qr - breeze.linalg.qr

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

Linear Supertypes

UFunc, AnyRef, Any

Type Members

type DenseQR = QR[DenseMatrix[Double]]
type Impl[V, VR] = UImpl[qr.this.type, V, VR]

Definition Classes
UFunc
type Impl2[V1, V2, VR] = UImpl2[qr.this.type, V1, V2, VR]

Definition Classes
UFunc
type Impl3[V1, V2, V3, VR] = UImpl3[qr.this.type, V1, V2, V3, VR]

Definition Classes
UFunc
type Impl4[V1, V2, V3, V4, VR] = UImpl4[qr.this.type, V1, V2, V3, V4, VR]

Definition Classes
UFunc
type InPlaceImpl[V] = generic.UFunc.InPlaceImpl[qr.this.type, V]

Definition Classes
UFunc
type InPlaceImpl2[V1, V2] = generic.UFunc.InPlaceImpl2[qr.this.type, V1, V2]

Definition Classes
UFunc
type InPlaceImpl3[V1, V2, V3] = generic.UFunc.InPlaceImpl3[qr.this.type, V1, V2, V3]

Definition Classes
UFunc
case class QR[M](q: M, r: M) extends Product with Serializable
type SDenseQR = QR[DenseMatrix[Float]]
type SinkImpl[S, V] = generic.UFunc.SinkImpl[qr.this.type, S, V]

Definition Classes
UFunc
type SinkImpl2[S, V1, V2] = generic.UFunc.SinkImpl2[qr.this.type, S, V1, V2]

Definition Classes
UFunc
type SinkImpl3[S, V1, V2, V3] = generic.UFunc.SinkImpl3[qr.this.type, S, V1, V2, V3]

Definition Classes
UFunc

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
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

Definition Classes
UFunc
final def apply[V1, V2, V3, VR](v1: V1, v2: V2, v3: V3)(implicit impl: Impl3[V1, V2, V3, VR]): VR

Definition Classes
UFunc
final def apply[V1, V2, VR](v1: V1, v2: V2)(implicit impl: Impl2[V1, V2, VR]): VR

Definition Classes
UFunc
final def apply[V, VR](v: V)(implicit impl: Impl[V, VR]): VR

Definition Classes
UFunc
final def asInstanceOf[T0]: T0

Definition Classes
Any
implicit def canZipMapValuesImpl[T, V1, VR, U](implicit handhold: ScalarOf[T, V1], impl: Impl2[V1, V1, VR], canZipMapValues: CanZipMapValues[T, V1, VR, U]): Impl2[T, T, U]

Definition Classes
UFunc
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
implicit object impl_DM_Double extends Impl[DenseMatrix[Double], DenseQR]
implicit object impl_DM_Float extends Impl[DenseMatrix[Float], SDenseQR]
final def inPlace[V, V2, V3](v: V, v2: V2, v3: V3)(implicit impl: generic.UFunc.InPlaceImpl3[qr.this.type, V, V2, V3]): V

Definition Classes
UFunc
final def inPlace[V, V2](v: V, v2: V2)(implicit impl: generic.UFunc.InPlaceImpl2[qr.this.type, V, V2]): V

Definition Classes
UFunc
final def inPlace[V](v: V)(implicit impl: generic.UFunc.InPlaceImpl[qr.this.type, V]): V

Definition Classes
UFunc
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
object justQ extends UFunc

QR that just returns Q.
object justR extends UFunc

QR that just returns R.
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
object reduced extends UFunc

QR Factorization that returns Q and R with dimensions (m, k), (k, n) where k = min(m, n)
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

Definition Classes
AnyRef → Any
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def withSink[S](s: S): WithSinkHelp[qr.this.type, S]

Definition Classes
UFunc

qr

Related Doc: package linalg

object qr extends UFunc

Type Members

type DenseQR = QR[DenseMatrix[Double]]

type Impl[V, VR] = UImpl[qr.this.type, V, VR]

type Impl2[V1, V2, VR] = UImpl2[qr.this.type, V1, V2, VR]

type Impl3[V1, V2, V3, VR] = UImpl3[qr.this.type, V1, V2, V3, VR]

type Impl4[V1, V2, V3, V4, VR] = UImpl4[qr.this.type, V1, V2, V3, V4, VR]

type InPlaceImpl[V] = generic.UFunc.InPlaceImpl[qr.this.type, V]

type InPlaceImpl2[V1, V2] = generic.UFunc.InPlaceImpl2[qr.this.type, V1, V2]

type InPlaceImpl3[V1, V2, V3] = generic.UFunc.InPlaceImpl3[qr.this.type, V1, V2, V3]

case class QR[M](q: M, r: M) extends Product with Serializable

type SDenseQR = QR[DenseMatrix[Float]]

type SinkImpl[S, V] = generic.UFunc.SinkImpl[qr.this.type, S, V]

type SinkImpl2[S, V1, V2] = generic.UFunc.SinkImpl2[qr.this.type, S, V1, V2]

type SinkImpl3[S, V1, V2, V3] = generic.UFunc.SinkImpl3[qr.this.type, S, V1, V2, V3]

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

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

final def apply[V1, V2, V3, VR](v1: V1, v2: V2, v3: V3)(implicit impl: Impl3[V1, V2, V3, VR]): VR

final def apply[V1, V2, VR](v1: V1, v2: V2)(implicit impl: Impl2[V1, V2, VR]): VR

final def apply[V, VR](v: V)(implicit impl: Impl[V, VR]): VR

final def asInstanceOf[T0]: T0

implicit def canZipMapValuesImpl[T, V1, VR, U](implicit handhold: ScalarOf[T, V1], impl: Impl2[V1, V1, VR], canZipMapValues: CanZipMapValues[T, V1, VR, U]): Impl2[T, T, U]

def clone(): AnyRef

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

implicit object impl_DM_Double extends Impl[DenseMatrix[Double], DenseQR]

implicit object impl_DM_Float extends Impl[DenseMatrix[Float], SDenseQR]

final def inPlace[V, V2, V3](v: V, v2: V2, v3: V3)(implicit impl: generic.UFunc.InPlaceImpl3[qr.this.type, V, V2, V3]): V

final def inPlace[V, V2](v: V, v2: V2)(implicit impl: generic.UFunc.InPlaceImpl2[qr.this.type, V, V2]): V

final def inPlace[V](v: V)(implicit impl: generic.UFunc.InPlaceImpl[qr.this.type, V]): V

final def isInstanceOf[T0]: Boolean

object justQ extends UFunc

object justR extends UFunc

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

object reduced extends UFunc

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

final def withSink[S](s: S): WithSinkHelp[qr.this.type, S]

Inherited from UFunc

Inherited from AnyRef

Inherited from Any

Ungrouped