scalation.linalgebra

MatrixD

class MatrixD extends Matrix with Error with Serializable

The MatrixD class stores and operates on Numeric Matrices of type Double. This class follows the MatrixN framework and is provided for efficieny.

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  1. MatrixD
  2. Serializable
  3. Serializable
  4. Matrix
  5. Error
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Instance Constructors

  1. new MatrixD(b: MatrixD)

    Construct a matrix and assign values from matrix u.

    Construct a matrix and assign values from matrix u.

    b

    the matrix of values to assign

  2. new MatrixD(u: Array[VectorD])

    Construct a matrix and assign values from array of vectors u.

    Construct a matrix and assign values from array of vectors u.

    u

    the 2D array of values to assign

  3. new MatrixD(dim: (Int, Int), u: Double*)

    Construct a matrix from repeated values.

    Construct a matrix from repeated values.

    dim

    the (row, column) dimensions

    u

    the repeated values

  4. new MatrixD(u: Array[Array[Double]])

    Construct a matrix and assign values from array of arrays u.

    Construct a matrix and assign values from array of arrays u.

    u

    the 2D array of values to assign

  5. new MatrixD(dim1: Int, dim2: Int, x: Double)

    Construct a dim1 by dim2 matrix and assign each element the value x.

    Construct a dim1 by dim2 matrix and assign each element the value x.

    dim1

    the row dimension

    dim2

    the column dimesion

    x

    the scalar value to assign

  6. new MatrixD(dim1: Int)

    Construct a dim1 by dim1 square matrix.

    Construct a dim1 by dim1 square matrix.

    dim1

    the row and column dimension

  7. new MatrixD(d1: Int, d2: Int, v: Array[Array[Double]] = null)

    d1

    the first/row dimension

    d2

    the second/column dimension

    v

    the 2D array used to store matrix elements

Value Members

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

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

    Definition Classes
    AnyRef → Any
  3. def *(x: Double): MatrixD

    Multiply this matrix by scalar x.

    Multiply this matrix by scalar x.

    x

    the scalar to multiply by

    Definition Classes
    MatrixDMatrix
  4. def *(u: VectorD): VectorD

    Multiply this matrix by vector u.

    Multiply this matrix by vector u.

    u

    the vector to multiply by

    Definition Classes
    MatrixDMatrix
  5. def *(b: MatrixD): MatrixD

    Multiply this matrix by matrix b, transposing b to improve efficiency.

    Multiply this matrix by matrix b, transposing b to improve efficiency. Use 'times' method to skip the transpose step.

    b

    the matrix to multiply by (requires sameCrossDimensions)

  6. def **(u: VectorD): MatrixD

    Multiply this matrix by vector u to produce another matrix (a_ij * u_j) E.

    Multiply this matrix by vector u to produce another matrix (a_ij * u_j) E.g., multiply a matrix by a diagonal matrix represented as a vector.

    u

    the vector to multiply by

    Definition Classes
    MatrixDMatrix
  7. def **=(u: VectorD): MatrixD

    Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)

    Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)

    u

    the vector to multiply by

    Definition Classes
    MatrixDMatrix
  8. def *=(x: Double): MatrixD

    Multiply in-place this matrix by scalar x.

    Multiply in-place this matrix by scalar x.

    x

    the scalar to multiply by

    Definition Classes
    MatrixDMatrix
  9. def *=(b: MatrixD): MatrixD

    Multiply in-place this matrix by matrix b, transposing b to improve efficiency.

    Multiply in-place this matrix by matrix b, transposing b to improve efficiency. Use 'times_ip' method to skip the transpose step.

    b

    the matrix to multiply by (requires square and sameCrossDimensions)

  10. def +(x: Double): MatrixD

    Add this matrix and scalar x.

    Add this matrix and scalar x.

    x

    the scalar to add

    Definition Classes
    MatrixDMatrix
  11. def +(u: VectorD): MatrixD

    Add this matrix and vector u.

    Add this matrix and vector u.

    u

    the vector to add

  12. def +(b: Matrix): MatrixD

    Add this matrix and matrix b.

