		                "Matrix(): "
		                "problem allocating data");
		return NULL;
	}

	self = BASE_MATH_NEW(MatrixObject, matrix_Type, base_type);
	if (self) {
		self->matrix = mat_alloc;
		self->num_col = num_col;
		self->num_row = num_row;

		/* init callbacks as NULL */
		self->cb_user = NULL;
		self->cb_type = self->cb_subtype = 0;

		if (mat) {  /*if a float array passed*/
			memcpy(self->matrix, mat, num_col * num_row * sizeof(float));
		}
		else if (num_col == num_row) {
			/* or if no arguments are passed return identity matrix for square matrices */
			matrix_identity_internal(self);
		}
		else {
			/* otherwise zero everything */
			memset(self->matrix, 0, num_col * num_row * sizeof(float));
		}
		self->flag = BASE_MATH_FLAG_DEFAULT;
	}
	else {
		PyMem_Free(mat_alloc);
	}

	return (PyObject *)self;
}

PyObject *Matrix_CreatePyObject_wrap(
        float *mat,
        const unsigned short num_col, const unsigned short num_row,
        PyTypeObject *base_type)
{
	MatrixObject *self;

	/* matrix objects can be any 2-4row x 2-4col matrix */
	if (num_col < 2 || num_col > 4 || num_row < 2 || num_row > 4) {
		PyErr_SetString(PyExc_RuntimeError,
		                "Matrix(): "
		                "row and column sizes must be between 2 and 4");
		return NULL;
	}

	self = BASE_MATH_NEW(MatrixObject, matrix_Type, base_type);
	if (self) {
		self->num_col = num_col;
		self->num_row = num_row;

		/* init callbacks as NULL */
		self->cb_user = NULL;
		self->cb_type = self->cb_subtype = 0;

		self->matrix = mat;
		self->flag = BASE_MATH_FLAG_DEFAULT | BASE_MATH_FLAG_IS_WRAP;
	}
	return (PyObject *) self;
}

PyObject *Matrix_CreatePyObject_cb(PyObject *cb_user,
                                   const unsigned short num_col, const unsigned short num_row,
                                   unsigned char cb_type, unsigned char cb_subtype)
{
	MatrixObject *self = (MatrixObject *)Matrix_CreatePyObject(NULL, num_col, num_row, NULL);
	if (self) {
		Py_INCREF(cb_user);
		self->cb_user         = cb_user;
		self->cb_type         = cb_type;
		self->cb_subtype      = cb_subtype;
		PyObject_GC_Track(self);
	}
	return (PyObject *) self;
}

/**
 * Use with PyArg_ParseTuple's "O&" formatting.
 */
static bool Matrix_ParseCheck(MatrixObject *pymat)
{
	if (!MatrixObject_Check(pymat)) {
		PyErr_Format(PyExc_TypeError,
		             "expected a mathutils.Matrix, not a %.200s",
		             Py_TYPE(pymat)->tp_name);
		return 0;
	}
	/* sets error */
	if (BaseMath_ReadCallback(pymat) == -1) {
		return 0;
	}
	return 1;
}

int Matrix_ParseAny(PyObject *o, void *p)
{
	MatrixObject **pymat_p = p;
	MatrixObject  *pymat = (MatrixObject *)o;

	if (!Matrix_ParseCheck(pymat)) {
		return 0;
	}
	*pymat_p = pymat;
	return 1;
}

int Matrix_Parse3x3(PyObject *o, void *p)
{
	MatrixObject **pymat_p = p;
	MatrixObject  *pymat = (MatrixObject *)o;

	if (!Matrix_ParseCheck(pymat)) {
		return 0;
	}
	if ((pymat->num_col != 3) ||
	    (pymat->num_row != 3))
	{
		PyErr_SetString(PyExc_ValueError, "matrix must be 3x3");
		return 0;
	}

	*pymat_p = pymat;
	return 1;
}

int Matrix_Parse4x4(PyObject *o, void *p)
{
	MatrixObject **pymat_p = p;
	MatrixObject  *pymat = (MatrixObject *)o;

	if (!Matrix_ParseCheck(pymat)) {
		return 0;
	}
	if ((pymat->num_col != 4) ||
	    (pymat->num_row != 4))
	{
		PyErr_SetString(PyExc_ValueError, "matrix must be 4x4");
		return 0;
	}

	*pymat_p = pymat;
	return 1;
}

/* ----------------------------------------------------------------------------
 * special type for alternate access */

typedef struct {
	PyObject_HEAD /* required python macro   */
	MatrixObject *matrix_user;
	eMatrixAccess_t type;
} MatrixAccessObject;

static int MatrixAccess_traverse(MatrixAccessObject *self, visitproc visit, void *arg)
{
	Py_VISIT(self->matrix_user);
	return 0;
}

static int MatrixAccess_clear(MatrixAccessObject *self)
{
	Py_CLEAR(self->matrix_user);
	return 0;
}

static void MatrixAccess_dealloc(MatrixAccessObject *self)
{
	if (self->matrix_user) {
		PyObject_GC_UnTrack(self);
		MatrixAccess_clear(self);
	}

	Py_TYPE(self)->tp_free(self);
}

/* sequence access */

static int MatrixAccess_len(MatrixAccessObject *self)
{
	return (self->type == MAT_ACCESS_ROW) ?
	       self->matrix_user->num_row :
	       self->matrix_user->num_col;
}

static PyObject *MatrixAccess_slice(MatrixAccessObject *self, int begin, int end)
{
	PyObject *tuple;
	int count;

	/* row/col access */
	MatrixObject *matrix_user = self->matrix_user;
	int matrix_access_len;
	PyObject *(*Matrix_item_new)(MatrixObject *, int);

	if (self->type == MAT_ACCESS_ROW) {
		matrix_access_len = matrix_user->num_row;
		Matrix_item_new = Matrix_item_row;
	}
	else { /* MAT_ACCESS_ROW */
		matrix_access_len = matrix_user->num_col;
		Matrix_item_new = Matrix_item_col;
	}

	CLAMP(begin, 0, matrix_access_len);
	if (end < 0) end = (matrix_access_len + 1) + end;
	CLAMP(end, 0, matrix_access_len);
	begin = MIN2(begin, end);

	tuple = PyTuple_New(end - begin);
	for (count = begin; count < end; count++) {
		PyTuple_SET_ITEM(tuple, count - begin, Matrix_item_new(matrix_user, count));
	}

	return tuple;
}

static PyObject *MatrixAccess_subscript(MatrixAccessObject *self, PyObject *item)
{
	MatrixObject *matrix_user = self->matrix_user;

	if (PyIndex_Check(item)) {
		Py_ssize_t i;
		i = PyNumber_AsSsize_t(item, PyExc_IndexError);
		if (i == -1 && PyErr_Occurred())
			return NULL;
		if (self->type == MAT_ACCESS_ROW) {
			if (i < 0)
				i += matrix_user->num_row;
			return Matrix_item_row(matrix_user, i);
		}
		else { /* MAT_ACCESS_ROW */
			if (i < 0)
				i += matrix_user->num_col;
			return Matrix_item_col(matrix_user, i);
		}
	}
	else if (PySlice_Check(item)) {
		Py_ssize_t start, stop, step, slicelength;

		if (PySlice_GetIndicesEx(item, MatrixAccess_len(self), &start, &stop, &step, &slicelength) < 0)
			return NULL;

		if (slicelength <= 0) {
			return PyTuple_New(0);
		}
		else if (step == 1) {
			return MatrixAccess_slice(self, start, stop);
		}
		else {
			PyErr_SetString(PyExc_IndexError,
			                "slice steps not supported with matrix accessors");
			return NULL;
		}
	}
	else {
		PyErr_Format(PyExc_TypeError,
		             "matrix indices must be integers, not %.200s",
		             Py_TYPE(item)->tp_name);
		return NULL;
	}
}

static int MatrixAccess_ass_subscript(MatrixAccessObject *self, PyObject *item, PyObject *value)
{
	MatrixObject *matrix_user = self->matrix_user;

	if (PyIndex_Check(item)) {
		Py_ssize_t i = PyNumber_AsSsize_t(item, PyExc_IndexError);
		if (i == -1 && PyErr_Occurred())
			return -1;

		if (self->type == MAT_ACCESS_ROW) {
			if (i < 0)
				i += matrix_user->num_row;
			return Matrix_ass_item_row(matrix_user, i, value);
		}
		else { /* MAT_ACCESS_ROW */
			if (i < 0)
				i += matrix_user->num_col;
			return Matrix_ass_item_col(matrix_user, i, value);
		}

	}
	/* TODO, slice */
	else {
		PyErr_Format(PyExc_TypeError,
		             "matrix indices must be integers, not %.200s",
		             Py_TYPE(item)->tp_name);
		return -1;
	}
}

static PyObject *MatrixAccess_iter(MatrixAccessObject *self)
{
	/* Try get values from a collection */
	PyObject *ret;
	PyObject *iter = NULL;
	ret = MatrixAccess_slice(self, 0, MATRIX_MAX_DIM);

	/* we know this is a tuple so no need to PyIter_Check
	 * otherwise it could be NULL (unlikely) if conversion failed */
	if (ret) {
		iter = PyObject_GetIter(ret);
		Py_DECREF(ret);
	}

	return iter;
}

static PyMappingMethods MatrixAccess_AsMapping = {
	(lenfunc)MatrixAccess_len,
	(binaryfunc)MatrixAccess_subscript,
	(objobjargproc) MatrixAccess_ass_subscript
};

PyTypeObject matrix_access_Type = {
	PyVarObject_HEAD_INIT(NULL, 0)
	"MatrixAccess",                     /*tp_name*/
	sizeof(MatrixAccessObject),         /*tp_basicsize*/
	0,                                  /*tp_itemsize*/
	(destructor)MatrixAccess_dealloc,   /*tp_dealloc*/
	NULL,                               /*tp_print*/
	NULL,                               /*tp_getattr*/
	NULL,                               /*tp_setattr*/
	NULL,                               /*tp_compare*/
	NULL,                               /*tp_repr*/
	NULL,                               /*tp_as_number*/
	NULL /*&MatrixAccess_SeqMethods*/ /* TODO */,           /*tp_as_sequence*/
	&MatrixAccess_AsMapping,            /*tp_as_mapping*/
	NULL,                               /*tp_hash*/
	NULL,                               /*tp_call*/
	NULL,                               /*tp_str*/
	NULL,                               /*tp_getattro*/
	NULL,                               /*tp_setattro*/
	NULL,                               /*tp_as_buffer*/
	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC, /*tp_flags*/
	NULL,                               /*tp_doc*/
	(traverseproc)MatrixAccess_traverse,/*tp_traverse*/
	(inquiry)MatrixAccess_clear,        /*tp_clear*/
	NULL /* (richcmpfunc)MatrixAccess_richcmpr */ /* TODO*/, /*tp_richcompare*/
	0,                                  /*tp_weaklistoffset*/
	(getiterfunc)MatrixAccess_iter, /* getiterfunc tp_iter; */
};

static PyObject *MatrixAccess_CreatePyObject(MatrixObject *matrix, const eMatrixAccess_t type)
{
	MatrixAccessObject *matrix_access = (MatrixAccessObject *)PyObject_GC_New(MatrixObject, &matrix_access_Type);

	matrix_access->matrix_user = matrix;
	Py_INCREF(matrix);

	matrix_access->type = type;

	return (PyObject *)matrix_access;
}

/* end special access
 * -------------------------------------------------------------------------- */