SquareMatrix in nalgebra::base - Rust
Description: A square matrix.
Keywords: rust, rustlang, rust-lang, SquareMatrix

# Type Definition nalgebra::base::SquareMatrix

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    pub type SquareMatrix<T, D, S> = Matrix<T, D, D, S>;

Expand description

A square matrix.

## Implementations§

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### impl<T, D1: Dim, S: StorageMut<T, D1, D1>> SquareMatrix<T, D1, S>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### 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.

##### Example

    // 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);

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#### 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.

##### Example

    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);

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#### 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.

##### Example

    // 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);

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#### 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.

##### Example

    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);

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### impl<T: Scalar + Zero + One + ClosedMul + ClosedAdd, D: DimName, S: Storage<T, D, D>> SquareMatrix<T, D, S>

#### Append/prepend translation and scaling

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#### 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.

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#### 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`.

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#### 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.

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#### 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`.

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#### 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.

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#### 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`.

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#### 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.

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#### 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`.

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#### 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.

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#### 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`.

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#### 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.

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#### 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`.

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### 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>>,

#### Transformation of vectors and points

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#### 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.

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### impl<T: RealField, S: Storage<T, Const<3>, Const<3>>> SquareMatrix<T, Const<3>, S>

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#### pub fn transform_point(&self, pt: &Point<T, 2>) -> Point<T, 2>

Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.

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### impl<T: RealField, S: Storage<T, Const<4>, Const<4>>> SquareMatrix<T, Const<4>, S>

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#### pub fn transform_point(&self, pt: &Point<T, 3>) -> Point<T, 3>

Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.

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### impl<T: Scalar, D: Dim, S: RawStorage<T, D, D>> SquareMatrix<T, D, S>

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#### pub fn diagonal(&self) -> OVector<T, D>where
DefaultAllocator: Allocator<T, D>,

The diagonal of this matrix.

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#### 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.

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#### pub fn trace(&self) -> Twhere
T: Scalar + Zero + ClosedAdd,

Computes a trace of a square matrix, i.e., the sum of its diagonal elements.

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### impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>

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#### pub fn symmetric_part(&self) -> OMatrix<T, D, D>where
DefaultAllocator: Allocator<T, D, D>,

The symmetric part of `self`, i.e., `0.5 * (self + self.transpose())`.

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#### pub fn hermitian_part(&self) -> OMatrix<T, D, D>where
DefaultAllocator: Allocator<T, D, D>,

The hermitian part of `self`, i.e., `0.5 * (self + self.adjoint())`.

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### impl<T: RealField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>where
DefaultAllocator: Allocator<T, D, D>,

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#### 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.

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#### pub fn is_invertible(&self) -> bool

Returns `true` if this matrix is invertible.

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### impl<T: ComplexField, D: DimMin<D, Output = D>, S: Storage<T, D, D>> SquareMatrix<T, D, S>

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#### pub fn determinant(&self) -> Twhere
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.

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### impl<T: ComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>

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#### pub fn try_inverse(self) -> Option<OMatrix<T, D, D>>where
DefaultAllocator: Allocator<T, D, D>,

Attempts to invert this square matrix.

##### Panics

Panics if `self` isn’t a square matrix.

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### impl<T: ComplexField, D: Dim, S: StorageMut<T, D, D>> SquareMatrix<T, D, S>

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#### pub fn try_inverse_mut(&mut self) -> bool where
DefaultAllocator: Allocator<T, D, D>,

Attempts to invert this square matrix in-place. Returns `false` and leaves `self` untouched if inversion fails.

##### Panics

Panics if `self` isn’t a square matrix.

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### impl<T: ComplexField, D, S: Storage<T, D, D>> SquareMatrix<T, D, S>where
D: DimSub<U1> + Dim,
DefaultAllocator: Allocator<T, D, DimDiff<D, U1>> + Allocator<T, DimDiff<D, U1>> + Allocator<T, D, D> + Allocator<T, D>,

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#### pub fn eigenvalues(&self) -> Option<OVector<T, D>>

Computes the eigenvalues of this matrix.

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#### pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D>where
T: RealField,
DefaultAllocator: Allocator<NumComplex<T>, D>,

Computes the eigenvalues of this matrix.

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### impl<T: ComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>

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#### 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.

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#### 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.

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#### 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.

source

#### 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.

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#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

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### impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>

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#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

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#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

source

#### 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.

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### impl<T: ComplexField, D: DimSub<U1>, S: Storage<T, D, D>> SquareMatrix<T, D, S>where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>> + Allocator<T::RealField, D> + Allocator<T::RealField, DimDiff<D, U1>>,

source

#### pub fn symmetric_eigenvalues(&self) -> OVector<T::RealField, D>

Computes the eigenvalues of this symmetric matrix.

Only the lower-triangular part of the matrix is read.