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class RleMatrixR extends MatriR with Error with Serializable

The RleMatrixR class stores and operates on Numeric Matrices of type Real. Rather than storing the matrix as a 2 dimensional array, it is stored as an array of RleVectorR's.

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Serializable, Serializable, MatriR, Error, AnyRef, Any
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  1. RleMatrixR
  2. Serializable
  3. Serializable
  4. MatriR
  5. Error
  6. AnyRef
  7. Any
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Instance Constructors

  1. new RleMatrixR(dim1: Int)

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

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

    dim1

    the row and column dimension

  2. new RleMatrixR(d1: Int, d2: Int, v: Array[RleVectorR] = null, deferred: Boolean = false)

    d1

    the first/row dimension

    d2

    the second/column dimension

    v

    the 1D 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 *(b: MatriR): MatriR

    Multiply 'this' matrix by matrix 'b'.

    Multiply 'this' matrix by matrix 'b'.

    b

    the matrix to multiply by (requires 'sameCrossDimensions')

    Definition Classes
    RleMatrixRMatriR
  4. def *(x: Real): RleMatrixR

    Multiply 'this' matrix by scalar 'x'.

    Multiply 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

    Definition Classes
    RleMatrixRMatriR
  5. def *(u: VectoR): VectoR

    Multiply 'this' matrix by (column) vector 'u'

    Multiply 'this' matrix by (column) vector 'u'

    u

    the vector to multiply by

    Definition Classes
    RleMatrixRMatriR
  6. def **(u: VectoR): MatriR

    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'. E.g., multiply a matrix by a diagonal matrix represented as a vector.

    u

    the vector to multiply by

    Definition Classes
    RleMatrixRMatriR
  7. def **(b: MatriR): MatriR

    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
    MatriR
    See also

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

  8. def **:(u: VectoR): MatriR

    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
    RleMatrixRMatriR
  9. def **=(u: VectoR): MatriR

    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
    RleMatrixRMatriR
  10. def *:(u: VectoR): VectoR

    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
    MatriR
  11. def *=(b: MatriR): MatriR

    Multiply in-place 'this' matrix by matrix 'b'

    Multiply in-place 'this' matrix by matrix 'b'

    b

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

    Definition Classes
    RleMatrixRMatriR
  12. def *=(x: Real): RleMatrixR

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

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

    x

    the matrix to multiply by

    Definition Classes
    RleMatrixRMatriR
  13. def +(u: VectoR): MatriR

    Add 'this' matrix and vector 'u'.

    Add 'this' matrix and vector 'u'.

    u

    the matrix to add (requires leDimensions)

    Definition Classes
    RleMatrixRMatriR
  14. def +(x: Real): RleMatrixR

    Add 'this' matrix and scalar 'x'.

    Add 'this' matrix and scalar 'x'.

    x

    the scalar to add

    Definition Classes
    RleMatrixRMatriR
  15. def +(b: MatriR): RleMatrixR

    Add 'this' matrix and matrix 'b'.

    Add 'this' matrix and matrix 'b'.

    b

    the matrix to add (requires leDimensions)

    Definition Classes
    RleMatrixRMatriR
  16. def ++(b: MatriR): RleMatrixR

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

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

    b

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

    Definition Classes
    RleMatrixRMatriR
  17. def ++^(b: MatriR): RleMatrixR

    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
    RleMatrixRMatriR
  18. def +:(u: VectoR): RleMatrixR

    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
    RleMatrixRMatriR
  19. def +=(b: MatriR): MatriR

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    RleMatrixRMatriR
  20. def +=(u: VectoR): MatriR

    Add in-place 'this' matrix and vector 'u'.

    Add in-place 'this' matrix and vector 'u'.

    u

    the vector to add

    Definition Classes
    RleMatrixRMatriR
  21. def +=(x: Real): MatriR

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

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

    x

    the scalar to add

    Definition Classes
    RleMatrixRMatriR
  22. def +^:(u: VectoR): RleMatrixR

    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
    RleMatrixRMatriR
  23. def -(b: MatriR): MatriR

    From 'this' matrix subtract matrix 'b'.

