Packages

class SparseMatrixD extends MatriD with Error with Serializable

The SparseMatrixD class stores and operates on Matrices of Doubles. Rather than storing the matrix as a 2 dimensional array, it is stored as an array of sorted-linked-maps, which record all the non-zero values for each particular row, along with their j-index as (j, v) pairs.

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  1. SparseMatrixD
  2. Serializable
  3. Serializable
  4. MatriD
  5. Error
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  7. Any
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Instance Constructors

  1. new SparseMatrixD(b: MatrixD)

    Construct a sparse matrix and assign values from dense matrix MatrixD 'b'.

    Construct a sparse matrix and assign values from dense matrix MatrixD 'b'.

    b

    the matrix of values to assign

  2. new SparseMatrixD(b: SparseMatrixD)

    Construct a sparse matrix and assign values from matrix 'b'.

    Construct a sparse matrix and assign values from matrix 'b'.

    b

    the matrix of values to assign

  3. new SparseMatrixD(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 SparseMatrixD(dim1: Int, dim2: Int, x: Double)

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

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

    dim1

    the row dimension

    dim2

    the column dimension

    x

    the scalar value to assign

  5. new SparseMatrixD(dim1: Int)

    Construct a 'dim1' by 'dim1' square sparse matrix.

    Construct a 'dim1' by 'dim1' square sparse matrix.

    dim1

    the row and column dimension

  6. new SparseMatrixD(dim1: Int, dim2: Int, u: Array[RowMap])

    Construct a 'dim1' by 'dim2' sparse matrix from an array of sorted-linked-maps.

    Construct a 'dim1' by 'dim2' sparse matrix from an array of sorted-linked-maps.

    dim1

    the row dimension

    dim2

    the column dimension

    u

    the array of sorted-linked-maps

  7. new SparseMatrixD(d1: Int, d2: Int)

    d1

    the first/row dimension

    d2

    the second/column dimension

Value Members

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

    Multiply 'this' sparse matrix by scalar 'x'.

    Multiply 'this' sparse matrix by scalar 'x'.

    x

    the scalar to multiply by

    Definition Classes
    SparseMatrixDMatriD
  4. def *(u: VectoD): VectorD

    Multiply 'this' sparse matrix by vector 'u' (vector elements beyond 'dim2' ignored).

    Multiply 'this' sparse matrix by vector 'u' (vector elements beyond 'dim2' ignored).

    u

    the vector to multiply by

    Definition Classes
    SparseMatrixDMatriD
  5. def *(b: MatriD): SparseMatrixD

    Multiply 'this' sparse matrix by dense matrix 'b'.

    Multiply 'this' sparse matrix by dense matrix 'b'.

    b

    the matrix to multiply by (requires 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  6. def *(b: SparseMatrixD): SparseMatrixD

    Multiply 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.

    Multiply 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.

    b

    the matrix to multiply by (requires 'sameCrossDimensions')

  7. def **(u: VectoD): SparseMatrixD

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

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

    u

    the vector to multiply by

    Definition Classes
    SparseMatrixDMatriD
  8. def **(b: MatriD): MatriD

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

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

    b

    the matrix to multiply by

    Definition Classes
    MatriD
    See also

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

  9. def **:(u: VectoD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  10. def **=(u: VectoD): SparseMatrixD

    Multiply in-place 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

    Multiply in-place 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

    u

    the vector to multiply by

    Definition Classes
    SparseMatrixDMatriD
  11. def *:(u: VectoD): VectoD

    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

    Definition Classes
    MatriD
  12. def *=(x: Double): SparseMatrixD

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

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

    x

    the scalar to multiply by

    Definition Classes
    SparseMatrixDMatriD
  13. def *=(b: MatriD): SparseMatrixD

    Multiply in-place 'this' sparse matrix by dense matrix 'b'.

    Multiply in-place 'this' sparse matrix by dense matrix 'b'.

    b

    the matrix to multiply by (requires square and 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  14. def *=(b: SparseMatrixD): SparseMatrixD

    Multiply in-place 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.

    Multiply in-place 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.

    b

    the matrix to multiply by (requires square and 'sameCrossDimensions')

  15. def +(x: Double): MatrixD

    Add 'this' sparse matrix and scalar 'x'.

    Add 'this' sparse matrix and scalar 'x'. Note: every element will be likely filled, hence the return type is a dense matrix.

    x

    the scalar to add

    Definition Classes
    SparseMatrixDMatriD
  16. def +(u: VectoD): SparseMatrixD

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

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

    u

    the vector to add

    Definition Classes
    SparseMatrixDMatriD
  17. def +(b: MatriD): SparseMatrixD

    Add 'this' sparse matrix and matrix 'b'.

    Add 'this' sparse matrix and matrix 'b'. 'b' may be any subtype of MatriD. Note, subtypes of MatriD should also implement a more efficient version, e.g., def + (b: SparseMatrixD): SparseMatrixD.

    b

    the matrix to add (requires 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  18. def +(b: SparseMatrixD): SparseMatrixD

    Add 'this' sparse matrix and sparse matrix 'b'.

    Add 'this' sparse matrix and sparse matrix 'b'.

    b

    the matrix to add (requires 'sameCrossDimensions')

  19. def ++(b: MatriD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  20. def ++^(b: MatriD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  21. def +:(u: VectoD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  22. def +=(x: Double): SparseMatrixD

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

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

    x

    the scalar to add

    Definition Classes
    SparseMatrixDMatriD
  23. def +=(u: VectoD): SparseMatrixD

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

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

    u

    the vector to add

    Definition Classes
    SparseMatrixDMatriD
  24. def +=(b: MatriD): SparseMatrixD

    Add in-place 'this' sparse matrix and matrix 'b'.

    Add in-place 'this' sparse matrix and matrix 'b'.

    b

    the matrix to add (requires 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  25. def +=(b: SparseMatrixD): SparseMatrixD

    Add in-place 'this' sparse matrix and sparse matrix 'b'.

    Add in-place 'this' sparse matrix and sparse matrix 'b'.

    b

    the matrix to add (requires 'sameCrossDimensions')

  26. def +^:(u: VectoD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  27. def -(x: Double): MatrixD

    From 'this' sparse matrix subtract scalar 'x'.

    From 'this' sparse matrix subtract scalar 'x'. Note: every element will be likely filled, hence the return type is a dense matrix.

    x

    the scalar to subtract

    Definition Classes
    SparseMatrixDMatriD
  28. def -(u: VectoD): SparseMatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    SparseMatrixDMatriD
  29. def -(b: MatriD): SparseMatrixD

    From 'this' sparse matrix subtract matrix 'b'.

    From 'this' sparse matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  30. def -(b: SparseMatrixD): SparseMatrixD

    From 'this' sparse matrix subtract matrix 'b'.

    From 'this' sparse matrix subtract matrix 'b'.

    b

    the sparse matrix to subtract (requires 'sameCrossDimensions')

  31. def -=(x: Double): SparseMatrixD

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

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

    x

    the scalar to subtract

    Definition Classes
    SparseMatrixDMatriD
  32. def -=(u: VectoD): SparseMatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    SparseMatrixDMatriD
  33. def -=(b: MatriD): SparseMatrixD

    From 'this' sparse matrix subtract in-place matrix 'b'.

    From 'this' sparse matrix subtract in-place matrix 'b'.

    b

    the matrix to subtract (requires 'sameCrossDimensions')

    Definition Classes
    SparseMatrixDMatriD
  34. def -=(b: SparseMatrixD): SparseMatrixD

    From 'this' sparse matrix subtract in-place sparse matrix 'b'.

    From 'this' sparse matrix subtract in-place sparse matrix 'b'.

    b

    the sparse matrix to subtract (requires 'sameCrossDimensions')

  35. def /(x: Double): SparseMatrixD

    Divide 'this' sparse matrix by scalar 'x'.

    Divide 'this' sparse matrix by scalar 'x'.

    x

    the scalar to divide by

    Definition Classes
    SparseMatrixDMatriD
  36. def /=(x: Double): SparseMatrixD

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

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

    x

    the scalar to divide by

    Definition Classes
    SparseMatrixDMatriD
  37. def :+(u: VectoD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  38. def :^+(u: VectoD): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  39. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  40. def apply(ir: Range, jr: Range): SparseMatrixD

    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
    SparseMatrixDMatriD
  41. def apply(i: Int): VectorD

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

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

    i

    the row index

    Definition Classes
    SparseMatrixDMatriD
  42. def apply(i: Int, j: Int): Double

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

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

    i

    the row index

    j

    the column index

    Definition Classes
    SparseMatrixDMatriD
  43. def apply(iv: VectoI): MatriD

    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

    Definition Classes
    MatriD
  44. def apply(i: Int, jr: Range): VectoD

    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
    MatriD
  45. def apply(ir: Range, j: Int): VectoD

    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
    MatriD
  46. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  47. def bsolve(y: VectoD): VectorD

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

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

    y

    the constant vector

    Definition Classes
    SparseMatrixDMatriD
  48. def clean(thres: Double, relative: Boolean = true): SparseMatrixD

    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
    SparseMatrixDMatriD
  49. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  50. 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
    SparseMatrixDMatriD
  51. def copy(): SparseMatrixD

    Create a clone of 'this' 'm-by-n' sparse matrix.

    Create a clone of 'this' 'm-by-n' sparse matrix.

    Definition Classes
    SparseMatrixDMatriD
  52. val d1: Int
  53. val d2: Int
  54. def det: Double

    Compute the determinant of 'this' sparse matrix.

    Compute the determinant of 'this' sparse matrix.

    Definition Classes
    SparseMatrixDMatriD
  55. def diag(p: Int, q: Int): SparseMatrixD

    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

    Definition Classes
    SparseMatrixDMatriD
  56. def diag(b: MatriD): SparseMatrixD

    Combine 'this' sparse 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' sparse 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

    Definition Classes
    SparseMatrixDMatriD
  57. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    SparseMatrixDMatriD
  58. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    SparseMatrixDMatriD
  59. def dot(b: MatriD): VectorD

    Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

    Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

    b

    the second matrix of the dot product

    Definition Classes
    SparseMatrixDMatriD
  60. def dot(u: VectoD): VectorD

    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)

    Definition Classes
    SparseMatrixDMatriD
  61. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  62. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  63. 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
    Definition Classes
    MatriD
  64. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  65. 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
  66. def foreach[U](f: (Array[Double]) ⇒ 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

    Definition Classes
    MatriD
  67. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  68. def getDiag(k: Int = 0): VectorD

    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)

    Definition Classes
    SparseMatrixDMatriD
  69. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  70. def inverse: SparseMatrixD

    Invert 'this' sparse matrix (requires a 'squareMatrix') using partial pivoting.

    Invert 'this' sparse matrix (requires a 'squareMatrix') using partial pivoting.

    Definition Classes
    SparseMatrixDMatriD
  71. def inverse_ip(): SparseMatrixD

    Invert in-place 'this' sparse matrix (requires a 'squareMatrix').

    Invert in-place 'this' sparse matrix (requires a 'squareMatrix'). This version uses partial pivoting.

    Definition Classes
    SparseMatrixDMatriD
  72. def inverse_npp: SparseMatrixD

    Invert 'this' sparse matrix (requires a 'squareMatrix') not using partial pivoting.

  73. 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.

    Definition Classes
    MatriD
  74. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  75. def isNonnegative: Boolean

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

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

    Definition Classes
    SparseMatrixDMatriD
  76. def isRectangular: Boolean

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

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

    Definition Classes
    SparseMatrixDMatriD
  77. 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
    MatriD
  78. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriD
  79. 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.

