Packages

class BidMatrixD extends MatriD with Error with Serializable

The BidMatrixD class stores and operates on square (upper) bidiagonal matrices. The elements are of type of Double. A matrix is stored as two vectors: the diagonal vector and the sup-diagonal vector.

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Serializable, Serializable, MatriD, Error, AnyRef, Any
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  1. BidMatrixD
  2. Serializable
  3. Serializable
  4. MatriD
  5. Error
  6. AnyRef
  7. Any
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Instance Constructors

  1. new BidMatrixD(b: MatriD)

    Construct a bidiagonal matrix from the given matrix.

    Construct a bidiagonal matrix from the given matrix.

    b

    the matrix of values to assign

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

    Construct a bidiagonal matrix with the given diagonal and sup-diagonal.

    Construct a bidiagonal matrix with the given diagonal and sup-diagonal.

    v1

    the diagonal vector

    v2

    the sup-diagonal vector

  3. new BidMatrixD(d1: Int)

    d1

    the first/row dimension (square => d2 = d1)

Value Members

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

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

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

    x

    the scalar to multiply by

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

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

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

    u

    the vector to multiply by

    Definition Classes
    BidMatrixDMatriD
  5. def *(b: BidMatrixD): MatrixD

    Multiply 'this' bidiagonal matrix by matrix 'b'.

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

    b

    the matrix to multiply by

  6. def *(b: MatriD): BidMatrixD

    Multiply 'this' bidiagonal matrix by matrix 'b'.

    Multiply 'this' bidiagonal matrix by matrix 'b'.

    b

    the matrix to multiply by

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

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

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

    u

    the vector to multiply by

    Definition Classes
    BidMatrixDMatriD
  8. def **:(u: VectoD): MatrixD

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

    Multiply vector 'u' by 'this' bidiagonal 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
    BidMatrixDMatriD
  9. def **=(u: VectoD): MatrixD

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

    Multiply in-place 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a diagonal matrix represented as a vector by a matrix.

    u

    the vector to multiply by

    Definition Classes
    BidMatrixDMatriD
  10. def *:(u: VectoD): VectoD

    Multiply (row) vector 'u' by 'this' matrix.

    Multiply (row) vector 'u' by 'this' matrix. Note '*:' is right associative. vector = vector *: matrix

    u

    the vector to multiply by

    Definition Classes
    MatriD
  11. def *=(x: Double): BidMatrixD

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

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

    x

    the scalar to multiply by

    Definition Classes
    BidMatrixDMatriD
  12. def *=(b: MatriD): BidMatrixD

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

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

    b

    the matrix to multiply by

    Definition Classes
    BidMatrixDMatriD
  13. def +(x: Double): BidMatrixD

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

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

    x

    the scalar to add

    Definition Classes
    BidMatrixDMatriD
  14. def +(u: VectoD): BidMatrixD

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

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

    u

    the vector to add

    Definition Classes
    BidMatrixDMatriD
  15. def +(b: MatriD): BidMatrixD

    Add 'this' bidiagonal matrix and matrix 'b'.

    Add 'this' bidiagonal matrix and matrix 'b'.

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    BidMatrixDMatriD
  16. def ++(b: MatriD): BidMatrixD

    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
    BidMatrixDMatriD
  17. def ++^(b: MatriD): BidMatrixD

    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
    BidMatrixDMatriD
  18. def +:(u: VectoD): BidMatrixD

    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
    BidMatrixDMatriD
  19. def +=(x: Double): BidMatrixD

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

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

    x

    the scalar to add

    Definition Classes
    BidMatrixDMatriD
  20. def +=(u: VectoD): MatrixD

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

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

    u

    the vector to add

    Definition Classes
    BidMatrixDMatriD
  21. def +=(b: MatriD): BidMatrixD

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

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

    b

    the matrix to add (requires 'leDimensions')

    Definition Classes
    BidMatrixDMatriD
  22. def +^:(u: VectoD): BidMatrixD

    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
    BidMatrixDMatriD
  23. def -(x: Double): BidMatrixD

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

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

    x

    the scalar to subtract

    Definition Classes
    BidMatrixDMatriD
  24. def -(u: VectoD): BidMatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    BidMatrixDMatriD
  25. def -(b: MatriD): BidMatrixD

    From 'this' bidiagonal matrix subtract matrix 'b'.

    From 'this' bidiagonal matrix subtract matrix 'b'.

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    BidMatrixDMatriD
  26. def -=(x: Double): BidMatrixD

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

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

    x

    the scalar to subtract

    Definition Classes
    BidMatrixDMatriD
  27. def -=(u: VectoD): BidMatrixD

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

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

    u

    the vector to subtract

    Definition Classes
    BidMatrixDMatriD
  28. def -=(b: MatriD): BidMatrixD

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

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

    b

    the matrix to subtract (requires 'leDimensions')

    Definition Classes
    BidMatrixDMatriD
  29. def /(x: Double): BidMatrixD

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

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

    x

    the scalar to divide by

    Definition Classes
    BidMatrixDMatriD
  30. def /=(x: Double): BidMatrixD

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

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

    x

    the scalar to divide by

    Definition Classes
    BidMatrixDMatriD
  31. def :+(u: VectoD): BidMatrixD

    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
    BidMatrixDMatriD
  32. def :^+(u: VectoD): BidMatrixD

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

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

    Get a slice 'this' bidiagonal 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
    BidMatrixDMatriD
  35. def apply(i: Int): VectorD

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

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

    i

    the row index

    Definition Classes
    BidMatrixDMatriD
  36. def apply(i: Int, j: Int): Double

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

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

    i

    the row index

    j

    the column index

    Definition Classes
    BidMatrixDMatriD
  37. def apply(i: Int, jr: Range): VectoD

    Get a slice 'this' matrix row-wise at index 'i' and column-wise on range 'jr'.

    Get a slice 'this' matrix row-wise at index 'i' and column-wise on range 'jr'. Ex: u = a(2, 3..5)

    i

    the row index

    jr

    the column range

    Definition Classes
    MatriD
  38. def apply(ir: Range, j: Int): VectoD

    Get a slice 'this' matrix row-wise on range 'ir' and column-wise at index j.

    Get a slice 'this' matrix row-wise on range 'ir' and column-wise at index j. Ex: u = a(2..4, 3)

    ir

    the row range

    j

    the column index

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

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

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

    i

    the row index

    j

    the column index

  41. def bsolve(y: VectoD): VectorD

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

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

    y

    the constant vector

    Definition Classes
    BidMatrixDMatriD
  42. def clean(thres: Double, relative: Boolean = true): BidMatrixD

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

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

    thres

    the cutoff threshold (a small value)

    relative

    whether to use relative or absolute cutoff

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

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

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

    col

    the column to extract from the matrix

    from

    the position to start extracting from

    Definition Classes
    BidMatrixDMatriD
  45. def copy(): BidMatrixD

    Create a clone of 'this' m-by-n matrix.

    Create a clone of 'this' m-by-n matrix.

    Definition Classes
    BidMatrixDMatriD
  46. val d1: Int
  47. def det: Double

    Compute the determinant of 'this' bidiagonal matrix.

    Compute the determinant of 'this' bidiagonal matrix.

    Definition Classes
    BidMatrixDMatriD
  48. def dg: VectorD

    Get the diagonal of 'this' bidiagonal matrix.

  49. def dg_(v: VectorD): Unit

    Set the diagonal of 'this' bidiagonal matrix.

    Set the diagonal of 'this' bidiagonal matrix.

    v

    the vector to assign to the diagonal

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

    Form a matrix '[Ip, this, Iq]' where Ir is a 'r-by-r' identity matrix, by positioning the three matrices 'Ip', 'this' and 'Iq' along the diagonal.

    Form a matrix '[Ip, this, Iq]' where Ir is a 'r-by-r' identity matrix, by positioning the three matrices 'Ip', 'this' and 'Iq' along the diagonal. Fill the rest of matrix with zeros.

    p

    the size of identity matrix Ip

    q

    the size of identity matrix Iq

    Definition Classes
    BidMatrixDMatriD
  51. def diag(b: MatriD): MatriD

    Combine 'this' bidiagonal 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' bidiagonal 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' bidiagonal matrix

    Definition Classes
    BidMatrixDMatriD
  52. lazy val dim1: Int

    Dimension 1

    Dimension 1

    Definition Classes
    BidMatrixDMatriD
  53. lazy val dim2: Int

    Dimension 2

    Dimension 2

    Definition Classes
    BidMatrixDMatriD
  54. def dot(b: MatriD): VectorD

    Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

    Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

    b

    the second matrix of the dot product

    Definition Classes
    BidMatrixDMatriD
  55. def dot(u: VectoD): VectorD

    Compute the dot product of 'this' matrix and vector 'u', by conceptually 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 conceptually 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
    BidMatrixDMatriD
  56. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  57. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  58. val fString: String

    Format string used for printing vector values (change using 'setFormat')

    Format string used for printing vector values (change using 'setFormat')

    Attributes
    protected
    Definition Classes
    MatriD
  59. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  60. 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
  61. def foreach[U](f: (Array[Double]) ⇒ U): Unit

    Iterate over 'this' matrix row by row applying method 'f'.

    Iterate over 'this' matrix row by row applying method 'f'.

    f

    the function to apply

    Definition Classes
    MatriD
  62. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  63. def getDiag(k: Int = 0): VectorD

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

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

    k

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

    Definition Classes
    BidMatrixDMatriD
  64. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  65. def inverse: MatriD

    Invert 'this' bidiagonal matrix.

    Invert 'this' bidiagonal matrix.

    Definition Classes
    BidMatrixDMatriD
  66. def inverse_ip(): BidMatrixD

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

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

    Definition Classes
    BidMatrixDMatriD
  67. 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).

    Definition Classes
    BidMatrixDMatriD
  68. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  69. def isNonnegative: Boolean

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

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

    Definition Classes
    BidMatrixDMatriD
  70. def isRectangular: Boolean

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

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

    Definition Classes
    BidMatrixDMatriD
  71. def isSquare: Boolean

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

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

    Definition Classes
    MatriD
  72. def isSymmetric: Boolean

    Check whether 'this' matrix is symmetric.

    Check whether 'this' matrix is symmetric.

    Definition Classes
    MatriD
  73. 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).

    Definition Classes
    BidMatrixDMatriD
  74. def leDimensions(b: MatriD): Boolean

    Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.

    Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.

    b

    the other matrix

    Definition Classes
    MatriD
  75. def lowerT: MatrixD

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

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

    Definition Classes
    BidMatrixDMatriD
  76. def lud_ip(): (MatriD, MatriD)

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

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

    Definition Classes
    BidMatrixDMatriD
  77. def lud_npp: (MatriD, MatriD)

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

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

    Definition Classes
    BidMatrixDMatriD
  78. def mag: Double

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

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

    Definition Classes
    MatriD
  79. def max(e: Int = dim1): Double

    Find the maximum element in 'this' bidiagonal matrix.

    Find the maximum element in 'this' bidiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    BidMatrixDMatriD
  80. def mdot(b: MatriD): MatrixD

    Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

    Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

    b

    the second matrix of the dot product

    Definition Classes
    BidMatrixDMatriD
  81. def mdot(b: BidMatrixD): MatrixD

    Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

    Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

    b

    the second matrix of the dot product

  82. def mean: VectoD

    Compute the column means of this matrix.

    Compute the column means of this matrix.

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

    Find the minimum element in 'this' bidiagonal matrix.

    Find the minimum element in 'this' bidiagonal matrix.

    e

    the ending row index (exclusive) for the search

    Definition Classes
    BidMatrixDMatriD
  84. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  85. def norm1: Double

    Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors.

    Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices '(a - b).norm1'.

    Definition Classes
    MatriD
  86. final def notify(): Unit
    Definition Classes
    AnyRef
  87. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  88. def nullspace: VectorD

    Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

    The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

    Definition Classes
    BidMatrixDMatriD
    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

  89. def nullspace_ip(): VectorD

    Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

    nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

    The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

    Definition Classes
    BidMatrixDMatriD
    See also

    /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf

    http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces

  90. val range1: Range

    Range for the storage array on dimension 1 (rows)

    Range for the storage array on dimension 1 (rows)

    Definition Classes
    MatriD
  91. val range2: Range

    Range for the storage array on dimension 2 (columns)

    Range for the storage array on dimension 2 (columns)

    Definition Classes
    MatriD
  92. def reduce: BidMatrixD

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

    Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix. A constraint on 'this' m by n matrix is that n >= m.

    Definition Classes
    BidMatrixDMatriD
  93. def reduce_ip(): Unit

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

    Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix. A constraint on 'this' m by n matrix is that n >= m.

    Definition Classes
    BidMatrixDMatriD
  94. def sameCrossDimensions(b: MatriD): Boolean

    Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.

    Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.

    b

    the other matrix

    Definition Classes
    MatriD
  95. def sameDimensions(b: MatriD): Boolean

    Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

    Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

    b

    the other matrix

    Definition Classes
    MatriD
  96. def sd: VectorD

    Get the sup-diagonal of this bidiagonal matrix.

  97. def sd_(v: VectorD): Unit

    Set the sup-diagonal of 'this' bidiagonal matrix.

    Set the sup-diagonal of 'this' bidiagonal matrix.

    v

    the vector to assign to the sup-diagonal

  98. def selectCols(colIndex: Array[Int]): BidMatrixD

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

    Select columns from 'this' bidiagonal 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
    BidMatrixDMatriD
  99. def selectRows(rowIndex: Array[Int]): BidMatrixD

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

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

    rowIndex

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

    Definition Classes
    BidMatrixDMatriD
  100. def set(i: Int, u: VectoD, j: Int = 0): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixDMatriD
  101. def set(u: Array[Array[Double]]): Unit

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

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

    u

    the 2D array of values to assign

    Definition Classes
    BidMatrixDMatriD
  102. def set(x: Double): Unit

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

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

    x

    the scalar value to assign

    Definition Classes
    BidMatrixDMatriD
  103. def setCol(col: Int, u: VectoD): Unit

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

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

    col

    the column to set

    u

    the vector to assign to the column

    Definition Classes
    BidMatrixDMatriD
  104. def setDiag(x: Double): Unit

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

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

    x

    the scalar to set the diagonal to

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

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

    Set the 'k'th diagonal of 'this' bidiagonal 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
    BidMatrixDMatriD
  106. def setFormat(newFormat: String): Unit

    Set the format to the 'newFormat'.

    Set the format to the 'newFormat'.

    newFormat

    the new format string

    Definition Classes
    MatriD
  107. def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): BidMatrixD

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

    Slice 'this' bidiagonal 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
    BidMatrixDMatriD
  108. def slice(from: Int, end: Int): BidMatrixD

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

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

    from

    the start row of the slice (inclusive)

    end

    the end row of the slice (exclusive)

    Definition Classes
    BidMatrixDMatriD
  109. def sliceCol(from: Int, end: Int): BidMatrixD

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

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

    from

    the start column of the slice (inclusive)

    end

    the end column of the slice (exclusive)

    Definition Classes
    BidMatrixDMatriD
  110. def sliceExclude(row: Int, col: Int): BidMatrixD

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

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

    row

    the row to exclude

    col

    the column to exclude

    Definition Classes
    BidMatrixDMatriD
  111. def solve(l: MatriD, u: MatriD, b: VectoD): VectorD

    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
    BidMatrixDMatriD
  112. def solve(b: VectoD): VectorD

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

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

    b

    the constant vector

    Definition Classes
    BidMatrixDMatriD
  113. def solve(lu: (MatriD, MatriD), b: VectoD): VectoD

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

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

    lu

    the lower and upper triangular matrices

    b

    the constant vector

    Definition Classes
    MatriD
  114. def sum: Double

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

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

    Definition Classes
    BidMatrixDMatriD
  115. def sumAbs: Double

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

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

    Definition Classes
    BidMatrixDMatriD
  116. def sumLower: Double

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

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

    Definition Classes
    BidMatrixDMatriD
  117. def swap(i: Int, k: Int, col: Int = 0): Unit

    Swap the elements in rows 'i' and 'k' starting from column 'col'.

    Swap the elements in rows 'i' and 'k' starting from column 'col'.

    i

    the first row in the swap

    k

    the second row in the swap

    col

    the starting column for the swap (default 0 => whole row)

    Definition Classes
    MatriD
  118. def swapCol(j: Int, l: Int, row: Int = 0): Unit

    Swap the elements in columns 'j' and 'l' starting from row 'row'.

    Swap the elements in columns 'j' and 'l' starting from row 'row'.

    j

    the first column in the swap

    l

    the second column in the swap

    row

    the starting row for the swap (default 0 => whole column)

    Definition Classes
    MatriD
  119. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  120. def t: BidMatrixD

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

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

    Definition Classes
    BidMatrixDMatriD
  121. def toDense: MatrixD

    Convert 'this' tridiagonal matrix to a dense matrix.

    Convert 'this' tridiagonal matrix to a dense matrix.

    Definition Classes
    BidMatrixDMatriD
  122. def toInt: BidMatrixI

    Convert 'this' BidMatrixD into a BidMatrixI.

    Convert 'this' BidMatrixD into a BidMatrixI.

    Definition Classes
    BidMatrixDMatriD
  123. def toString(): String

    Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

    Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

    Definition Classes
    BidMatrixD → AnyRef → Any
  124. def trace: Double

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

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

    Definition Classes
    BidMatrixDMatriD
    See also

    Eigen.scala

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

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

    Set a slice 'this' bidiagonal 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
    BidMatrixDMatriD
  126. def update(i: Int, u: VectoD): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixDMatriD
  127. def update(i: Int, j: Int, x: Double): Unit

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

    Set 'this' bidiagonal 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
    BidMatrixDMatriD
  128. def update(i: Int, jr: Range, u: VectoD): Unit

    Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'.

    Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'. Ex: a(2, 3..5) = u

    i

    the row index

    jr

    the column range

    u

    the vector to assign

    Definition Classes
    MatriD
  129. def update(ir: Range, j: Int, u: VectoD): Unit

    Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'.

    Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'. Ex: a(2..4, 3) = u

    ir

    the row range

    j

    the column index

    u

    the vector to assign

    Definition Classes
    MatriD
  130. def upperT: MatrixD

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

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

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

    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
    BidMatrixDMatriD
  136. def ~^(p: Int): BidMatrixD

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

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

    p

    the power to raise 'this' matrix to

    Definition Classes
    BidMatrixDMatriD

Inherited from Serializable

Inherited from Serializable

Inherited from MatriD

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped