breeze.linalg

pinv

object pinv extends UFunc with pinvLowPrio

Computes the Moore-Penrose pseudo inverse of the given real matrix X.

The pseudo inverse is nothing but the least-squares solution to AX=B, hence: d/dX 1/2 (AX-B)2 = AT (AX-B) Solving AT (AX-B) = 0 for X yields AT AX = A^T B

> X

Linear Supertypes
pinvLowPrio, UFunc, AnyRef, Any
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  2. pinvLowPrio
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Type Members

  1. type Impl[V, VR] = UImpl[pinv.this.type, V, VR]

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

  5. type InPlaceImpl[V] = generic.UFunc.InPlaceImpl[pinv.this.type, V]

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  6. 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

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

  10. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  11. 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

  12. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  13. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  14. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  15. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  16. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  17. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  18. implicit def implFromTransposeAndSolve[T, TransT, MulRes, Result](implicit numericT: (T) ⇒ NumericOps[T], trans: CanTranspose[T, TransT], numericTrans: (TransT) ⇒ NumericOps[TransT], mul: operators.OpMulMatrix.Impl2[TransT, T, MulRes], numericMulRes: (MulRes) ⇒ NumericOps[MulRes], solve: operators.OpSolveMatrixBy.Impl2[MulRes, TransT, Result]): Impl[T, Result]

    pinv for anything that can be transposed, multiplied with that transposed, and then solved.

    pinv for anything that can be transposed, multiplied with that transposed, and then solved. This signature looks intense, but take it one step at a time.

    T

    the type of matrix

    TransT

    the transpose of that matrix

    MulRes

    the result of TransT * T

    Result

    the result of MulRes \ TransT

    numericT

    : Do I support operators

    trans

    : Can I be transposed?

    numericTrans

    : Does my transpose support operators

    mul

    : Can I multiply T and TransT?

    numericMulRes

    : Does the result of that multiplication support operators?

    solve

    : Can I solve the system of equations MulRes * x = TransT

    returns

    Definition Classes
    pinvLowPrio

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

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

    Definition Classes
    UFunc

  22. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  23. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  24. final def notify(): Unit

    Definition Classes
    AnyRef

  25. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  26. implicit val pinvFromSVD_Double: Impl[DenseMatrix[Double], DenseMatrix[Double]]

  27. implicit val pinvFromSVD_Float: Impl[DenseMatrix[Float], DenseMatrix[Float]]

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

    Definition Classes
    AnyRef

  29. def toString(): String

    Definition Classes
    AnyRef → Any

  30. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  32. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    UFunc

Inherited from pinvLowPrio

Inherited from UFunc

Inherited from AnyRef

Inherited from Any

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