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trait MatriQ extends Error

The MatriQ trait specifies the operations to be defined by the concrete classes implementing Rational matrices, i.e., MatrixQ - dense matrix BidMatrixQ - bidiagonal matrix - useful for computing Singular Values RleMatrixQ - compressed matrix - Run Length Encoding (RLE) SparseMatrixQ - sparse matrix - majority of elements should be zero SymTriMatrixQ - symmetric triangular matrix - useful for computing Eigenvalues par.MatrixQ - parallel dense matrix par.SparseMatrixQ - parallel sparse matrix Some of the classes provide a few custom methods, e.g., methods beginning with "times" or ending with 'npp'. ------------------------------------------------------------------------------ row-wise column-wise Prepend: vector +: matrix vector +: matrix (right associative) Append: matrix :+ vector matrix :+ vector Concatenate: matrix ++ matrix matrix ++^ matrix

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Error, AnyRef, Any
Known Subclasses
BidMatrixQ, MatrixQ, RleMatrixQ, SparseMatrixQ, SymTriMatrixQ
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Abstract Value Members

  1. abstract def *(x: Rational): MatriQ

    Multiply 'this' matrix by scalar 'x'.

    Multiply 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

  2. abstract def *(u: VectoQ): VectoQ

    Multiply 'this' matrix by vector 'u'.

    Multiply 'this' matrix by vector 'u'.

    u

    the vector to multiply by

  3. abstract def *(b: MatriQ): MatriQ

    Multiply 'this' matrix and matrix 'b' for any type extending MatriQ.

    Multiply 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def * (b: MatrixQ): MatrixQ.

    b

    the matrix to add (requires 'leDimensions')

  4. abstract def **(u: VectoQ): MatriQ

    Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

    Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

    u

    the vector to multiply by

  5. abstract def **:(u: VectoQ): MatriQ

    Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'.

    Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'. E.g., multiply a diagonal matrix represented as a vector by a matrix. This operator is right associative.

    u

    the vector to multiply by

  6. abstract def **=(u: VectoQ): MatriQ

    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

  7. abstract def *=(x: Rational): MatriQ

    Multiply in-place 'this' matrix by scalar 'x'.

    Multiply in-place 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

  8. abstract def *=(b: MatriQ): MatriQ

    Multiply in-place 'this' matrix and matrix 'b' for any type extending MatriQ.

    Multiply in-place 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def *= (b: MatrixQ): MatrixQ.

    b

    the matrix to multiply by (requires 'leDimensions')

  9. abstract def +(x: Rational): MatriQ

    Add 'this' matrix and scalar 'x'.

    Add 'this' matrix and scalar 'x'.

    x

    the scalar to add

  10. abstract def +(u: VectoQ): MatriQ

    Add 'this' matrix and (row) vector 'u'.

    Add 'this' matrix and (row) vector 'u'.

    u

    the vector to add

  11. abstract def +(b: MatriQ): MatriQ

    Add 'this' matrix and matrix 'b' for any type extending MatriQ.

    Add 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def + (b: MatrixQ): MatrixQ.

    b

    the matrix to add (requires 'leDimensions')

  12. abstract def ++(b: MatriQ): MatriQ

    Concatenate (row-wise) 'this' matrix and matrix 'b'.

    Concatenate (row-wise) 'this' matrix and matrix 'b'.

    b

    the matrix to be concatenated as the new last rows in new matrix

  13. abstract def ++^(b: MatriQ): MatriQ

    Concatenate (column-wise) 'this' matrix and matrix 'b'.

    Concatenate (column-wise) 'this' matrix and matrix 'b'.

    b

    the matrix to be concatenated as the new last columns in new matrix

  14. abstract def +:(u: VectoQ): MatriQ

    Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

    Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

    u

    the vector to be prepended as the new first row in new matrix

  15. abstract def +=(x: Rational): MatriQ

    Add in-place 'this' matrix and scalar 'x'.

    Add in-place 'this' matrix and scalar 'x'.

    x

    the scalar to add

  16. abstract def +=(u: VectoQ): MatriQ

    Add in-place 'this' matrix and (row) vector 'u'.

    Add in-place 'this' matrix and (row) vector 'u'.

    u

    the vector to add

  17. abstract def +=(b: MatriQ): MatriQ

    Add in-place 'this' matrix and matrix 'b' for any type extending MatriQ.

    Add in-place 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def += (b: MatrixQ): MatrixQ.

    b

    the matrix to add (requires 'leDimensions')

  18. abstract def +^:(u: VectoQ): MatriQ

    Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

    Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

    u

    the vector to be prepended as the new first column in new matrix

  19. abstract def -(x: Rational): MatriQ

    From 'this' matrix subtract scalar 'x'.

    From 'this' matrix subtract scalar 'x'.

    x

    the scalar to subtract

  20. abstract def -(u: VectoQ): MatriQ

    From 'this' matrix subtract (row) vector 'u'.

    From 'this' matrix subtract (row) vector 'u'.

    u

    the vector to subtract

  21. abstract def -(b: MatriQ): MatriQ

    From 'this' matrix subtract matrix 'b' for any type extending MatriQ.

    From 'this' matrix subtract matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def - (b: MatrixQ): MatrixQ.

    b

    the matrix to subtract (requires 'leDimensions')

  22. abstract def -=(x: Rational): MatriQ

    From 'this' matrix subtract in-place scalar 'x'.

    From 'this' matrix subtract in-place scalar 'x'.

    x

    the scalar to subtract

  23. abstract def -=(u: VectoQ): MatriQ

    From 'this' matrix subtract in-place (row) vector 'u'.

    From 'this' matrix subtract in-place (row) vector 'u'.

    u

    the vector to subtract

  24. abstract def -=(b: MatriQ): MatriQ

    From 'this' matrix subtract in-place matrix 'b' for any type extending MatriQ.

    From 'this' matrix subtract in-place matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def -= (b: MatrixQ): MatrixQ.

    b

    the matrix to subtract (requires 'leDimensions')

  25. abstract def /(x: Rational): MatriQ

    Divide 'this' matrix by scalar 'x'.

    Divide 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

  26. abstract def /=(x: Rational): MatriQ

    Divide in-place 'this' matrix by scalar 'x'.

    Divide in-place 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

  27. abstract def :+(u: VectoQ): MatriQ

    Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.

    Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.

    u

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

  28. abstract def :^+(u: VectoQ): MatriQ

    Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.

    Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.

    u

    the vector to be appended as the new last column in new matrix

  29. abstract def apply(ir: Range, jr: Range): MatriQ

    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

  30. abstract def apply(i: Int): VectoQ

    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

  31. abstract def apply(i: Int, j: Int): Rational

    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

  32. abstract def bsolve(y: VectoQ): VectoQ

    Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud' above).

    Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud' above).

    y

    the constant vector

  33. abstract def clean(thres: Double, relative: Boolean = true): MatriQ

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

    Clean values in 'this' matrix at or below the threshold 'thres' 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

  34. abstract def col(col: Int, from: Int = 0): VectoQ

    Get column 'col' starting 'from' in 'this' matrix, returning it as a vector.

    Get column 'col' starting 'from' in 'this' matrix, returning it as a vector.

    col

    the column to extract from the matrix

    from

    the position to start extracting from

  35. abstract def copy: MatriQ

    Create an exact copy of 'this' m-by-n matrix.

  36. abstract def det: Rational

    Compute the determinant of 'this' matrix.

  37. abstract def diag(p: Int, q: Int = 0): MatriQ

    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.

    p

    the size of identity matrix Ip

    q

    the size of identity matrix Iq

  38. abstract def diag(b: MatriQ): MatriQ

    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. abstract val dim1: Int

    Matrix dimension 1 (# rows)

  40. abstract val dim2: Int

    Matrix dimension 2 (# columns)

  41. abstract def dot(b: MatriQ): VectoQ

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    b

    the matrix to multiply by (requires same first dimensions)

    See also

    www.mathworks.com/help/matlab/ref/dot.html

  42. abstract def dot(u: VectoQ): VectoQ

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

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

    u

    the vector to multiply by (requires same first dimensions)

  43. abstract def getDiag(k: Int = 0): VectoQ

    Get the 'k'th diagonal of 'this' matrix.

    Get the 'k'th diagonal of 'this' matrix. Assumes dim2 >= dim1.

    k

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

  44. abstract def inverse: MatriQ

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

  45. abstract def inverse_ip(): MatriQ

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

  46. abstract def isRectangular: Boolean

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

  47. abstract def lowerT: MatriQ

    Return the lower triangular of 'this' matrix (rest are zero).

  48. abstract def lud_ip(): (MatriQ, MatriQ)

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

  49. abstract def lud_npp: (MatriQ, MatriQ)

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

  50. abstract def max(e: Int = dim1): Rational

    Find the maximum element in 'this' matrix.

    Find the maximum element in 'this' matrix.

    e

    the ending row index (exclusive) for the search

  51. abstract def mdot(b: MatriQ): MatriQ

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

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

    b

    the matrix to multiply by (requires same first dimensions)

  52. abstract def min(e: Int = dim1): Rational

    Find the minimum element in 'this' matrix.

    Find the minimum element in 'this' matrix.

    e

    the ending row index (exclusive) for the search

  53. abstract def nullspace: VectoQ

    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.

    nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

    The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

    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

  54. abstract def nullspace_ip(): VectoQ

    Compute in-place 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 in-place 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.

    nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

    The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

    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

  55. abstract def reduce: MatriQ

    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.

  56. abstract def reduce_ip(): MatriQ

    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.

  57. abstract def selectCols(colIndex: Array[Int]): MatriQ

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

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

  58. abstract def selectRows(rowIndex: Array[Int]): MatriQ

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

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

    rowIndex

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

  59. abstract def set(i: Int, u: VectoQ, j: Int = 0): Unit

    Set 'this' matrix's 'i'th row starting a column 'j' to the vector 'u'.

    Set 'this' matrix's 'i'th row starting a column 'j' to the vector 'u'.

    i

    the row index

    u

    the vector value to assign

    j

    the starting column index

  60. abstract def set(u: MatriQ): Unit

    Set the values in 'this' matrix as copies of the values in matrix 'u'.

    Set the values in 'this' matrix as copies of the values in matrix 'u'.

    u

    the matrix of values to assign

  61. abstract def set(u: Array[Array[Rational]]): Unit

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

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

    u

    the 2D array of values to assign

  62. abstract def set(x: Rational): 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

  63. abstract def setCol(col: Int, u: VectoQ): Unit

    Set column 'col' of 'this' matrix to vector 'u'.

    Set column 'col' of 'this' matrix to vector 'u'.

    col

    the column to set

    u

    the vector to assign to the column

  64. abstract def setDiag(x: Rational): 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

  65. abstract def setDiag(u: VectoQ, k: Int = 0): Unit

    Set the 'k'th diagonal of 'this' matrix to the vector 'u'.

    Set the 'k'th 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)

  66. abstract def slice(from: Int, end: Int): MatriQ

    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)

  67. abstract def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatriQ

    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 (inclusive)

    r_end

    the end of the row slice (exclusive)

    c_from

    the start of the column slice (inclusive)

    c_end

    the end of the column slice (exclusive)

  68. abstract def sliceCol(from: Int, end: Int): MatriQ

    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)

  69. abstract def sliceEx(row: Int, col: Int): MatriQ

    Slice 'this' matrix excluding the given 'row' and 'column'.

    Slice 'this' matrix excluding the given 'row' and 'column'.

    row

    the row to exclude

    col

    the column to exclude

  70. abstract def solve(b: VectoQ): VectoQ

    Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.

    Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.

    b

    the constant vector.

  71. abstract def solve(l: MatriQ, u: MatriQ, b: VectoQ): VectoQ

    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

  72. abstract def sum: Rational

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

  73. abstract def sumAbs: Rational

    Compute the 'abs' sum of 'this' matrix, i.e., the sum of the absolute value of its elements.

    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'.

  74. abstract def sumLower: Rational

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

  75. abstract def t: MatriQ

    Transpose 'this' matrix (rows => columns).

  76. abstract def toDense: MatriQ

    Convert 'this' matrix to a dense matrix.

  77. abstract def toDouble: MatriD

    Convert 'this' MatriQ into a double matrix MatriD.

  78. abstract def toInt: MatriI

    Convert 'this' MatriQ into an integer matrix MatriI.

  79. abstract def trace: Rational

    Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal.

    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.

    See also

    Eigen.scala

  80. abstract def update(ir: Range, jr: Range, b: MatriQ): Unit

    Set a slice of 'this' matrix row-wise on range 'ir' and column-wise on range 'jr' to matrix 'b'.

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

    ir

    the row range

    jr

    the column range

    b

    the matrix to assign

  81. abstract def update(i: Int, u: VectoQ): 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

  82. abstract def update(i: Int, j: Int, x: Rational): 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

  83. abstract def upperT: MatriQ

    Return the upper triangular of 'this' matrix (rest are zero).

  84. abstract def write(fileName: String): Unit

    Write 'this' matrix to a CSV-formatted text file with name 'fileName'.

    Write 'this' matrix to a CSV-formatted text file with name 'fileName'.

    fileName

    the name of file to hold the data

  85. abstract def zero(m: Int = dim1, n: Int = dim2): MatriQ

    Create an m-by-n matrix with all elements initialized to zero.

    Create an m-by-n matrix with all elements initialized to zero.

    m

    the number of rows

    n

    the number of columns

  86. abstract def ~^(p: Int): MatriQ

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

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

    p

    the power to raise 'this' matrix to

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def **(b: MatriQ): MatriQ

    Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

    Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

    b

    the matrix to multiply by

    See also

    en.wikipedia.org/wiki/Hadamard_product_(matrices) FIX - remove ??? and implement in all implementing classes

  4. def *:(u: VectoQ): VectoQ

    Multiply (row) vector 'u' by 'this' matrix.

    Multiply (row) vector 'u' by 'this' matrix. Note '*:' is right associative. vector = vector *: matrix

    u

    the vector to multiply by

  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def apply(iv: VectoI): MatriQ

    Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes

    Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes

    iv

    the vector of row indices

  7. def apply(i: Int, jr: Range): VectoQ

    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

  8. def apply(ir: Range, j: Int): VectoQ

    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

  9. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  10. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  13. val fString: String

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

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

    Attributes
    protected
  14. def flatten: VectoQ

    Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.

  15. final 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
  16. def foreach[U](f: (Array[Rational]) => U): Unit

    Iterate over 'this' matrix row by row applying method 'f'.

    Iterate over 'this' matrix row by row applying method 'f'.

    f

    the function to apply

  17. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. def isBidiagonal: Boolean

    Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).

    Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.

  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. def isNonnegative: Boolean

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

  22. def isSquare: Boolean

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

  23. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

  24. def isTridiagonal: Boolean

    Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).

    Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.

  25. def leDimensions(b: MatriQ): Boolean

    Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.

    Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.

    b

    the other matrix

  26. def mag: Rational

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

  27. def map(f: (VectoQ) => VectoQ): MatriQ

    Map the elements of 'this' matrix by applying the mapping function 'f'.

    Map the elements of 'this' matrix by applying the mapping function 'f'. FIX - remove ??? and implement in all implementing classes

    f

    the function to apply

  28. def mean: VectoQ

    Compute the column means of 'this' matrix.

  29. def meanNZ: VectoQ

    Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

  30. def meanR: VectoQ

    Compute the row means of 'this' matrix.

  31. def meanRNZ: VectoQ

    Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

  32. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  33. def norm1: Rational

    Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors.

    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'.

    See also

    en.wikipedia.org/wiki/Matrix_norm

  34. def normF: Rational

    Compute the Frobenius-norm of 'this' matrix, i.e., the square root of the sum of the squared values over all the elements (sqrt (sse)).

    Compute the Frobenius-norm of 'this' matrix, i.e., the square root of the sum of the squared values over all the elements (sqrt (sse)). FIX: for MatriC should take absolute values, first.

    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  35. def normFSq: Rational

    Compute the sqaure of the Frobenius-norm of 'this' matrix, i.e., the sum of the squared values over all the elements (sse).

    Compute the sqaure of the Frobenius-norm of 'this' matrix, i.e., the sum of the squared values over all the elements (sse). FIX: for MatriC should take absolute values, first.

    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  36. def normINF: Rational

    Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

    Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

    See also

    en.wikipedia.org/wiki/Matrix_norm

  37. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  38. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  39. val range1: Range

    Range for the storage array on dimension 1 (rows)

  40. val range2: Range

    Range for the storage array on dimension 2 (columns)

  41. def sameCrossDimensions(b: MatriQ): Boolean

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

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

    b

    the other matrix

  42. def sameDimensions(b: MatriQ): Boolean

    Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

    Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

    b

    the other matrix

  43. def selectRows(rowIndex: VectoI): MatriQ

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

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

    rowIndex

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

  44. def selectRowsEx(rowIndex: VectoI): MatriQ

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    rowIndex

    the row indices to exclude

  45. def selectRowsEx(rowIndex: Array[Int]): MatriQ

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    rowIndex

    the row indices to exclude

  46. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

  47. def slice(rg: Range): MatriQ

    Slice 'this' matrix row-wise over the given range 'rg'.

    Slice 'this' matrix row-wise over the given range 'rg'.

    rg

    the range specifying the slice

  48. def sliceEx(rg: Range): MatriQ

    Slice 'this' matrix row-wise excluding the given range 'rg'.

    Slice 'this' matrix row-wise excluding the given range 'rg'.

    rg

    the excluded range of the slice

  49. def solve(lu: (MatriQ, MatriQ), b: VectoQ): VectoQ

    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

  50. def splitRows(rowIndex: VectoI): (MatriQ, MatriQ)

    Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

    Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

    rowIndex

    the row indices to include/exclude

  51. def splitRows(rowIndex: Array[Int]): (MatriQ, MatriQ)

    Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

    Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

    rowIndex

    the row indices to include/exclude

  52. 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)

  53. 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)

  54. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  55. def toString(): String
    Definition Classes
    AnyRef → Any
  56. def update(i: Int, jr: Range, u: VectoQ): Unit

    Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'.

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

    i

    the row index

    jr

    the column range

    u

    the vector to assign

  57. def update(ir: Range, j: Int, u: VectoQ): Unit

    Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'.

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

    ir

    the row range

    j

    the column index

    u

    the vector to assign

  58. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  59. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  60. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
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    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

Inherited from Error

Inherited from AnyRef

Inherited from Any

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