README
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Complex Linear Algebra cmplxalg
A complex linear algebra package written in golang.
Implements many common linear algebra algorithms for complex-valued matrices and vectors.
This package implements the types Matrix and Vector, both of which are arrays of complex numbers. It can utilize these types to perform many different operations such as examining if two vectors are parallell, finding the angle between them, and calculating the inverse of a matrix. All of this with fully-fledged support for complex numbers.
Documentation
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Index ¶
- Constants
- func Angle(v, w *Vector) complex128
- func DotProduct(v, w *Vector) complex128
- func Parallell(v, w *Vector) bool
- func Perpendicular(v, w *Vector) bool
- func TestAll()
- type Matrix
- func (m *Matrix) Augment(a *Matrix)
- func (m *Matrix) Columns() int
- func (m *Matrix) Conjugate()
- func (m *Matrix) Copy() *Matrix
- func (m *Matrix) Determinant() complex128
- func (a *Matrix) Equal(b *Matrix) bool
- func (m *Matrix) GetColumn(index int) *Vector
- func (m *Matrix) GetRow(index int) *Vector
- func (m *Matrix) HermitianTranspose()
- func (m *Matrix) Inverse()
- func (m *Matrix) IsHermitian() bool
- func (m *Matrix) IsInvertible() bool
- func (m *Matrix) IsSingular() bool
- func (m *Matrix) MatrixMultiply(a *Matrix)
- func (m *Matrix) RR()
- func (m *Matrix) RREF()
- func (m *Matrix) RealString() string
- func (m *Matrix) Rows() int
- func (m *Matrix) ScalarAdd(f complex128)
- func (m *Matrix) ScalarMultiply(f complex128)
- func (m *Matrix) SetColumn(index int, col *Vector)
- func (m *Matrix) SetRow(index int, row *Vector)
- func (m *Matrix) String() string
- func (m *Matrix) Transpose()
- type Vector
- func (v *Vector) Add(w *Vector)
- func (v *Vector) Conjugate()
- func (v *Vector) Copy() *Vector
- func (v *Vector) Equal(w *Vector) bool
- func (v *Vector) Magnitude() complex128
- func (v *Vector) MatrixMultiply(a *Matrix)
- func (v *Vector) Normalize()
- func (v *Vector) ScalarMultiply(factor complex128)
- func (v *Vector) Sub(w *Vector)
Constants ¶
const ERR_AUGM_ROW = "Cannot augment matrices with differing amount of rows"
const ERR_CRSP_DIM = "Can only calculate cross product of 3-dimensional vectors"
const ERR_DETM_SQR = "Cannot calculate inverse of non-square matrix"
const ERR_DOTP_DIM = "Cannot calculate dot-product of vectors with different dimensions"
Panic Messages --------------------------------------------------------------
const ERR_INVR_SNG = "Cannot calculate inverse of singular matrix"
const ERR_INVR_SQR = "Cannot calculate inverse of non-square matrix"
const ERR_MTRX_DIM = "Incompatible matrix dimensions"
const ERR_MTRX_RNG = "The index to get/set is out of range"
const ERR_MTRX_SNG = "Cannot row-reduce singular matrix"
const ERR_NORM_ZER = "Cannot normalize the zero-vector"
const ERR_PARA_ZER = "Cannot determine if zero-vector is parallell to another vector"
const ERR_PERP_ZER = "Cannot determine if zero-vector is perpendicular to another vector"
Variables ¶
This section is empty.
Functions ¶
func DotProduct ¶
func DotProduct(v, w *Vector) complex128
Returns dot product 'v*w'. Panics if 'v' and 'w' differs in dimension. O(n)
func Parallell ¶
Returns whether 'v' and 'w' are perpendicular. If 'v' and 'w' differ in dimension it pads the smaller one with zeroes. Panics if 'v' or 'w' are zero-vectors O(n)
func Perpendicular ¶
Returns whether 'v' and 'w' are perpendicular. Panics if 'v' or 'w' are zero-vectors O(n)
Types ¶
type Matrix ¶
type Matrix [][]complex128
func Zeroes ¶
Returns matrix with specified size filled with zeroes. O(n*m) TODO: Panic if rows or columns == 0
func (*Matrix) Augment ¶
Augments matrix 'm' with matrix 'a'. Panics if sizes are incompatible. O(n*m + p*q)
func (*Matrix) Determinant ¶
func (m *Matrix) Determinant() complex128
Returns determinant of square matrix 'm' Panics if 'm' is not square. TODO: Unsure if works for complex matrices
func (*Matrix) GetColumn ¶
Get column 'index' of matrix 'm' starting at 0. Panics if out of range. O(n)
func (*Matrix) HermitianTranspose ¶
func (m *Matrix) HermitianTranspose()
Transposes and conjugates matrix 'm'. O(n*m)
func (*Matrix) Inverse ¶
func (m *Matrix) Inverse()
Inverses matrix 'm'. Panics if matrix isn't invertible.
func (*Matrix) IsHermitian ¶
Returns whether matrix 'm' is hermitian or not. O(n*m)
func (*Matrix) IsInvertible ¶
Returns whether 'm' is invertible or not.
func (*Matrix) IsSingular ¶
Returns whether 'm' is singular or not. TODO: Defer to recover from singular matrix panic in Determinant()
func (*Matrix) MatrixMultiply ¶
Multiplies matrix 'm' by matrix 'a' O(n^3)
func (*Matrix) RR ¶
func (m *Matrix) RR()
Perform row reduction on matrix 'm'. Panics if singular matrix.
func (*Matrix) RREF ¶
func (m *Matrix) RREF()
Find Row-Reduced Echelon Form of matrix 'm'. Panics if singular matrix.
func (*Matrix) RealString ¶
Return string representation of real matrix 'm' O(n*m)
func (*Matrix) ScalarAdd ¶
func (m *Matrix) ScalarAdd(f complex128)
Adds scalar 'f' to each element in matrix 'm' O(n*m)
func (*Matrix) ScalarMultiply ¶
func (m *Matrix) ScalarMultiply(f complex128)
Multiplies each element in matrix 'm' by scalar 'f' O(n*m)
func (*Matrix) SetColumn ¶
Set column 'index' of matrix 'm' to 'col'. Column index starts at 0. Panics if out of range. O(n)
func (*Matrix) SetRow ¶
Set column 'index' of matrix 'm' to 'row'. Column index starts at 0. Panics if out of range. O(n)
type Vector ¶
type Vector []complex128
func CrossProduct ¶
Returns cross product 'vxw'. Panics if 'v' or 'w' not 3-dimensional. O(1)
func (*Vector) Add ¶
Add 'w' to vector 'v'. Pads vector with zeroes if different sizes O(n), n is highest dimension of 'v', 'w'
func (*Vector) MatrixMultiply ¶
Multiply vector 'v' by matrix 'a'. O(n)
func (*Vector) ScalarMultiply ¶
func (v *Vector) ScalarMultiply(factor complex128)
Multiply 'v' by complex factor. O(n)
Source Files