    Definition Classes
    MatriD
  80. def leDimensions(b: MatriD): 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

    Definition Classes
    MatriD
  81. def lowerT: SparseMatrixD

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

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

    Definition Classes
    SparseMatrixDMatriD
  82. def lud_ip(): (SparseMatrixD, SparseMatrixD)

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

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

    Definition Classes
    SparseMatrixDMatriD
  83. def lud_npp: (SparseMatrixD, SparseMatrixD)

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

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

    Definition Classes
    SparseMatrixDMatriD
  84. 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
    MatriD
  85. def map(f: (VectoD) ⇒ VectoD): MatriD

    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

    Definition Classes
    MatriD
  86. def max(e: Int = dim1): Double

    Find the maximum element in 'this' sparse matrix.

    Find the maximum element in 'this' sparse matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    SparseMatrixDMatriD
  87. def mdot(b: MatriD): SparseMatrixD

    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)

    Definition Classes
    SparseMatrixDMatriD
  88. def mean: VectoD

    Compute the column means of 'this' matrix.

    Compute the column means of 'this' matrix.

    Definition Classes
    MatriD
  89. def meanNZ: VectoD

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

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

    Definition Classes
    MatriD
  90. def meanR: VectoD

    Compute the row means of 'this' matrix.

    Compute the row means of 'this' matrix.

    Definition Classes
    MatriD
  91. def meanRNZ: VectoD

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

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

    Definition Classes
    MatriD
  92. def min(e: Int = dim1): Double

    Find the minimum element in 'this' sparse matrix.

    Find the minimum element in 'this' sparse matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    SparseMatrixDMatriD
  93. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  94. def norm1: Double

    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'.

    Definition Classes
    MatriD
    See also

    en.wikipedia.org/wiki/Matrix_norm

  95. def normF: Double

    Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.

    Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.

    Definition Classes
    MatriD
    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  96. def normINF: Double

    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.

    Definition Classes
    MatriD
    See also

    en.wikipedia.org/wiki/Matrix_norm

  97. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  98. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  99. 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.

    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.

    Definition Classes
    SparseMatrixDMatriD
    See also

    /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces

  100. def nullspace_ip(): VectorD

    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.

    Definition Classes
    SparseMatrixDMatriD
    See also

    /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces

  101. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriD
  102. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriD
  103. def reduce: SparseMatrixD

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

    Use Gauss-Jordan reduction on 'this' sparse matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

    Definition Classes
    SparseMatrixDMatriD
  104. def reduce_ip(): Unit

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

    Use Gauss-Jordan reduction in-place on 'this' sparse matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

    Definition Classes
    SparseMatrixDMatriD
  105. def sameCrossDimensions(b: MatriD): 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

    Definition Classes
    MatriD
  106. def sameDimensions(b: MatriD): 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

    Definition Classes
    MatriD
  107. def selectCols(colIndex: Array[Int]): SparseMatrixD

    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
    SparseMatrixDMatriD
  108. def selectRows(rowIndex: Array[Int]): SparseMatrixD

    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
    SparseMatrixDMatriD
  109. def selectRowsEx(rowIndex: Array[Int]): MatriD

    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

    Definition Classes
    MatriD
  110. def set(i: Int, u: VectoD, j: Int = 0): Unit

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

    Set this matrix's 'i'th 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
    SparseMatrixDMatriD
  111. 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
    SparseMatrixDMatriD
  112. 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
    SparseMatrixDMatriD
  113. def setCol(col: Int, u: VectoD): 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
    SparseMatrixDMatriD
  114. 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
    SparseMatrixDMatriD
  115. def setDiag(u: VectoD, 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)

    Definition Classes
    SparseMatrixDMatriD
  116. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

    Definition Classes
    MatriD
  117. def showAll(): Unit

    Show all elements in 'this' sparse matrix.

  118. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): SparseMatrixD

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

    Slice 'this' sparse 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
    SparseMatrixDMatriD
  119. def slice(from: Int, end: Int): SparseMatrixD

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

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

    from

    the start row of the slice

    end

    the end row of the slice

    Definition Classes
    SparseMatrixDMatriD
  120. def slice(rg: Range): MatriD

    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

    Definition Classes
    MatriD
  121. def sliceCol(from: Int, end: Int): SparseMatrixD

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

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

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

    Definition Classes
    SparseMatrixDMatriD
  122. def sliceEx(row: Int, col: Int): SparseMatrixD

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

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

    row

    the row to exclude

    col

    the column to exclude

    Definition Classes
    SparseMatrixDMatriD
  123. def sliceEx(rg: Range): MatriD

    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

    Definition Classes
    MatriD
  124. def solve(b: VectoD): VectoD

    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.

    Definition Classes
    SparseMatrixDMatriD
  125. def solve(l: MatriD, u: MatriD, b: VectoD): VectoD

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

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

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    SparseMatrixDMatriD
  126. def solve(lu: (MatriD, MatriD), b: VectoD): VectoD

    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
    MatriD
  127. def sum: Double

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

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

    Definition Classes
    SparseMatrixDMatriD
  128. def sumAbs: Double

    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'.

    Definition Classes
    SparseMatrixDMatriD
  129. def sumLower: Double

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

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

    Definition Classes
    SparseMatrixDMatriD
  130. 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)

    Definition Classes
    MatriD
  131. 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)

    Definition Classes
    MatriD
  132. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  133. def t: SparseMatrixD

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

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

    Definition Classes
    SparseMatrixDMatriD
  134. def times_s(b: SparseMatrixD): SparseMatrixD

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

    Multiply 'this' sparse matrix by sparse 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

  135. def toDense: MatrixD

    Convert this sparse matrix to a dense matrix.

    Convert this sparse matrix to a dense matrix. FIX - new builder

    Definition Classes
    SparseMatrixDMatriD
  136. def toInt: MatrixI

    Convert 'this' SparseMatrixD into a MatrixI.

    Convert 'this' SparseMatrixD into a MatrixI.

    Definition Classes
    SparseMatrixDMatriD
  137. def toString(): String

    Show the non-zero elements in 'this' sparse matrix.

    Show the non-zero elements in 'this' sparse matrix.

    Definition Classes
    SparseMatrixD → AnyRef → Any
  138. def trace: Double

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

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

    Definition Classes
    SparseMatrixDMatriD
    See also

    Eigen.scala

  139. def update(ir: Range, jr: Range, b: MatriD): Unit

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

    Set a slice 'this' sparse 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

    Definition Classes
    SparseMatrixDMatriD
  140. def update(i: Int, u: RowMap): Unit

    Set 'this' sparse matrix's row at the 'i'-th index position to the sorted-linked-map 'u'.

    Set 'this' sparse matrix's row at the 'i'-th index position to the sorted-linked-map 'u'.

    i

    the row index

    u

    the sorted-linked-map of non-zero values to assign

  141. def update(i: Int, u: VectoD): Unit

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

    Set 'this' sparse 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
    SparseMatrixDMatriD
  142. def update(i: Int, j: Int, x: Double): Unit

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

    Set 'this' sparse matrix's element at the 'i,j'-th index position to the scalar 'x'. Only store 'x' if it is non-zero.

    i

    the row index

    j

    the column index

    x

    the scalar value to assign

    Definition Classes
    SparseMatrixDMatriD
  143. def update(i: Int, jr: Range, u: VectoD): 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

    Definition Classes
    MatriD
  144. def update(ir: Range, j: Int, u: VectoD): 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

    Definition Classes
    MatriD
  145. def upperT: SparseMatrixD

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

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

    Definition Classes
    SparseMatrixDMatriD
  146. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  147. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  148. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  149. 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

    Definition Classes
    SparseMatrixDMatriD
  150. def zero(m: Int = dim1, n: Int = dim2): SparseMatrixD

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

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

    m

    the number of rows

    n

    the number of columns

    Definition Classes
    SparseMatrixDMatriD
  151. def ~^(p: Int): SparseMatrixD

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

    Raise 'this' sparse matrix to the 'p'th 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
    SparseMatrixDMatriD

Inherited from Serializable

Inherited from Serializable

Inherited from MatriD

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped