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class SymTriMatrixC extends MatriC with Error with Serializable

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

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Serializable, Serializable, MatriC, Error, AnyRef, Any
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  1. SymTriMatrixC
  2. Serializable
  3. Serializable
  4. MatriC
  5. Error
  6. AnyRef
  7. Any
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Instance Constructors

  1. new SymTriMatrixC(b: MatriC)

    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 SymTriMatrixC(v1: VectoC, v2: VectoC)

    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 SymTriMatrixC(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: Complex): SymTriMatrixC

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

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

    x

    the scalar to multiply by

    Definition Classes
    SymTriMatrixCMatriC
  4. def *(u: VectoC): VectorC

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

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

    u

    the vector to multiply by

    Definition Classes
    SymTriMatrixCMatriC
  5. def *(b: SymTriMatrixC): MatrixC

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

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

    b

    the matrix to multiply by

  6. def *(b: MatriC): SymTriMatrixC

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

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

    b

    the matrix to multiply by

    Definition Classes
    SymTriMatrixCMatriC
  7. def **(u: VectoC): MatrixC

    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
    SymTriMatrixCMatriC
  8. def **:(u: VectoC): MatrixC

    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
    SymTriMatrixCMatriC
  9. def **=(u: VectoC): MatrixC

    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
    SymTriMatrixCMatriC
  10. def *:(u: VectoC): VectoC

    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
    MatriC
  11. def *=(x: Complex): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  12. def *=(b: MatriC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  13. def +(x: Complex): SymTriMatrixC

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

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

    x

    the scalar to add

    Definition Classes
    SymTriMatrixCMatriC
  14. def +(u: VectoC): MatrixC

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

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

    u

    the vector to add

    Definition Classes
    SymTriMatrixCMatriC
  15. def +(b: MatriC): SymTriMatrixC

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    SymTriMatrixCMatriC
  16. def ++(b: MatriC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  17. def ++^(b: MatriC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  18. def +:(u: VectoC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  19. def +=(x: Complex): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  20. def +=(u: VectoC): MatrixC

    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
    SymTriMatrixCMatriC
  21. def +=(b: MatriC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  22. def +^:(u: VectoC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  23. def -(x: Complex): SymTriMatrixC

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

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

    x

    the scalar to subtract

    Definition Classes
    SymTriMatrixCMatriC
  24. def -(u: VectoC): MatrixC

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

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

    u

    the vector to subtract

    Definition Classes
    SymTriMatrixCMatriC
  25. def -(b: MatriC): SymTriMatrixC

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    SymTriMatrixCMatriC
  26. def -=(x: Complex): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  27. def -=(u: VectoC): MatrixC

    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
    SymTriMatrixCMatriC
  28. def -=(b: MatriC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  29. def /(x: Complex): SymTriMatrixC

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

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

    x

    the scalar to divide by

    Definition Classes
    SymTriMatrixCMatriC
  30. def /=(x: Complex): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  31. def :+(u: VectoC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  32. def :^+(u: VectoC): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  33. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  34. def apply(ir: Range, jr: Range): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  35. def apply(i: Int): VectorC

    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
    SymTriMatrixCMatriC
  36. def apply(i: Int, j: Int): Complex

    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
    SymTriMatrixCMatriC
  37. def apply(i: Int, jr: Range): VectoC

    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
    MatriC
  38. def apply(ir: Range, j: Int): VectoC

    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
    MatriC
  39. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  40. def at(i: Int, j: Int): Complex

    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

  41. def bsolve(y: VectoC): VectorC

    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
    SymTriMatrixCMatriC
  42. def clean(thres: Double, relative: Boolean = true): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  43. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  44. def col(col: Int, from: Int = 0): VectorC

    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
    SymTriMatrixCMatriC
  45. def copy(): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  46. val d1: Int
  47. def det: Complex

    Compute the determinant of 'this' tridiagonal matrix.

    Compute the determinant of 'this' tridiagonal matrix.

    Definition Classes
    SymTriMatrixCMatriC
  48. def dg: VectorC

    Get the diagonal of 'this' tridiagonal matrix.

  49. def dg_(v: VectorC): Unit

    Set the diagonal of 'this' tridiagonal matrix.

    Set the diagonal of 'this' tridiagonal matrix.

    v

    the vector to assign to the diagonal

  50. def diag(p: Int, q: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  51. def diag(b: MatriC): MatriC

    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
    SymTriMatrixCMatriC
  52. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    SymTriMatrixCMatriC
  53. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    SymTriMatrixCMatriC
  54. def dot(b: MatriC): VectorC

    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
    SymTriMatrixCMatriC
  55. def dot(b: SymTriMatrixC): VectorC

    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

  56. def dot(u: VectoC): VectorC

    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
    SymTriMatrixCMatriC
  57. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  58. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  59. 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
    MatriC
  60. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  61. 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
  62. def foreach[U](f: (Array[Complex]) ⇒ 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
    MatriC
  63. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  64. def getDiag(k: Int = 0): VectorC

    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
    SymTriMatrixCMatriC
  65. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  66. def inverse: MatriC

    Invert 'this' tridiagonal matrix.

    Invert 'this' tridiagonal matrix.

    Definition Classes
    SymTriMatrixCMatriC
    See also

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

  67. def inverse_ip(): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  68. 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
    MatriC
  69. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  70. 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
    SymTriMatrixCMatriC
  71. 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
    SymTriMatrixCMatriC
  72. 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
    MatriC
  73. def isSymmetric: Boolean

    Check whether 'this' tridiagonal matrix is symmetric.

    Check whether 'this' tridiagonal matrix is symmetric.

    Definition Classes
    SymTriMatrixCMatriC
  74. 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
    SymTriMatrixCMatriC
  75. def leDimensions(b: MatriC): 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
    MatriC
  76. def lowerT: SymTriMatrixC

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

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

    Definition Classes
    SymTriMatrixCMatriC
  77. def lud_ip(): (MatriC, MatriC)

    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
    SymTriMatrixCMatriC
  78. def lud_npp: (MatriC, MatriC)

    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
    SymTriMatrixCMatriC
    See also

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

  79. def mag: Complex

    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
    MatriC
  80. def max(e: Int = dim1): Complex

    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
    SymTriMatrixCMatriC
  81. def mdot(b: MatriC): MatrixC

    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
    SymTriMatrixCMatriC
  82. def mdot(b: SymTriMatrixC): MatrixC

    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

  83. def mean: VectoC

    Compute the column means of this matrix.

    Compute the column means of this matrix.

    Definition Classes
    MatriC
  84. def min(e: Int = dim1): Complex

    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
    SymTriMatrixCMatriC
  85. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  86. def norm1: Complex

    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
    MatriC
  87. final def notify(): Unit
    Definition Classes
    AnyRef
  88. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  89. def nullspace: VectorC

    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
    SymTriMatrixCMatriC
    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

  90. def nullspace_ip(): VectorC

    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
    SymTriMatrixCMatriC
    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

  91. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriC
  92. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriC
  93. def reduce: SymTriMatrixC

    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
    SymTriMatrixCMatriC
  94. 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
    SymTriMatrixCMatriC
  95. def sameCrossDimensions(b: MatriC): 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
    MatriC
  96. def sameDimensions(b: MatriC): 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
    MatriC
  97. def sd: VectorC

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

  98. def sd_(v: VectorC): 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

  99. def selectCols(colIndex: Array[Int]): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  100. def selectRows(rowIndex: Array[Int]): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  101. def set(i: Int, u: VectoC, 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
    SymTriMatrixCMatriC
  102. def set(u: Array[Array[Complex]]): 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
    SymTriMatrixCMatriC
  103. def set(x: Complex): 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
    SymTriMatrixCMatriC
  104. def setCol(col: Int, u: VectoC): 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
    SymTriMatrixCMatriC
  105. def setDiag(x: Complex): 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
    SymTriMatrixCMatriC
  106. def setDiag(u: VectoC, 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
    SymTriMatrixCMatriC
  107. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

    Definition Classes
    MatriC
  108. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  109. def slice(from: Int, end: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  110. def sliceCol(from: Int, end: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  111. def sliceExclude(row: Int, col: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  112. def solve(b: VectoC): VectoC

    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
    SymTriMatrixCMatriC
    See also

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

  113. def solve(l: MatriC, u: MatriC, b: VectoC): VectoC

    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
    SymTriMatrixCMatriC
  114. def solve(lu: (MatriC, MatriC), b: VectoC): VectoC

    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
    MatriC
  115. def sum: Complex

    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
    SymTriMatrixCMatriC
  116. def sumAbs: Complex

    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
    SymTriMatrixCMatriC
  117. def sumLower: Complex

    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
    SymTriMatrixCMatriC
  118. 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
    MatriC
  119. 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
    MatriC
  120. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  121. def t: SymTriMatrixC

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

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

    Definition Classes
    SymTriMatrixCMatriC
  122. def toDense: MatrixC

    Convert 'this' tridiagonal matrix to a dense matrix.

    Convert 'this' tridiagonal matrix to a dense matrix.

    Definition Classes
    SymTriMatrixCMatriC
  123. def toInt: SymTriMatrixI

    Convert 'this' SymTriMatrixC into a SymTriMatrixI.

    Convert 'this' SymTriMatrixC into a SymTriMatrixI.

    Definition Classes
    SymTriMatrixCMatriC
  124. 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
    SymTriMatrixC → AnyRef → Any
  125. def trace: Complex

    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
    SymTriMatrixCMatriC
    See also

    Eigen.scala

  126. def update(ir: Range, jr: Range, b: MatriC): 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
    SymTriMatrixCMatriC
  127. def update(i: Int, u: VectoC): 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
    SymTriMatrixCMatriC
  128. def update(i: Int, j: Int, x: Complex): 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
    SymTriMatrixCMatriC
  129. def update(i: Int, jr: Range, u: VectoC): 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
    MatriC
  130. def update(ir: Range, j: Int, u: VectoC): 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
    MatriC
  131. def upperT: SymTriMatrixC

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

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

    Definition Classes
    SymTriMatrixCMatriC
  132. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  133. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  134. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  135. 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
    SymTriMatrixCMatriC
  136. def zero(m: Int = dim1, n: Int = dim2): SymTriMatrixC

    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
    SymTriMatrixCMatriC
  137. def ~^(p: Int): SymTriMatrixC

    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
    SymTriMatrixCMatriC

Inherited from Serializable

Inherited from Serializable

Inherited from MatriC

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped