breeze/breeze.linalg/qr

qr

object qr extends UFunc

QR Factorization

Previous versions of Breeze had qr(m, skipQ), where we could skip the computation in making Q if we didn't want it. That is now supplanted by qr.justR(m)

Supports complete and reduced mode of factorization of matrix A with dimensions (m, n). If mode is complete matrices Q and R have dimensions (m, m), (m, n). If mode is reduced matrices Q and R have dimensions (m, k), (k, n) with k = min(m, n).

Complete QR factorization can be called by qr(A).

Reduced QR factorization can be called by qr.reduced(A). If computation of Q is unnecessary, it can be skipped by qr.reduced.justR(A)

Returns

(Q, R) Q - A matrix with orthonormal columns R - The upper-triangular matrix

trait UFunc
trait HasOps
class Object
trait Matchable
class Any

Type members

Classlikes

case class QR[M](q: M, r: M)
object impl_DM_Double extends Impl[DenseMatrix[Double], DenseQR]
object impl_DM_Float extends Impl[DenseMatrix[Float], SDenseQR]
object justQ extends UFunc

QR that just returns Q.

QR that just returns Q.

object justR extends UFunc

QR that just returns R.

QR that just returns R.

object reduced extends UFunc

QR Factorization that returns Q and R with dimensions (m, k), (k, n) where k = min(m, n)

QR Factorization that returns Q and R with dimensions (m, k), (k, n) where k = min(m, n)

Types

type DenseQR = QR[DenseMatrix[Double]]
type SDenseQR = QR[DenseMatrix[Float]]

Inherited types

type Impl[V, VR] = UImpl[UFunc, V, VR]
Inherited from
UFunc
type Impl2[V1, V2, VR] = UImpl2[UFunc, V1, V2, VR]
Inherited from
UFunc
type Impl3[V1, V2, V3, VR] = UImpl3[UFunc, V1, V2, V3, VR]
Inherited from
UFunc
type Impl4[V1, V2, V3, V4, VR] = UImpl4[UFunc, V1, V2, V3, V4, VR]
Inherited from
UFunc
type InPlaceImpl[V] = InPlaceImpl[UFunc, V]
Inherited from
UFunc
type InPlaceImpl2[V1, V2] = InPlaceImpl2[UFunc, V1, V2]
Inherited from
UFunc
type InPlaceImpl3[V1, V2, V3] = InPlaceImpl3[UFunc, V1, V2, V3]
Inherited from
UFunc
type SinkImpl[S, V] = SinkImpl[UFunc, S, V]
Inherited from
UFunc
type SinkImpl2[S, V1, V2] = SinkImpl2[UFunc, S, V1, V2]
Inherited from
UFunc
type SinkImpl3[S, V1, V2, V3] = SinkImpl3[UFunc, S, V1, V2, V3]
Inherited from
UFunc

Value members

Inherited methods

final def apply[V1, V2, V3, V4, VR](v1: V1, v2: V2, v3: V3, v4: V4)(implicit impl: Impl4[V1, V2, V3, V4, VR]): VR
Inherited from
UFunc
final def apply[V1, @specialized(Int, Double, Float) V2, @specialized(Int, Double, Float) V3, @specialized(Int, Double, Float) VR](v1: V1, v2: V2, v3: V3)(implicit impl: Impl3[V1, V2, V3, VR]): VR
Inherited from
UFunc
final def apply[@specialized(Int, Double, Float) V1, @specialized(Int, Double, Float) V2, @specialized(Int, Double, Float) VR](v1: V1, v2: V2)(implicit impl: Impl2[V1, V2, VR]): VR
Inherited from
UFunc
final def apply[@specialized(Int, Double, Float) V, @specialized(Int, Double, Float) VR](v: V)(implicit impl: Impl[V, VR]): VR
Inherited from
UFunc
final def inPlace[V, V2, V3](v: V, v2: V2, v3: V3)(implicit impl: InPlaceImpl3[qr, V, V2, V3]): V
Inherited from
UFunc
final def inPlace[V, V2](v: V, v2: V2)(implicit impl: InPlaceImpl2[qr, V, V2]): V
Inherited from
UFunc
final def inPlace[V](v: V)(implicit impl: InPlaceImpl[qr, V]): V
Inherited from
UFunc
final def withSink[S](s: S): WithSinkHelp[qr, S]
Inherited from
UFunc