Packages

trait MatriQ extends Error

The MatriQ trait specifies the operations to be defined by the concrete classes implementing Rational matrices, i.e., MatrixQ - dense matrix BidMatrixQ - bidiagonal matrix - useful for computing Singular Values SparseMatrixQ - sparse matrix - majority of elements should be zero SymTriMatrixQ - symmetric triangular matrix - useful for computing Eigenvalues par.MatrixQ - parallel dense matrix par.SparseMatrixQ - parallel sparse matrix Some of the classes provide a few custom methods, e.g., methods beginning with "times" or ending with "npp". ------------------------------------------------------------------------------ row-wise column-wise Append: matrix +: vector matrix +: vector Concatenate: matrix ++ matrix matrix ++ matrix

Linear Supertypes
Error, AnyRef, Any
Known Subclasses
MatrixQ
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. MatriQ
  2. Error
  3. AnyRef
  4. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def *(x: Rational): MatriQ

    Multiply 'this' matrix by scalar 'x'.

    Multiply 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

  2. abstract def *(u: VectorQ): VectorQ

    Multiply 'this' matrix by vector 'u'.

    Multiply 'this' matrix by vector 'u'.

    u

    the vector to multiply by

  3. abstract def *(b: MatriQ): MatriQ

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

    Multiply 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def * (b: MatrixD): MatrixD.

    b

    the matrix to add (requires leDimensions)

  4. abstract def **(u: VectorQ): MatriQ

    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)

    u

    the vector to multiply by

  5. abstract def **=(u: VectorQ): MatriQ

    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

  6. abstract def *=(x: Rational): MatriQ

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

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

    x

    the scalar to multiply by

  7. abstract def *=(b: MatriQ): MatriQ

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

    Multiply in-place 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def *= (b: MatrixD): MatrixD.

    b

    the matrix to multiply by (requires leDimensions)

  8. abstract def +(x: Rational): MatriQ

    Add 'this' matrix and scalar 'x'.

    Add 'this' matrix and scalar 'x'.

    x

    the scalar to add

  9. abstract def +(u: VectorQ): MatriQ

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

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

    u

    the vector to add

  10. abstract def +(b: MatriQ): MatriQ

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

    Add 'this' matrix and matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def + (b: MatrixD): MatrixD.

    b

    the matrix to add (requires leDimensions)

  11. abstract def ++(b: MatriQ): MatriQ

    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

  12. abstract def ++^(b: MatriQ): MatriQ

    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

  13. abstract def +:(u: VectorQ): MatriQ

    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

  14. abstract def +=(x: Rational): MatriQ

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

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

    x

    the scalar to add

  15. abstract def +=(u: VectorQ): MatriQ

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

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

    u

    the vector to add

  16. abstract def +=(b: MatriQ): MatriQ

    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. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def += (b: MatrixD): MatrixD.

    b

    the matrix to add (requires leDimensions)

  17. abstract def +^:(u: VectorQ): MatriQ

    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

  18. abstract def -(x: Rational): MatriQ

    From 'this' matrix subtract scalar 'x'.

    From 'this' matrix subtract scalar 'x'.

    x

    the scalar to subtract

  19. abstract def -(u: VectorQ): MatriQ

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

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

    u

    the vector to subtract

  20. abstract def -(b: MatriQ): MatriQ

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

    From 'this' matrix subtract matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def - (b: MatrixD): MatrixD.

    b

    the matrix to subtract (requires leDimensions)

  21. abstract def -=(x: Rational): MatriQ

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

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

    x

    the scalar to subtract

  22. abstract def -=(u: VectorQ): MatriQ

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

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

    u

    the vector to subtract

  23. abstract def -=(b: MatriQ): MatriQ

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

    From 'this' matrix subtract in-place matrix 'b' for any type extending MatriQ. Note, subtypes of MatriQ should also implement a more efficient version, e.g., def -= (b: MatrixD): MatrixD.

    b

    the matrix to subtract (requires leDimensions)

  24. abstract def /(x: Rational): MatriQ

    Divide 'this' matrix by scalar 'x'.

    Divide 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

  25. abstract def /=(x: Rational): MatriQ

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

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

    x

    the scalar to divide by

  26. abstract def :+(u: VectorQ): MatriQ

    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

  27. abstract def :^+(u: VectorQ): MatriQ

    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

  28. abstract def apply(ir: Range, jr: Range): MatriQ

    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

  29. abstract 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

  30. abstract 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

  31. abstract def clean(thres: Double, relative: Boolean = true): MatriQ

    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

  32. abstract def col(col: Int, from: Int = 0): VectorQ

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

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

    col

    the column to extract from the matrix

    from

    the position to start extracting from

  33. abstract def det: Rational

    Compute the determinant of 'this' matrix.

  34. abstract def diag(p: Int, q: Int = 0): MatriQ

    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.

    p

    the size of identity matrix Ip

    q

    the size of identity matrix Iq

  35. abstract def diag(b: MatriQ): MatriQ

    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

  36. abstract val dim1: Int

    Matrix dimension 1 (# rows)

  37. abstract val dim2: Int

    Matrix dimension 2 (# columns)

  38. abstract 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)

  39. abstract def getDiag(k: Int = 0): VectorQ

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

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

    k

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

  40. abstract def inverse: MatriQ

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

  41. abstract def inverse_ip: MatriQ

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

  42. abstract def isRectangular: Boolean

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

  43. abstract def lud: (MatriQ, MatriQ)

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

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

  44. abstract def lud_ip: (MatriQ, MatriQ)

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

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

  45. abstract 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

  46. abstract 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

  47. abstract 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.

    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

  48. abstract 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.

    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

  49. abstract def reduce: MatriQ

    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.

  50. abstract 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.

  51. abstract def selectCols(colIndex: Array[Int]): MatriQ

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

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

  52. abstract def selectRows(rowIndex: Array[Int]): MatriQ

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

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

    rowIndex

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

  53. abstract def set(i: Int, u: VectorQ, j: Int = 0): Unit

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

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

    i

    the row index

    u

    the vector value to assign

    j

    the starting column index

  54. abstract def set(u: Array[Array[Rational]]): Unit

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

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

    u

    the 2D array of values to assign

  55. abstract 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

  56. abstract def setCol(col: Int, u: VectorQ): Unit

    Set column 'col' of 'this' matrix to vector 'u'.

    Set column 'col' of 'this' matrix to vector 'u'.

    col

    the column to set

    u

    the vector to assign to the column

  57. abstract 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

  58. abstract def setDiag(u: VectorQ, k: Int = 0): Unit

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

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

    u

    the vector to set the diagonal to

    k

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

  59. abstract def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatriQ

    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 (inclusive)

    r_end

    the end of the row slice (exclusive)

    c_from

    the start of the column slice (inclusive)

    c_end

    the end of the column slice (exclusive)

  60. abstract def slice(from: Int, end: Int): MatriQ

    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)

  61. abstract def sliceCol(from: Int, end: Int): MatriQ

    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)

  62. abstract def sliceExclude(row: Int, col: Int): MatriQ

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

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

    row

    the row to exclude

    col

    the column to exclude

  63. abstract 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.

  64. abstract 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

  65. abstract def sum: Rational

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

  66. abstract 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

  67. abstract def sumLower: Rational

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

  68. abstract def t: MatriQ

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

  69. abstract 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.

    See also

    Eigen.scala

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

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

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

    ir

    the row range

    jr

    the column range

    b

    the matrix to assign

  71. abstract 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

  72. abstract 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

  73. abstract 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

  74. abstract def ~^(p: Int): MatriQ

    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).

    p

    the power to raise 'this' matrix to

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. 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

  5. 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

  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  8. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  9. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  10. 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
  11. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  12. 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
  13. 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

  14. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  15. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  16. 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.

  17. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  18. def isNonnegative: Boolean

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

  19. def isSquare: Boolean

    Check whether 'this' matrix is square (same row and column dimensions).

  20. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

  21. 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.

  22. 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

  23. def mag: Rational

    Find the magnitude of 'this' matrix, the element value farthest from zero.

  24. def mean: VectorQ

    Compute the column means of this matrix.

  25. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  26. 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'.

  27. final def notify(): Unit
    Definition Classes
    AnyRef
  28. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  29. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Attributes
    protected
  30. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Attributes
    protected
  31. 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).

    See also

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

  32. 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

  33. 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

  34. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

  35. 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

  36. 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)

  37. 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)

  38. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  39. def toString(): String
    Definition Classes
    AnyRef → Any
  40. 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

  41. 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

  42. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  43. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  44. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped