Struct SymmetricDMat6

pub struct SymmetricDMat6 {
    pub a: SymmetricDMat3,
    pub b: DMat3,
    pub d: SymmetricDMat3,
}

The bottom left triangle (including the diagonal) of a symmetric 6x6 column-major matrix.

This is useful for storing a symmetric 6x6 matrix in a more compact form and performing some matrix operations more efficiently.

Some defining properties of symmetric matrices include:

• The matrix is equal to its transpose.
• The matrix has real eigenvalues.
• The eigenvectors corresponding to the eigenvalues are orthogonal.
• The matrix is always diagonalizable.

The sum and difference of two symmetric matrices is always symmetric. However, the product of two symmetric matrices is only symmetric if the matrices are commutable, meaning that AB = BA.

The 6x6 matrix is represented as:

[ A  BT ]
[ B  D  ]

Fields

a: SymmetricDMat3

The bottom left triangle of the top left 3x3 block of the matrix, including the diagonal.

b: DMat3

The bottom left 3x3 block of the matrix.

d: SymmetricDMat3

The bottom left triangle of the bottom right 3x3 block of the matrix, including the diagonal.

Implementations

impl SymmetricDMat6

pub const ZERO: Self

A symmetric 6x6 matrix with all elements set to 0.0.

pub const IDENTITY: Self

A symmetric 6x6 identity matrix, where all diagonal elements are 1.0, and all off-diagonal elements are 0.0.

pub const NAN: Self

All NaNs.

pub const fn new(a: SymmetricDMat3, b: DMat3, d: SymmetricDMat3) -> Self

Creates a new symmetric 6x6 matrix from its bottom left triangle, including diagonal elements.

The matrix is represented as:

[ A  BT ]
[ B  D  ]

pub fn from_outer_product(v1: DVec3, v2: DVec3) -> Self

Creates a new symmetric 6x6 matrix from the outer product [v1, v2] * [v1, v2]^T.

pub fn is_finite(&self) -> bool

Returns true if, and only if, all elements are finite. If any element is either NaN or positive or negative infinity, this will return false.

pub fn is_nan(&self) -> bool

Returns true if any elements are NaN.

pub fn abs(&self) -> Self

Takes the absolute value of each element in self.

pub fn mul_vec6(&self, rhs1: DVec3, rhs2: DVec3) -> (DVec3, DVec3)

Transforms a 6x1 vector that is split into two 3x1 vectors.

pub fn ldlt_solve(&self, rhs1: DVec3, rhs2: DVec3) -> (DVec3, DVec3)

Solves self * [x1, x2] = [rhs1, rhs2] for x1 and x2 using the LDLT decomposition.

self must be a positive semidefinite matrix.

pub fn add_symmetric_mat6(&self, rhs: &Self) -> Self

Adds two symmetric 6x6 matrices.

pub fn sub_symmetric_mat6(&self, rhs: &Self) -> Self

Subtracts two symmetric 6x6 matrices.

pub fn mul_scalar(&self, rhs: f64) -> Self

Multiplies a 6x6 matrix by a scalar.

pub fn div_scalar(&self, rhs: f64) -> Self

Divides a 6x6 matrix by a scalar.

impl SymmetricDMat6

pub fn as_symmetric_mat6(&self) -> SymmetricMat6

Returns the single precision version of self.

Trait Implementations

impl Add<&&SymmetricDMat6> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl Add<&SymmetricDMat6> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl Add for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl Add for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign<&SymmetricDMat6> for SymmetricDMat6

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl AddAssign for SymmetricDMat6

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for SymmetricDMat6

fn clone(&self) -> SymmetricDMat6

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SymmetricDMat6

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for SymmetricDMat6

fn default() -> Self

Returns the “default value” for a type.

impl Display for SymmetricDMat6

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Div<&SymmetricDMat6> for &f64

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: &SymmetricDMat6) -> Self::Output

Performs the / operation.

impl Div<&SymmetricDMat6> for f64

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: &SymmetricDMat6) -> Self::Output

Performs the / operation.

impl Div<&f64> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: &f64) -> Self::Output

Performs the / operation.

impl Div<&f64> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: &f64) -> Self::Output

Performs the / operation.

impl Div<SymmetricDMat6> for &f64

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: SymmetricDMat6) -> Self::Output

Performs the / operation.

impl Div<SymmetricDMat6> for f64

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: SymmetricDMat6) -> Self::Output

Performs the / operation.

impl Div<f64> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> Self::Output

Performs the / operation.

impl Div<f64> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> Self::Output

Performs the / operation.

impl DivAssign<&f64> for SymmetricDMat6

fn div_assign(&mut self, rhs: &f64)

Performs the /= operation.

impl DivAssign<f64> for SymmetricDMat6

fn div_assign(&mut self, rhs: f64)

Performs the /= operation.

impl FromReflect for SymmetricDMat6

fn from_reflect(reflect: &dyn PartialReflect) -> Option<Self>

Constructs a concrete instance of Self from a reflected value.

fn take_from_reflect( reflect: Box<dyn PartialReflect>, ) -> Result<Self, Box<dyn PartialReflect>>

Attempts to downcast the given value to Self using, constructing the value using from_reflect if that fails.

impl GetTypeRegistration for SymmetricDMat6

fn get_type_registration() -> TypeRegistration

Returns the default TypeRegistration for this type.

fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this type.

impl Mul<&SymmetricDMat6> for &f64

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricDMat6) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricDMat6> for f64

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricDMat6) -> Self::Output

Performs the * operation.

impl Mul<&f64> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: &f64) -> Self::Output

Performs the * operation.

impl Mul<&f64> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: &f64) -> Self::Output

Performs the * operation.

impl Mul<SymmetricDMat6> for &f64

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricDMat6) -> Self::Output

Performs the * operation.

impl Mul<SymmetricDMat6> for f64

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricDMat6) -> Self::Output

Performs the * operation.

impl Mul<f64> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> Self::Output

Performs the * operation.

impl Mul<f64> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> Self::Output

Performs the * operation.

impl MulAssign<&f64> for SymmetricDMat6

fn mul_assign(&mut self, rhs: &f64)

Performs the *= operation.

impl MulAssign<f64> for SymmetricDMat6

fn mul_assign(&mut self, rhs: f64)

Performs the *= operation.

impl Neg for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for SymmetricDMat6

fn eq(&self, other: &SymmetricDMat6) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialReflect for SymmetricDMat6

fn get_represented_type_info(&self) -> Option<&'static TypeInfo>

Returns the TypeInfo of the type represented by this value.

fn try_apply(&mut self, value: &dyn PartialReflect) -> Result<(), ApplyError>

Tries to apply a reflected value to this value.

fn reflect_kind(&self) -> ReflectKind

Returns a zero-sized enumeration of “kinds” of type.

fn reflect_ref(&self) -> ReflectRef<'_>

Returns an immutable enumeration of “kinds” of type.

fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type.

fn reflect_owned(self: Box<Self>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type.

fn try_into_reflect( self: Box<Self>, ) -> Result<Box<dyn Reflect>, Box<dyn PartialReflect>>

Attempts to cast this type to a boxed, fully-reflected value.

fn try_as_reflect(&self) -> Option<&dyn Reflect>

Attempts to cast this type to a fully-reflected value.

fn try_as_reflect_mut(&mut self) -> Option<&mut dyn Reflect>

Attempts to cast this type to a mutable, fully-reflected value.

fn into_partial_reflect(self: Box<Self>) -> Box<dyn PartialReflect>

Casts this type to a boxed, reflected value.

fn as_partial_reflect(&self) -> &dyn PartialReflect

Casts this type to a reflected value.

fn as_partial_reflect_mut(&mut self) -> &mut dyn PartialReflect

Casts this type to a mutable, reflected value.

fn reflect_partial_eq(&self, value: &dyn PartialReflect) -> Option<bool>

Returns a “partial equality” comparison result.

fn reflect_clone(&self) -> Result<Box<dyn Reflect>, ReflectCloneError>

Attempts to clone Self using reflection.

fn apply(&mut self, value: &(dyn PartialReflect + 'static))

Applies a reflected value to this value.

fn to_dynamic(&self) -> Box<dyn PartialReflect>

Converts this reflected value into its dynamic representation based on its kind.

fn reflect_clone_and_take<T>(&self) -> Result<T, ReflectCloneError>

where T: 'static, Self: Sized + TypePath,

For a type implementing PartialReflect, combines reflect_clone and take in a useful fashion, automatically constructing an appropriate ReflectCloneError if the downcast fails.

fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type).

fn debug(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Debug formatter for the value.

fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type.

impl Reflect for SymmetricDMat6

fn into_any(self: Box<Self>) -> Box<dyn Any>

Returns the value as a Box<dyn Any>.

fn as_any(&self) -> &dyn Any

Returns the value as a &dyn Any.

fn as_any_mut(&mut self) -> &mut dyn Any

Returns the value as a &mut dyn Any.

fn into_reflect(self: Box<Self>) -> Box<dyn Reflect>

Casts this type to a boxed, fully-reflected value.

fn as_reflect(&self) -> &dyn Reflect

Casts this type to a fully-reflected value.

fn as_reflect_mut(&mut self) -> &mut dyn Reflect

Casts this type to a mutable, fully-reflected value.

fn set(&mut self, value: Box<dyn Reflect>) -> Result<(), Box<dyn Reflect>>

Performs a type-checked assignment of a reflected value to this value.

impl Struct for SymmetricDMat6

fn field(&self, name: &str) -> Option<&dyn PartialReflect>

Returns a reference to the value of the field named name as a &dyn PartialReflect.

fn field_mut(&mut self, name: &str) -> Option<&mut dyn PartialReflect>

Returns a mutable reference to the value of the field named name as a &mut dyn PartialReflect.

fn field_at(&self, index: usize) -> Option<&dyn PartialReflect>

Returns a reference to the value of the field with index index as a &dyn PartialReflect.

fn field_at_mut(&mut self, index: usize) -> Option<&mut dyn PartialReflect>

Returns a mutable reference to the value of the field with index index as a &mut dyn PartialReflect.

fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index index.

fn field_len(&self) -> usize

Returns the number of fields in the struct.

fn iter_fields(&self) -> FieldIter<'_>

Returns an iterator over the values of the reflectable fields for this struct.

fn to_dynamic_struct(&self) -> DynamicStruct

Creates a new DynamicStruct from this struct.

fn get_represented_struct_info(&self) -> Option<&'static StructInfo>

Will return None if TypeInfo is not available.

impl Sub<&&SymmetricDMat6> for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl Sub<&SymmetricDMat6> for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl Sub for &SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl Sub for SymmetricDMat6

type Output = SymmetricDMat6

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl SubAssign<&SymmetricDMat6> for SymmetricDMat6

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl SubAssign for SymmetricDMat6

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> Sum<&'a SymmetricDMat6> for SymmetricDMat6

fn sum<I: Iterator<Item = &'a SymmetricDMat6>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for SymmetricDMat6

fn sum<I: Iterator<Item = SymmetricDMat6>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl TypePath for SymmetricDMat6

fn type_path() -> &'static str

Returns the fully qualified path of the underlying type.

fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type.

fn type_ident() -> Option<&'static str>

Returns the name of the type, or None if it is anonymous.

fn crate_name() -> Option<&'static str>

Returns the name of the crate the type is in, or None if it is anonymous.

fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or None if it is anonymous.

impl Typed for SymmetricDMat6

fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.

impl Copy for SymmetricDMat6

impl StructuralPartialEq for SymmetricDMat6