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class MatrixC extends MatriC with Error with Serializable

The MatrixC class stores and operates on Numeric Matrices of type Complex. This class follows the gen.MatrixN framework and is provided for efficiency. Caveat: Only works for rectangular matrices. For matrix-like structures based on jagged arrays, where the second dimension varies,

See also

scalation.linalgebra.gen.HMatrix2

Linear Supertypes
Serializable, Serializable, MatriC, Error, AnyRef, Any
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  1. MatrixC
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Instance Constructors

  1. new MatrixC(b: MatriC)

    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 MatrixC(dim: (Int, Int), u: Complex*)

    Construct a matrix from repeated values.

    Construct a matrix from repeated values.

    dim

    the (row, column) dimensions

    u

    the repeated values

  3. new MatrixC(u: Array[Array[Complex]])

    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 MatrixC(dim1: Int, dim2: Int, x: Complex)

    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 dimension

    x

    the scalar value to assign

  5. new MatrixC(dim1: Int)

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

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

    dim1

    the row and column dimension

  6. new MatrixC(d1: Int, d2: Int, v: Array[Array[Complex]] = 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: Complex): MatrixC

    Multiply 'this' matrix by scalar 'x'.

    Multiply 'this' matrix by scalar 'x'.

    x

    the scalar to multiply by

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

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

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

    u

    the vector to multiply by

    Definition Classes
    MatrixCMatriC
  5. def *(b: MatriC): MatrixC

    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
    MatrixCMatriC
  6. def *(b: MatrixC): MatrixC

    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 **(b: MatriC): MatrixC

    Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

    Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

    b

    the matrix to multiply by

    Definition Classes
    MatrixCMatriC
    See also

    en.wikipedia.org/wiki/Hadamard_product_(matrices)

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

    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
    MatrixCMatriC
  9. def **:(u: VectoC): MatrixC

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

    Multiply vector 'u' by 'this' 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
    MatrixCMatriC
  10. def **=(u: VectoC): MatrixC

    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
    MatrixCMatriC
  11. 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
  12. def *=(x: Complex): MatrixC

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

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

    x

    the scalar to multiply by

    Definition Classes
    MatrixCMatriC
  13. def *=(b: MatriC): MatrixC

    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
    MatrixCMatriC
  14. def *=(b: MatrixC): MatrixC

    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')

  15. def +(x: Complex): MatrixC

    Add 'this' matrix and scalar 'x'.

    Add 'this' matrix and scalar 'x'.

    x

    the scalar to add

    Definition Classes
    MatrixCMatriC
  16. def +(u: VectoC): MatrixC

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

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

    u

    the vector to add

    Definition Classes
    MatrixCMatriC
  17. def +(b: MatriC): MatrixC

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    MatrixCMatriC
  18. def +(b: MatrixC): MatrixC

    Add 'this' matrix and matrix 'b'.

    Add 'this' matrix and matrix 'b'.

    b

    the matrix to add (requires 'leDimensions')

  19. def ++(b: MatriC): MatrixC

    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
    MatrixCMatriC
  20. def ++^(b: MatriC): MatrixC

    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
    MatrixCMatriC
  21. def +:(u: VectoC): MatrixC

    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
    MatrixCMatriC
  22. def +=(x: Complex): MatrixC

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

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

    x

    the scalar to add

    Definition Classes
    MatrixCMatriC
  23. def +=(u: VectoC): MatrixC

    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
    MatrixCMatriC
  24. def +=(b: MatriC): MatrixC

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    MatrixCMatriC
  25. def +=(b: MatrixC): MatrixC

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

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

    b

    the matrix to add (requires 'leDimensions')

  26. def +^:(u: VectoC): MatrixC

    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
    MatrixCMatriC
  27. def -(x: Complex): MatrixC

    From 'this' matrix subtract scalar 'x'.

    From 'this' matrix subtract scalar 'x'.

    x

    the scalar to subtract

    Definition Classes
    MatrixCMatriC
  28. def -(u: VectoC): MatrixC

    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
    MatrixCMatriC
  29. def -(b: MatriC): MatrixC

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    MatrixCMatriC
  30. def -(b: MatrixC): MatrixC

    From 'this' matrix subtract matrix 'b'.

    From 'this' matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires 'leDimensions')

  31. def -=(x: Complex): MatrixC

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

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

    x

    the scalar to subtract

    Definition Classes
    MatrixCMatriC
  32. def -=(u: VectoC): MatrixC

    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
    MatrixCMatriC
  33. def -=(b: MatriC): MatrixC

    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
    MatrixCMatriC
  34. def -=(b: MatrixC): MatrixC

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

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

    b

    the matrix to subtract (requires 'leDimensions')

  35. def /(x: Complex): MatrixC

    Divide 'this' matrix by scalar 'x'.

    Divide 'this' matrix by scalar 'x'.

    x

    the scalar to divide by

    Definition Classes
    MatrixCMatriC
  36. def /=(x: Complex): MatrixC

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

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

    x

    the scalar to divide by

    Definition Classes
    MatrixCMatriC
  37. def :+(u: VectoC): MatrixC

    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
    MatrixCMatriC
  38. def :^+(u: VectoC): MatrixC

    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
    MatrixCMatriC
  39. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  40. def apply(iv: VectoI): MatrixC

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

    Get the rows from 'this' matrix according to the given index/basis. The new matrix is formed by referencing rows in the current matrix, thereby saving space.

    iv

    the row index vector

    Definition Classes
    MatrixCMatriC
  41. def apply(): Array[Array[Complex]]

    Get the underlying 2D array for 'this' matrix.

  42. def apply(ir: Range, jr: Range): MatrixC

    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
    MatrixCMatriC
  43. def apply(i: Int): VectorC

    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
    MatrixCMatriC
  44. def apply(i: Int, j: Int): Complex

    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
    MatrixCMatriC
  45. 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
  46. 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
  47. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  48. 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_npp' above).

    Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud_npp' above).

    y

    the constant vector

    Definition Classes
    MatrixCMatriC
  49. def clean(thres: Double = TOL, relative: Boolean = true): MatrixC

    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
    MatrixCMatriC
  50. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  51. def col(col: Int, from: Int = 0): VectorC

    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
    MatrixCMatriC
  52. def copy(): MatrixC

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

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

    Definition Classes
    MatrixCMatriC
  53. def det: Complex

    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
    MatrixCMatriC
  54. def diag(p: Int, q: Int = 0): MatrixC

    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
    MatrixCMatriC
  55. def diag(b: MatriC): MatrixC

    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
    MatrixCMatriC
  56. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    MatrixCMatriC
  57. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    MatrixCMatriC
  58. def dot(b: MatrixC): VectorC

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    b

    the matrix to multiply by (requires same first dimensions)

    See also

    www.mathworks.com/help/matlab/ref/dot.html

  59. def dot(b: MatriC): VectorC

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.

    b

    the matrix to multiply by (requires same first dimensions)

    Definition Classes
    MatrixCMatriC
    See also

    www.mathworks.com/help/matlab/ref/dot.html

  60. def dot(u: VectoC): VectorC

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

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

    u

    the vector to multiply by (requires same first dimensions)

    Definition Classes
    MatrixCMatriC
  61. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  62. def equals(b: Any): Boolean

    Override equals to determine whether 'this' matrix equals matrix 'b'.

    Override equals to determine whether 'this' matrix equals matrix 'b'.

    b

    the matrix to compare with this

    Definition Classes
    MatrixC → AnyRef → Any
  63. 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
  64. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  65. 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
  66. 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
  67. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  68. def getDiag(k: Int = 0): VectorC

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

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

    k

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

    Definition Classes
    MatrixCMatriC
  69. def hashCode(): Int

    Must also override hashCode for 'this' matrix to be compatible with equals.

    Must also override hashCode for 'this' matrix to be compatible with equals.

    Definition Classes
    MatrixC → AnyRef → Any
  70. def inverse: MatrixC

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

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

    Definition Classes
    MatrixCMatriC
  71. def inverse_ip(): MatrixC

    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 original matrix into the identity matrix. The inverse is returned and is captured by assignment.

    Definition Classes
    MatrixCMatriC
  72. def inverse_npp: MatrixC

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

  73. 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
  74. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  75. 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
    MatriC
  76. 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
    MatrixCMatriC
  77. 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
  78. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriC
  79. def isTridiagonal: Boolean

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

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

    Definition Classes
    MatriC
  80. 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
  81. def lowerT: MatrixC

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

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

    Definition Classes
    MatrixCMatriC
  82. def lud_ip(): (MatrixC, MatrixC)

    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.

    Definition Classes
    MatrixCMatriC
  83. def lud_npp: (MatrixC, MatrixC)

    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. Caveat: This version requires square matrices and performs no partial pivoting.

    Definition Classes
    MatrixCMatriC
    See also

    Fac_LU for a more complete implementation

  84. 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
  85. def map(f: (VectoC) ⇒ VectoC): MatrixC

    Map the elements of 'this' matrix by applying the mapping function 'f'.

    Map the elements of 'this' matrix by applying the mapping function 'f'.

    f

    the function to apply

    Definition Classes
    MatrixCMatriC
  86. def max(e: Int = dim1): Complex

    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
    MatrixCMatriC
  87. def mdot(b: MatrixC): MatrixC

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

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

    b

    the matrix to multiply by (requires same first dimensions)

  88. def mdot(b: MatriC): MatrixC

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

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

    b

    the matrix to multiply by (requires same first dimensions)

    Definition Classes
    MatrixCMatriC
  89. def mean: VectoC

    Compute the column means of 'this' matrix.

    Compute the column means of 'this' matrix.

    Definition Classes
    MatriC
  90. def meanNZ: VectoC

    Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

    Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

    Definition Classes
    MatriC
  91. def meanR: VectoC

    Compute the row means of 'this' matrix.

    Compute the row means of 'this' matrix.

    Definition Classes
    MatriC
  92. def meanRNZ: VectoC

    Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

    Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

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

    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
    MatrixCMatriC
  94. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  95. 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
    See also

    en.wikipedia.org/wiki/Matrix_norm

  96. def normF: Complex

    Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.

    Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.

    Definition Classes
    MatriC
    See also

    en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

  97. def normINF: Complex

    Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

    Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

    Definition Classes
    MatriC
    See also

    en.wikipedia.org/wiki/Matrix_norm

  98. def normalizeU: MatrixC

    Create a normalized version of 'this' matrix.

  99. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  100. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  101. 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
    MatrixCMatriC
    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

  102. 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
    MatrixCMatriC
    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

  103. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriC
  104. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriC
  105. def reduce: MatrixC

    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
    MatrixCMatriC
  106. 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
    MatrixCMatriC
  107. 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
  108. 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
  109. def selectCols(colIndex: Array[Int]): MatrixC

    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
    MatrixCMatriC
  110. def selectRows(rowIndex: Array[Int]): MatrixC

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

    Select rows from 'this' matrix according to the given index/basis. The new matrix is formed by copying rows from the current matrix.

    rowIndex

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

    Definition Classes
    MatrixCMatriC
  111. def selectRowsEx(rowIndex: Array[Int]): MatriC

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

    rowIndex

    the row indices to exclude

    Definition Classes
    MatriC
  112. def set(i: Int, u: VectoC, 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
    MatrixCMatriC
  113. def set(u: Array[Array[Complex]]): 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
    MatrixCMatriC
  114. def set(x: Complex): 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
    MatrixCMatriC
  115. def setCol(col: Int, u: VectoC): 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
    MatrixCMatriC
  116. def setDiag(x: Complex): Unit

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

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

    x

    the scalar to set the diagonal to

    Definition Classes
    MatrixCMatriC
  117. def setDiag(u: VectoC, 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'.

    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
    MatrixCMatriC
  118. 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
  119. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixC

    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
    MatrixCMatriC
  120. def slice(from: Int, end: Int): MatrixC

    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
    MatrixCMatriC
  121. def slice(rg: Range): MatriC

    Slice 'this' matrix row-wise over the given range 'rg'.

    Slice 'this' matrix row-wise over the given range 'rg'.

    rg

    the range specifying the slice

    Definition Classes
    MatriC
  122. def sliceCol(from: Int, end: Int): MatrixC

    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
    MatrixCMatriC
  123. def sliceEx(row: Int, col: Int): MatrixC

    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
    MatrixCMatriC
  124. def sliceEx(rg: Range): MatriC

    Slice 'this' matrix row-wise excluding the given range 'rg'.

    Slice 'this' matrix row-wise excluding the given range 'rg'.

    rg

    the excluded range of the slice

    Definition Classes
    MatriC
  125. def solve(b: VectoC): VectoC

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

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

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

    l

    the lower triangular matrix

    u

    the upper triangular matrix

    b

    the constant vector

    Definition Classes
    MatrixCMatriC
  127. 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
  128. def sum: Complex

    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
    MatrixCMatriC
  129. def sumAbs: Complex

    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
    MatrixCMatriC
  130. def sumLower: Complex

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

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

    Definition Classes
    MatrixCMatriC
  131. 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
  132. 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
  133. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  134. def t: MatrixC

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

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

    Definition Classes
    MatrixCMatriC
  135. def times(b: MatrixC): MatrixC

    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')

  136. def times_d(b: MatriC): MatrixC

    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')

  137. def times_ip(b: MatrixC): 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')

  138. def times_ip_pre(b: MatrixC, d: Int = 0): Unit

    Pre-multiply in-place 'this' ('a') matrix by matrix 'b', starting with column 'd'.

    Pre-multiply in-place 'this' ('a') matrix by matrix 'b', starting with column 'd'.

    a(d:m, d:n) = b a(d:m, d:n)

    b

    the matrix to pre-multiply by 'this' (requires square and 'sameCrossDimensions')

    d

    the column to start with

  139. def times_s(b: MatrixC): MatrixC

    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

  140. def tip(): MatrixC

    Transpose, in-place, 'this' matrix (columns => rows).

    Transpose, in-place, 'this' matrix (columns => rows). FIX: may wish to use algorithm with better data locality.

  141. def toDense: MatrixC

    Convert 'this' matrix to a dense matrix.

    Convert 'this' matrix to a dense matrix.

    Definition Classes
    MatrixCMatriC
  142. def toDouble: MatrixD

    Convert 'this' MatrixC into a double matrix MatrixD.

  143. def toInt: MatrixI

    Convert 'this' MatrixC into an integer matrix MatrixI.

    Convert 'this' MatrixC into an integer matrix MatrixI.

    Definition Classes
    MatrixCMatriC
  144. def toString(): String

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

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

    Definition Classes
    MatrixC → AnyRef → Any
  145. def trace: Complex

    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
    MatrixCMatriC
    See also

    Eigen.scala

  146. def update(ir: Range, jr: Range, b: MatriC): 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
    MatrixCMatriC
  147. def update(i: Int, u: VectoC): 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
    MatrixCMatriC
  148. def update(i: Int, j: Int, x: Complex): 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
    MatrixCMatriC
  149. 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
  150. 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
  151. def upperT: MatrixC

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

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

    Definition Classes
    MatrixCMatriC
  152. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  153. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  154. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  155. 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
    MatrixCMatriC
  156. def zero(m: Int = dim1, n: Int = dim2): MatrixC

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

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

    m

    the number of rows

    n

    the number of columns

    Definition Classes
    MatrixCMatriC
  157. def ~^(p: Int): MatrixC

    Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 1) using a divide and conquer algorithm.

    Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 1) using a divide and conquer algorithm.

    p

    the power to raise 'this' matrix to

    Definition Classes
    MatrixCMatriC

Inherited from Serializable

Inherited from Serializable

Inherited from MatriC

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped