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class SymTriMatrixD extends MatriD with Error with Serializable

The SymTriMatrixD class stores and operates on symmetric tridiagonal matrices. The elements are of type of Double. A matrix is stored as two vectors: the diagonal vector and the sub-diagonal vector.

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

  1. new SymTriMatrixD(b: MatriD)

    Construct a symmetric tridiagonal matrix from the given matrix.

    Construct a symmetric tridiagonal matrix from the given matrix.

    b

    the matrix of values to assign

  2. new SymTriMatrixD(v1: VectoD, v2: VectoD)

    Construct a symmetric tridiagonal matrix with the given diagonal and sub-diagonal.

    Construct a symmetric tridiagonal matrix with the given diagonal and sub-diagonal.

    v1

    the diagonal vector

    v2

    the sub-diagonal vector

  3. new SymTriMatrixD(d1: Int)

    d1

    the first/row dimension (symmetric => 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: Double): SymTriMatrixD

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

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

    x

    the scalar to multiply by

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

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

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

    u

    the vector to multiply by

    Definition Classes
    SymTriMatrixDMatriD
  5. def *(b: SymTriMatrixD): MatrixD

    Multiply 'this' tridiagonal matrix by matrix 'b'.

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

    b

    the matrix to multiply by

  6. def *(b: MatriD): SymTriMatrixD

    Multiply 'this' tridiagonal matrix by matrix 'b'.

    Multiply 'this' tridiagonal matrix by matrix 'b'.

    b

    the matrix to multiply by

    Definition Classes
    SymTriMatrixDMatriD
  7. def **(u: VectoD): MatrixD

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

    Multiply 'this' tridiagonal 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
    SymTriMatrixDMatriD
  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): MatrixD

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

    Multiply vector 'u' by 'this' tridiagonal 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
    SymTriMatrixDMatriD
  10. def **=(u: VectoD): MatrixD

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

    Multiply in-place 'this' tridiagonal 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
    SymTriMatrixDMatriD
  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): SymTriMatrixD

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

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

    x

    the scalar to multiply by

    Definition Classes
    SymTriMatrixDMatriD
  13. def *=(b: MatriD): SymTriMatrixD

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

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

    b

    the matrix to multiply by

    Definition Classes
    SymTriMatrixDMatriD
  14. def +(x: Double): SymTriMatrixD

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

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

    x

    the scalar to add

    Definition Classes
    SymTriMatrixDMatriD
  15. def +(u: VectoD): MatrixD

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

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

    u

    the vector to add

    Definition Classes
    SymTriMatrixDMatriD
  16. def +(b: MatriD): SymTriMatrixD

    Add 'this' tridiagonal matrix and matrix 'b'.

    Add 'this' tridiagonal matrix and matrix 'b'.

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    SymTriMatrixDMatriD
  17. def ++(b: MatriD): SymTriMatrixD

    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
    SymTriMatrixDMatriD
  18. def ++^(b: MatriD): SymTriMatrixD

    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
    SymTriMatrixDMatriD
  19. def +:(u: VectoD): SymTriMatrixD

    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
    SymTriMatrixDMatriD
  20. def +=(x: Double): SymTriMatrixD

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

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

    x

    the scalar to add

    Definition Classes
    SymTriMatrixDMatriD
  21. def +=(u: VectoD): MatrixD

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

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

    u

    the vector to add

    Definition Classes
    SymTriMatrixDMatriD
  22. def +=(b: MatriD): SymTriMatrixD

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    SymTriMatrixDMatriD
  23. def +^:(u: VectoD): SymTriMatrixD

    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
    SymTriMatrixDMatriD
  24. def -(x: Double): SymTriMatrixD

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

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

    x

    the scalar to subtract

    Definition Classes
    SymTriMatrixDMatriD
  25. def -(u: VectoD): MatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    SymTriMatrixDMatriD
  26. def -(b: MatriD): SymTriMatrixD

    From 'this' tridiagonal matrix subtract matrix 'b'.

    From 'this' tridiagonal matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    SymTriMatrixDMatriD
  27. def -=(x: Double): SymTriMatrixD

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

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

    x

    the scalar to subtract

    Definition Classes
    SymTriMatrixDMatriD
  28. def -=(u: VectoD): MatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    SymTriMatrixDMatriD
  29. def -=(b: MatriD): SymTriMatrixD

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    SymTriMatrixDMatriD
  30. def /(x: Double): SymTriMatrixD

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

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

    x

    the scalar to divide by

    Definition Classes
    SymTriMatrixDMatriD
  31. def /=(x: Double): SymTriMatrixD

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

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

    x

    the scalar to divide by

    Definition Classes
    SymTriMatrixDMatriD
  32. def :+(u: VectoD): SymTriMatrixD

    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
    SymTriMatrixDMatriD
  33. def :^+(u: VectoD): SymTriMatrixD

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

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

    Get a slice 'this' tridiagonal 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
    SymTriMatrixDMatriD
  36. def apply(i: Int): VectorD

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

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

    i

    the row index

    Definition Classes
    SymTriMatrixDMatriD
  37. def apply(i: Int, j: Int): Double

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

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

    i

    the row index

    j

    the column index

    Definition Classes
    SymTriMatrixDMatriD
  38. 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
  39. 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
  40. 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
  41. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  42. def at(i: Int, j: Int): Double

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

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

    i

    the row index

    j

    the column index

  43. 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' 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
    SymTriMatrixDMatriD
  44. def clean(thres: Double, relative: Boolean = true): SymTriMatrixD

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

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

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

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

    col

    the column to extract from the matrix

    from

    the position to start extracting from

    Definition Classes
    SymTriMatrixDMatriD
  47. def copy(): SymTriMatrixD

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

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

    Definition Classes
    SymTriMatrixDMatriD
  48. val d1: Int
  49. def det: Double

    Compute the determinant of 'this' tridiagonal matrix.

    Compute the determinant of 'this' tridiagonal matrix.

    Definition Classes
    SymTriMatrixDMatriD
  50. def dg: VectorD

    Get the diagonal of 'this' tridiagonal matrix.

  51. def dg_(v: VectorD): Unit

    Set the diagonal of 'this' tridiagonal matrix.

    Set the diagonal of 'this' tridiagonal matrix.

    v

    the vector to assign to the diagonal

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

    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
    SymTriMatrixDMatriD
  53. def diag(b: MatriD): MatriD

    Combine 'this' tridiagonal 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' tridiagonal 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' tridiagonal matrix

    Definition Classes
    SymTriMatrixDMatriD
  54. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    SymTriMatrixDMatriD
  55. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    SymTriMatrixDMatriD
  56. 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
    SymTriMatrixDMatriD
  57. def dot(b: SymTriMatrixD): 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

  58. def dot(u: VectoD): VectorD

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

    Compute the dot product of 'this' tridiagonal matrix and vector 'u', by first transposing 'this' tridiagonal matrix and then multiplying by 'u' (i.e., 'a dot u = a.t * u'). Since 'this' is symmetric, the result is the same as 'a * u'.

    u

    the vector to multiply by (requires same first dimensions)

    Definition Classes
    SymTriMatrixDMatriD
  59. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  60. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  61. 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
  62. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  63. 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
  64. 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
  65. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  66. def getDiag(k: Int = 0): VectorD

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

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

    k

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

    Definition Classes
    SymTriMatrixDMatriD
  67. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  68. def inverse: MatriD

    Invert 'this' tridiagonal matrix.

    Invert 'this' tridiagonal matrix.

    Definition Classes
    SymTriMatrixDMatriD
    See also

    www.amm.shu.edu.cn/EN/article/downloadArticleFile.do?attachType=PDF&id=4339

  69. def inverse_ip(): SymTriMatrixD

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

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

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

    Definition Classes
    SymTriMatrixDMatriD
  73. def isRectangular: Boolean

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

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

    Definition Classes
    SymTriMatrixDMatriD
  74. 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
  75. def isSymmetric: Boolean

    Check whether 'this' tridiagonal matrix is symmetric.

    Check whether 'this' tridiagonal matrix is symmetric.

    Definition Classes
    SymTriMatrixDMatriD
  76. def isTridiagonal: Boolean

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

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

    Definition Classes
    SymTriMatrixDMatriD
  77. 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
  78. def lowerT: SymTriMatrixD

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

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

    Definition Classes
    SymTriMatrixDMatriD
  79. def lud_ip(): (MatriD, MatriD)

    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
    SymTriMatrixDMatriD
  80. def lud_npp: (MatriD, MatriD)

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

    Factor 'this' tridiagonal matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Factorization algorithm. 'l' is lower bidiagonal and 'u' is upper bidiagonal. FIX: would be more efficient to use tridiagonal matrices than dense matrices.

    Definition Classes
    SymTriMatrixDMatriD
    See also

    www.webpages.uidaho.edu/~barannyk/Teaching/LU_factorization_tridiagonal.pdf

  81. 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
  82. 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
  83. def max(e: Int = dim1): Double

    Find the maximum element in 'this' tridiagonal matrix.

    Find the maximum element in 'this' tridiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    SymTriMatrixDMatriD
  84. def mdot(b: MatriD): MatrixD

    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
    SymTriMatrixDMatriD
  85. def mdot(b: SymTriMatrixD): MatrixD

    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

  86. def mean: VectoD

    Compute the column means of 'this' matrix.

    Compute the column means of 'this' matrix.

    Definition Classes
    MatriD
  87. 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
  88. def meanR: VectoD

    Compute the row means of 'this' matrix.

    Compute the row means of 'this' matrix.

    Definition Classes
    MatriD
  89. 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
  90. def min(e: Int = dim1): Double

    Find the minimum element in 'this' tridiagonal matrix.

    Find the minimum element in 'this' tridiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    SymTriMatrixDMatriD
  91. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  92. 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

  93. 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

  94. 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

  95. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  96. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  97. 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
    SymTriMatrixDMatriD
    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. 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
    SymTriMatrixDMatriD
    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

  99. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriD
  100. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriD
  101. def reduce: SymTriMatrixD

    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
    SymTriMatrixDMatriD
  102. 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
    SymTriMatrixDMatriD
  103. 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
  104. 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
  105. def sd: VectorD

    Get the sub-diagonal of 'this' tridiagonal matrix.

  106. def sd_(v: VectorD): Unit

    Set the sub-diagonal of 'this' tridiagonal matrix.

    Set the sub-diagonal of 'this' tridiagonal matrix.

    v

    the vector to assign to the sub-diagonal

  107. def selectCols(colIndex: Array[Int]): SymTriMatrixD

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

    Select columns from 'this' tridiagonal 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
    SymTriMatrixDMatriD
  108. def selectRows(rowIndex: Array[Int]): SymTriMatrixD

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

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

    rowIndex

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

    Definition Classes
    SymTriMatrixDMatriD
  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' tridiagonal matrix's 'i'th row starting at column 'j' to the vector 'u'.

    Set 'this' tridiagonal 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
    SymTriMatrixDMatriD
  111. def set(u: Array[Array[Double]]): Unit

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

    Set all the values in 'this' tridiagonal matrix as copies of the values in 2D array 'u'. Ignore parts of array not corresponding to tridiagonal.

    u

    the 2D array of values to assign

    Definition Classes
    SymTriMatrixDMatriD
  112. def set(x: Double): Unit

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

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

    x

    the scalar value to assign

    Definition Classes
    SymTriMatrixDMatriD
  113. def setCol(col: Int, u: VectoD): Unit

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

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

    col

    the column to set

    u

    the vector to assign to the column

    Definition Classes
    SymTriMatrixDMatriD
  114. def setDiag(x: Double): Unit

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

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

    x

    the scalar to set the diagonal to

    Definition Classes
    SymTriMatrixDMatriD
  115. def setDiag(u: VectoD, k: Int = 0): Unit

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

    Set the 'k'th diagonal of 'this' tridiagonal 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
    SymTriMatrixDMatriD
  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 slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): SymTriMatrixD

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

    Slice 'this' tridiagonal 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
    SymTriMatrixDMatriD
  118. def slice(from: Int, end: Int): SymTriMatrixD

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

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

    from

    the start row of the slice (inclusive)

    end

    the end row of the slice (exclusive)

    Definition Classes
    SymTriMatrixDMatriD
  119. 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
  120. def sliceCol(from: Int, end: Int): SymTriMatrixD

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

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

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

    Definition Classes
    SymTriMatrixDMatriD
  121. def sliceEx(row: Int, col: Int): SymTriMatrixD

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

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

    row

    the row to exclude

    col

    the column to exclude

    Definition Classes
    SymTriMatrixDMatriD
  122. 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
  123. def solve(b: VectoD): VectoD

    Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' tridiagonal matrix, using the Thomas Algorithm.

    Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' tridiagonal matrix, using the Thomas Algorithm. Caveat: Stability vs. diagonal dominance. This method is more efficient, since a 'lud_npp' creates dense matrices.

    b

    the constant vector

    Definition Classes
    SymTriMatrixDMatriD
    See also

    en.wikibooks.org/wiki/Algorithm_Implementation/Linear_Algebra/Tridiagonal_matrix_algorithm

  124. def solve(l: MatriD, u: MatriD, b: VectoD): VectoD

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

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

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    SymTriMatrixDMatriD
  125. 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
  126. def sum: Double

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

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

    Definition Classes
    SymTriMatrixDMatriD
  127. def sumAbs: Double

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

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

    Definition Classes
    SymTriMatrixDMatriD
  128. def sumLower: Double

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

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

    Definition Classes
    SymTriMatrixDMatriD
  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
    MatriD
  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
    MatriD
  131. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  132. def t: SymTriMatrixD

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

    Transpose 'this' tridiagonal matrix (rows => columns). Note, since the matrix is symmetric, it returns itself.

    Definition Classes
    SymTriMatrixDMatriD
  133. def toDense: MatrixD

    Convert 'this' tridiagonal matrix to a dense matrix.

    Convert 'this' tridiagonal matrix to a dense matrix.

    Definition Classes
    SymTriMatrixDMatriD
  134. def toInt: SymTriMatrixI

    Convert 'this' SymTriMatrixD into a SymTriMatrixI.

    Convert 'this' SymTriMatrixD into a SymTriMatrixI.

    Definition Classes
    SymTriMatrixDMatriD
  135. def toString(): String

    Convert 'this' tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.

    Convert 'this' tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.

    Definition Classes
    SymTriMatrixD → AnyRef → Any
  136. def trace: Double

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

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

    Definition Classes
    SymTriMatrixDMatriD
    See also

    Eigen.scala

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

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

    Set a slice 'this' tridiagonal 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
    SymTriMatrixDMatriD
  138. def update(i: Int, u: VectoD): Unit

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

    Set 'this' tridiagonal 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
    SymTriMatrixDMatriD
  139. def update(i: Int, j: Int, x: Double): Unit

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

    Set 'this' tridiagonal 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
    SymTriMatrixDMatriD
  140. 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
  141. 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
  142. def upperT: SymTriMatrixD

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

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

    Definition Classes
    SymTriMatrixDMatriD
  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' tridiagonal matrix to a CSV-formatted text file with name 'fileName'.

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

    fileName

    the name of file to hold the data

    Definition Classes
    SymTriMatrixDMatriD
  147. def zero(m: Int = dim1, n: Int = dim2): SymTriMatrixD

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

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

    m

    the number of rows

    n

    the number of columns

    Definition Classes
    SymTriMatrixDMatriD
  148. def ~^(p: Int): SymTriMatrixD

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

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

    p

    the power to raise this tridiagonal matrix to

    Definition Classes
    SymTriMatrixDMatriD

Inherited from Serializable

Inherited from Serializable

Inherited from MatriD

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped