class LA::BandedMatrix(T)

Overview

banded matrix, heap-allocated

Defined in:

matrix/banded_matrix.cr

Constructors

Class Method Summary

Instance Method Summary

Instance methods inherited from class LA::Matrix(T)

*(k : Number)
*(k : Complex)
*(m : Matrix(T)) *, **(other : Int) **, +(k : Number)
+(k : Complex)
+(m : Matrix(T)) +, -(k : Number | Complex)
-(m : Matrix(T))
- -, /(k : Number | Complex) /, ==(other) ==, [](i : Int32, j : Int32)
[](arows : Range(Int32 | Nil, Int32 | Nil), acolumns : Range(Int32 | Nil, Int32 | Nil))
[](row : Int32, acolumns : Range(Int32 | Nil, Int32 | Nil))
[](arows : Range(Int32 | Nil, Int32 | Nil), column : Int32) [], []=(i : Int32, j : Int32, value)
[]=(arows : Range(Int32, Int32), acolumns : Range(Int32, Int32), value)
[]=(row : Int32, acolumns : Range(Int32, Int32), value)
[]=(nrows : Range(Int32, Int32), column : Int32, value) []=, abs(kind : MatrixNorm = MatrixNorm::Frobenius) abs, add!(k : Number, m : Matrix)
add!(m) add!, add_mult(a, b : Matrix(T), *, alpha = 1.0, beta = 1.0) add_mult, almost_eq(other : Matrix(T), eps)
almost_eq(other : Matrix(T)) almost_eq, assume!(flag : MatrixFlags, value : Bool = true) assume!, balance(*, permute = true, scale = true, separate = false) balance, balance!(*, permute = true, scale = true, separate = false) balance!, cat(other : Matrix(T), axis : Axis) cat, cho_solve(b : self, *, overwrite_b = false) cho_solve, cholesky(*, lower = false, dont_clean = false) cholesky, cholesky!(*, lower = false, dont_clean = false) cholesky!, chop(eps = self.tolerance) chop, clear_flags clear_flags, columns columns, conjt conjt, conjt! conjt!, conjtranspose conjtranspose, coshm coshm, cosm cosm, det(*, overwrite_a = false) det, detect(aflags : MatrixFlags = MatrixFlags::All, eps = tolerance) detect, detect?(aflags : MatrixFlags = MatrixFlags::All, eps = tolerance) detect?, diag(offset = 0) diag, each(*, all = false, &) each, each_index(*, all = false, &) each_index, each_lower(*, diagonal = true, all = false, &) each_lower, each_upper(*, diagonal = true, all = false, &) each_upper, each_with_index(*, all = false, &) each_with_index, eigs(*, left = false, overwrite_a = false)
eigs(*, need_left : Bool, need_right : Bool, overwrite_a = false)
eigs(*, b : Matrix(T), need_left : Bool, need_right : Bool, overwrite_a = false, overwrite_b = false) eigs, eigvals(*, overwrite_a = false) eigvals, expm(*, schur_fact = false) expm, flags : MatrixFlags flags, hcat(other) hcat, hessenberg
hessenberg(*, calc_q = false) hessenberg, hessenberg!
hessenberg!(*, calc_q = false) hessenberg!, inspect(io) inspect, inv inv, inv! inv!, kron(b : Matrix(T)) kron, lq(*, overwrite_a = false) lq, lq_r(*, overwrite_a = false) lq_r, lstsq(b : self, method : LSMethod = LSMethod::Auto, *, overwrite_a = false, overwrite_b = false, cond = -1) lstsq, lu(*, overwrite_a = false) lu, lu_factor : LUMatrix(T) lu_factor, lu_factor! : LUMatrix(T) lu_factor!, map(&) map, map!(&) map!, map_with_index(&) map_with_index, map_with_index!(&) map_with_index!, max(axis : Axis) max, min(axis : Axis) min, ncolumns : Int32 ncolumns, norm(kind : MatrixNorm = MatrixNorm::Frobenius) norm, nrows : Int32 nrows, pinv pinv, product(axis : Axis) product, ql(*, overwrite_a = false) ql, ql_r(*, overwrite_a = false) ql_r, qr(*, overwrite_a = false, pivoting = false) qr, qr_r(*, overwrite_a = false, pivoting = false) qr_r, qr_raw(*, overwrite_a = false, pivoting = false) qr_raw, qz(b, overwrite_a = false, overwrite_b = false) qz, rank(eps = self.tolerance, *, method : RankMethod = RankMethod::SVD, overwrite_a = false) rank, reduce(axis : Axis, initial, &) reduce, repmat(arows, acolumns) repmat, rows rows, rq(*, overwrite_a = false) rq, rq_r(*, overwrite_a = false) rq_r, save_csv(filename) save_csv, scale!(k : Number | Complex) scale!, schur(*, overwrite_a = false) schur, shape shape, sinhm sinhm, sinm sinm, size : Tuple(Int32, Int32) size, solve(b : self, *, overwrite_a = false, overwrite_b = false) solve, solvels(b : self, *, overwrite_a = false, overwrite_b = false, cond = -1) solvels, square? square?, sum(axis : Axis) sum, svd(*, overwrite_a = false) svd, svdvals(*, overwrite_a = false) svdvals, t t, t! t!, tanhm tanhm, tanm tanm, to_custom(io, prefix, columns_separator, rows_separator, postfix)
to_custom(prefix, columns_separator, rows_separator, postfix) to_custom, to_general to_general, to_imag to_imag, to_matlab(io)
to_matlab to_matlab, to_real to_real, to_s(io) to_s, to_unsafe to_unsafe, tolerance tolerance, tr_mult!(a : Matrix(T), *, alpha = 1.0, left = false) tr_mult!, trace trace, transpose transpose, tril(k = 0) tril, tril!(k = 0) tril!, triu(k = 0) triu, triu!(k = 0) triu!, vcat(other) vcat

Class methods inherited from class LA::Matrix(T)

arange(start_val : T, end_val : T, delta = 1.0) arange, block_diag(*args) block_diag, circulant(c) circulant, column(values) column, companion(a) companion, dft(n, scale : DFTScale = DFTScale::None) dft, diag(nrows, ncolumns, value : Number | Complex)
diag(nrows, ncolumns, values)
diag(values)
diag(nrows, ncolumns, &) diag, eye(n) eye, fiedler(values) fiedler, from_custom(str : String, prefix, columns_separator, rows_separator, postfix)
from_custom(io, prefix, columns_separator, rows_separator, postfix) from_custom, from_matlab(s) from_matlab, hadamard(n) hadamard, hankel(column : Indexable | Matrix, row : Indexable | Matrix | Nil = nil) hankel, helmert(n, full = false) helmert, hilbert(n) hilbert, identity(n) identity, invhilbert(n) invhilbert, invpascal(n, kind : PascalKind = PascalKind::Symmetric) invpascal, kron(a, b) kron, leslie(f, s) leslie, load_csv(filename) load_csv, ones(nrows, ncolumns) ones, pascal(n, kind : PascalKind = PascalKind::Symmetric) pascal, rand(nrows, ncolumns, rng = Random::DEFAULT) rand, repmat(a : Matrix(T), nrows, ncolumns) repmat, row(values) row, toeplitz(column : Indexable | Matrix, row : Indexable | Matrix | Nil = nil) toeplitz, tri(nrows, ncolumns, k = 0) tri, zeros(nrows, ncolumns) zeros

Instance methods inherited from module Enumerable(T)

product(initial : Complex)
product(initial : Complex, &) product

Constructor Detail

def self.new(nrows : Int32, ncolumns : Int32, upper_band : Int32, lower_band : Int32, values : Indexable) #

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def self.new(nrows, ncolumns, upper_band, values : Indexable) #

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def self.new(nrows : Int32, ncolumns : Int32, upper_band : Int32, lower_band : Int32 = upper_band, flags : LA::MatrixFlags = MatrixFlags::None) #

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def self.new(nrows : Int32, ncolumns : Int32, upper_band : Int32, lower_band : Int32 = upper_band, flags : LA::MatrixFlags = MatrixFlags::None, &) #

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def self.new(matrix : BandedMatrix) #

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def self.new(matrix : Matrix, tolerance = matrix.tolerance) #

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Class Method Detail

def self.diag(nrows, ncolumns, values) #

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def self.estimate(matrix : Matrix(T), tolerance = matrix.tolerance) #

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def self.rand(nrows, ncolumns, upper_band : Int32, lower_band : Int32, rng : Random = Random::DEFAULT) #

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def self.rand(nrows, ncolumns, upper_band : Int32, rng : Random = Random::DEFAULT) #

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Instance Method Detail

def +(m : BandedMatrix(T)) #

returns element-wise sum


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def +(m : LA::Matrix) #

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def -(m : BandedMatrix(T)) #

returns element-wise subtract


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def -(m : LA::Matrix) #

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def ==(other : BandedMatrix(T)) #

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def add!(k : Number, m : BandedMatrix) #

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def add!(k : Number, m : Matrix) #
Description copied from class LA::Matrix(T)

Perform inplace addition with matrix m multiplied to scalar k

a.add!(k, b) is equal to a = a + k * b, but faster as no new matrix is allocated


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def clone #

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def conjtranspose #

returns conjtransposed matrix


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def det(*, overwrite_a = false) #
Description copied from class LA::Matrix(T)

Calculates determinant for a square matrix

if overwrite_a is true, a will be overriden in process of calculation

Uses getrf LAPACK routine


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def dup #
Description copied from class Reference

Returns a shallow copy of this object.

This allocates a new object and copies the contents of self into it.


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def each_index(*, all = false, &) #
Description copied from class LA::Matrix(T)

Yields every index

all argument controls whether to yield all or non-empty elements for banded\sparse matrices Example: m.each_index { |i, j| m[i, j] = -m[i, j] }


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def flags : MatrixFlags #
Description copied from class LA::Matrix(T)

Returns flags of matrix (see MatrixFlags)


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def flags=(flags : MatrixFlags) #
Description copied from class LA::Matrix(T)

Returns flags of matrix (see MatrixFlags)


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def lower_band : Int32 #

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def lower_band=(value) #

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def map_with_index(&) #
Description copied from class LA::Matrix(T)

Returns result of appliyng block to every element with index


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def map_with_index_complex(&) #

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def map_with_index_f64(&) #
Description copied from class LA::Matrix(T)

TODO - macro magic?


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def ncolumns : Int32 #
Description copied from class LA::Matrix(T)

Returns number of columns in matrix


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def norm(kind : MatrixNorm = MatrixNorm::Frobenius) #

returns matrix norm


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def nrows : Int32 #
Description copied from class LA::Matrix(T)

Returns number of rows in matrix


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def set_bands(aupper, alower) : Nil #

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def solve(b : GeneralMatrix(T), *, overwrite_a = false, overwrite_b = false) #

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def to_unsafe #
Description copied from class LA::Matrix(T)

Returns pointer to underlying data

Storage format depends of matrix type This method raises at runtime if matrix doesn't have raw pointer


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def transpose #

returns transposed matrix


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def transpose! #

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def tril(k = 0) #
Description copied from class LA::Matrix(T)

Same as tril in scipy - returns lower triangular or trapezoidal part of matrix

Returns a matrix with all elements above k-th diagonal zeroed


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def tril!(k = 0) #
Description copied from class LA::Matrix(T)

Works like a tril in scipy - remove all elements above k-diagonal


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def triu(k = 0) #
Description copied from class LA::Matrix(T)

Same as triu in scipy - returns upper triangular or trapezoidal part of matrix

Returns a matrix with all elements below k-th diagonal zeroed


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def triu!(k = 0) #
Description copied from class LA::Matrix(T)

Works like a triu in scipy - remove all elements below k-diagonal


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def unsafe_fetch(i, j) #

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def unsafe_set(i, j, value) #

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def upper_band : Int32 #

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def upper_band=(value) #

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