breeze.linalg

pinv

object pinv extends UFunc

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

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

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

    Definition Classes
    UFunc
  6. type InPlaceImpl3[V1, V2, V3] = generic.UFunc.InPlaceImpl3[pinv.this.type, 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, VR](v1: V1, v2: V2, v3: V3)(implicit impl: Impl3[V1, V2, V3, VR]): VR

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

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

    Definition Classes
    UFunc
  9. final def asInstanceOf[T0]: T0

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

    Definition Classes
    UFunc
  11. def clone(): AnyRef

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

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

    Definition Classes
    AnyRef → Any
  14. def finalize(): Unit

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

    Definition Classes
    AnyRef → Any
  16. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  17. 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

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

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

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

    Definition Classes
    UFunc
  21. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  22. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  23. final def notify(): Unit

    Definition Classes
    AnyRef
  24. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  25. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  26. def toString(): String

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

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

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from UFunc

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