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class MatrixQ extends MatriQ with Error with Serializable

The MatrixQ class stores and operates on Numeric Matrices of type Rational. This class follows the gen.MatrixN framework and is provided for efficiency.

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Serializable, Serializable, MatriQ, Error, AnyRef, Any
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  1. MatrixQ
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Instance Constructors

  1. new MatrixQ(b: MatrixQ)

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

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

    b

    the matrix of values to assign

  2. new MatrixQ(dim: (Int, Int), u: Rational*)

    Construct a matrix from repeated values.

    Construct a matrix from repeated values.

    dim

    the (row, column) dimensions

    u

    the repeated values

  3. new MatrixQ(u: Array[MM_ArrayQ])

    Construct a matrix and assign values from array of arrays 'u'.

    Construct a matrix and assign values from array of arrays 'u'.

    u

    the 2D array of values to assign

  4. new MatrixQ(dim1: Int, dim2: Int, x: Rational)

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

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

    dim1

    the row dimension

    dim2

    the column dimesion

    x

    the scalar value to assign

  5. new MatrixQ(dim1: Int)

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

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

    dim1

    the row and column dimension

  6. new MatrixQ(d1: Int, d2: Int, v: Array[MM_ArrayQ] = null)

    d1

    the first/row dimension

    d2

    the second/column dimension

    v

    the 2D array used to store matrix elements

Value Members

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

    Multiply 'this' matrix by scalar 'x'.

    Multiply 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

    Definition Classes
    MatrixQMatriQ
  4. def *(u: VectorQ): VectorQ

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

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

    u

    the vector to multiply by

    Definition Classes
    MatrixQMatriQ
  5. def *(b: MatriQ): MatrixQ

    Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.

    Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times' method to skip the transpose step.

    b

    the matrix to multiply by (requires sameCrossDimensions)

    Definition Classes
    MatrixQMatriQ
  6. def *(b: MatrixQ): MatrixQ

    Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.

    Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times' method to skip the transpose step.

    b

    the matrix to multiply by (requires sameCrossDimensions)

  7. def **(u: VectorQ): MatrixQ

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

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

    u

    the vector to multiply by

    Definition Classes
    MatrixQMatriQ
  8. def **=(u: VectorQ): MatrixQ

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

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

    u

    the vector to multiply by

    Definition Classes
    MatrixQMatriQ
  9. def *=(x: Rational): MatrixQ

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

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

    x

    the scalar to multiply by

    Definition Classes
    MatrixQMatriQ
  10. def *=(b: MatriQ): MatrixQ

    Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.

    Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times_ip' method to skip the transpose step.

    b

    the matrix to multiply by (requires square and sameCrossDimensions)

    Definition Classes
    MatrixQMatriQ
  11. def *=(b: MatrixQ): MatrixQ

    Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.

    Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times_ip' method to skip the transpose step.

    b

    the matrix to multiply by (requires square and sameCrossDimensions)

  12. def +(x: Rational): MatrixQ

    Add 'this' matrix and scalar 'x'.

    Add 'this' matrix and scalar 'x'.

    x

    the scalar to add

    Definition Classes
    MatrixQMatriQ
  13. def +(u: VectorQ): MatrixQ

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

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

    u

    the vector to add

    Definition Classes
    MatrixQMatriQ
  14. def +(b: MatriQ): MatrixQ

    Add 'this' matrix and matrix 'b' for any type extending MatriQ.

    Add 'this' matrix and matrix 'b' for any type extending MatriQ.

    b

    the matrix to add (requires leDimensions)

    Definition Classes
    MatrixQMatriQ
  15. def +(b: MatrixQ): MatrixQ

    Add 'this' matrix and matrix 'b'.

    Add 'this' matrix and matrix 'b'.

    b

    the matrix to add (requires leDimensions)

  16. def ++(b: MatriQ): MatrixQ

    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
    MatrixQMatriQ
  17. def ++^(b: MatriQ): MatrixQ

    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
    MatrixQMatriQ
  18. def +:(u: VectorQ): MatrixQ

    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
    MatrixQMatriQ
  19. def +=(x: Rational): MatrixQ

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

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

    x

    the scalar to add

    Definition Classes
    MatrixQMatriQ
  20. def +=(u: VectorQ): MatrixQ

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

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

    u

    the vector to add

    Definition Classes
    MatrixQMatriQ
  21. def +=(b: MatriQ): MatrixQ

    Add in-place 'this' matrix and matrix 'b' for any type extending MatriQ.

    Add in-place 'this' matrix and matrix 'b' for any type extending MatriQ.

    b

    the matrix to add (requires leDimensions)

    Definition Classes
    MatrixQMatriQ
  22. def +=(b: MatrixQ): MatrixQ

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

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

    b

    the matrix to add (requires leDimensions)

  23. def +^:(u: VectorQ): MatrixQ

    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
    MatrixQMatriQ
  24. def -(x: Rational): MatrixQ

    From 'this' matrix subtract scalar 'x'.

    From 'this' matrix subtract scalar 'x'.

    x

    the scalar to subtract

    Definition Classes
    MatrixQMatriQ
  25. def -(u: VectorQ): MatrixQ

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

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

    u

    the vector to subtract@param b the vector to subtract

    Definition Classes
    MatrixQMatriQ
  26. def -(b: MatriQ): MatrixQ

    From 'this' matrix subtract matrix 'b' for any type extending MatriQ.

    From 'this' matrix subtract matrix 'b' for any type extending MatriQ.

    b

    the matrix to subtract (requires leDimensions)

    Definition Classes
    MatrixQMatriQ
  27. def -(b: MatrixQ): MatrixQ

    From 'this' matrix subtract matrix 'b'.

    From 'this' matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires leDimensions)

  28. def -=(x: Rational): MatrixQ

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

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

    x

    the scalar to subtract

    Definition Classes
    MatrixQMatriQ
  29. def -=(u: VectorQ): MatrixQ

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

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

    u

    the vector to subtract@param b the vector to subtract

    Definition Classes
    MatrixQMatriQ
  30. def -=(b: MatriQ): MatrixQ

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

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

    b

    the matrix to subtract (requires leDimensions)

    Definition Classes
    MatrixQMatriQ
  31. def -=(b: MatrixQ): MatrixQ

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

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

    b

    the matrix to subtract (requires leDimensions)

  32. def /(x: Rational): MatrixQ

    Divide 'this' matrix by scalar 'x'.

    Divide 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

    Definition Classes
    MatrixQMatriQ
  33. def /=(x: Rational): MatrixQ

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

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

    x

    the scalar to divide by

    Definition Classes
    MatrixQMatriQ
  34. def :+(u: VectorQ): MatrixQ

    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
    MatrixQMatriQ
  35. def :^+(u: VectorQ): MatrixQ

    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
    MatrixQMatriQ
  36. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  37. def apply(ir: Range, jr: Range): MatrixQ

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

    Get a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: b = a(2..4, 3..5)

    ir

    the row range

    jr

    the column range

    Definition Classes
    MatrixQMatriQ
  38. def apply(i: Int): VectorQ

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

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

    i

    the row index

    Definition Classes
    MatrixQMatriQ
  39. def apply(i: Int, j: Int): Rational

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

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

    i

    the row index

    j

    the column index

    Definition Classes
    MatrixQMatriQ
  40. def apply(i: Int, jr: Range): VectorQ

    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
    MatriQ
  41. def apply(ir: Range, j: Int): VectorQ

    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
    MatriQ
  42. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  43. def clean(thres: Double, relative: Boolean = true): MatrixQ

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

    Clean values in 'this' matrix at or below the threshold 'thres' by setting them to zero. Iterative algorithms give approximate values and if very close to zero, may throw off other calculations, e.g., in computing eigenvectors.

    thres

    the cutoff threshold (a small value)

    relative

    whether to use relative or absolute cutoff

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

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

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

    col

    the column to extract from the matrix

    from

    the position to start extracting from

    Definition Classes
    MatrixQMatriQ
  46. val d1: Int
  47. val d2: Int
  48. def det: Rational

    Compute the determinant of 'this' matrix.

    Compute the determinant of 'this' matrix. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).

    Definition Classes
    MatrixQMatriQ
  49. def diag(p: Int, q: Int = 0): MatrixQ

    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
    MatrixQMatriQ
  50. def diag(b: MatriQ): MatrixQ

    Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.

    Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.

    b

    the matrix to combine with 'this' matrix

    Definition Classes
    MatrixQMatriQ
  51. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    MatrixQMatriQ
  52. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    MatrixQMatriQ
  53. def dot(u: VectorQ): VectorQ

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

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

    u

    the vector to multiply by (requires same first dimensions)

    Definition Classes
    MatrixQMatriQ
  54. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  55. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  56. 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
    MatriQ
  57. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  58. 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
  59. def foreach[U](f: (MM_ArrayQ) ⇒ 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
    MatriQ
  60. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  61. def getDiag(k: Int = 0): VectorQ

    Get the kth diagonal of 'this' matrix.

    Get the kth diagonal of 'this' matrix. Assumes 'dim2 >= dim1'.

    k

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

    Definition Classes
    MatrixQMatriQ
  62. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  63. def inverse: MatrixQ

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

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

    Definition Classes
    MatrixQMatriQ
  64. def inverse_ip: MatrixQ

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

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

    Definition Classes
    MatrixQMatriQ
  65. def inverse_npp: MatrixQ

    Invert 'this' matrix (requires a square matrix) and does not use partial pivoting.

  66. def isBidiagonal: Boolean

    Check whether 'this' matrix is bidiagonal (has non-zreo elements only in main diagonal and superdiagonal).

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

    Definition Classes
    MatriQ
  67. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  68. def isNonnegative: Boolean

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

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

    Definition Classes
    MatriQ
  69. def isRectangular: Boolean

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

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

    Definition Classes
    MatrixQMatriQ
  70. 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
    MatriQ
  71. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriQ
  72. def isTridiagonal: Boolean

    Check whether 'this' matrix is bidiagonal (has non-zreo elements only in main diagonal and superdiagonal).

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

    Definition Classes
    MatriQ
  73. def leDimensions(b: MatriQ): 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
    MatriQ
  74. def lud: (MatrixQ, MatrixQ)

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

    Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the LU Factorization algorithm. This version uses partial pivoting.

    Definition Classes
    MatrixQMatriQ
  75. def lud_ip: (MatrixQ, MatrixQ)

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

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

    Definition Classes
    MatrixQMatriQ
  76. def lud_npp: (MatrixQ, MatrixQ)

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

    Factor 'this' matrix into the product of upper and lower triangular matrices '(l, u)' using the LU Factorization algorithm. This version uses no partial pivoting.

  77. def mag: Rational

    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
    MatriQ
  78. def max(e: Int = dim1): Rational

    Find the maximum element in 'this' matrix.

    Find the maximum element in 'this' matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    MatrixQMatriQ
  79. def mean: VectorQ

    Compute the column means of this matrix.

    Compute the column means of this matrix.

    Definition Classes
    MatriQ
  80. def min(e: Int = dim1): Rational

    Find the minimum element in 'this' matrix.

    Find the minimum element in 'this' matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    MatrixQMatriQ
  81. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  82. def norm1: Rational

    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
    MatriQ
  83. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  84. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  85. def nullspace: VectorQ

    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
    MatrixQMatriQ
    See also

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

  86. def nullspace_ip: VectorQ

    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
    MatrixQMatriQ
    See also

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

  87. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Attributes
    protected
    Definition Classes
    MatriQ
  88. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Attributes
    protected
    Definition Classes
    MatriQ
  89. def rank: Int

    Determine the rank of 'this' m-by-n matrix by taking the upper triangular matrix 'u' from the LU Decomposition and counting the number of non-zero diagonal elements.

    Determine the rank of 'this' m-by-n matrix by taking the upper triangular matrix 'u' from the LU Decomposition and counting the number of non-zero diagonal elements. Implementing classes may override this method with a better one (e.g., SVD or Rank Revealing QR).

    Definition Classes
    MatriQ
    See also

    http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29

  90. def reduce: MatrixQ

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

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

    Definition Classes
    MatrixQMatriQ
  91. def reduce_ip(): Unit

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

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

    Definition Classes
    MatrixQMatriQ
  92. def sameCrossDimensions(b: MatriQ): 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
    MatriQ
  93. def sameDimensions(b: MatriQ): 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
    MatriQ
  94. def selectCols(colIndex: Array[Int]): MatrixQ

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

    Select columns from 'this' matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.

    colIndex

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

    Definition Classes
    MatrixQMatriQ
  95. def selectRows(rowIndex: Array[Int]): MatrixQ

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

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

    rowIndex

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

    Definition Classes
    MatrixQMatriQ
  96. def set(i: Int, u: VectorQ, j: Int = 0): Unit

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

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

    i

    the row index

    u

    the vector value to assign

    j

    the starting column index

    Definition Classes
    MatrixQMatriQ
  97. def set(u: Array[Array[Rational]]): Unit

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

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

    u

    the 2D array of values to assign

    Definition Classes
    MatrixQMatriQ
  98. def set(x: Rational): Unit

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

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

    x

    the scalar value to assign

    Definition Classes
    MatrixQMatriQ
  99. def setCol(col: Int, u: VectorQ): Unit

    Set column 'col' of the matrix to a vector.

    Set column 'col' of the matrix to a vector.

    col

    the column to set

    u

    the vector to assign to the column

    Definition Classes
    MatrixQMatriQ
  100. def setDiag(x: Rational): Unit

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

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

    x

    the scalar to set the diagonal to

    Definition Classes
    MatrixQMatriQ
  101. def setDiag(u: VectorQ, k: Int = 0): Unit

    Set the kth diagonal of 'this' matrix to the vector 'u'.

    Set the kth diagonal of 'this' matrix to the vector 'u'. Assumes 'dim2 >= dim1'.

    u

    the vector to set the diagonal to

    k

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

    Definition Classes
    MatrixQMatriQ
  102. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

    Definition Classes
    MatriQ
  103. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixQ

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

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

    r_from

    the start of the row slice

    r_end

    the end of the row slice

    c_from

    the start of the column slice

    c_end

    the end of the column slice

    Definition Classes
    MatrixQMatriQ
  104. def slice(from: Int, end: Int): MatrixQ

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

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

    from

    the start row of the slice (inclusive)

    end

    the end row of the slice (exclusive)

    Definition Classes
    MatrixQMatriQ
  105. def sliceCol(from: Int, end: Int): MatrixQ

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

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

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

    Definition Classes
    MatrixQMatriQ
  106. def sliceExclude(row: Int, col: Int): MatrixQ

    Slice 'this' matrix excluding the given row and/or column.

    Slice 'this' matrix excluding the given row and/or column.

    row

    the row to exclude (0 until dim1, set to dim1 to keep all rows)

    col

    the column to exclude (0 until dim2, set to dim2 to keep all columns)

    Definition Classes
    MatrixQMatriQ
  107. def solve(b: VectorQ): VectorQ

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

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

    b

    the constant vector.

    Definition Classes
    MatrixQMatriQ
  108. def solve(u: MatriQ, b: VectorQ): VectorQ

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

    Solve for 'x' in the equation 'l*u*x = b' where 'l = this'. Requires 'l' to be lower triangular.

    u

    the upper triangular matrix

    b

    the constant vector

  109. def solve(l: MatriQ, u: MatriQ, b: VectorQ): VectorQ

    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
    MatrixQMatriQ
  110. def solve(lu: (MatriQ, MatriQ), b: VectorQ): VectorQ

    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
    MatriQ
  111. def sum: Rational

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

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

    Definition Classes
    MatrixQMatriQ
  112. def sumAbs: Rational

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

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

    Definition Classes
    MatrixQMatriQ
  113. def sumLower: Rational

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

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

    Definition Classes
    MatrixQMatriQ
  114. 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
    MatriQ
  115. 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
    MatriQ
  116. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  117. def t: MatrixQ

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

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

    Definition Classes
    MatrixQMatriQ
  118. def times(b: MatrixQ): MatrixQ

    Multiply 'this' matrix by matrix 'b' without first transposing 'b'.

    Multiply 'this' matrix by matrix 'b' without first transposing 'b'.

    b

    the matrix to multiply by (requires sameCrossDimensions)

  119. def times_d(b: MatriQ): MatrixQ

    Multiply 'this' matrix by matrix 'b' using 'dot' product (concise solution).

    Multiply 'this' matrix by matrix 'b' using 'dot' product (concise solution).

    b

    the matrix to multiply by (requires sameCrossDimensions)

  120. def times_ip(b: MatrixQ): Unit

    Multiply in-place 'this' matrix by matrix 'b' without first transposing 'b'.

    Multiply in-place 'this' matrix by matrix 'b' without first transposing 'b'. If b and this reference the same matrix (b == this), a copy of the this matrix is made.

    b

    the matrix to multiply by (requires square and sameCrossDimensions)

  121. def times_s(b: MatrixQ): MatrixQ

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

    Multiply 'this' matrix by matrix b using the Strassen matrix multiplication algorithm. Both matrices ('this' and 'b') must be square. Although the algorithm is faster than the traditional cubic algorithm, its requires more memory and is often less stable (due to round-off errors). FIX: could be make more efficient using a virtual slice (vslice) method.

    b

    the matrix to multiply by (it has to be a square matrix)

    See also

    http://en.wikipedia.org/wiki/Strassen_algorithm

  122. def toString(): String

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

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

    Definition Classes
    MatrixQ → AnyRef → Any
  123. def trace: Rational

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

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

    Definition Classes
    MatrixQMatriQ
    See also

    Eigen.scala

  124. def update(ir: Range, jr: Range, b: MatriQ): Unit

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

    Set a slice 'this' matrix row-wise on range ir and column-wise on range 'jr'. Ex: a(2..4, 3..5) = b

    ir

    the row range

    jr

    the column range

    b

    the matrix to assign

    Definition Classes
    MatrixQMatriQ
  125. def update(i: Int, u: VectorQ): Unit

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

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

    i

    the row index

    u

    the vector value to assign

    Definition Classes
    MatrixQMatriQ
  126. def update(i: Int, j: Int, x: Rational): Unit

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

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

    i

    the row index

    j

    the column index

    x

    the scalar value to assign

    Definition Classes
    MatrixQMatriQ
  127. def update(i: Int, jr: Range, u: VectorQ): 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
    MatriQ
  128. def update(ir: Range, j: Int, u: VectorQ): 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
    MatriQ
  129. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  130. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  131. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  132. 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
    MatrixQMatriQ
  133. def ~^(p: Int): MatrixQ

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

    Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 2). Caveat: should be replace by a divide and conquer algorithm.

    p

    the power to raise 'this' matrix to

    Definition Classes
    MatrixQMatriQ

Inherited from Serializable

Inherited from Serializable

Inherited from MatriQ

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped