rust-ndarray/ndarray-linalg

Linear algebra package for rust-ndarray using LAPACK binding

ndarray-linalg's Issues

You code does not work on mac os

You code does not work on mac os

= note: ld: library not found for -lgfortran
clang: error: linker command failed with exit code 1 (use -v to see invocation)

How do I resolve? Or is this codebase no longer valid

Random array for integers

ndarray_linalg::generate::random only supports f32, f64, c32, and c64. It should use rand::Rand trait
https://doc.rust-lang.org/rand/rand/trait.Rand.html

Write Test for eigh()

• write test
• add test phase on werker

Support ArrayView or ArrayBase

I have no idea for supporting LAPACK binding to general ArrayBase.

Suggestions for cross compiling to armv7-unknown-linux-gnueabihf

cargo build works correctly on my host using features=["openblas"]. However, when cross compiling to armv7-unknown-linux-gnueabihf, I get the following (truncated) error:

error: linking with `arm-linux-gnueabihf-gcc` failed: exit code: 1
= note: /target/armv7-unknown-linux-gnueabihf/debug/deps/libopenblas_src-75b3c950014242b8.rlib: error adding symbols: File format not recognized

I assumed the openblas-src crate would have taken care of acquiring the correct armv7 libs, but it looks like I'm mistaken. Any suggestions? Should I take my question to openblas-src?

Eigenvalue analysis for general matrices

As argued in #29

test cholesky_solve ... FAILED

Sometimes this test fails
https://app.wercker.com/termoshtt/ndarray-linalg/runs/test-openblas/59f195128e888f0001cf3ef5?step=59f19584791109000146172c

Support macOS with OpenBLAS/Netlib backend

macOS CI has been introduced at #141 only intel-mkl. backend.

TODO

• Create a compilable environment on macOS virtual machine with gfortran and cmake

make UPLO and Transpose are private

Related to #66 #70
Some are removed in v0.6

qr_mut is lacking

assert_close_l2! cannot be called without `use ndarray_linalg::*`

Compiling error using `det()` method

I have this error using the det() method in a function

undefined reference to `LAPACKE_dgetrf`

in Archlinux

Thanks in advance

Krylov subspace methods, Arnoldi method

Arnoldi method is a fundamental component of Krylov subspace method, which is used in sparse matrix context. However, the idea of Arnoldi method can be extended to general linear operators.

TODO

• Iterative QR decomposition #150
  • modified Gram-Schmit #149
  • Householder #154
• Interface of Arnoldi #155
• Implement GMRES (as an example and test)

Development discussion and dashboard

Any suggestions are welcome :)

Algorithms to be implemented

• eig: Eigenvalue analysis for general matrix (#40)
• outer: Outer product
• deth: Determinant for Hermite/Symmetric matrices
• dmd: Dynamics mode decomposition
• pca: Principal components analysis

Default Backend

Related: #102, #103

The default backend features is omitted at version 0.8 when we switch to LAPACKE implementation.
See also how BLAS/LAPACK wrappers select their backend: https://github.com/blas-lapack-rs/blas-lapack-rs.github.io/wiki
Current empty default feature causes an issue as reported in #102, we cannot run cargo test without specifying the backend. The merit of empty default is that we can avoid duplicated dependencies.

Feature for switching BLAS/LAPACK backend

lapack has switch to select the LAPACK backend.
https://github.com/stainless-steel/lapack/blob/master/Cargo.toml

Add `expm` (exponential matrix) implementation

https://en.wikipedia.org/wiki/Matrix_exponential

Move to rust-ndarray organization?

Related to rust-ndarray/ndarray#424

Rename *_mut to *_inplace and change return type

Methods that modify the input array in-place, such as solve_mut and cholesky_mut, would be better named *_inplace, such as solve_inplace and cholesky_inplace, to maintain consistency with ndarray. (See ArrayBase::map_inplace and ArrayBase::mapv_inplace.) Additionally, it would be clearer for those methods not to return a reference to the array that is being modified. In other words, I suggest changing:

fn solve_mut<'a, Sb: DataMut<Elem = A>>(&self, b: &'a mut ArrayBase<Sb, Ix1>) -> Result<&'a mut ArrayBase<Sb, Ix1>>;

to

fn solve_inplace<'a, Sb: DataMut<Elem = A>>(&self, b: &'a mut ArrayBase<Sb, Ix1>) -> Result<()>;

and

fn cholesky_mut(&mut self, uplo: UPLO) -> Result<&mut Self>;

to

fn cholesky_inplace(&mut self, uplo: UPLO) -> Result<()>;

etc.

What do you think? I can submit a PR with this change.

Complete QR-decomposition

Consider the following code

let a = arr2(&[[1.], [0.]]);
let (q, r) = a.qr().unwrap();
println!("q = {}", q);
println!("r = {}", r);

The output is

q = [[1],
 [0]]
r = [[1]]

however I was expecting q to be of size 2 x 2 and r of size 2 x 1.
For instance, in Matlab, [q, r] = qr([1; 0]) prints

q =

   1   0
  -0   1

r =

   1
   0

Generators for specific matrices

LAPACK bindings

Implement basic subroutines:

• lu: LU factorization
• qr: QR factorization
• cholesky: Cholesky decomposition
• svd: singular-value decomposition (SVD)
• inv: inverse matrix
• eig: eigenvalue analysis for general matrix
• eigh: eigenvalue analysis for Hermite matrix
• norm_{1,i,f}: norms of matrix
• ssqrt: symmetric square root of Hermite matrix

General Dot

ndarray::linalg::Dot is limited to use Array and the RHS must be reference. We can loosen this restriction, and more general Dot should be defined in this crate.

SVD segfaults on 2x2 matrices

https://github.com/bbrener1/dylib_linking_test

Minimum reproducible case in repo above

When SVD is performed on a 2x2 matrix, for example a an identity matrix containing f64s, the program terminates with a segfault.

I have reproduced this bug on Ubuntu and OSX, and have reproduced it using Intel-MKL and OpenBlas backends.

Bug is also apparent in a docker container using run -it rust:latest, so versioning is unlikely to be at issue.

Please see if you can reproduce and track down the cause

blas in ndarray

ndarray needs the "blas" feature to enable using blas for its matrix multiplication (and dot product).

That feature enables calling blas without explicitly picking any particular backend.

Picking backend is tricky in general; indeed none of our libraries should pick one, but enable the end user, final application, to pick the blas/lapack provider.

I was made aware of this crate today, and feel free to report any issues with upstream ndarray. Please note that it's best to migrate to the Ix1, Ix2 etc dimensionality type aliases, for compatibility with future versions.

Add Examples

det_empty test fail

https://circleci.com/gh/termoshtt/ndarray-linalg/124

Intel MKL ERROR: Parameter 4 was incorrect on entry to DGETRF.
test det_empty ... FAILED
test det_zero_nonsquare ... ok
test det_zero ... ok
test det_nonsquare ... ok
test det ... ok

failures:

---- det_empty stdout ----
thread 'det_empty' panicked at 'called `Result::unwrap()` on an `Err` value: Lapack { return_code: -5 }', src/libcore/result.rs:997:5
note: Run with `RUST_BACKTRACE=1` environment variable to display a backtrace.


failures:
    det_empty

Intel MKL ERROR: Parameter 4 was incorrect on entry to DGETRF.

Parameter 4 is LDA and 0 is passed, but LDA must be lager than 1.

Matrix on Complex numbers

Inherited from #17

Current code only supports real numbers, i.e. f32 and f64.
Some algorithm in the linear algebra are closed in real number, but others are not.

Create module for test

There are many duplicated codes in tests/ directory

Fill lower part of matrix in SolveH

Related to #76

• SolveH does not fill the lower matrix while others (e.g. EigH) fill.
• Test for SolveH is missing

Methods for Hermite matrices

Following features are lacking:

• inverse matrix of Hermite matrix: invh, invh_into
• solve for Hermite matrix: solveh, factorizeh

Use LAPACK instead of LAPACKE

Note that using row-major ordering may require more memory and time than column-major ordering, because the routine must transpose the row-major order to the column-major order required by the underlying LAPACK routine.

http://www.netlib.org/lapack/lapacke.html

I found while implementing rust-ndarray/ndarray#445 that the interface between CBLAS and LAPACKE around UPLO and other parameter are incompatible. I will use BLAS instead of CBLAS for it since the interface of BLAS is compatible with LAPACK (use u8 always). We should use LAPACK instead of LAPACKE (´・ω・｀)

Scalar Operations

Float and Complex traits in num crate support same functions, e.g. sin, ln, and so on.
Since real number can be regarded as a complex number naturally, all methods for Complex can be implemented for Scalar.

Outer product

Restore outer product removed in #41

Buffer overflow on shape mismatch

Some functions (including solve_inplace but probably many others) are missing checks that the input arrays have matching shapes. As a result, the current implementation of solve_inplace can lead to buffer overflow if the shapes don't match (e.g. if the number of rows in b is less than the number of rows/columns in a).

Example with ndarray 0.12 and ndarray-linalg 0.10:

extern crate ndarray;
extern crate ndarray_linalg;

use ndarray::array;
use ndarray::prelude::*;
use ndarray_linalg::solve::Solve;

fn main() {
    let a = array![[1., 2.], [3., 4.]];
    let mut b = array![1.];

    // This is a read of uninitialized memory one past the end of `b`. This is
    // undefined behavior, but the point of this print statement is to show
    // that calling `a.solve_inplace(&mut b)` changes the value of the element
    // one past the end of `b`.
    //
    // On my system, this prints `0`, but it could print anything because the
    // memory is uninitialized.
    println!("{}", unsafe { *b.as_ptr().wrapping_offset(1) } );

    // This should panic or return an error because `a` is `2x2` and `b` has
    // length `1`.
    a.solve_inplace(&mut b).unwrap();

    // Prints `[-1.9999999999999998]` on my system, which corresponds to the
    // first element in the solution if `b` was `array![1., 0.]`.
    println!("{}", b);

    // This is another read of uninitialized memory one past the end of `b`.
    // This is undefined behavior, but the point of this print statement is to
    // show that calling `a.solve_inplace(&mut b)` changes the value of the
    // element one past the end of `b`.
    //
    // On my system, this prints `1.4999999999999998`, which corresponds to the
    // second element in the solution if `b` was `array![1., 0.]`.
    println!("{}", unsafe { *b.as_ptr().wrapping_offset(1) } );
}

Remove prelude module

Compilation on windows fails

Hallo rustaceans, so I am having an issue compiling this library on windows.

Here is what is happening. I am trying to use ndarray-linalg with ndarray to compute some inverses. So I added ndarray-linalg to dependencies in cargo.toml , and I also added openblas-src and included both as extern crates in my main. Here is what that looks like in code:

MY TOML:

[package]
name = "kalman"
version = "0.1.0"
authors = ["VanioBegic <[email protected]>"]
edition = "2018"

[dependencies]
ndarray = "0.12.1"
ndarray-linalg = "0.10"
openblas-src = "0.7.0"

MY EXTERN CRATES:

extern crate ndarray;
extern crate ndarray_linalg;
extern crate openblas_src;

With stable-gnu toolchain I get :

     Running `rustc --edition=2018 --crate-name kalman src\main.rs --color always --crate-type bin --emit=dep-info,link
-C debuginfo=2 -C metadata=3ba5ee5205741b31 -C extra-filename=-3ba5ee5205741b31 --out-dir D:\rust\kalman\target\debug\de
ps -C incremental=D:\rust\kalman\target\debug\incremental -L dependency=D:\rust\kalman\target\debug\deps --extern ndarra
y=D:\rust\kalman\target\debug\deps\libndarray-3abb85534de560ac.rlib --extern ndarray_linalg=D:\rust\kalman\target\debug\
deps\libndarray_linalg-837a2f143f8d01ff.rlib --extern openblas_src=D:\rust\kalman\target\debug\deps\libopenblas_src-98bd
3a2195e9d264.rlib -L native=C:\Users\py-goku\.cargo\registry\src\github.com-1ecc6299db9ec823\winapi-x86_64-pc-windows-gn
u-0.4.0\lib -L D:/rust/kalman/target/debug/build/openblas-src-f55a152752440e9e/out\opt/OpenBLAS/lib`
warning: unused variable: `meas`
  --> src\main.rs:11:9
   |
11 |     let meas: Array1<f64> = array![1., 0., 0., 0.];
   |         ^^^^ help: consider prefixing with an underscore: `_meas`
   |
   = note: #[warn(unused_variables)] on by default

error: linking with `gcc` failed: exit code: 1
  |
  = note: "gcc" "-Wl,--enable-long-section-names" "-fno-use-linker-plugin" "-Wl,--nxcompat" "-nostdlib" "-m64" "C:\\User
s\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\crt2.o" "C:\\Us
ers\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\rsbegin.o" "-
L" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib" "D:
\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.102bwz4cwkffz5vr.rcgu.o" "D:\\rust\\kalman\\target\\debug\\
deps\\kalman-3ba5ee5205741b31.12v645j3ed9vrayd.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.1
6isqldkpweo3rur.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.19slj34d2n53xkag.rcgu.o" "D:\\ru
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0b1ftzhvbs8.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.1oe1wuyo9u1furts.rcgu.o" "D:\\rust\\
kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.1oh0kko3nivgxo4g.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\ka
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w595mwz.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.1ycderw9dyln7txc.rcgu.o" "D:\\rust\\kalm
an\\target\\debug\\deps\\kalman-3ba5ee5205741b31.21gxnztygpshb3j3.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman
-3ba5ee5205741b31.23aglk462cweq2tu.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.25jhqgnco7q8c
e6l.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.28kn6i6qj0xoc7ih.rcgu.o" "D:\\rust\\kalman\\
target\\debug\\deps\\kalman-3ba5ee5205741b31.2d335ex5ci33x0mu.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba
5ee5205741b31.2mbo2q1by6etfp1v.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.2o3xqkkxkz4hk56d.
rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.2oreuwq78gy19k4p.rcgu.o" "D:\\rust\\kalman\\targ
et\\debug\\deps\\kalman-3ba5ee5205741b31.2s0woql8r85jpm93.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5
205741b31.2syhpmbs0vt23e9e.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.2xmrc77t5vpuds2v.rcgu
.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.2y0eikb0ni9mvbuh.rcgu.o" "D:\\rust\\kalman\\target\\
debug\\deps\\kalman-3ba5ee5205741b31.322s0azx0gvb6foz.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee52057
41b31.3274hbhvixc0fczt.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.360iu1b8mfs2nysh.rcgu.o"
"D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.36yroxof3ov7rqre.rcgu.o" "D:\\rust\\kalman\\target\\debu
g\\deps\\kalman-3ba5ee5205741b31.38kyfr76uj2a2bza.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b3
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\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.3gb6svwqmw2d3cuv.rcgu.o" "D:\\rust\\kalman\\target\\debug\\d
eps\\kalman-3ba5ee5205741b31.3npev0sfva8zu3rl.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.3u
4nqwy6op7z7z3p.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.432otjgawcbviyn0.rcgu.o" "D:\\rus
t\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.43f2vnho2v4js9zn.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\
\kalman-3ba5ee5205741b31.44dho71mqna2nsji.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4m1wx1
nlnneqswvs.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4mu15vejcyr6v0ak.rcgu.o" "D:\\rust\\k
alman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4pfvogc8v3bidymm.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kal
man-3ba5ee5205741b31.4rmsuic72egughkf.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4vl37wzs3p
aztefe.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4w7xz6zu7lkiyx9n.rcgu.o" "D:\\rust\\kalma
n\\target\\debug\\deps\\kalman-3ba5ee5205741b31.4xatvkvk6hhumofn.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-
3ba5ee5205741b31.527sx3hb26ryx334.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.54pg963me85rnq
0j.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.62a08qibvfulcfp.rcgu.o" "D:\\rust\\kalman\\ta
rget\\debug\\deps\\kalman-3ba5ee5205741b31.9jf9aw94plte2d2.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee
5205741b31.cramvzkpulzdyt3.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.dlwfetkynhnb8dp.rcgu.
o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.jxoz41mcrc3c5a4.rcgu.o" "D:\\rust\\kalman\\target\\de
bug\\deps\\kalman-3ba5ee5205741b31.tlpcufstnrcyjhv.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b
31.tqza18r74x5zojf.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.u8dbchyx23lmf04.rcgu.o" "D:\\
rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.wn17a3u9d8xnqvi.rcgu.o" "D:\\rust\\kalman\\target\\debug\\dep
s\\kalman-3ba5ee5205741b31.xr1bibrv3g4cpex.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.zwnpc
s8vp2qvpeu.rcgu.o" "-o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-3ba5ee5205741b31.exe" "D:\\rust\\kalman\\target\\
debug\\deps\\kalman-3ba5ee5205741b31.25gr5761hlccinua.rcgu.o" "-Wl,--gc-sections" "-nodefaultlibs" "-L" "D:\\rust\\kalma
n\\target\\debug\\deps" "-L" "C:\\Users\\py-goku\\.cargo\\registry\\src\\github.com-1ecc6299db9ec823\\winapi-x86_64-pc-w
indows-gnu-0.4.0\\lib" "-L" "D:/rust/kalman/target/debug/build/openblas-src-f55a152752440e9e/out\\opt/OpenBLAS/lib" "-L"
 "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib" "-Wl,
-Bstatic" "D:\\rust\\kalman\\target\\debug\\deps\\libopenblas_src-98bd3a2195e9d264.rlib" "D:\\rust\\kalman\\target\\debu
g\\deps\\libndarray_linalg-837a2f143f8d01ff.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\librand-86be185ec55e8bfa.rlib"
 "D:\\rust\\kalman\\target\\debug\\deps\\libwinapi-700386b500e7fb4f.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libran
d_core-eb435bcd66f10ec7.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\librand_core-38a8cdd77640f568.rlib" "D:\\rust\\kal
man\\target\\debug\\deps\\liblapacke-85b05e19e76f0926.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\liblapacke_sys-0de30
ba7859d1867.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libndarray-3abb85534de560ac.rlib" "D:\\rust\\kalman\\target\\d
ebug\\deps\\libnum_complex-82363a479edd90b7.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libnum_traits-553d440d3fe42740
.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libitertools-18b588cfb0c0e6f0.rlib" "D:\\rust\\kalman\\target\\debug\\dep
s\\libeither-5ee002a6bfa0d5e3.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libmatrixmultiply-e5bbb7c57020595e.rlib" "D:
\\rust\\kalman\\target\\debug\\deps\\librawpointer-419e217115828537.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libbla
s_src-2127476f8a7e5e4a.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libcblas_sys-124fa1b3851d4c83.rlib" "D:\\rust\\kalm
an\\target\\debug\\deps\\liblibc-08ef32ba80f20c5a.rlib" "-Wl,--start-group" "C:\\Users\\py-goku\\.rustup\\toolchains\\st
able-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\libstd-744703a485660c1e.rlib" "C:\\Users\\py-goku\
\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\libpanic_unwind-28c855288f
12d465.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu
\\lib\\libbacktrace_sys-1f1894ea56815eb1.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\l
ib\\rustlib\\x86_64-pc-windows-gnu\\lib\\librustc_demangle-54d77c07f0360832.rlib" "C:\\Users\\py-goku\\.rustup\\toolchai
ns\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\libunwind-4a1182a5162d96f6.rlib" "C:\\Users\
\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\liblibc-f110a63e7
9ca9506.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gn
u\\lib\\liballoc-72088863526c7b10.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rus
tlib\\x86_64-pc-windows-gnu\\lib\\librustc_std_workspace_core-8bdc5136c286e0c9.rlib" "C:\\Users\\py-goku\\.rustup\\toolc
hains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\libcore-493ddf3b73736766.rlib" "-Wl,--end
-group" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib
\\libcompiler_builtins-7bd2330f2cf0f215.rlib" "-Wl,-Bdynamic" "-lgfortran" "-lopenblas" "-lwinapi_advapi32" "-lwinapi_cr
edui" "-lwinapi_kernel32" "-lwinapi_secur32" "-ladvapi32" "-lws2_32" "-luserenv" "-Wl,-Bstatic" "-lgcc_eh" "-lpthread" "
-Wl,-Bdynamic" "-lmingwex" "-lmingw32" "-lgcc" "-lmsvcrt" "-lmsvcrt" "-luser32" "-lkernel32" "C:\\Users\\py-goku\\.rustu
p\\toolchains\\stable-x86_64-pc-windows-gnu\\lib\\rustlib\\x86_64-pc-windows-gnu\\lib\\rsend.o"
  = note: ld: cannot find -lgfortran


error: aborting due to previous error

error: Could not compile `kalman`.

Caused by:
  process didn't exit successfully: `rustc --edition=2018 --crate-name kalman src\main.rs --color always --crate-type bi
n --emit=dep-info,link -C debuginfo=2 -C metadata=3ba5ee5205741b31 -C extra-filename=-3ba5ee5205741b31 --out-dir D:\rust
\kalman\target\debug\deps -C incremental=D:\rust\kalman\target\debug\incremental -L dependency=D:\rust\kalman\target\deb
ug\deps --extern ndarray=D:\rust\kalman\target\debug\deps\libndarray-3abb85534de560ac.rlib --extern ndarray_linalg=D:\ru
st\kalman\target\debug\deps\libndarray_linalg-837a2f143f8d01ff.rlib --extern openblas_src=D:\rust\kalman\target\debug\de
ps\libopenblas_src-98bd3a2195e9d264.rlib -L native=C:\Users\py-goku\.cargo\registry\src\github.com-1ecc6299db9ec823\wina
pi-x86_64-pc-windows-gnu-0.4.0\lib -L D:/rust/kalman/target/debug/build/openblas-src-f55a152752440e9e/out\opt/OpenBLAS/l
ib` (exit code: 1)

With stable-msvc toolchain I get:

     Running `rustc --edition=2018 --crate-name kalman src\main.rs --color always --crate-type bin --emit=dep-info,link -C debuginfo=2 -C metadata=a95edc84d22c3dfb -C extra-filename=-a95edc84d22c3dfb --out-dir D:\rust\kalman\target\debug\deps -C incremental=D:\rust\kalma
n\target\debug\incremental -L dependency=D:\rust\kalman\target\debug\deps --extern ndarray=D:\rust\kalman\target\debug\deps\libndarray-92e0395f476950e1.rlib --extern ndarray_linalg=D:\rust\kalman\target\debug\deps\libndarray_linalg-6df84c958c2578c8.rlib --extern openblas
_src=D:\rust\kalman\target\debug\deps\libopenblas_src-016fb3f34a35b405.rlib -L D:/rust/kalman/target/debug/build/openblas-src-a9fb8b5975a41b99/out\opt/OpenBLAS/lib`
warning: unused variable: `meas`
  --> src\main.rs:11:9
   |
11 |     let meas: Array1<f64> = array![1., 0., 0., 0.];
   |         ^^^^ help: consider prefixing with an underscore: `_meas`
   |
   = note: #[warn(unused_variables)] on by default

error: linking with `link.exe` failed: exit code: 1181
  |
  = note: "C:\\Program Files (x86)\\Microsoft Visual Studio 14.0\\VC\\bin\\amd64\\link.exe" "/NOLOGO" "/NXCOMPAT" "/LIBPATH:C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib" "D:\\rust\\kalman\\target\\debug
\\deps\\kalman-a95edc84d22c3dfb.122vu3aswteipqb1.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.13n2vnuws66j8mdj.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.18s60t46xaif3zvh.rcgu.o" "D:\\rust\\kalman\\target\\debug\\de
ps\\kalman-a95edc84d22c3dfb.1b2yvh7shw587of6.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1ei9wegjtim2kqzm.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1fcfzl6oev6xtzn2.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\
kalman-a95edc84d22c3dfb.1g4ggp65vsdblzgl.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1giie7bs78k2xt7g.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1mr47t1oyy5rsiji.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalm
an-a95edc84d22c3dfb.1ruoctt7ijlljoa6.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1uqshpy4sa4v8an5.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.1vsy0yg9o5par3rq.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a
95edc84d22c3dfb.1x6x3ihj3p13mkpl.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.267zx13kij34u4gt.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.28z5jtqzf4zk6a0a.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95ed
c84d22c3dfb.2bxn7d495r83on0.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.2cx67c2sbouecr3a.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.2lnkm8nbhamz2ufu.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d2
2c3dfb.2nkqt0oi23x4dkb2.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.2r3702bguifhe1jl.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.2wmpnjhzx5ckvomx.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3d
fb.2x9yfmm614o259ap.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.2z0546q3cydrchmp.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.316d728p18tkmmro.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3
a2ku7c0vf58tous.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3cx29zlj5pu8cuam.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3ed27cw63udeet3a.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3foqq
kqh31cmszrd.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3lqkhyitdp1nktxu.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3svekdg01vbp0bpx.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3tcg78kh8
idwv97l.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.3zv7fin0xq29c9p.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.40xcvq6efvpjc1p0.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4fhamr92tvi952
1c.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4i1nreuqah7u98m.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4onj8ou682kjo2i8.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4qy0lcg90jnqzi0c.rc
gu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4sdn6qh9f71x312t.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4sf841ra9wnj9x20.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4tj3u3whifcu6itg.rcgu.o
" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4uxpa4iussens7p4.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4v417z274elxthgp.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.4ykvifozynxio5sa.rcgu.o" "D
:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.53pnp4acasjjvyae.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.53zvmjwduisgidcn.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.56ggjxtlgj7yd2ox.rcgu.o" "D:\\r
ust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.5aikzwzau7elumzl.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.5bvixrabzl8kcjxo.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.5cglmdh2g96jcky7.rcgu.o" "D:\\rust\
\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.cc6kpbki57wosm1.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.e4ki9k9ygqbxw4r.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.ehx25eu8sfjc690.rcgu.o" "D:\\rust\\kalman
\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.esvadvlq5jzkjv.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.jhh6ixa44l796ko.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.jstaw6vryzqt12p.rcgu.o" "D:\\rust\\kalman\\target
\\debug\\deps\\kalman-a95edc84d22c3dfb.y5xv86bej16ece7.rcgu.o" "D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.ykgc0dyjx9fo2jc.rcgu.o" "/OUT:D:\\rust\\kalman\\target\\debug\\deps\\kalman-a95edc84d22c3dfb.exe" "D:\\rust\\kalman\\target\\debug\\deps\\kalman
-a95edc84d22c3dfb.4p8ztpguotmgsgor.rcgu.o" "/OPT:REF,NOICF" "/DEBUG" "/NATVIS:C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\etc\\intrinsic.natvis" "/NATVIS:C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib
\\rustlib\\etc\\liballoc.natvis" "/NATVIS:C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\etc\\libcore.natvis" "/LIBPATH:D:\\rust\\kalman\\target\\debug\\deps" "/LIBPATH:D:/rust/kalman/target/debug/build/openblas-src-a9fb8b5975a41b99
/out\\opt/OpenBLAS/lib" "/LIBPATH:C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib" "D:\\rust\\kalman\\target\\debug\\deps\\libopenblas_src-016fb3f34a35b405.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\lib
ndarray_linalg-6df84c958c2578c8.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\librand-56bb68fe717a7c52.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libwinapi-4124b515ecc34851.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\librand_core-dd076e771b70d107.rlib" "D:\\rust\\ka
lman\\target\\debug\\deps\\librand_core-095a947572badebd.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\liblapacke-f3b07a3205e00851.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\liblapacke_sys-c47da9062b715d2a.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libndarray-92e03
95f476950e1.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libnum_complex-40b449ee04f55cb0.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libnum_traits-71b583abd7fc37da.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libitertools-96a05f8e8fe0d445.rlib" "D:\\rust\\kalman\\tar
get\\debug\\deps\\libeither-8d7f83e59ef4d65d.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libmatrixmultiply-7843eba1b0a23445.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\librawpointer-472e64f4ec8e6401.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libblas_src-a832735ffc
b26e90.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\libcblas_sys-a5e84083ce548fc0.rlib" "D:\\rust\\kalman\\target\\debug\\deps\\liblibc-017498fec30aa81b.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\
lib\\libstd-b37071b9e2cd3aa5.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\libpanic_unwind-80ad24dd9399543e.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rus
tlib\\x86_64-pc-windows-msvc\\lib\\librustc_demangle-dd79d3cff78d66ff.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\libunwind-25039ae4abdf00f4.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stab
le-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\liblibc-372f2e64ad75cbde.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\liballoc-89af1159cf06a551.rlib" "C:\\Users\\py-goku\\.
rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\librustc_std_workspace_core-ab52a96521eb83dc.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\libcore-ed
3299f47397f63d.rlib" "C:\\Users\\py-goku\\.rustup\\toolchains\\stable-x86_64-pc-windows-msvc\\lib\\rustlib\\x86_64-pc-windows-msvc\\lib\\libcompiler_builtins-3d0709ec5c75f4fa.rlib" "gfortran.lib" "openblas.lib" "advapi32.lib" "credui.lib" "kernel32.lib" "secur32.lib" "ad
vapi32.lib" "ws2_32.lib" "userenv.lib" "msvcrt.lib"
  = note: LINK : fatal error LNK1181: cannot open input file 'gfortran.lib'


error: aborting due to previous error

error: Could not compile `kalman`.

Caused by:
  process didn't exit successfully: `rustc --edition=2018 --crate-name kalman src\main.rs --color always --crate-type bin --emit=dep-info,link -C debuginfo=2 -C metadata=a95edc84d22c3dfb -C extra-filename=-a95edc84d22c3dfb --out-dir D:\rust\kalman\target\debug\deps -C in
cremental=D:\rust\kalman\target\debug\incremental -L dependency=D:\rust\kalman\target\debug\deps --extern ndarray=D:\rust\kalman\target\debug\deps\libndarray-92e0395f476950e1.rlib --extern ndarray_linalg=D:\rust\kalman\target\debug\deps\libndarray_linalg-6df84c958c2578c8
.rlib --extern openblas_src=D:\rust\kalman\target\debug\deps\libopenblas_src-016fb3f34a35b405.rlib -L D:/rust/kalman/target/debug/build/openblas-src-a9fb8b5975a41b99/out\opt/OpenBLAS/lib` (exit code: 1)

Now some may be aware then when compiled from powershell, openblas-src does not compile, but these same errors persist when trying to build from MSYS2 MinGW 64bit.

I hope we can resolve this, because without ndarray-linalg the ndarray is useless for Numpy users.

Calc norm

• norm for vector from dot-product (Hilbert)
• norm for matrix, using {d,c}lange in LAPACK #6
  • http://www.netlib.org/lapack/explore-3.1.1-html/dlange.f.html

This issue is necessary for testing #7 #8

Travis CI fails to compile OpenBLAS

Possible answers:

• use sudo in Travis CI
• use another CI service (e.g. Circle CI, wercher) to use docker

Unexpected output when using linalg.inv with OpenBLAS backend

When I run the following code:

use ndarray::*;
use ndarray_linalg::*;

#[test]
fn inv_test() {
    let a: Array2<f64> = array!([1.0, 2.0], [3.0, 4.0]);
    let a_inv = a.inv().unwrap();
    assert!(a_inv.all_close(&array!([-2.0, 1.0], [1.5, -0.5]), 1e-5));
}

it produces the following output (running the command cargo test --features=openblas:

thread 'tests::inv_test' panicked at 'assertion failed: a_inv.all_close(&array!([ - 2.0 , 1.0 ] , [ 1.5 , - 0.5 ]), 1e-5)', src/main.rs:355:9
note: Some details are omitted, run with `RUST_BACKTRACE=full` for a verbose backtrace.

The value of a_inv is vec![2, -1, -0.5, 0.5]

I would expect the value to be the same as the example using the equivalent using numpy:

>>> from numpy.linalg import inv
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = inv(np.matrix(a))
>>> ainv
matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])

macOS High Sierra Linking Fails

Encountering problems when building with ndarray-linalg as a dependency

Versions:

OSX: 10.13.4 (17E199)

clang: Apple LLVM version 9.1.0 (clang-902.0.39.2)
Target: x86_64-apple-darwin17.5.0
Thread model: posix
InstalledDir: /Library/Developer/CommandLineTools/usr/bin

blas and openblas installed via conda, versions are:

blas 1.0 openblas anaconda
openblas 0.3.3 3 anaconda
openblas-devel 0.3.3 3 anaconda

gfortran was installed via homebrew:

boris@Boriss-MacBook-Pro-2:~/haxx/python/gravity_clustering$ gfortran -v
Using built-in specs.
COLLECT_GCC=gfortran
COLLECT_LTO_WRAPPER=/usr/local/Cellar/gcc/8.2.0/libexec/gcc/x86_64-apple-darwin17.7.0/8.2.0/lto-wrapper
Target: x86_64-apple-darwin17.7.0
Configured with: ../configure --build=x86_64-apple-darwin17.7.0 --prefix=/usr/local/Cellar/gcc/8.2.0 --libdir=/usr/local/Cellar/gcc/8.2.0/lib/gcc/8 --enable-languages=c,c++,objc,obj-c++,fortran --program-suffix=-8 --with-gmp=/usr/local/opt/gmp --with-mpfr=/usr/local/opt/mpfr --with-mpc=/usr/local/opt/libmpc --with-isl=/usr/local/opt/isl --with-system-zlib --enable-checking=release --with-pkgversion='Homebrew GCC 8.2.0' --with-bugurl=https://github.com/Homebrew/homebrew-core/issues --disable-nls
Thread model: posix
gcc version 8.2.0 (Homebrew GCC 8.2.0)

Error text is as follows:

error: linking with `cc` failed: exit code: 1
  |
  = note: "cc" "-m64" "-L" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering0-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering1-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering10-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering11-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering12-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering13-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering14-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering15-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering2-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering3-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering4-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering5-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering6-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering7-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering8-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.gravity_clustering9-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o" "-o" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/gravity_clustering-af9a185107b464a2.crate.allocator.rcgu.o" "-Wl,-dead_strip" "-nodefaultlibs" "-L" "/Users/boris/haxx/python/gravity_clustering/target/release/deps" "-L" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librayon-4b02d786d1bd55a5.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librayon_core-6ad42d4bfe037261.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libcrossbeam_deque-3e4d4acc829c5c73.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libcrossbeam_epoch-ca8363f9197e111f.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libscopeguard-b6ce87978007c9eb.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libmemoffset-19ba1fa21caf0388.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/liblazy_static-f9f2f60147bdfdf0.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libcrossbeam_utils-025f80d9e0908a5b.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libcfg_if-31e57d1f0d09db98.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libarrayvec-b72cb89b05274aca.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libnodrop-a40abb48bf76c4e6.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libndarray_linalg-b74f9ca68324d40e.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/liblapacke-4b6143a9e09368de.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/liblapacke_sys-fa7f00acac0e1073.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libndarray-9ae38c327d6212ae.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libnum_complex-e1f6eb9ac6503af6.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libnum_traits-03eef3ab8946d374.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libitertools-9016f082db60a7a7.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libeither-fcfc96e5a4db8cce.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libmatrixmultiply-817168ed32bf0403.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librawpointer-d8a37321df43ac4b.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libblas_src-772e556da810a4d4.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libcblas_sys-9a2f33c41b92c395.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/libnum_cpus-eaf59e66f6f31242.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librand-800929ac40d24603.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/liblibc-3c1946dd65acb4d1.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librand_core-3b99e0cebd545167.rlib" "/Users/boris/haxx/python/gravity_clustering/target/release/deps/librand_core-d541ebf4a966e2be.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/libstd-03b901326ae24853.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/libpanic_unwind-6ff7c563e703aab0.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/liballoc_jemalloc-5bcc251fd166dc12.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/libunwind-3af07b1997da2eea.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/liballoc_system-f2d882c31340c020.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/liblibc-c27b8d1b261d1a71.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/liballoc-a8adffd320893f05.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/libcore-095d0e0c6f534dd1.rlib" "/Users/boris/.rustup/toolchains/stable-x86_64-apple-darwin/lib/rustlib/x86_64-apple-darwin/lib/libcompiler_builtins-5bd49e510cc11ed9.rlib" "-framework" "Security" "-lSystem" "-lresolv" "-lpthread" "-lc" "-lm"
  = note: Undefined symbols for architecture x86_64:
            "_LAPACKE_dgesvd", referenced from:
                _$LT$f64$u20$as$u20$ndarray_linalg..lapack_traits..svd..SVD_$GT$::svd::hfaf0e8598dff5bc2 in libndarray_linalg-b74f9ca68324d40e.rlib(ndarray_linalg-b74f9ca68324d40e.ndarray_linalg4-18283fb439679ae1ca7e2ec2221088bb.rs.rcgu.o)
            "_cblas_ddot", referenced from:
                ndarray::linalg::impl_linalg::_$LT$impl$u20$ndarray..ArrayBase$LT$S$C$$u20$ndarray..dimension..dim..Dim$LT$$u5b$usize$u3b$$u20$_$u5d$$GT$$GT$$GT$::dot::h714423fc9780e798 in gravity_clustering-af9a185107b464a2.gravity_clustering1-b7d3c0d45745af024f0794934bb8388b.rs.rcgu.o
          ld: symbol(s) not found for architecture x86_64
          clang: error: linker command failed with exit code 1 (use -v to see invocation)

Cargo.toml is:

[package]
name = "gravity_clustering"
version = "0.1.0"
authors = ["boris"]

[dependencies]
ndarray = "0.12"
ndarray-linalg = { version = "0.10", features = ["openblas"] }
#(I have tried this with "ndarray-linalg = "0.10"" as well)
rand = "0.5.5"
num_cpus = "1.8.0"
rayon = "1.0.2"

Please advise on options, so far I have solved this by creating a symlink in usr/local/bin for cc to link to G++-8, however this is terrifying and terrible, and I would like another way to solve. Issue doesn't appear to be platform dependent, as this build also fails on Ubuntu.

EDIT(by @termoshtt): Fix markdown

Threading behavior depends on backend?

I recently played around with Rust for a stochastic simulation (dynamical Monte Carlo via Gillespie's algorithm). In order to increase the performance, I parallelized it via std::thread over different initial conditions. The state space I use is a lattice in several dimensions, represented by Array1<u64> from ndarray. So far nothing worth mentioning.

Now I had to adapt the stochastic simulation to do some additional linear algebra along the way (nothing too crazy – just some dozen-dimensional linear problems) and decided to go for ndarray-linalg with its recommended backend openblas – instead of re-implementing linear algebra routines or pulling in another linear algebra package. However, this caused the parallelization via std::threads to not work anymore: The threads were still visible in htop, but they all stayed on the same core – not speeding up the calculation as intended. The only way I could get it to work as expected was to switch to the backend netlib. Now my threads populate different cores again and, in this sense, I do not have a problem that needs fixing anymore.

However, it took me a long time to figure this out. I am not an expert in the different backends. Is this known and expected behavior? Is it even intended? Is my "solution" to use netlib a true solution or is it a weird workaround, possibly causing some other problems in the future?

A simple example project reproducing the observation is given below. With openblas it does not distribute over several cores. With netlib instead it does. Note that the linear algebra operations in this example only appear at the very end – and just once per thread.

Cargo.toml
---
[package]
name = "example"
version = "0.1.0"

[dependencies]
rand = "0.5"
ndarray = "0.11"
# ndarray-linalg = {version = "0.9", features=["netlib"]}
ndarray-linalg = {version = "0.9", features=["openblas"]}

main.rs
---
extern crate rand;
extern crate ndarray;
extern crate ndarray_linalg;

use std::thread;

use rand::Rng;
use ndarray::{arr1, Array1};
use ndarray::{arr2, Array2};

use ndarray_linalg::Solve;

fn main() {
    println!("Hello, world!");

    let mut handles = vec![];

    let n = 1000000000;

    for idx in 0..4 {
        let handle = thread::spawn(move || {

            let mut rng = rand::thread_rng();

            let mut x: f64 = 0.;

            for _ in 0..n {
                x += rng.gen::<f64>();
            }
            
            println!("Thread no {} finished averaging {} random numbers. \
                     Result: {}", idx, n, x/(n as f64));

            let matrix: Array2<f64> = arr2(&[[1., 1., 0.],[0., 2., 0.], [0., 0., 3.]]);
            let vector: Array1<f64> = arr1(&[rng.gen(), rng.gen(), rng.gen()]);

            let result = matrix.solve_into(vector).unwrap();

            println!("Thread no {} says: result = {}", idx, result);

        });

        handles.push(handle);
    }

    for handle in handles {
        handle.join().unwrap();
    }

}

serde feature

To switch two features

• num-complex/serde rust-num/num-complex#7
• ndarray/serde1

Test coverage

Current test does not cover all implementations, especially for complex matrices.

https://github.com/codecov/example-rust

will be a good example :)

wasm-pack libc error

Hi there,

I understand that it's not exactly the aim of this package, but I'm trying to do linear algebra in the browser with a ndarray web assembly module. When I use wasm-pack build workflow to run the factorize examples I get a number of libc related errors that aren't present in the standard system build. What's strange (or not at all) is that the rest of the ndarray crate lends itself nicely to wasm conversion.

If you have a second, could you briefly glance over these errors, and help me determine whether there's any workaround? I'd love to be able to use the developing ndarray-linalg crate to handle the transformation, and factorization needs that folks may have.

If this is way out of the scope of your tool, then feel free to pass on this issue. Thanks!

//lib.rs
extern crate cfg_if;
extern crate wasm_bindgen;

mod utils;

use cfg_if::cfg_if;
use wasm_bindgen::prelude::*;

cfg_if! {
    // When the `wee_alloc` feature is enabled, use `wee_alloc` as the global
    // allocator.
    if #[cfg(feature = "wee_alloc")] {
        extern crate wee_alloc;
        #[global_allocator]
        static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT;
    }
}

extern crate ndarray;
extern crate ndarray_linalg;

use ndarray::*;
use ndarray_linalg::*;

// Solve `Ax=b`
fn solve() -> Result<(), error::LinalgError> {
    let a: Array2<f64> = random((3, 3));
    let b: Array1<f64> = random(3);
    let _x = a.solve(&b)?;
    println!("in solve {:?}",_x);
    Ok(())
}

// Solve `Ax=b` for many b with fixed A
fn factorize() -> Result<String, error::LinalgError> {
    let a: Array2<f64> = random((3, 3));
    let f = a.factorize_into()?; // LU factorize A (A is consumed)
    let mut ret_string = String::new();
    for _ in 0..10 {
        let b: Array1<f64> = random(3);
        let _x = f.solve_into(b)?; // solve Ax=b using factorized L, U
        ret_string += format!("in factorize {:?}",_x);
    }
    Ok(ret_string)
}

#[wasm_bindgen]
extern {
    fn alert(s: &str);
}

#[wasm_bindgen]
pub fn greet() -> String {
    match factorize() {
        Ok(st) => st,
        Err(e) => format!("broke something")
    }
}

//cargo.toml
[package]
name = "test-linalgwasm"
version = "0.1.0"
authors = [""]

[lib]
crate-type = ["cdylib", "rlib"]

[features]
default = ["console_error_panic_hook"]

[dependencies]
cfg-if = "0.1.2"
ndarray= "0.12"
ndarray-linalg = { version = "0.10", features = ["openblas"] }
wasm-bindgen = "0.2"

# The `console_error_panic_hook` crate provides better debugging of panics by
# logging them with `console.error`. This is great for development, but requires
# all the `std::fmt` and `std::panicking` infrastructure, so isn't great for
# code size when deploying.
console_error_panic_hook = { version = "0.1.1", optional = true }

# `wee_alloc` is a tiny allocator for wasm that is only ~1K in code size
# compared to the default allocator's ~10K. It is slower than the default
# allocator, however.
#
# Unfortunately, `wee_alloc` requires nightly Rust when targeting wasm for now.
wee_alloc = { version = "0.4.2", optional = true }

[dev-dependencies]
wasm-bindgen-test = "0.2"

[profile.release]
# Tell `rustc` to optimize for small code size.
opt-level = "s

build error

  [1/9] Checking `rustc` version...
  [2/9] Checking crate configuration...
  [3/9] Adding WASM target...
  info: component 'rust-std' for target 'wasm32-unknown-unknown' is up to date
  [4/9] Compiling to WASM...
      Updating crates.io index
     Compiling proc-macro2 v0.4.23
     Compiling unicode-xid v0.1.0
     Compiling wasm-bindgen-shared v0.2.28
     Compiling cfg-if v0.1.6
     Compiling num-traits v0.2.6
     Compiling lazy_static v1.2.0
     Compiling openblas-src v0.6.1
     Compiling matrixmultiply v0.1.15
     Compiling num-complex v0.2.1
     Compiling rawpointer v0.1.0
     Compiling ndarray v0.12.0
     Compiling libc v0.2.43
     Compiling rand_core v0.3.0
     Compiling either v1.5.0
     Compiling wasm-bindgen v0.2.28
     Compiling log v0.4.6
     Compiling cblas-sys v0.1.4
     Compiling lapacke-sys v0.1.4
  error[E0432]: unresolved imports `libc::c_char`, `libc::c_double`, `libc::c_float`, `libc::c_int`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/cblas-sys-0.1.4/src/lib.rs:13:12
     |
  13 | use libc::{c_char, c_double, c_float, c_int};
     |            ^^^^^^  ^^^^^^^^  ^^^^^^^  ^^^^^ no `c_int` in the root
     |            |       |         |
     |            |       |         no `c_float` in the root
     |            |       no `c_double` in the root
     |            no `c_char` in the root
  
  error[E0412]: cannot find type `c_double` in module `libc`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/cblas-sys-0.1.4/src/lib.rs:17:36
     |
  17 | pub type c_double_complex = [libc::c_double; 2];
     |                                    ^^^^^^^^ not found in `libc`
  
  error[E0412]: cannot find type `c_float` in module `libc`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/cblas-sys-0.1.4/src/lib.rs:21:35
     |
  21 | pub type c_float_complex = [libc::c_float; 2];
     |                                   ^^^^^^^ not found in `libc`
  
  error: aborting due to 3 previous errors
  
  Some errors occurred: E0412, E0432.
  For more information about an error, try `rustc --explain E0412`.
  error: Could not compile `cblas-sys`.
  warning: build failed, waiting for other jobs to finish...
  error[E0432]: unresolved imports `libc::c_char`, `libc::c_double`, `libc::c_float`, `libc::c_int`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/lapacke-sys-0.1.4/src/lib.rs:13:12
     |
  13 | use libc::{c_char, c_double, c_float, c_int};
     |            ^^^^^^  ^^^^^^^^  ^^^^^^^  ^^^^^ no `c_int` in the root
     |            |       |         |
     |            |       |         no `c_float` in the root
     |            |       no `c_double` in the root
     |            no `c_char` in the root
  
  error[E0412]: cannot find type `c_double` in module `libc`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/lapacke-sys-0.1.4/src/lib.rs:17:36
     |
  17 | pub type c_double_complex = [libc::c_double; 2];
     |                                    ^^^^^^^^ not found in `libc`
  
  error[E0412]: cannot find type `c_float` in module `libc`
    --> ~/.cargo/registry/src/github.com-1ecc6299db9ec823/lapacke-sys-0.1.4/src/lib.rs:21:35
     |
  21 | pub type c_float_complex = [libc::c_float; 2];
     |                                   ^^^^^^^ not found in `libc`
  
  error: aborting due to 3 previous errors
  
  Some errors occurred: E0412, E0432.
  For more information about an error, try `rustc --explain E0412`.
  error: Could not compile `lapacke-sys`.
\ warning: build failed, waiting for other jobs to finish...

Rewrite tests

Restore ssqrt and deth

Support RcArray

This will be possible without cloning Array.

Rewrite solve_triangular

DGEMV throws error on stdout but does not panic

I have tried running some code with the Intel MKL backend and the OpenBLAS backend, both spew out warnings like

Intel MKL ERROR: Parameter 7 was incorrect on entry to cblas_dgemv.

The only ndarray-linalg routine I use is Solve and I use ndarray without the blas feature.

So far I have been unable to replicate the error with a simple example.

This sounds quite ominous, either the dimension parameter is wrong or my vector is somehow invalid (nans maybe?), but somehow my code doesn't halt. After browsing the source for a morning I haven't been able to find where this message originates or why my code doesn't panic. I'd be happy to solve the issue myself but I really need some pointers on where to start. Your help is appreciated!