    Add this matrix and matrix b.

    b

    the matrix to add (requires leDimensions)

    Definition Classes
    MatrixDMatrix
  13. def +(b: MatrixD): MatrixD

    Add this matrix and matrix b.

    Add this matrix and matrix b.

    b

    the matrix to add (requires leDimensions)

  14. def ++(u: VectorD): MatrixD

    Concatenate this matrix and vector u.

    Concatenate this matrix and vector u.

    u

    the vector to be concatenated as the new last row in matrix

    Definition Classes
    MatrixDMatrix
  15. def +=(x: Double): MatrixD

    Add in-place this matrix and scalar x.

    Add in-place this matrix and scalar x.

    x

    the scalar to add

    Definition Classes
    MatrixDMatrix
  16. def +=(b: MatrixD): MatrixD

    Add in-place this matrix and matrix b.

    Add in-place this matrix and matrix b.

    b

    the matrix to add (requires leDimensions)

  17. def -(x: Double): MatrixD

    From this matrix subtract scalar x.

    From this matrix subtract scalar x.

    x

    the scalar to subtract

    Definition Classes
    MatrixDMatrix
  18. def -(b: MatrixD): MatrixD

    From this matrix subtract matrix b.

    From this matrix subtract matrix b.

    b

    the matrix to subtract (requires leDimensions)

  19. def -=(x: Double): MatrixD

    From this matrix subtract in-place scalar x.

    From this matrix subtract in-place scalar x.

    x

    the scalar to subtract

    Definition Classes
    MatrixDMatrix
  20. def -=(b: MatrixD): MatrixD

    From this matrix subtract in-place matrix b.

    From this matrix subtract in-place matrix b.

    b

    the matrix to subtract (requires leDimensions)

  21. def /(x: Double): MatrixD

    Divide this matrix by scalar x.

    Divide this matrix by scalar x.

    x

    the scalar to divide by

    Definition Classes
    MatrixDMatrix
  22. def /=(x: Double): MatrixD

    Divide in-place this matrix by scalar x.

    Divide in-place this matrix by scalar x.

    x

    the scalar to divide by

    Definition Classes
    MatrixDMatrix
  23. final def ==(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  24. def apply(i: Int, jr: Range): VectorD

    Get a slice this matrix row-wise at index i and column-wise on range jr.

    Get a slice this matrix row-wise at index i and column-wise on range jr. Ex: u = a(2, 3..5)

    i

    the row index

    jr

    the column range

    Definition Classes
    MatrixDMatrix
  25. def apply(ir: Range, j: Int): VectorD

    Get a slice this matrix row-wise on range ir and column-wise at index j.

    Get a slice this matrix row-wise on range ir and column-wise at index j. Ex: u = a(2..4, 3)

    ir

    the row range

    j

    the column index

    Definition Classes
    MatrixDMatrix
  26. def apply(ir: Range, jr: Range): MatrixD

    Get a slice this matrix row-wise on range ir and column-wise on range jr.

    Get a slice this matrix row-wise on range ir and column-wise on range jr. Ex: b = a(2..4, 3..5)

    ir

    the row range

    jr

    the column range

    Definition Classes
    MatrixDMatrix
  27. def apply(i: Int): VectorD

    Get this matrix's vector at the i-th index position (i-th row).

    Get this matrix's vector at the i-th index position (i-th row).

    i

    the row index

    Definition Classes
    MatrixDMatrix
  28. def apply(i: Int, j: Int): Double

    Get this matrix's element at the i,j-th index position.

    Get this matrix's element at the i,j-th index position.

    i

    the row index

    j

    the column index

    Definition Classes
    MatrixDMatrix
  29. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  30. def clean(thres: Double, relative: Boolean = true): MatrixD

    Clean values in matrix at or below the threshold by setting them to zero.

    Clean values in matrix at or below the threshold by setting them to zero. Iterative algorithms give approximate values and if very close to zero, may throw off other calculations, e.g., in computing eigenvectors.

    thres

    the cutoff threshold (a small value)

    relative

    whether to use relative or absolute cutoff

    Definition Classes
    MatrixDMatrix
  31. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  32. def col(col: Int, from: Int = 0): VectorD

    Get column 'col' from the matrix, returning it as a vector.

    Get column 'col' from the matrix, returning it as a vector.

    col

    the column to extract from the matrix

    from

    the position to start extracting from

    Definition Classes
    MatrixDMatrix
  33. val d1: Int

    the first/row dimension

  34. val d2: Int

    the second/column dimension

  35. def det: Double

    Compute the determinant of this matrix.

    Compute the determinant of this matrix. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).

    Definition Classes
    MatrixDMatrix
  36. def diag(p: Int, q: Int): MatrixD

    Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by positioning the three matrices Ip, this and Iq along the diagonal.

    Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by positioning the three matrices Ip, this and Iq along the diagonal. Fill the rest of matrix with zeros.

    p

    the size of identity matrix Ip

    q

    the size of identity matrix Iq

    Definition Classes
    MatrixDMatrix
  37. def diag(p: Int): MatrixD

    Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal.

    Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal. Fill the rest of matrix with zeros.

    p

    the size of identity matrix Ip

  38. def diag(b: MatrixD): MatrixD

    Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeros; [this, b].

    Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeros; [this, b].

    b

    the matrix to combine with this matrix

  39. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    MatrixDMatrix
  40. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    MatrixDMatrix
  41. def dot(u: VectorD): VectorD

    Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (ie.

    Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (ie., 'a dot u = a.t * u').

    u

    the vector to multiply by (requires same first dimensions)

  42. def dot(b: MatrixD): MatrixD

    Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie.

    Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie., 'a dot b = a.t * b').

    b

    the matrix to multiply by (requires same first dimensions)

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

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

    Definition Classes
    AnyRef → Any
  45. var fString: String

    Format string used for printing vector values (change using setFormat)

    Format string used for printing vector values (change using setFormat)

    Attributes
    protected
    Definition Classes
    Matrix
  46. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  47. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  48. def foreach[U](f: (Array[Double]) ⇒ U): Unit

    Iterate over the matrix row by row.

    Iterate over the matrix row by row.

    f

    the function to apply

    Definition Classes
    Matrix
  49. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  50. def getDiag(k: Int = 0): VectorD

    Get the kth diagonal of this matrix.

    Get the kth diagonal of this matrix. Assumes dim2 >= dim1.

    k

    how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)

    Definition Classes
    MatrixDMatrix
  51. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  52. def inverse: MatrixD

    Invert this matrix (requires a squareMatrix) and use partial pivoting.

    Invert this matrix (requires a squareMatrix) and use partial pivoting.

    Definition Classes
    MatrixDMatrix
  53. def inverse_ip: MatrixD

    Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting.

    Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting. Note: this method turns the orginal matrix into the identity matrix. The inverse is returned and is captured by assignment.

    Definition Classes
    MatrixDMatrix
  54. def inverse_npp: MatrixD

    Invert this matrix (requires a squareMatrix) and does not use partial pivoting.

    Invert this matrix (requires a squareMatrix) and does not use partial pivoting.

    Definition Classes
    MatrixDMatrix
  55. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  56. def isNonnegative: Boolean

    Check whether this matrix is nonnegative (has no negative elements).

    Check whether this matrix is nonnegative (has no negative elements).

    Definition Classes
    MatrixDMatrix
  57. def isRectangular: Boolean

    Check whether this matrix is rectangular (all rows have the same number of columns).

    Check whether this matrix is rectangular (all rows have the same number of columns).

    Definition Classes
    MatrixDMatrix
  58. def isSquare: Boolean

    Check whether this matrix is square (same row and column dimensions).

    Check whether this matrix is square (same row and column dimensions).

    Definition Classes
    Matrix
  59. def isSymmetric: Boolean

    Check whether this matrix is symmetric.

    Check whether this matrix is symmetric.

    Definition Classes
    Matrix
  60. def leDimensions(b: Matrix): Boolean

    Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.

    Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.

    b

    the other matrix

    Definition Classes
    Matrix
  61. def lud: (MatrixD, MatrixD)

    Decompose this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm.

    Decompose this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm. This version uses partial pivoting.

    Definition Classes
    MatrixDMatrix
  62. def lud_ip: (MatrixD, MatrixD)

    Decompose in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm.

    Decompose in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm. This version uses partial pivoting.

    Definition Classes
    MatrixDMatrix
  63. def lud_npp: (MatrixD, MatrixD)

    Decompose this matrix into the product of upper and lower triangular matrices (l, u) using the LU Decomposition algorithm.

    Decompose this matrix into the product of upper and lower triangular matrices (l, u) using the LU Decomposition algorithm. This version uses no partial pivoting.

  64. def mag: Double

    Find the magnitude of this matrix, the element value farthest from zero.

    Find the magnitude of this matrix, the element value farthest from zero.

    Definition Classes
    Matrix
  65. def max(e: Int = dim1): Double

    Find the maximum element in this matrix.

    Find the maximum element in this matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    MatrixDMatrix
  66. def min(e: Int = dim1): Double

    Find the minimum element in this matrix.

    Find the minimum element in this matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    MatrixDMatrix
  67. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  68. def norm1: Double

    Compute the 1-norm of this matrix, i.

    Compute the 1-norm of this matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices (a - b).norm1

    Definition Classes
    MatrixDMatrix
  69. final def notify(): Unit

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

    Definition Classes
    AnyRef
  71. def nullspace: VectorD

    Compute the (right) nullspace of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    Compute the (right) nullspace of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose). FIX: need a more robust algorithm for computing nullspace (@see QRDecomp.scala)

    Definition Classes
    MatrixDMatrix
    See also

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

  72. def nullspace_ip: VectorD

    Compute the (right) nullspace in-place of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    Compute the (right) nullspace in-place of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose).

    Definition Classes
    MatrixDMatrix
  73. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Attributes
    protected
    Definition Classes
    Matrix
  74. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Attributes
    protected
    Definition Classes
    Matrix
  75. def rank: Int

    Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements.

    Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements.

    Definition Classes
    Matrix
  76. def reduce: MatrixD

    Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix.

    Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m.

    Definition Classes
    MatrixDMatrix
  77. def reduce_ip: Unit

    Use Gauss-Jordan reduction in-place on this matrix to make the left part embed an identity matrix.

    Use Gauss-Jordan reduction in-place on this matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m.

    Definition Classes
    MatrixDMatrix
  78. def sameCrossDimensions(b: Matrix): Boolean

    Check whether this matrix and the other matrix have the same cross dimensions.

    Check whether this matrix and the other matrix have the same cross dimensions.

    b

    the other matrix

    Definition Classes
    Matrix
  79. def sameDimensions(b: Matrix): Boolean

    Check whether this matrix and the other Matrix have the same dimensions.

    Check whether this matrix and the other Matrix have the same dimensions.

    b

    the other matrix

    Definition Classes
    Matrix
  80. def selectCols(colIndex: Array[Int]): MatrixD

    Select columns from this matrix according to the given index/basis.

    Select columns from this matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.

    colIndex

    the column index positions (e.g., (0, 2, 5))

    Definition Classes
    MatrixDMatrix
  81. def selectRows(rowIndex: Array[Int]): MatrixD

    Select rows from this matrix according to the given index/basis.

    Select rows from this matrix according to the given index/basis.

    rowIndex

    the row index positions (e.g., (0, 2, 5))

    Definition Classes
    MatrixDMatrix
  82. def set(i: Int, u: VectorD, j: Int = 0): Unit

    Set this matrix's ith row starting at column j to the vector u.

    Set this matrix's ith row starting at column j to the vector u.

    i

    the row index

    u

    the vector value to assign

    j

    the starting column index

    Definition Classes
    MatrixDMatrix
  83. def set(u: Array[Array[Double]]): Unit

    Set all the values in this matrix as copies of the values in 2D array u.

    Set all the values in this matrix as copies of the values in 2D array u.

    u

    the 2D array of values to assign

    Definition Classes
    MatrixDMatrix
  84. def set(x: Double): Unit

    Set all the elements in this matrix to the scalar x.

    Set all the elements in this matrix to the scalar x.

    x

    the scalar value to assign

    Definition Classes
    MatrixDMatrix
  85. def setCol(col: Int, u: VectorD): Unit

    Set column 'col' of the matrix to a vector.

    Set column 'col' of the matrix to a vector.

    col

    the column to set

    u

    the vector to assign to the column

    Definition Classes
    MatrixDMatrix
  86. def setDiag(x: Double): Unit

    Set the main diagonal of this matrix to the scalar x.

    Set the main diagonal of this matrix to the scalar x. Assumes dim2 >= dim1.

    x

    the scalar to set the diagonal to

    Definition Classes
    MatrixDMatrix
  87. def setDiag(u: VectorD, k: Int = 0): Unit

    Set the kth diagonal of this matrix to the vector u.

    Set the kth diagonal of this matrix to the vector u. Assumes dim2 >= dim1.

    u

    the vector to set the diagonal to

    k

    how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)

    Definition Classes
    MatrixDMatrix
  88. def setFormat(newFormat: String): Unit

    Set the format to the newFormat.

    Set the format to the newFormat.

    newFormat

    the new format string

    Definition Classes
    Matrix
  89. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixD

    Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.

    Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.

    r_from

    the start of the row slice

    r_end

    the end of the row slice

    c_from

    the start of the column slice

    c_end

    the end of the column slice

    Definition Classes
    MatrixDMatrix
  90. def slice(from: Int, end: Int): MatrixD

    Slice this matrix row-wise 'from' to 'end'.

    Slice this matrix row-wise 'from' to 'end'.

    from

    the start row of the slice (inclusive)

    end

    the end row of the slice (exclusive)

    Definition Classes
    MatrixDMatrix
  91. def sliceCol(from: Int, end: Int): MatrixD

    Slice this matrix column-wise 'from' to 'end'.

    Slice this matrix column-wise 'from' to 'end'.

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

  92. def sliceExclude(row: Int, col: Int): MatrixD

    Slice this matrix excluding the given row and/or column.

    Slice this matrix excluding the given row and/or column.

    row

    the row to exclude (0 until dim1, set to dim1 to keep all rows)

    col

    the column to exclude (0 until dim2, set to dim2 to keep all columns)

    Definition Classes
    MatrixDMatrix
  93. def solve(b: VectorD): VectorD

    Solve for x in the equation a*x = b where a is this matrix (see lud above).

    Solve for x in the equation a*x = b where a is this matrix (see lud above).

    b

    the constant vector.

    Definition Classes
    MatrixDMatrix
  94. def solve(lu: (Matrix, Matrix), b: VectorD): VectorD

    Solve for x in the equation l*u*x = b (see lud above).

    Solve for x in the equation l*u*x = b (see lud above).

    lu

    the lower and upper triangular matrices

    b

    the constant vector

    Definition Classes
    MatrixDMatrix
  95. def solve(l: Matrix, u: Matrix, b: VectorD): VectorD

    Solve for x in the equation l*u*x = b (see lud above).

    Solve for x in the equation l*u*x = b (see lud above).

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    MatrixDMatrix
  96. def sum: Double

    Compute the sum of this matrix, i.

    Compute the sum of this matrix, i.e., the sum of its elements.

    Definition Classes
    MatrixDMatrix
  97. def sumAbs: Double

    Compute the abs sum of this matrix, i.

    Compute the abs sum of this matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices (a - b).sumAbs

    Definition Classes
    MatrixDMatrix
  98. def sumLower: Double

    Compute the sum of the lower triangular region of this matrix.

    Compute the sum of the lower triangular region of this matrix.

    Definition Classes
    MatrixDMatrix
  99. def swap(i: Int, k: Int, col: Int = 0): Unit

    Swap the elements in rows 'i' and 'k' starting from column 'col'.

    Swap the elements in rows 'i' and 'k' starting from column 'col'.

    i

    the first row in the swap

    k

    the second row in the swap

    col

    the starting column for the swap (default 0 => whole row)

  100. def swapCol(j: Int, l: Int, row: Int = 0): Unit

    Swap the elements in columns 'j' and 'l' starting from row 'row'.

    Swap the elements in columns 'j' and 'l' starting from row 'row'.

    j

    the first column in the swap

    l

    the second column in the swap

    row

    the starting row for the swap (default 0 => whole column)

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

    Definition Classes
    AnyRef
  102. def t: MatrixD

    Transpose this matrix (rows => columns).

    Transpose this matrix (rows => columns).

    Definition Classes
    MatrixDMatrix
  103. def times(b: MatrixD): MatrixD

    Multiply this matrix by matrix b without first transposing b.

    Multiply this matrix by matrix b without first transposing b.

    b

    the matrix to multiply by (requires sameCrossDimensions)

  104. def times_d(b: Matrix): MatrixD

    Multiply this matrix by matrix b using dot product (concise solution).

    Multiply this matrix by matrix b using dot product (concise solution).

    b

    the matrix to multiply by (requires sameCrossDimensions)

  105. def times_ip(b: MatrixD): Unit

    Multiply in-place this matrix by matrix b without first transposing b.

    Multiply in-place this matrix by matrix b without first transposing b. If b and this reference the same matrix (b == this), a copy of the this matrix is made.

    b

    the matrix to multiply by (requires square and sameCrossDimensions)

  106. def times_s(b: MatrixD): MatrixD

    Multiply this matrix by matrix b using the Strassen matrix multiplication algorithm.

    Multiply this matrix by matrix b using the Strassen matrix multiplication algorithm. Both matrices (this and b) must be square. Although the algorithm is faster than the traditional cubic algorithm, its requires more memory and is often less stable (due to round-off errors). FIX: could be make more efficient using a virtual slice (vslice) method.

    b

    the matrix to multiply by (it has to be a square matrix)

    See also

    http://en.wikipedia.org/wiki/Strassen_algorithm

  107. def toString(): String

    Convert this real (double precision) matrix to a string.

    Convert this real (double precision) matrix to a string.

    Definition Classes
    MatrixD → AnyRef → Any
  108. def trace: Double

    Compute the trace of this matrix, i.

    Compute the trace of this matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.

    Definition Classes
    MatrixDMatrix
    See also

    Eigen.scala

  109. def update(i: Int, jr: Range, u: VectorD): Unit

    Set a slice this matrix row-wise at index i and column-wise on range jr.

    Set a slice this matrix row-wise at index i and column-wise on range jr. Ex: a(2, 3..5) = u

    i

    the row index

    jr

    the column range

    u

    the vector to assign

    Definition Classes
    MatrixDMatrix
  110. def update(ir: Range, j: Int, u: VectorD): Unit

    Set a slice this matrix row-wise on range ir and column-wise at index j.

    Set a slice this matrix row-wise on range ir and column-wise at index j. Ex: a(2..4, 3) = u

    ir

    the row range

    j

    the column index

    u

    the vector to assign

    Definition Classes
    MatrixDMatrix
  111. def update(ir: Range, jr: Range, b: MatrixD): Unit

    Set a slice this matrix row-wise on range ir and column-wise on range jr.

    Set a slice this matrix row-wise on range ir and column-wise on range jr. Ex: a(2..4, 3..5) = b

    ir

    the row range

    jr

    the column range

    b

    the matrix to assign

  112. def update(i: Int, u: VectorD): Unit

    Set this matrix's row at the i-th index position to the vector u.

    Set this matrix's row at the i-th index position to the vector u.

    i

    the row index

    u

    the vector value to assign

    Definition Classes
    MatrixDMatrix
  113. def update(i: Int, j: Int, x: Double): Unit

    Set this matrix's element at the i,j-th index position to the scalar x.

    Set this matrix's element at the i,j-th index position to the scalar x.

    i

    the row index

    j

    the column index

    x

    the scalar value to assign

    Definition Classes
    MatrixDMatrix
  114. final def wait(): Unit

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

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  117. def write(fileName: String): Unit

    Write this matrix to a CSV-formatted text file.

    Write this matrix to a CSV-formatted text file.

    fileName

    the name of file holding the data

  118. def ~^(p: Int): MatrixD

    Raise this matrix to the pth power (for some integer p >= 2).

    Raise this matrix to the pth power (for some integer p >= 2). Caveat: should be replace by a divide and conquer algorithm.

    p

    the power to raise this matrix to

    Definition Classes
    MatrixDMatrix

Inherited from Serializable

Inherited from Serializable

Inherited from Matrix

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped