List of all items
Structs
Enums
Traits
- Cholesky_
- Eig_
- Eigh_
- Lapack
- LeastSquaresSvdDivideConquer_
- OperatorNorm_
- QR_
- Rcond_
- SVDDC_
- SVD_
- Solve_
- Solveh_
- Triangular_
- Tridiagonal_
- error::AsLapackResult
Redirecting to ../../lax/trait.Cholesky_.html...
+ + + \ No newline at end of file diff --git a/lax/eig/trait.Eig_.html b/lax/eig/trait.Eig_.html new file mode 100644 index 00000000..218d77c9 --- /dev/null +++ b/lax/eig/trait.Eig_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.Eig_.html...
+ + + \ No newline at end of file diff --git a/lax/eigh/trait.Eigh_.html b/lax/eigh/trait.Eigh_.html new file mode 100644 index 00000000..44c09209 --- /dev/null +++ b/lax/eigh/trait.Eigh_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.Eigh_.html...
+ + + \ No newline at end of file diff --git a/lax/enum.Diag.html b/lax/enum.Diag.html new file mode 100644 index 00000000..09c52d2c --- /dev/null +++ b/lax/enum.Diag.html @@ -0,0 +1,47 @@ +#[repr(u8)]
+pub enum Diag {
+ Unit,
+ NonUnit,
+}Variants
Unit
NonUnit
Trait Implementations
Auto Trait Implementations
impl RefUnwindSafe for Diag
impl Send for Diag
impl Sync for Diag
impl Unpin for Diag
impl UnwindSafe for Diag
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
+ Enum lax::
source · [−]
Enum lax::EigenVectorFlag
source · [−]#[repr(u8)]
+pub enum EigenVectorFlag {
+ Calc,
+ Not,
+}Expand description
Flag for calculating eigenvectors or not
+Variants
Calc
Not
Implementations
Trait Implementations
sourceimpl Clone for EigenVectorFlag
impl Clone for EigenVectorFlag
sourcefn clone(&self) -> EigenVectorFlag
fn clone(&self) -> EigenVectorFlag
Returns a copy of the value. Read more
+1.0.0 · sourcefn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
Performs copy-assignment from source. Read more
sourceimpl Debug for EigenVectorFlag
impl Debug for EigenVectorFlag
sourceimpl PartialEq<EigenVectorFlag> for EigenVectorFlag
impl PartialEq<EigenVectorFlag> for EigenVectorFlag
impl Copy for EigenVectorFlag
impl Eq for EigenVectorFlag
impl StructuralEq for EigenVectorFlag
impl StructuralPartialEq for EigenVectorFlag
Auto Trait Implementations
impl RefUnwindSafe for EigenVectorFlag
impl Send for EigenVectorFlag
impl Sync for EigenVectorFlag
impl Unpin for EigenVectorFlag
impl UnwindSafe for EigenVectorFlag
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
#[repr(u8)]
+pub enum NormType {
+ One,
+ Infinity,
+ Frobenius,
+}Variants
One
Infinity
Frobenius
Implementations
Trait Implementations
Auto Trait Implementations
impl RefUnwindSafe for NormType
impl Send for NormType
impl Sync for NormType
impl Unpin for NormType
impl UnwindSafe for NormType
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
#[repr(u8)]
+pub enum Transpose {
+ No,
+ Transpose,
+ Hermite,
+}Variants
No
Transpose
Hermite
Implementations
Trait Implementations
Auto Trait Implementations
impl RefUnwindSafe for Transpose
impl Send for Transpose
impl Sync for Transpose
impl Unpin for Transpose
impl UnwindSafe for Transpose
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
#[repr(u8)]
+pub enum UPLO {
+ Upper,
+ Lower,
+}Expand description
Upper/Lower specification for seveal usages
+Variants
Upper
Lower
Implementations
Trait Implementations
Auto Trait Implementations
impl RefUnwindSafe for UPLO
impl Send for UPLO
impl Sync for UPLO
impl Unpin for UPLO
impl UnwindSafe for UPLO
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
#[repr(u8)]
+pub enum UVTFlag {
+ Full,
+ Some,
+ None,
+}Expand description
Specifies how many of the columns of U and rows of Vᵀ are computed and returned.
+For an input array of shape m×n, the following are computed:
+Variants
Full
All m columns of U and all n rows of Vᵀ.
+Some
The first min(m,n) columns of U and the first min(m,n) rows of Vᵀ.
+None
No columns of U or rows of Vᵀ.
+Trait Implementations
impl Copy for UVTFlag
impl Eq for UVTFlag
impl StructuralEq for UVTFlag
impl StructuralPartialEq for UVTFlag
Auto Trait Implementations
impl RefUnwindSafe for UVTFlag
impl Send for UVTFlag
impl Sync for UVTFlag
impl Unpin for UVTFlag
impl UnwindSafe for UVTFlag
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
pub enum Error {
+ LapackInvalidValue {
+ return_code: i32,
+ },
+ LapackComputationalFailure {
+ return_code: i32,
+ },
+ InvalidShape,
+}Variants
LapackInvalidValue
Fields
return_code: i32LapackComputationalFailure
Fields
return_code: i32InvalidShape
Strides of the array is not supported
+Trait Implementations
sourceimpl Error for Error
impl Error for Error
1.30.0 · sourcefn source(&self) -> Option<&(dyn Error + 'static)>
fn source(&self) -> Option<&(dyn Error + 'static)>
The lower-level source of this error, if any. Read more
+sourcefn backtrace(&self) -> Option<&Backtrace>
fn backtrace(&self) -> Option<&Backtrace>
🔬 This is a nightly-only experimental API. (
backtrace)Returns a stack backtrace, if available, of where this error occurred. Read more
+1.0.0 · sourcefn description(&self) -> &str
fn description(&self) -> &str
👎 Deprecated since 1.42.0:
use the Display impl or to_string()
+Auto Trait Implementations
impl RefUnwindSafe for Error
impl Send for Error
impl Sync for Error
impl Unpin for Error
impl UnwindSafe for Error
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
+ Trait lax::
source · [−]
Trait lax::error::AsLapackResult
source · [−]pub trait AsLapackResult {
+ fn as_lapack_result(self) -> Result<()>;
+}Required Methods
fn as_lapack_result(self) -> Result<()>
Implementations on Foreign Types
sourceimpl AsLapackResult for i32
impl AsLapackResult for i32
fn as_lapack_result(self) -> Result<()>
Implementors
Expand description
Linear Algebra eXtension (LAX)
+ndarray-free safe Rust wrapper for LAPACK FFI
+Linear equation, Inverse matrix, Condition number
+As the property of $A$, several types of triangular factorization are used:
+-
+
- LU-decomposition for general matrix
+
-
+
- $PA = LU$, where $L$ is lower matrix, $U$ is upper matrix, and $P$ is permutation matrix +
+ - Bunch-Kaufman diagonal pivoting method for nonpositive-definite Hermitian matrix
+
-
+
- $A = U D U^\dagger$, where $U$ is upper matrix, +$D$ is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. +
+
| matrix type | Triangler factorization (TRF) | Solve (TRS) | Inverse matrix (TRI) | Reciprocal condition number (CON) |
|---|---|---|---|---|
| General (GE) | lu | solve | inv | rcond |
| Symmetric (SY) / Hermitian (HE) | bk | solveh | invh | - |
Eigenvalue Problem
+Solve eigenvalue problem for a matrix $A$
+$$ Av_i = \lambda_i v_i $$
+or generalized eigenvalue problem
+$$ Av_i = \lambda_i B v_i $$
+| matrix type | Eigenvalue (EV) | Generalized Eigenvalue Problem (EG) |
|---|---|---|
| General (GE) | eig | - |
| Symmetric (SY) / Hermitian (HE) | eigh | eigh_generalized |
Singular Value Decomposition (SVD), Least square problem
| matrix type | Singular Value Decomposition (SVD) | SVD with divided-and-conquer (SDD) | Least square problem (LSD) |
|---|---|---|---|
| General (GE) | svd | svddc | least_squares |
Modules
+Structs
+Represents the LU factorization of a tridiagonal matrix A as A = P*L*U.
Result of LeastSquares
+Result of SVD
+Represents a tridiagonal matrix as 3 one-dimensional vectors.
+Enums
+Flag for calculating eigenvectors or not
+Upper/Lower specification for seveal usages
+Specifies how many of the columns of U and rows of Vᵀ are computed and returned.
+Traits
+Wraps *geev for general matrices
Trait for primitive types which implements LAPACK subroutines
+Wraps *gelsd
Wraps *gesvd
Wraps *trtri and *trtrs
Wraps *gttrf, *gtcon and *gttrs
Type Definitions
+
+ Enum lax::
source · [−]
Enum lax::layout::MatrixLayout
source · [−]Variants
C
F
Implementations
sourceimpl MatrixLayout
impl MatrixLayout
pub fn size(&self) -> (i32, i32)
pub fn resized(&self, row: i32, col: i32) -> MatrixLayout
pub fn lda(&self) -> i32
pub fn len(&self) -> i32
pub fn is_empty(&self) -> bool
pub fn same_order(&self, other: &MatrixLayout) -> bool
pub fn toggle_order(&self) -> Self
sourcepub fn t(&self) -> Self
pub fn t(&self) -> Self
Transpose without changing memory representation
+C-contigious row=2, lda=3
+[[1, 2, 3]
+ [4, 5, 6]]and F-contigious col=2, lda=3
+[[1, 4]
+ [2, 5]
+ [3, 6]]have same memory representation [1, 2, 3, 4, 5, 6], and this toggles them.
let layout = MatrixLayout::C { row: 2, lda: 3 };
+assert_eq!(layout.t(), MatrixLayout::F { col: 2, lda: 3 });Trait Implementations
sourceimpl Clone for MatrixLayout
impl Clone for MatrixLayout
sourcefn clone(&self) -> MatrixLayout
fn clone(&self) -> MatrixLayout
Returns a copy of the value. Read more
+1.0.0 · sourcefn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
Performs copy-assignment from source. Read more
sourceimpl Debug for MatrixLayout
impl Debug for MatrixLayout
sourceimpl PartialEq<MatrixLayout> for MatrixLayout
impl PartialEq<MatrixLayout> for MatrixLayout
sourcefn eq(&self, other: &MatrixLayout) -> bool
fn eq(&self, other: &MatrixLayout) -> bool
This method tests for self and other values to be equal, and is used
+by ==. Read more
sourcefn ne(&self, other: &MatrixLayout) -> bool
fn ne(&self, other: &MatrixLayout) -> bool
This method tests for !=.
impl Copy for MatrixLayout
impl Eq for MatrixLayout
impl StructuralEq for MatrixLayout
impl StructuralPartialEq for MatrixLayout
Auto Trait Implementations
impl RefUnwindSafe for MatrixLayout
impl Send for MatrixLayout
impl Sync for MatrixLayout
impl Unpin for MatrixLayout
impl UnwindSafe for MatrixLayout
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
+impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
fn vzip(self) -> V
+ Function lax::
source · [−]
Function lax::layout::square_transpose
source · [−]pub fn square_transpose<T: Copy>(layout: MatrixLayout, a: &mut [T])Expand description
In-place transpose of a square matrix by keeping F/C layout
+Transpose for C-continuous array
+ +let layout = MatrixLayout::C { row: 2, lda: 2 };
+let mut a = vec![1., 2., 3., 4.];
+square_transpose(layout, &mut a);
+assert_eq!(a, &[1., 3., 2., 4.]);Transpose for F-continuous array
+ +let layout = MatrixLayout::F { col: 2, lda: 2 };
+let mut a = vec![1., 3., 2., 4.];
+square_transpose(layout, &mut a);
+assert_eq!(a, &[1., 2., 3., 4.]);Panics
+-
+
- If size of
aandlayoutsize mismatch
+
pub fn transpose<T: Copy>(
layout: MatrixLayout,
input: &[T]
) -> (MatrixLayout, Vec<T>)Expand description
Out-place transpose for general matrix
+Examples
+let layout = MatrixLayout::C { row: 2, lda: 3 };
+let a = vec![1., 2., 3., 4., 5., 6.];
+let (l, b) = transpose(layout, &a);
+assert_eq!(l, MatrixLayout::F { col: 3, lda: 2 });
+assert_eq!(b, &[1., 4., 2., 5., 3., 6.]);let layout = MatrixLayout::F { col: 2, lda: 3 };
+let a = vec![1., 2., 3., 4., 5., 6.];
+let (l, b) = transpose(layout, &a);
+assert_eq!(l, MatrixLayout::C { row: 3, lda: 2 });
+assert_eq!(b, &[1., 4., 2., 5., 3., 6.]);Panics
+-
+
- If input array size and
layoutsize mismatch
+
+ Function lax::
source · [−]
Function lax::layout::transpose_over
source · [−]pub fn transpose_over<T: Copy>(
layout: MatrixLayout,
from: &[T],
to: &mut [T]
) -> MatrixLayoutExpand description
Out-place transpose for general matrix
+Examples
+let layout = MatrixLayout::C { row: 2, lda: 3 };
+let a = vec![1., 2., 3., 4., 5., 6.];
+let mut b = vec![0.0; a.len()];
+let l = transpose_over(layout, &a, &mut b);
+assert_eq!(l, MatrixLayout::F { col: 3, lda: 2 });
+assert_eq!(b, &[1., 4., 2., 5., 3., 6.]);let layout = MatrixLayout::F { col: 2, lda: 3 };
+let a = vec![1., 2., 3., 4., 5., 6.];
+let mut b = vec![0.0; a.len()];
+let l = transpose_over(layout, &a, &mut b);
+assert_eq!(l, MatrixLayout::C { row: 3, lda: 2 });
+assert_eq!(b, &[1., 4., 2., 5., 3., 6.]);Panics
+-
+
- If input array sizes and
layoutsize mismatch
+
Expand description
Memory layout of matrices
+Different from ndarray format which consists of shape and strides, +matrix format in LAPACK consists of row or column size and leading dimension.
+ndarray format and stride
+Let us consider 3-dimensional array for explaining ndarray structure.
+The address of (x,y,z)-element in ndarray satisfies following relation:
shape = [Nx, Ny, Nz]
+ where Nx > 0, Ny > 0, Nz > 0
+stride = [Sx, Sy, Sz]
+
+&data[(x, y, z)] = &data[(0, 0, 0)] + Sx*x + Sy*y + Sz*z
+ for x < Nx, y < Ny, z < NzThe array is called
+-
+
- C-continuous if
[Sx, Sy, Sz] = [Nz*Ny, Nz, 1]
+ - F(Fortran)-continuous if
[Sx, Sy, Sz] = [1, Nx, Nx*Ny]
+
Strides of ndarray [Sx, Sy, Sz] take arbitrary value,
+e.g. it can be non-ordered Sy > Sx > Sz, or can be negative Sx < 0.
+If the minimum of [Sx, Sy, Sz] equals to 1,
+the value of elements fills data memory region and called “continuous”.
+Non-continuous ndarray is useful to get sub-array without copying data.
Matrix layout for LAPACK
+LAPACK interface focuses on the linear algebra operations for F-continuous 2-dimensional array.
+Under this restriction, stride becomes far simpler; we only have to consider the case [1, S]
+This S for a matrix A is called “leading dimension of the array A” in LAPACK document, and denoted by lda.
Enums
+Functions
+In-place transpose of a square matrix by keeping F/C layout
+Out-place transpose for general matrix
+Out-place transpose for general matrix
+Redirecting to ../../lax/struct.LeastSquaresOutput.html...
+ + + \ No newline at end of file diff --git a/lax/least_squares/trait.LeastSquaresSvdDivideConquer_.html b/lax/least_squares/trait.LeastSquaresSvdDivideConquer_.html new file mode 100644 index 00000000..f22e21b4 --- /dev/null +++ b/lax/least_squares/trait.LeastSquaresSvdDivideConquer_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.LeastSquaresSvdDivideConquer_.html...
+ + + \ No newline at end of file diff --git a/lax/opnorm/trait.OperatorNorm_.html b/lax/opnorm/trait.OperatorNorm_.html new file mode 100644 index 00000000..67e3c9e1 --- /dev/null +++ b/lax/opnorm/trait.OperatorNorm_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.OperatorNorm_.html...
+ + + \ No newline at end of file diff --git a/lax/qr/trait.QR_.html b/lax/qr/trait.QR_.html new file mode 100644 index 00000000..3816fd9e --- /dev/null +++ b/lax/qr/trait.QR_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.QR_.html...
+ + + \ No newline at end of file diff --git a/lax/rcond/trait.Rcond_.html b/lax/rcond/trait.Rcond_.html new file mode 100644 index 00000000..ffaf0032 --- /dev/null +++ b/lax/rcond/trait.Rcond_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.Rcond_.html...
+ + + \ No newline at end of file diff --git a/lax/sidebar-items.js b/lax/sidebar-items.js new file mode 100644 index 00000000..2df28d13 --- /dev/null +++ b/lax/sidebar-items.js @@ -0,0 +1 @@ +window.SIDEBAR_ITEMS = {"enum":[["Diag",""],["EigenVectorFlag","Flag for calculating eigenvectors or not"],["NormType",""],["Transpose",""],["UPLO","Upper/Lower specification for seveal usages"],["UVTFlag","Specifies how many of the columns of U and rows of Vᵀ are computed and returned."]],"mod":[["error",""],["layout","Memory layout of matrices"]],"struct":[["LUFactorizedTridiagonal","Represents the LU factorization of a tridiagonal matrix `A` as `A = P*L*U`."],["LeastSquaresOutput","Result of LeastSquares"],["SVDOutput","Result of SVD"],["Tridiagonal","Represents a tridiagonal matrix as 3 one-dimensional vectors."]],"trait":[["Cholesky_",""],["Eig_","Wraps `*geev` for general matrices"],["Eigh_",""],["Lapack","Trait for primitive types which implements LAPACK subroutines"],["LeastSquaresSvdDivideConquer_","Wraps `*gelsd`"],["OperatorNorm_",""],["QR_",""],["Rcond_",""],["SVDDC_",""],["SVD_","Wraps `*gesvd`"],["Solve_",""],["Solveh_",""],["Triangular_","Wraps `*trtri` and `*trtrs`"],["Tridiagonal_","Wraps `*gttrf`, `*gtcon` and `*gttrs`"]],"type":[["Pivot",""]]}; \ No newline at end of file diff --git a/lax/solve/trait.Solve_.html b/lax/solve/trait.Solve_.html new file mode 100644 index 00000000..ebecf200 --- /dev/null +++ b/lax/solve/trait.Solve_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.Solve_.html...
+ + + \ No newline at end of file diff --git a/lax/solveh/trait.Solveh_.html b/lax/solveh/trait.Solveh_.html new file mode 100644 index 00000000..ce928e41 --- /dev/null +++ b/lax/solveh/trait.Solveh_.html @@ -0,0 +1,11 @@ + + + + +Redirecting to ../../lax/trait.Solveh_.html...
+ + + \ No newline at end of file diff --git a/lax/src/alloc.rs b/lax/src/alloc.rs deleted file mode 100644 index 63458818..00000000 --- a/lax/src/alloc.rs +++ /dev/null @@ -1,78 +0,0 @@ -use cauchy::*; -use std::mem::MaybeUninit; - -/// Helper for getting pointer of slice -pub(crate) trait AsPtr: Sized { - type Elem; - fn as_ptr(vec: &[Self]) -> *const Self::Elem; - fn as_mut_ptr(vec: &mut [Self]) -> *mut Self::Elem; -} - -macro_rules! impl_as_ptr { - ($target:ty, $elem:ty) => { - impl AsPtr for $target { - type Elem = $elem; - fn as_ptr(vec: &[Self]) -> *const Self::Elem { - vec.as_ptr() as *const _ - } - fn as_mut_ptr(vec: &mut [Self]) -> *mut Self::Elem { - vec.as_mut_ptr() as *mut _ - } - } - }; -} -impl_as_ptr!(i32, i32); -impl_as_ptr!(f32, f32); -impl_as_ptr!(f64, f64); -impl_as_ptr!(c32, lapack_sys::__BindgenComplex