kaleidic.lubeck

Public Imports

mir.lapack

public import mir.lapack : lapackint;

Members

Aliases

BlasType

alias BlasType(Iterators...) = CommonType!(staticMap!(IterationType, Iterators))

Gets the type that can be used with Blas routines that all types can be implicitly converted to.

Enums

fastmath

anonymousenum fastmath

Undocumented in source.

Functions

choleskyDecomp

auto choleskyDecomp(char uplo, Slice!(Iterator, 2, kind) a)

Computs Cholesky decomposition of symmetric positive definite matrix 'A'. The factorization has the form: \A = U**T * U, if UPLO = 'U', or \A = L * L**T, if UPLO = 'L' Where U is an upper triangular matrix and L is lower triangular.

choleskySolve

auto choleskySolve(char uplo, Slice!(IteratorC, 2, Canonical) c, Slice!(IteratorB, N, kindB) b)

Solves a system of linear equations A * X = B with a symmetric matrix A using the Cholesky factorization: \A = U**T * U or \A = L * L**T computed by choleskyDecomp.

cov

Slice!(BlasType!Iterator*, 2) cov(Slice!(Iterator, 2, kind) matrix)

Covariance matrix.

det

auto det(Slice!(Iterator, 2, kind) a)

Matrix determinant.

detSymmetric

auto detSymmetric(char store, Slice!(Iterator, 2, kind) a)

Matrix determinant.

eigSymmetric

auto eigSymmetric(char store, Slice!(Iterator, 2, kind) a)

Eigenvalues and eigenvectors of symmetric matrix.

inv

auto inv(Slice!(Iterator, 2, kind) a)

Calculates the inverse of a matrix.

ldlDecomp

auto ldlDecomp(char uplo, Slice!(Iterator, 2, kind) a)

Computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The for of the factorization is: \A = L*D*L**T Where L is product if permutation and unit lower triangular matrices, and D is symmetric and block diagonal with '1 x 1' and '2 x 2' diagonal blocks.

ldlSolve

auto ldlSolve(char uplo, Slice!(IteratorA, 2, Canonical) a, Slice!(lapackint*) ipiv, Slice!(IteratorB, N, kindB) b)

Solves a system of linear equations \A * X = B with symmetric matrix 'A' using the factorization \A = U * D * U**T, or \A = L * D * L**T computed by ldlDecomp.

luDecomp

auto luDecomp(Slice!(Iterator, 2, kind) a)

Computes LU factorization of a general 'M x N' matrix 'A' using partial pivoting with row interchanges. The factorization has the form: \A = P * L * U Where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

luSolve

auto luSolve(char trans, Slice!(IteratorLU, 2, Canonical) lut, Slice!(lapackint*) ipiv, Slice!(IteratorB, N, kindB) b)

Solves a system of linear equations \A * X = B, or \A**T * X = B with a general 'N x N' matrix 'A' using the LU factorization computed by luDecomp.

mldivide

Slice!(BlasType!(IteratorA, IteratorB)*, 2) mldivide(Slice!(IteratorA, 2, kindA) a, Slice!(IteratorB, 2, kindB) b)

Slice!(BlasType!(IteratorA, IteratorB)*) mldivide(Slice!(IteratorA, 2, kindA) a, Slice!(IteratorB, 1, kindB) b)

Solve systems of linear equations AX = B for X. Computes minimum-norm solution to a linear least squares problem if A is not a square matrix.

mtimes

Slice!(BlasType!(IteratorA, IteratorB)*, 2) mtimes(Slice!(IteratorA, 2, kindA) a, Slice!(IteratorB, 2, kindB) b)

General matrix-matrix multiplication. Allocates result to an uninitialized slice using GC.

mtimes

Slice!(BlasType!(IteratorA, IteratorB)*) mtimes(Slice!(IteratorA, 2, kindA) a, Slice!(IteratorB, 1, kindB) b)

General matrix-matrix multiplication. Allocates result to an uninitialized slice using GC.

mtimes

Slice!(BlasType!(IteratorA, IteratorB)*) mtimes(Slice!(IteratorB, 1, kindB) a, Slice!(IteratorA, 2, kindA) b)

General matrix-matrix multiplication.

mtimes

CommonType!(BlasType!IteratorA, BlasType!IteratorB) mtimes(Slice!(IteratorB, 1, kindB) a, Slice!(IteratorA, 1, kindA) b)

Vector-vector multiplication (dot product).

pca

auto pca(Slice!(Iterator, 2, kind) matrix, Flag!"centerColumns" cc)

Principal component analysis of raw data.

pinv

Slice!(BlasType!Iterator*, 2) pinv(Slice!(Iterator, 2, kind) matrix, double tolerance)

Computes Moore-Penrose pseudoinverse of matrix.

qrDecomp

auto qrDecomp(Slice!(Iterator, 2, kind) a)

Computes a QR factorization of matrix 'a'.

qrSolve

auto qrSolve(Slice!(IteratorA, 2, Canonical) a, Slice!(IteratorT) tau, Slice!(IteratorB, N, kindB) b)

Solve the least squares problem: \min ||A * X - B|| Using the QR factorization: \A = Q * R computed by qrDecomp.

svd

auto svd(Slice!(Iterator, 2, kind) matrix, Flag!"slim" slim)

Computes the singular value decomposition.

Structs

EigSymmetricResult

struct EigSymmetricResult(T)

Eigenvalues and eigenvectors POD.

LDLResult

struct LDLResult(T)

Consist LDL factorization;

LUResult

struct LUResult(T)

LUResult consist lu factorization.

PcaResult

struct PcaResult(T)

Principal component analises result.

QRResult

struct QRResult(T)

SvdResult

struct SvdResult(T)

choleskyResult

struct choleskyResult(T)

Undocumented in source.

Templates

CommonType

template CommonType(A)

Undocumented in source.

CommonType

template CommonType(A, B)

Undocumented in source.

• lubeck
• lubeck2