Modules
		scitbx.array_family.flex math

Classes
		__builtin__.object rec col diag identity inversion row sqr sym rt   class col(rec)       Method resolution order: col rec __builtin__.object Methods defined here: __init__(self, elems) Class methods defined here: random(cls, n, a, b) from __builtin__.type Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class diag(rec)       Method resolution order: diag rec __builtin__.object Methods defined here: __init__(self, diag_elems) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class identity(diag)       Method resolution order: identity diag rec __builtin__.object Methods defined here: __init__(self, n) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class inversion(diag)       Method resolution order: inversion diag rec __builtin__.object Methods defined here: __init__(self, n) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class rec(__builtin__.object)       Methods defined here: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __init__(self, elems, n) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors defined here: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class row(rec)       Method resolution order: row rec __builtin__.object Methods defined here: __init__(self, elems) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class rt(__builtin__.object)       Methods defined here: __add__(self, other) __init__(self, tuple_r_t) __mul__(self, other) __sub__(self, other) as_augmented_matrix(self) as_float(self) inverse(self) inverse_assuming_orthogonal_r(self) Data descriptors defined here: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class sqr(rec)       Method resolution order: sqr rec __builtin__.object Methods defined here: __init__(self, elems) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)   class sym(rec)       Method resolution order: sym rec __builtin__.object Methods defined here: __init__(self, elems=None, sym_mat3=None) Methods inherited from rec: __abs__(self) __add__(self, other) __call__(self, ir, ic) __div__(self, other) __eq__(self, other) __floordiv__(self, other) __getitem__(self, i) __len__(self) __mod__(self, other) __mul__(self, other) __neg__(self) __repr__(self) __rmul__(self, other) scalar * matrix __str__(self) __sub__(self, other) __truediv__(self, other) accute_angle(self, other, value_if_undefined=None, deg=False) angle(self, other, value_if_undefined=None, deg=False) as_boost_rational(self) as_flex_double_matrix(self) as_float(self) as_int(self, rounding=True) as_list_of_lists(self) as_mat3(self) as_sym_mat3(self) axis_and_angle_as_r3_rotation_matrix(self, angle, deg=False) axis_and_angle_as_unit_quaternion(self, angle, deg=False) co_factor_matrix_transposed(self) cos_angle(self, other, value_if_undefined=None) cross(self, other) determinant(self) dot(self, other=None) each_abs(self) extract_block(self, stop, start=(0, 0), step=(1, 1)) inverse(self) is_r3_rotation_matrix(self, rms_tolerance=1e-08) is_r3_rotation_matrix_rms(self) is_square(self) mathematica_form(self, label='', one_row_per_line=False, format=None, prefix='', matrix_form=False) matlab_form(self, label='', one_row_per_line=False, format=None, prefix='') max(self) max_index(self) min(self) min_index(self) n_columns(self) n_rows(self) norm_sq(self) normalize(self) ortho(self) outer_product(self, other=None) product(self) r3_rotation_matrix_as_unit_quaternion(self) resolve_partitions(self) rotate(self, axis, angle, deg=False) rt_for_rotation_around_axis_through(self, point, angle, deg=False) sum(self) trace(self) transpose(self) transpose_multiply(self, other=None) unit_quaternion_as_r3_rotation_matrix(self) unit_quaternion_product(self, other) vector_to_001_rotation(self, sin_angle_is_zero_threshold=1e-10, is_normal_vector_threshold=1e-10) Data descriptors inherited from rec: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined)

Functions
		col_list(seq) cross_product_matrix((v0, v1, v2)) Matrix associated with vector cross product:   a.cross(b) is equivalent to cross_product_matrix(a) * b Useful for simplification of equations. Used frequently in robotics and classical mechanics literature. determinant_via_lu(m) exercise() inverse_via_lu(m) lu_back_substitution(a, n, pivot_indices, b, raise_if_singular=True) lu_decomposition_in_place(a, n, raise_if_singular=True) row_list(seq) zeros(n)

Data
		division = _Feature((2, 2, 0, 'alpha', 2), (3, 0, 0, 'alpha', 0), 8192) numpy = None