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class BidMatrixL extends MatriL with Error with Serializable

The BidMatrixL class stores and operates on square (upper) bidiagonal matrices. The elements are of type of Long. A matrix is stored as two vectors: the diagonal vector and the sup-diagonal vector.

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Serializable, Serializable, MatriL, Error, AnyRef, Any
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  1. BidMatrixL
  2. Serializable
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  4. MatriL
  5. Error
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Instance Constructors

  1. new BidMatrixL(b: MatriL)

    Construct a bidiagonal matrix from the given matrix.

    Construct a bidiagonal matrix from the given matrix.

    b

    the matrix of values to assign

  2. new BidMatrixL(v1: VectoL, v2: VectoL)

    Construct a bidiagonal matrix with the given diagonal and sup-diagonal.

    Construct a bidiagonal matrix with the given diagonal and sup-diagonal.

    v1

    the diagonal vector

    v2

    the sup-diagonal vector

  3. new BidMatrixL(d1: Int)

    d1

    the first/row dimension (square => d2 = d1)

Value Members

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

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

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

    x

    the scalar to multiply by

    Definition Classes
    BidMatrixLMatriL
  4. def *(u: VectoL): VectorL

    Multiply 'this' bidiagonal matrix by vector 'u'.

    Multiply 'this' bidiagonal matrix by vector 'u'.

    u

    the vector to multiply by

    Definition Classes
    BidMatrixLMatriL
  5. def *(b: BidMatrixL): MatrixL

    Multiply 'this' bidiagonal matrix by matrix 'b'.

    Multiply 'this' bidiagonal matrix by matrix 'b'. Requires 'b' to have type BidMatrixL, but returns a more general type of matrix.

    b

    the matrix to multiply by

  6. def *(b: MatriL): BidMatrixL

    Multiply 'this' bidiagonal matrix by matrix 'b'.

    Multiply 'this' bidiagonal matrix by matrix 'b'.

    b

    the matrix to multiply by

    Definition Classes
    BidMatrixLMatriL
  7. def **(u: VectoL): MatrixL

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

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

    u

    the vector to multiply by

    Definition Classes
    BidMatrixLMatriL
  8. def **(b: MatriL): MatriL

    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
    MatriL
    See also

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

  9. def **:(u: VectoL): MatrixL

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

    Multiply vector 'u' by 'this' bidiagonal 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
    BidMatrixLMatriL
  10. def **=(u: VectoL): MatrixL

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

    Multiply in-place 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a diagonal matrix represented as a vector by a matrix.

    u

    the vector to multiply by

    Definition Classes
    BidMatrixLMatriL
  11. def *:(u: VectoL): VectoL

    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
    MatriL
  12. def *=(x: Long): BidMatrixL

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

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

    x

    the scalar to multiply by

    Definition Classes
    BidMatrixLMatriL
  13. def *=(b: MatriL): BidMatrixL

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

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

    b

    the matrix to multiply by

    Definition Classes
    BidMatrixLMatriL
  14. def +(x: Long): BidMatrixL

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

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

    x

    the scalar to add

    Definition Classes
    BidMatrixLMatriL
  15. def +(u: VectoL): BidMatrixL

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

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

    u

    the vector to add

    Definition Classes
    BidMatrixLMatriL
  16. def +(b: MatriL): BidMatrixL

    Add 'this' bidiagonal matrix and matrix 'b'.

    Add 'this' bidiagonal matrix and matrix 'b'.

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    BidMatrixLMatriL
  17. def ++(b: MatriL): BidMatrixL

    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
    BidMatrixLMatriL
  18. def ++^(b: MatriL): BidMatrixL

    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
    BidMatrixLMatriL
  19. def +:(u: VectoL): BidMatrixL

    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
    BidMatrixLMatriL
  20. def +=(x: Long): BidMatrixL

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

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

    x

    the scalar to add

    Definition Classes
    BidMatrixLMatriL
  21. def +=(u: VectoL): MatrixL

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

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

    u

    the vector to add

    Definition Classes
    BidMatrixLMatriL
  22. def +=(b: MatriL): BidMatrixL

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    BidMatrixLMatriL
  23. def +^:(u: VectoL): BidMatrixL

    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
    BidMatrixLMatriL
  24. def -(x: Long): BidMatrixL

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

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

    x

    the scalar to subtract

    Definition Classes
    BidMatrixLMatriL
  25. def -(u: VectoL): BidMatrixL

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

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

    u

    the vector to subtract

    Definition Classes
    BidMatrixLMatriL
  26. def -(b: MatriL): BidMatrixL

    From 'this' bidiagonal matrix subtract matrix 'b'.

    From 'this' bidiagonal matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    BidMatrixLMatriL
  27. def -=(x: Long): BidMatrixL

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

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

    x

    the scalar to subtract

    Definition Classes
    BidMatrixLMatriL
  28. def -=(u: VectoL): BidMatrixL

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

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

    u

    the vector to subtract

    Definition Classes
    BidMatrixLMatriL
  29. def -=(b: MatriL): BidMatrixL

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    BidMatrixLMatriL
  30. def /(x: Long): BidMatrixL

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

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

    x

    the scalar to divide by

    Definition Classes
    BidMatrixLMatriL
  31. def /=(x: Long): BidMatrixL

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

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

    x

    the scalar to divide by

    Definition Classes
    BidMatrixLMatriL
  32. def :+(u: VectoL): BidMatrixL

    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
    BidMatrixLMatriL
  33. def :^+(u: VectoL): BidMatrixL

    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
    BidMatrixLMatriL
  34. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  35. def apply(ir: Range, jr: Range): BidMatrixL

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

    Get a slice 'this' bidiagonal 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
    BidMatrixLMatriL
  36. def apply(i: Int): VectorL

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

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

    i

    the row index

    Definition Classes
    BidMatrixLMatriL
  37. def apply(i: Int, j: Int): Long

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

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

    i

    the row index

    j

    the column index

    Definition Classes
    BidMatrixLMatriL
  38. def apply(iv: VectoI): MatriL

    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
    MatriL
  39. def apply(i: Int, jr: Range): VectoL

    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
    MatriL
  40. def apply(ir: Range, j: Int): VectoL

    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
    MatriL
  41. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  42. def at(i: Int, j: Int): Long

    Get 'this' bidiagonal matrix's element at the 'i,j'-th index position, returning 0, if off bidiagonal.

    Get 'this' bidiagonal matrix's element at the 'i,j'-th index position, returning 0, if off bidiagonal.

    i

    the row index

    j

    the column index

  43. def bsolve(y: VectoL): VectorL

    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

    Definition Classes
    BidMatrixLMatriL
  44. def clean(thres: Double, relative: Boolean = true): BidMatrixL

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

    Clean values in 'this' bidiagonal 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
    BidMatrixLMatriL
  45. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  46. def col(col: Int, from: Int = 0): VectorL

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

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

    col

    the column to extract from the matrix

    from

    the position to start extracting from

    Definition Classes
    BidMatrixLMatriL
  47. def copy(): BidMatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  48. val d1: Int
  49. def det: Long

    Compute the determinant of 'this' bidiagonal matrix.

    Compute the determinant of 'this' bidiagonal matrix.

    Definition Classes
    BidMatrixLMatriL
  50. def dg: VectorL

    Get the diagonal of 'this' bidiagonal matrix.

  51. def dg_(v: VectorL): Unit

    Set the diagonal of 'this' bidiagonal matrix.

    Set the diagonal of 'this' bidiagonal matrix.

    v

    the vector to assign to the diagonal

  52. def diag(p: Int, q: Int): SymTriMatrixL

    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
    BidMatrixLMatriL
  53. def diag(b: MatriL): MatriL

    Combine 'this' bidiagonal 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' bidiagonal 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' bidiagonal matrix

    Definition Classes
    BidMatrixLMatriL
  54. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    BidMatrixLMatriL
  55. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    BidMatrixLMatriL
  56. def dot(b: MatriL): VectorL

    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
    BidMatrixLMatriL
  57. def dot(u: VectoL): VectorL

    Compute the dot product of 'this' matrix and vector 'u', by conceptually 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 conceptually 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
    BidMatrixLMatriL
  58. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  59. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  60. 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
    MatriL
  61. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  62. 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
  63. def foreach[U](f: (Array[Long]) ⇒ 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
    MatriL
  64. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  65. def getDiag(k: Int = 0): VectorL

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

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

    k

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

    Definition Classes
    BidMatrixLMatriL
  66. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  67. def inverse: MatriL

    Invert 'this' bidiagonal matrix.

    Invert 'this' bidiagonal matrix.

    Definition Classes
    BidMatrixLMatriL
  68. def inverse_ip(): BidMatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  69. 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).

    Definition Classes
    BidMatrixLMatriL
  70. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  71. def isNonnegative: Boolean

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

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

    Definition Classes
    BidMatrixLMatriL
  72. def isRectangular: Boolean

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

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

    Definition Classes
    BidMatrixLMatriL
  73. 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
    MatriL
  74. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriL
  75. 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).

    Definition Classes
    BidMatrixLMatriL
  76. def leDimensions(b: MatriL): 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
    MatriL
  77. def lowerT: MatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  78. def lud_ip(): (MatriL, MatriL)

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

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

    Definition Classes
    BidMatrixLMatriL
  79. def lud_npp: (MatriL, MatriL)

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

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

    Definition Classes
    BidMatrixLMatriL
  80. def mag: Long

    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
    MatriL
  81. def map(f: (VectoL) ⇒ VectoL): MatriL

    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
    MatriL
  82. def max(e: Int = dim1): Long

    Find the maximum element in 'this' bidiagonal matrix.

    Find the maximum element in 'this' bidiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    BidMatrixLMatriL
  83. def mdot(b: MatriL): MatrixL

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

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

    b

    the second matrix of the dot product

    Definition Classes
    BidMatrixLMatriL
  84. def mdot(b: BidMatrixL): MatrixL

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

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

    b

    the second matrix of the dot product

  85. def mean: VectoL

    Compute the column means of 'this' matrix.

    Compute the column means of 'this' matrix.

    Definition Classes
    MatriL
  86. def meanNZ: VectoL

    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
    MatriL
  87. def meanR: VectoL

    Compute the row means of 'this' matrix.

    Compute the row means of 'this' matrix.

    Definition Classes
    MatriL
  88. def meanRNZ: VectoL

    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
    MatriL
  89. def min(e: Int = dim1): Long

    Find the minimum element in 'this' bidiagonal matrix.

    Find the minimum element in 'this' bidiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    BidMatrixLMatriL
  90. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  91. def norm1: Long

    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
    MatriL
    See also

    en.wikipedia.org/wiki/Matrix_norm

  92. def normF: Long

    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
    MatriL
    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  93. def normINF: Long

    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
    MatriL
    See also

    en.wikipedia.org/wiki/Matrix_norm

  94. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  95. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  96. def nullspace: VectorL

    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
    BidMatrixLMatriL
    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

  97. def nullspace_ip(): VectorL

    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
    BidMatrixLMatriL
    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

  98. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriL
  99. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriL
  100. def reduce: BidMatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  101. def reduce_ip(): Unit

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

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

    Definition Classes
    BidMatrixLMatriL
  102. def sameCrossDimensions(b: MatriL): 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
    MatriL
  103. def sameDimensions(b: MatriL): 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
    MatriL
  104. def sd: VectorL

    Get the sup-diagonal of this bidiagonal matrix.

  105. def sd_(v: VectorL): Unit

    Set the sup-diagonal of 'this' bidiagonal matrix.

    Set the sup-diagonal of 'this' bidiagonal matrix.

    v

    the vector to assign to the sup-diagonal

  106. def selectCols(colIndex: Array[Int]): BidMatrixL

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

    Select columns from 'this' bidiagonal 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
    BidMatrixLMatriL
  107. def selectRows(rowIndex: Array[Int]): BidMatrixL

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

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

    rowIndex

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

    Definition Classes
    BidMatrixLMatriL
  108. def set(i: Int, u: VectoL, j: Int = 0): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixLMatriL
  109. def set(u: Array[Array[Long]]): Unit

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

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

    u

    the 2D array of values to assign

    Definition Classes
    BidMatrixLMatriL
  110. def set(x: Long): Unit

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

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

    x

    the scalar value to assign

    Definition Classes
    BidMatrixLMatriL
  111. def setCol(col: Int, u: VectoL): Unit

    Set column 'col' of 'this' bidiagonal matrix to a vector.

    Set column 'col' of 'this' bidiagonal matrix to a vector.

    col

    the column to set

    u

    the vector to assign to the column

    Definition Classes
    BidMatrixLMatriL
  112. def setDiag(x: Long): Unit

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

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

    x

    the scalar to set the diagonal to

    Definition Classes
    BidMatrixLMatriL
  113. def setDiag(u: VectoL, k: Int = 0): Unit

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

    Set the 'k'th diagonal of 'this' bidiagonal 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
    BidMatrixLMatriL
  114. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

    Definition Classes
    MatriL
  115. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): BidMatrixL

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

    Slice 'this' bidiagonal 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
    BidMatrixLMatriL
  116. def slice(from: Int, end: Int): BidMatrixL

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

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

    from

    the start row of the slice (inclusive)

    end

    the end row of the slice (exclusive)

    Definition Classes
    BidMatrixLMatriL
  117. def slice(rg: Range): MatriL

    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
    MatriL
  118. def sliceCol(from: Int, end: Int): BidMatrixL

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

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

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

    Definition Classes
    BidMatrixLMatriL
  119. def sliceEx(row: Int, col: Int): BidMatrixL

    Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.

    Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.

    row

    the row to exclude

    col

    the column to exclude

    Definition Classes
    BidMatrixLMatriL
  120. def sliceEx(rg: Range): MatriL

    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
    MatriL
  121. def solve(l: MatriL, u: MatriL, b: VectoL): VectorL

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

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

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    BidMatrixLMatriL
  122. def solve(b: VectoL): VectorL

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

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

    b

    the constant vector

    Definition Classes
    BidMatrixLMatriL
  123. def solve(lu: (MatriL, MatriL), b: VectoL): VectoL

    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
    MatriL
  124. def sum: Long

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

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

    Definition Classes
    BidMatrixLMatriL
  125. def sumAbs: Long

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

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

    Definition Classes
    BidMatrixLMatriL
  126. def sumLower: Long

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

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

    Definition Classes
    BidMatrixLMatriL
  127. 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
    MatriL
  128. 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
    MatriL
  129. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  130. def t: BidMatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  131. def toDense: MatrixL

    Convert 'this' tridiagonal matrix to a dense matrix.

    Convert 'this' tridiagonal matrix to a dense matrix.

    Definition Classes
    BidMatrixLMatriL
  132. def toInt: BidMatrixI

    Convert 'this' BidMatrixL into a BidMatrixI.

    Convert 'this' BidMatrixL into a BidMatrixI.

    Definition Classes
    BidMatrixLMatriL
  133. def toString(): String

    Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

    Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

    Definition Classes
    BidMatrixL → AnyRef → Any
  134. def trace: Long

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

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

    Definition Classes
    BidMatrixLMatriL
    See also

    Eigen.scala

  135. def update(ir: Range, jr: Range, b: MatriL): Unit

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

    Set a slice 'this' bidiagonal 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
    BidMatrixLMatriL
  136. def update(i: Int, u: VectoL): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixLMatriL
  137. def update(i: Int, j: Int, x: Long): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixLMatriL
  138. def update(i: Int, jr: Range, u: VectoL): 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
    MatriL
  139. def update(ir: Range, j: Int, u: VectoL): 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
    MatriL
  140. def upperT: MatrixL

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

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

    Definition Classes
    BidMatrixLMatriL
  141. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  142. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  143. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  144. 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
    BidMatrixLMatriL
  145. def zero(m: Int = dim1, n: Int = dim2): BidMatrixL

    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

    Definition Classes
    BidMatrixLMatriL
  146. def ~^(p: Int): BidMatrixL

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

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

    p

    the power to raise 'this' matrix to

    Definition Classes
    BidMatrixLMatriL

Inherited from Serializable

Inherited from Serializable

Inherited from MatriL

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped