Struct extendr_api::prelude::solvers::ColPivQr

pub struct ColPivQr<E>
where E: Entity,
{ factors: Mat<E>, householder: Mat<E>, col_perm: Vec<usize>, col_perm_inv: Vec<usize>, }
Expand description

QR decomposition with column pivoting.

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§factors: Mat<E>§householder: Mat<E>§col_perm: Vec<usize>§col_perm_inv: Vec<usize>

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impl<E> ColPivQr<E>
where E: ComplexField,

pub fn new<ViewE>(matrix: MatRef<'_, ViewE>) -> ColPivQr<E>
where ViewE: Conjugate<Canonical = E>,

Returns the QR decomposition of the input matrix with column pivoting.

The factorization is such that $AP^\top = QR$, where $R$ is upper trapezoidal, $Q$ is unitary, and $P$ is a permutation matrix.

pub fn col_permutation(&self) -> PermRef<'_, usize>

Returns the column permutation matrix $P$ of the QR decomposition.

pub fn compute_r(&self) -> Mat<E>

Returns the factor $R$ of the QR decomposition.

pub fn compute_q(&self) -> Mat<E>

Returns the factor $Q$ of the QR decomposition.

pub fn compute_thin_r(&self) -> Mat<E>

Returns the top $r$ rows of the factor $R$ of the QR decomposition, where $r = \min(\text{nrows}(A), \text{ncols}(A))$.

pub fn compute_thin_q(&self) -> Mat<E>

Returns the leftmost $r$ columns of the factor $R$ of the QR decomposition, where $r = \min(\text{nrows}(A), \text{ncols}(A))$.

Trait Implementations§

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impl<E> Debug for ColPivQr<E>
where E: Debug + Entity,

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

Formats the value using the given formatter. Read more
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impl<E> SolverCore<E> for ColPivQr<E>
where E: ComplexField,

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fn reconstruct(&self) -> Mat<E>

Reconstructs the original matrix using the decomposition.
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fn inverse(&self) -> Mat<E>

Computes the inverse of the original matrix using the decomposition. Read more
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impl<E> SpSolverCore<E> for ColPivQr<E>
where E: ComplexField,

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fn nrows(&self) -> usize

Returns the number of rows of the matrix used to construct this decomposition.
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fn ncols(&self) -> usize

Returns the number of columns of the matrix used to construct this decomposition.
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impl<E> SolverLstsqCore<E> for ColPivQr<E>
where E: ComplexField,

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impl<E> SpSolverLstsqCore<E> for ColPivQr<E>
where E: ComplexField,

Auto Trait Implementations§

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impl<E> Freeze for ColPivQr<E>
where <<E as Entity>::Group as ForCopyType>::FaerOfCopy<NonNull<<E as Entity>::Unit>>: Freeze,

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impl<E> RefUnwindSafe for ColPivQr<E>
where <<E as Entity>::Group as ForCopyType>::FaerOfCopy<NonNull<<E as Entity>::Unit>>: RefUnwindSafe, E: RefUnwindSafe,

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impl<E> Send for ColPivQr<E>

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impl<E> Sync for ColPivQr<E>

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impl<E> Unpin for ColPivQr<E>
where <<E as Entity>::Group as ForCopyType>::FaerOfCopy<NonNull<<E as Entity>::Unit>>: Unpin, E: Unpin,

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impl<E> UnwindSafe for ColPivQr<E>
where <<E as Entity>::Group as ForCopyType>::FaerOfCopy<NonNull<<E as Entity>::Unit>>: UnwindSafe, E: UnwindSafe,

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<T> Pointable for T

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const ALIGN: usize = _

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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impl<E, Dec> SpSolver<E> for Dec
where E: ComplexField, Dec: SpSolverCore<E> + ?Sized,

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fn solve_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation self * X = rhs, and stores the result in rhs.
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fn solve_conj_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation conjugate(self) * X = rhs, and stores the result in rhs.
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fn solve_transpose_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation transpose(self) * X = rhs, and stores the result in rhs.
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fn solve_conj_transpose_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation adjoint(self) * X = rhs, and stores the result in rhs.
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fn solve<ViewE, B>(&self, rhs: B) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation self * X = rhs, and returns the result.
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fn solve_conj<ViewE, B>(&self, rhs: B) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation conjugate(self) * X = rhs, and returns the result.
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fn solve_transpose<ViewE, B>(&self, rhs: B) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation transpose(self) * X = rhs, and returns the result.
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fn solve_conj_transpose<ViewE, B>( &self, rhs: B, ) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation adjoint(self) * X = rhs, and returns the result.
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impl<E, Dec> SpSolverLstsq<E> for Dec
where E: ComplexField, Dec: SpSolverLstsqCore<E> + ?Sized,

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fn solve_lstsq_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation self * X = rhs, in the sense of least squares, and stores the result in the top rows of rhs.
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fn solve_lstsq_conj_in_place(&self, rhs: impl ColBatchMut<E>)

Solves the equation conjugate(self) * X = rhs, in the sense of least squares, and stores the result in the top rows of rhs.
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fn solve_lstsq<ViewE, B>(&self, rhs: B) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation self * X = rhs, and returns the result.
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fn solve_lstsq_conj<ViewE, B>(&self, rhs: B) -> <B as ColBatch<ViewE>>::Owned
where ViewE: Conjugate<Canonical = E>, B: ColBatch<ViewE>,

Solves the equation conjugate(self) * X = rhs, and returns the result.
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<E, Dec> Solver<E> for Dec
where E: ComplexField, Dec: SolverCore<E> + ?Sized,

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impl<E, Dec> SolverLstsq<E> for Dec
where E: ComplexField, Dec: SolverLstsqCore<E> + ?Sized,