Type Definition nalgebra::base::SquareMatrix [−][src]
pub type SquareMatrix<T, D, S> = Matrix<T, D, D, S>;
Expand description
A square matrix.
Implementations
impl<T, D1: Dim, S: StorageMut<T, D1, D1>> SquareMatrix<T, D1, S> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
impl<T, D1: Dim, S: StorageMut<T, D1, D1>> SquareMatrix<T, D1, S> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T
) where
D2: Dim,
R3: Dim,
C3: Dim,
D4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,
pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T
) where
D2: Dim,
R3: Dim,
C3: Dim,
D4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,
Computes the quadratic form self = alpha * lhs * mid * lhs.transpose() + beta * self
.
This uses the provided workspace work
to avoid allocations for intermediate results.
Examples:
// Note that all those would also work with statically-sized matrices.
// We use DMatrix/DVector since that's the only case where pre-allocating the
// workspace is actually useful (assuming the same workspace is re-used for
// several computations) because it avoids repeated dynamic allocations.
let mut mat = DMatrix::identity(2, 2);
let lhs = DMatrix::from_row_slice(2, 3, &[1.0, 2.0, 3.0,
4.0, 5.0, 6.0]);
let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
0.5, 0.6, 0.7,
0.9, 1.0, 1.1]);
// The random shows that values on the workspace do not
// matter as they will be overwritten.
let mut workspace = DVector::new_random(2);
let expected = &lhs * &mid * lhs.transpose() * 10.0 + &mat * 5.0;
mat.quadform_tr_with_workspace(&mut workspace, 10.0, &lhs, &mid, 5.0);
assert_relative_eq!(mat, expected);
pub fn quadform_tr<R3, C3, S3, D4, S4>(
&mut self,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T
) where
R3: Dim,
C3: Dim,
D4: Dim,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
DefaultAllocator: Allocator<T, D1>,
pub fn quadform_tr<R3, C3, S3, D4, S4>(
&mut self,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T
) where
R3: Dim,
C3: Dim,
D4: Dim,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
DefaultAllocator: Allocator<T, D1>,
Computes the quadratic form self = alpha * lhs * mid * lhs.transpose() + beta * self
.
This allocates a workspace vector of dimension D1 for intermediate results.
If D1
is a type-level integer, then the allocation is performed on the stack.
Use .quadform_tr_with_workspace(...)
instead to avoid allocations.
Examples:
let mut mat = Matrix2::identity();
let lhs = Matrix2x3::new(1.0, 2.0, 3.0,
4.0, 5.0, 6.0);
let mid = Matrix3::new(0.1, 0.2, 0.3,
0.5, 0.6, 0.7,
0.9, 1.0, 1.1);
let expected = lhs * mid * lhs.transpose() * 10.0 + mat * 5.0;
mat.quadform_tr(10.0, &lhs, &mid, 5.0);
assert_relative_eq!(mat, expected);
pub fn quadform_with_workspace<D2, S2, D3, S3, R4, C4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
mid: &SquareMatrix<T, D3, S3>,
rhs: &Matrix<T, R4, C4, S4>,
beta: T
) where
D2: Dim,
D3: Dim,
R4: Dim,
C4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, D3, D3>,
S4: Storage<T, R4, C4>,
ShapeConstraint: DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
pub fn quadform_with_workspace<D2, S2, D3, S3, R4, C4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
mid: &SquareMatrix<T, D3, S3>,
rhs: &Matrix<T, R4, C4, S4>,
beta: T
) where
D2: Dim,
D3: Dim,
R4: Dim,
C4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, D3, D3>,
S4: Storage<T, R4, C4>,
ShapeConstraint: DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
Computes the quadratic form self = alpha * rhs.transpose() * mid * rhs + beta * self
.
This uses the provided workspace work
to avoid allocations for intermediate results.
// Note that all those would also work with statically-sized matrices.
// We use DMatrix/DVector since that's the only case where pre-allocating the
// workspace is actually useful (assuming the same workspace is re-used for
// several computations) because it avoids repeated dynamic allocations.
let mut mat = DMatrix::identity(2, 2);
let rhs = DMatrix::from_row_slice(3, 2, &[1.0, 2.0,
3.0, 4.0,
5.0, 6.0]);
let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
0.5, 0.6, 0.7,
0.9, 1.0, 1.1]);
// The random shows that values on the workspace do not
// matter as they will be overwritten.
let mut workspace = DVector::new_random(3);
let expected = rhs.transpose() * &mid * &rhs * 10.0 + &mat * 5.0;
mat.quadform_with_workspace(&mut workspace, 10.0, &mid, &rhs, 5.0);
assert_relative_eq!(mat, expected);
pub fn quadform<D2, S2, R3, C3, S3>(
&mut self,
alpha: T,
mid: &SquareMatrix<T, D2, S2>,
rhs: &Matrix<T, R3, C3, S3>,
beta: T
) where
D2: Dim,
R3: Dim,
C3: Dim,
S2: Storage<T, D2, D2>,
S3: Storage<T, R3, C3>,
ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>,
DefaultAllocator: Allocator<T, D2>,
pub fn quadform<D2, S2, R3, C3, S3>(
&mut self,
alpha: T,
mid: &SquareMatrix<T, D2, S2>,
rhs: &Matrix<T, R3, C3, S3>,
beta: T
) where
D2: Dim,
R3: Dim,
C3: Dim,
S2: Storage<T, D2, D2>,
S3: Storage<T, R3, C3>,
ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>,
DefaultAllocator: Allocator<T, D2>,
Computes the quadratic form self = alpha * rhs.transpose() * mid * rhs + beta * self
.
This allocates a workspace vector of dimension D2 for intermediate results.
If D2
is a type-level integer, then the allocation is performed on the stack.
Use .quadform_with_workspace(...)
instead to avoid allocations.
let mut mat = Matrix2::identity();
let rhs = Matrix3x2::new(1.0, 2.0,
3.0, 4.0,
5.0, 6.0);
let mid = Matrix3::new(0.1, 0.2, 0.3,
0.5, 0.6, 0.7,
0.9, 1.0, 1.1);
let expected = rhs.transpose() * mid * rhs * 10.0 + mat * 5.0;
mat.quadform(10.0, &mid, &rhs, 5.0);
assert_relative_eq!(mat, expected);
pub fn append_scaling(&self, scaling: T) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
DefaultAllocator: Allocator<T, D, D>,
pub fn append_scaling(&self, scaling: T) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
DefaultAllocator: Allocator<T, D, D>,
Computes the transformation equal to self
followed by an uniform scaling factor.
pub fn prepend_scaling(&self, scaling: T) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
DefaultAllocator: Allocator<T, D, D>,
pub fn prepend_scaling(&self, scaling: T) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
DefaultAllocator: Allocator<T, D, D>,
Computes the transformation equal to an uniform scaling factor followed by self
.
pub fn append_nonuniform_scaling<SB>(
&self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
pub fn append_nonuniform_scaling<SB>(
&self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
Computes the transformation equal to self
followed by a non-uniform scaling factor.
pub fn prepend_nonuniform_scaling<SB>(
&self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
pub fn prepend_nonuniform_scaling<SB>(
&self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
Computes the transformation equal to a non-uniform scaling factor followed by self
.
pub fn append_translation<SB>(
&self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
pub fn append_translation<SB>(
&self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D>,
Computes the transformation equal to self
followed by a translation.
pub fn prepend_translation<SB>(
&self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimNameDiff<D, U1>>,
pub fn prepend_translation<SB>(
&self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) -> OMatrix<T, D, D> where
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimNameDiff<D, U1>>,
Computes the transformation equal to a translation followed by self
.
pub fn append_scaling_mut(&mut self, scaling: T) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
pub fn append_scaling_mut(&mut self, scaling: T) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
Computes in-place the transformation equal to self
followed by an uniform scaling factor.
pub fn prepend_scaling_mut(&mut self, scaling: T) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
pub fn prepend_scaling_mut(&mut self, scaling: T) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
Computes in-place the transformation equal to an uniform scaling factor followed by self
.
pub fn append_nonuniform_scaling_mut<SB>(
&mut self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
pub fn append_nonuniform_scaling_mut<SB>(
&mut self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
Computes in-place the transformation equal to self
followed by a non-uniform scaling factor.
pub fn prepend_nonuniform_scaling_mut<SB>(
&mut self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
pub fn prepend_nonuniform_scaling_mut<SB>(
&mut self,
scaling: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
Computes in-place the transformation equal to a non-uniform scaling factor followed by self
.
pub fn append_translation_mut<SB>(
&mut self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
pub fn append_translation_mut<SB>(
&mut self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) where
S: StorageMut<T, D, D>,
D: DimNameSub<U1>,
SB: Storage<T, DimNameDiff<D, U1>>,
Computes the transformation equal to self
followed by a translation.
pub fn prepend_translation_mut<SB>(
&mut self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) where
D: DimNameSub<U1>,
S: StorageMut<T, D, D>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, DimNameDiff<D, U1>>,
pub fn prepend_translation_mut<SB>(
&mut self,
shift: &Vector<T, DimNameDiff<D, U1>, SB>
) where
D: DimNameSub<U1>,
S: StorageMut<T, D, D>,
SB: Storage<T, DimNameDiff<D, U1>>,
DefaultAllocator: Allocator<T, DimNameDiff<D, U1>>,
Computes the transformation equal to a translation followed by self
.
impl<T: RealField, D: DimNameSub<U1>, S: Storage<T, D, D>> SquareMatrix<T, D, S> where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimNameDiff<D, U1>> + Allocator<T, DimNameDiff<D, U1>, DimNameDiff<D, U1>>,
impl<T: RealField, D: DimNameSub<U1>, S: Storage<T, D, D>> SquareMatrix<T, D, S> where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimNameDiff<D, U1>> + Allocator<T, DimNameDiff<D, U1>, DimNameDiff<D, U1>>,
pub fn transform_vector(
&self,
v: &OVector<T, DimNameDiff<D, U1>>
) -> OVector<T, DimNameDiff<D, U1>>
pub fn transform_vector(
&self,
v: &OVector<T, DimNameDiff<D, U1>>
) -> OVector<T, DimNameDiff<D, U1>>
Transforms the given vector, assuming the matrix self
uses homogeneous coordinates.
Transforms the given point, assuming the matrix self
uses homogeneous coordinates.
Transforms the given point, assuming the matrix self
uses homogeneous coordinates.
The diagonal of this matrix.
pub fn map_diagonal<T2: Scalar>(&self, f: impl FnMut(T) -> T2) -> OVector<T2, D> where
DefaultAllocator: Allocator<T2, D>,
pub fn map_diagonal<T2: Scalar>(&self, f: impl FnMut(T) -> T2) -> OVector<T2, D> where
DefaultAllocator: Allocator<T2, D>,
Apply the given function to this matrix’s diagonal and returns it.
This is a more efficient version of self.diagonal().map(f)
since this
allocates only once.
The symmetric part of self
, i.e., 0.5 * (self + self.transpose())
.
The hermitian part of self
, i.e., 0.5 * (self + self.adjoint())
.
impl<T: RealField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S> where
DefaultAllocator: Allocator<T, D, D>,
impl<T: RealField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S> where
DefaultAllocator: Allocator<T, D, D>,
pub fn is_special_orthogonal(&self, eps: T) -> bool where
D: DimMin<D, Output = D>,
DefaultAllocator: Allocator<(usize, usize), D>,
pub fn is_special_orthogonal(&self, eps: T) -> bool where
D: DimMin<D, Output = D>,
DefaultAllocator: Allocator<(usize, usize), D>,
Checks that this matrix is orthogonal and has a determinant equal to 1.
Returns true
if this matrix is invertible.
pub fn determinant(&self) -> T where
DefaultAllocator: Allocator<T, D, D> + Allocator<(usize, usize), D>,
pub fn determinant(&self) -> T where
DefaultAllocator: Allocator<T, D, D> + Allocator<(usize, usize), D>,
Computes the matrix determinant.
If the matrix has a dimension larger than 3, an LU decomposition is used.
pub fn try_inverse(self) -> Option<OMatrix<T, D, D>> where
DefaultAllocator: Allocator<T, D, D>,
pub fn try_inverse(self) -> Option<OMatrix<T, D, D>> where
DefaultAllocator: Allocator<T, D, D>,
Attempts to invert this matrix.
Attempts to invert this matrix in-place. Returns false
and leaves self
untouched if
inversion fails.
Computes the eigenvalues of this matrix.
pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D> where
T: RealField,
DefaultAllocator: Allocator<NumComplex<T>, D>,
pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D> where
T: RealField,
DefaultAllocator: Allocator<NumComplex<T>, D>,
Computes the eigenvalues of this matrix.
pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_with_diag_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>,
diag: T
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular_with_diag_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>,
diag: T
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
lower-triangular part of self
is considered not-zero. The diagonal is never read as it is
assumed to be equal to diag
. Returns false
and does not modify its inputs if diag
is zero.
pub fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.transpose() . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.transpose() . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.transpose() . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.transpose() . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.adjoint() . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.adjoint() . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.adjoint() . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> bool where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.adjoint() . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_with_diag_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>,
diag: T
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_lower_triangular_with_diag_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>,
diag: T
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
lower-triangular part of self
is considered not-zero. The diagonal is never read as it is
assumed to be equal to diag
. Returns false
and does not modify its inputs if diag
is zero.
pub fn solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.transpose() . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.transpose() . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.transpose() . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn tr_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn tr_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.transpose() . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.adjoint() . x = b
where x
is the unknown and only
the lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2> where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Computes the solution of the linear system self.adjoint() . x = b
where x
is the unknown and only
the upper-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.adjoint() . x = b
where x
is the unknown and only the
lower-triangular part of self
(including the diagonal) is considered not-zero.
pub fn ad_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn ad_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the linear system self.adjoint() . x = b
where x
is the unknown and only the
upper-triangular part of self
(including the diagonal) is considered not-zero.
Computes the eigenvalues of this symmetric matrix.
Only the lower-triangular part of the matrix is read.