LinearAlgebra

Value Members

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

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

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3. final def ##(): Int

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

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

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6. def LU[T](X: Matrix[T])(implicit td: (T) ⇒ Double): (DenseMatrix[Double], Array[Int])

   Computes the LU factorization of the given real M-by-N matrix X such that X = P * L * U where P is a permutation matrix (row exchanges).

   Computes the LU factorization of the given real M-by-N matrix X such that X = P * L * U where P is a permutation matrix (row exchanges).

   Upon completion, a tuple consisting of a matrix A and an integer array P.

   The upper triangular portion of A resembles U whereas the lower triangular portion of A resembles L up to but not including the diagonal elements of L which are all equal to 1.

   For 0 <= i < M, each element P(i) denotes whether row i of the matrix X was exchanged with row P(i-1) during computation (the offset is caused by the internal call to LAPACK).

7. final def asInstanceOf[T0]: T0

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8. def cholesky(X: Matrix[Double]): DenseMatrix[Double]

   Computes the cholesky decomposition A of the given real symmetric positive definite matrix X such that X = A A.

   Computes the cholesky decomposition A of the given real symmetric positive definite matrix X such that X = A A.t.

   XXX: For higher dimensionalities, the return value really should be a sparse matrix due to its inherent lower triangular nature.

9. def clone(): AnyRef

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10. def cross[V1](a: DenseVector[V1], b: DenseVector[V1])(implicit ring: Ring[V1], man: ClassTag[V1]): DenseVector[V1]

    Vector cross product of 3D vectors a and b.

11. def det[T](X: Matrix[T])(implicit td: (T) ⇒ Double): Double

    Computes the determinant of the given real matrix.

12. def eig(m: Matrix[Double]): (DenseVector[Double], DenseVector[Double], DenseMatrix[Double])

    Eigenvalue decomposition (right eigenvectors)

    Eigenvalue decomposition (right eigenvectors)

    This function returns the real and imaginary parts of the eigenvalues, and the corresponding eigenvectors. For most (?) interesting matrices, the imaginary part of all eigenvalues will be zero (and the corresponding eigenvectors will be real). Any complex eigenvalues will appear in complex-conjugate pairs, and the real and imaginary components of the eigenvector for each pair will be in the corresponding columns of the eigenvector matrix. Take the complex conjugate to find the second eigenvector.

    Based on EVD.java from MTJ 0.9.12

13. def eigSym(X: Matrix[Double], rightEigenvectors: Boolean): (DenseVector[Double], Option[DenseMatrix[Double]])

    Computes all eigenvalues (and optionally right eigenvectors) of the given real symmetric matrix X.

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

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15. def equals(arg0: Any): Boolean

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16. def finalize(): Unit

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

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18. def hashCode(): Int

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19. def inv[T](X: Matrix[T])(implicit td: (T) ⇒ Double): DenseMatrix[Double]

    Computes the inverse of a given real matrix.

20. final def isInstanceOf[T0]: Boolean

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21. def kron[V1, V2, M, RV](a: DenseMatrix[V1], b: M)(implicit mul: BinaryOp[V1, M, OpMulScalar, DenseMatrix[RV]], asMat: <:<[M, Matrix[V2]], man: ClassTag[RV], dfv: DefaultArrayValue[RV]): DenseMatrix[RV]

    Returns the Kronecker product of the two matrices a and b, usually denoted a ⊗ b.

22. def lowerTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

    The lower triangular portion of the given real quadratic matrix X.

    The lower triangular portion of the given real quadratic matrix X. Note that no check will be performed regarding the symmetry of X.

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

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24. final def notify(): Unit

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25. final def notifyAll(): Unit

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26. def pinv[V](X: DenseMatrix[V])(implicit cast: (V) ⇒ Double): DenseMatrix[Double]

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

27. def pinv(X: DenseMatrix[Double]): DenseMatrix[Double]

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

28. def pow(m: DenseMatrix[Double], exp: Double): DenseMatrix[Double]

    Raises m to the exp'th power via eigenvalue decomposition.

    Raises m to the exp'th power via eigenvalue decomposition. Currently requires that m's eigenvalues are real.

    m

    exp

29. def qr(A: DenseMatrix[Double], skipQ: Boolean = false): (DenseMatrix[Double], DenseMatrix[Double])

    QR Factorization

    QR Factorization

    A

    m x n matrix

    skipQ

    (optional) if true, don't reconstruct orthogonal matrix Q (instead returns (null,R))

    returns

    (Q,R) Q: m x m R: m x n

30. def qrp(A: DenseMatrix[Double]): (DenseMatrix[Double], DenseMatrix[Double], DenseMatrix[Int], Array[Int])

    QR Factorization with pivoting

    QR Factorization with pivoting

    input: A m x n matrix output: (Q,R,P,pvt) where AP = QR Q: m x m R: m x n P: n x n : permutation matrix (P(pvt(i),i) = 1) pvt : pivot indices

31. def rank(m: DenseMatrix[Double], tol: Option[Double] = None): Int

    Computes the rank of a DenseMatrix[Double].

    Computes the rank of a DenseMatrix[Double].

    The rank of the matrix is computed using the SVD method. The singular values of the SVD which are greater than a specified tolerance are counted.

    m

    matrix for which to compute the rank

    tol

    optional tolerance for singular values. If not supplied, the default tolerance is: max(m.cols, m.rows) * eps * sigma_max, where eps is the machine epsilon and sigma_max is the largest singular value of m.

    returns

    the rank of the matrix (number of singular values)

32. def ranks[V](x: Vector[V])(implicit arg0: Ordering[V]): Array[Double]

    Returns the rank of each element in the given vector, adjusting for ties.

33. def svd(mat: DenseMatrix[Double]): (DenseMatrix[Double], DenseVector[Double], DenseMatrix[Double])

    Computes the SVD of a m by n matrix Returns an m*m matrix U, a vector of singular values, and a n*n matrix V'

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

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35. def toString(): String

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36. def upperTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

    The upper triangular portion of the given real quadratic matrix X.

    The upper triangular portion of the given real quadratic matrix X. Note that no check will be performed regarding the symmetry of X.

37. final def wait(): Unit

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

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

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