    From 'this' matrix subtract matrix 'b'.

    b

    the matrix to subtract

    Definition Classes
    RleMatrixRMatriR
  24. def -(u: VectoR): RleMatrixR

    From 'this' matrix subtract vector 'u'.

    From 'this' matrix subtract vector 'u'.

    u

    the vector to subtract

    Definition Classes
    RleMatrixRMatriR
  25. def -(x: Real): MatriR

    From 'this' matrix subtract scalar 'x'.

    From 'this' matrix subtract scalar 'x'.

    x

    the scalar to subtract

    Definition Classes
    RleMatrixRMatriR
  26. def -=(b: MatriR): MatriR

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    RleMatrixRMatriR
  27. def -=(u: VectoR): MatriR

    From 'this' matrix subtract in-place vector 'u'.

    From 'this' matrix subtract in-place vector 'u'.

    u

    the vector to subtract

    Definition Classes
    RleMatrixRMatriR
  28. def -=(x: Real): MatriR

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

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

    x

    the scalar to subtract

    Definition Classes
    RleMatrixRMatriR
  29. def /(x: Real): MatriR

    Divide 'this' matrix by scalar 'x'.

    Divide 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

    Definition Classes
    RleMatrixRMatriR
  30. def /=(x: Real): MatriR

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

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

    x

    the scalar to divide by

    Definition Classes
    RleMatrixRMatriR
  31. def :+(u: VectoR): RleMatrixR

    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
    RleMatrixRMatriR
  32. def :^+(u: VectoR): RleMatrixR

    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
    RleMatrixRMatriR
  33. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  34. def apply(): Array[RleVectorR]

    Get the underlying 1D array for 'this' matrix.

  35. def apply(ir: Range, jr: Range): MatriR

    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
    RleMatrixRMatriR
  36. def apply(i: Int): RleVectorR

    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
    RleMatrixRMatriR
  37. def apply(i: Int, j: Int): Real

    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
    RleMatrixRMatriR
  38. def apply(iv: VectoI): MatriR

    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
    MatriR
  39. def apply(i: Int, jr: Range): VectoR

    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
    MatriR
  40. def apply(ir: Range, j: Int): VectoR

    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
    MatriR
  41. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  42. def bsolve(y: VectoR): RleVectorR

    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
    RleMatrixRMatriR
  43. def clean(thres: Double = TOL, relative: Boolean = true): MatriR

    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

    Definition Classes
    RleMatrixRMatriR
  44. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  45. def col(col: Int, from: Int = 0): VectorR

    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
    RleMatrixRMatriR
  46. def col(col: Int): RleVectorR

    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

  47. def copy(): RleMatrixR

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

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

    Definition Classes
    RleMatrixRMatriR
  48. def csize: VectorI

    Get size of each column of 'this' RleMatrix

  49. val d1: Int
  50. val d2: Int
  51. val deferred: Boolean
  52. def det: Real

    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
    RleMatrixRMatriR
  53. def diag(b: MatriR): RleMatrixR

    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

    Definition Classes
    RleMatrixRMatriR
  54. def diag(p: Int, q: Int = 0): MatriR

    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
    RleMatrixRMatriR
  55. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    RleMatrixRMatriR
  56. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    RleMatrixRMatriR
  57. def dot(b: RleMatrixR): RleVectorR

    Compute the dot product of 'this' matrix and matrix 'b'.

    Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.

    b

    the matrix to multiply by (requires same first dimensions)

  58. def dot(b: MatriR): RleVectorR

    Compute the dot product of 'this' matrix and matrix 'b'.

    Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.

    b

    the matrix to multiply by (requires same first dimensions)

    Definition Classes
    RleMatrixRMatriR
  59. def dot(b: VectoR): VectoR

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

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

    b

    the vector to multiply by (requires same first dimensions)

    Definition Classes
    RleMatrixRMatriR
  60. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  61. def equals(b: Any): Boolean

    Override equals to determine whether 'this' vector equals vector 'b'.

    Override equals to determine whether 'this' vector equals vector 'b'.

    b

    the vector to compare with this

    Definition Classes
    RleMatrixR → AnyRef → Any
  62. 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
    MatriR
  63. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  64. 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
  65. def foreach[U](f: (Array[Real]) ⇒ 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
    MatriR
  66. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  67. def getDiag(k: Int = 0): RleVectorR

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

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

    k

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

    Definition Classes
    RleMatrixRMatriR
  68. def hashCode(): Int

    Must also override hashCode for 'this' vector to be compatible with equals.

    Must also override hashCode for 'this' vector to be compatible with equals.

    Definition Classes
    RleMatrixR → AnyRef → Any
  69. def inverse: MatriR

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

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

    Definition Classes
    RleMatrixRMatriR
  70. def inverse_ip(): MatriR

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

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

    Definition Classes
    RleMatrixRMatriR
  71. 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
    MatriR
  72. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  73. 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
    MatriR
  74. 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
    RleMatrixRMatriR
  75. 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
    MatriR
  76. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriR
  77. 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
    MatriR
  78. def leDimensions(b: MatriR): 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
    MatriR
  79. def lowerT: RleMatrixR

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

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

    Definition Classes
    RleMatrixRMatriR
  80. def lud_ip(): (RleMatrixR, RleMatrixR)

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

    Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).

    Definition Classes
    RleMatrixRMatriR
  81. def lud_npp: (RleMatrixR, RleMatrixR)

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

    Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).

    Definition Classes
    RleMatrixRMatriR
  82. def mag: Real

    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
    MatriR
  83. def map(f: (VectoR) ⇒ VectoR): MatriR

    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
    MatriR
  84. def max(e: Int = dim1): Real

    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
    RleMatrixRMatriR
  85. def mdot(b: RleMatrixR): RleMatrixR

    Compute the matrix dot product of 'this' matrix and matrix 'b'.

    Compute the matrix dot product of 'this' matrix and matrix 'b'.

    b

    the matrix to multiply by (requires same first dimensions)

  86. def mdot(b: MatriR): RleMatrixR

    Compute the matrix dot product of 'this' matrix and matrix 'b'.

    Compute the matrix dot product of 'this' matrix and matrix 'b'.

    b

    the matrix to multiply by (requires same first dimensions)

    Definition Classes
    RleMatrixRMatriR
  87. def mean: VectoR

    Compute the column means of 'this' matrix.

    Compute the column means of 'this' matrix.

    Definition Classes
    MatriR
  88. def meanNZ: VectoR

    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
    MatriR
  89. def meanR: VectoR

    Compute the row means of 'this' matrix.

    Compute the row means of 'this' matrix.

    Definition Classes
    MatriR
  90. def meanRNZ: VectoR

    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
    MatriR
  91. def min(e: Int = dim1): Real

    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
    RleMatrixRMatriR
  92. def mul2(u: RleVectorR): RleVectorR

    Multiply 'this' matrix by (column) vector 'u'

    Multiply 'this' matrix by (column) vector 'u'

    u

    the vector to multiply by

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

    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
    MatriR
    See also

    en.wikipedia.org/wiki/Matrix_norm

  95. def normF: Real

    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
    MatriR
    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  96. def normINF: Real

    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
    MatriR
    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: VectoR

    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
    RleMatrixRMatriR
    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(): VectoR

    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
    RleMatrixRMatriR
    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
    MatriR
  102. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriR
  103. def reduce: RleMatrixR

    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'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

    Definition Classes
    RleMatrixRMatriR
  104. 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'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

    Definition Classes
    RleMatrixRMatriR
  105. def sameCrossDimensions(b: MatriR): 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
    MatriR
  106. def sameDimensions(b: MatriR): 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
    MatriR
  107. def selectCols(colIndex: Array[Int]): RleMatrixR

    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
    RleMatrixRMatriR
  108. def selectRows(rowIndex: Array[Int]): RleMatrixR

    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
    RleMatrixRMatriR
  109. def selectRowsEx(rowIndex: Array[Int]): MatriR

    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
    MatriR
  110. def set(u: Array[Array[Real]]): 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
    RleMatrixRMatriR
  111. def set(i: Int, u: VectoR, 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
    RleMatrixRMatriR
  112. def set(x: Real): 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
    RleMatrixRMatriR
  113. def setCol(col: Int, u: VectoR): 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
    RleMatrixRMatriR
  114. def setDiag(u: VectoR, 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
    RleMatrixRMatriR
  115. def setDiag(x: Real): Unit

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

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

    x

    the scalar to set the diagonal to

    Definition Classes
    RleMatrixRMatriR
  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
    MatriR
  117. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): RleMatrixR

    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
    RleMatrixRMatriR
  118. def slice(from: Int, end: Int): RleMatrixR

    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
    RleMatrixRMatriR
  119. def slice(rg: Range): MatriR

    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
    MatriR
  120. def sliceCol(from: Int, end: Int): RleMatrixR

    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)

    Definition Classes
    RleMatrixRMatriR
  121. def sliceEx(row: Int, col: Int): RleMatrixR

    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

    col

    the column to exclude

    Definition Classes
    RleMatrixRMatriR
  122. def sliceEx(rg: Range): MatriR

    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
    MatriR
  123. def solve(b: VectoR): VectoR

    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
    RleMatrixRMatriR
  124. def solve(l: MatriR, u: MatriR, b: VectoR): VectoR

    Solve for 'x' in the equation 'l*u*x = b'

    Solve for 'x' in the equation 'l*u*x = b'

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    RleMatrixRMatriR
  125. def solve(lu: (MatriR, MatriR), b: VectoR): VectoR

    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
    MatriR
  126. def sum: Real

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

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

    Definition Classes
    RleMatrixRMatriR
  127. def sumAbs: Real

    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
    RleMatrixRMatriR
  128. def sumLower: Real

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

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

    Definition Classes
    RleMatrixRMatriR
  129. 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
    MatriR
  130. 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
    MatriR
  131. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  132. def t: RleMatrixR

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

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

    Definition Classes
    RleMatrixRMatriR
  133. def toDense: MatrixR

    Convert 'this' matrix to a dense matrix.

    Convert 'this' matrix to a dense matrix.

    Definition Classes
    RleMatrixRMatriR
  134. def toInt: MatrixI

    Convert 'this' RleMatrixR into a MatrixI.

    Convert 'this' RleMatrixR into a MatrixI.

    Definition Classes
    RleMatrixRMatriR
  135. def toString(): String

    Convert 'this' real (Real precision) matrix to a string.

    Convert 'this' real (Real precision) matrix to a string.

    Definition Classes
    RleMatrixR → AnyRef → Any
  136. def trace: Real

    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.

    Definition Classes
    RleMatrixRMatriR
    See also

    Eigen.scala

  137. def update(ir: Range, jr: Range, b: MatriR): 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

    Definition Classes
    RleMatrixRMatriR
  138. def update(i: Int, u: VectoR): 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
    RleMatrixRMatriR
  139. def update(i: Int, j: Int, x: Real): 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
    RleMatrixRMatriR
  140. def update(i: Int, jr: Range, u: VectoR): 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
    MatriR
  141. def update(ir: Range, j: Int, u: VectoR): 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
    MatriR
  142. def upperT: RleMatrixR

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

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

    Definition Classes
    RleMatrixRMatriR
  143. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  144. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  145. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  146. 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
    RleMatrixRMatriR
  147. def zero(mm: Int, nn: Int): RleMatrixR

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

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

    Definition Classes
    RleMatrixRMatriR
  148. def ~^(p: Int): RleMatrixR

    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). FIX - make compatible with imple in BldMatrix

    p

    the power to raise 'this' matrix to

    Definition Classes
    RleMatrixRMatriR

Inherited from Serializable

Inherited from Serializable

Inherited from MatriR

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped