Blasjs NPM | npm.io

BLASjs (Basic Linear Algebra Subprograms)

This is a 100% Pure Javascript ( TypeScript ) re-write of the reference implementation Basic Linear Algebra SubPrograms (BLAS) numerical library found here. This is a full manual re-write, "emscripten" was not used.

summary

BLASjs contains all the functions (Complex, Real) of the reference implementation capable for 32 bit and 64 bit floating point arithmatic:

:ok_hand: 100% code coverage
1005 tests
Output off all tests equal to the BLAS FORTRAN reference implementation.
Level 1: all vector-vector operations implemented.
Level 2: all vector-matrix operations implemented.
Level 3: all matrix-matrix operations implemented.
Helper functions to ease the porting of FORTRAN BLAS usage to Javascript.

Node and Web

The resulting bundled blasjs file is an agnostic UMD library, it can be used in a web client as-well as in a server side node environment.

Installation

node

$ npm i blasjs

Usage:

//node
   const blas = require('blasjs');
//or typescript
   import * as blas from 'blasjs';

web

The module directory contains a standalone bundle for use in html <script> insertion. The library assigns window.BLAS after loading.

<!-- <script src="your_server_url/blasjs.min.js"></script> -->
<!-- this example uses unpkg as CDN -->
<script src="https://unpkg.com/blasjs@latest/dist/lib/blasjs.min.js"></script>
<script>
  const blas = window.BLAS; //UMD exposes it as BLAS

  //fetch some level3 complex 64 bit precision matrix-matrix operations
  const {
      level3: { zsyrk, ztrmm, ztrsm }
   } = blas;
</script>

Language differences with FORTRAN/BLAS

FORTRAN language can instrinsicly work with non-zero based multidimensional arrays and complex numbers. Below are some examples from FORTRAN that have no Javascript counterpart. The reference implementation of BLAS functions expect inputs of these types.

The FORTRAN complex scalar, complex array and complex "Matrix"

!    double precision Complex number
     COMPLEX*16 alpha
!
!    double precision Complex array with offset 2
     COMPLEX*16 vector(2,10)
!
!    double precision complex MultiDimensional Array (matrix)
!    rows 1 to 5 , columns 1 to 10
     COMPLEX*16 A(1:5,1:10)

To work with the concept of non-zero based arrays and complex numbers in JS, these FORTRAN constructs have equivalents in the blasjs library.

The blasjs helpers to create complex scalar, complex array and complex "Matrix" objects

  const blas = require('blasjs');

  const {
      helper:{
        /* create complex Object from 2 real numbers */
        complex,

        /* create single precision Real/complex arrays, */
        fortranArrComplex32,

        /* create double precision Real/Complex arrays */
        fortranArrComplex64,

        /* create single precision 2 dimensional Real/Complex arrays */
        fortranMatrixComplex32,

        /* Double precision 2 dimensional Real/Complex arrays */
        fortranMatrixComplex64,
      }
  } = blas;

These functions are extensively documented in the helper functions. It is recommended you read this introductory part of the documentation first. before anything else.

Helper functions

blasjs uses "FORTRAN like" complex number 32/64 bit precision multidimensional complex/real data. These helper functions have been designed to significantly ease the use of working with these data types in JavaScript.

Types

Typescript types/interfaces to mimic FORTRAN native (complex) multidimensional arrays.

`fpArray`

Wraps JS types Float32Array and Float64Array into a single type.

decl:

export type fpArray = Float32Array | Float64Array;

`FortranArr`

Abstraction of a 1 dimensional single/double precision complex/real FORTRAN array. Used by level 1 and level 2 blasjs functions. FortranArrobjects should be created by the fortranArrComplex32 and fortranArrComplex64 helper functions.

decl:

export declare type FortranArr = {
    base: number;
    r: fpArray;
    i?: fpArray;
    s: (index: number) => (re?: number, im?: number) => number | Complex;
    toArr: () => Complex[] | number[];
};

fields:

base: fortran by default has a 1-value based array. Mimiced by this property.
r: See decl fpArray. The Real part of complex array.
i: (optional). See decl fpArray. The Imaginary part of the complex array.
s: set, get values of the array. Uses FORTRAN style array indexes taking the value of base into account.
toArr generates an JavaScript array from the r and i (optional) data.

Usage:

const blas = require('blasjs');

const { helper: { fortranArrComplex64 } } = blas;

// You can also use the helper "complex" or "muxComplex"
// to generate JS complex arrays
const complexDataArr = [
    { re: 1.8, im: -0.2 },
    { re: 2.3, im: 0.6 }
];

// Create an object that mimics FORTRAN COMPLEX*16 SP(2:3)
//    and fill it with above data
const sp = fortranArrComplex64(complexArr)(2);

// fast! normal JS TypedArray access
let re = sp.r[ 2 - sp.base ];
// 1.8

let  im = sp.i[ 2 - sp.base ];
// -0.2

// not so fast, but easier syntax
let v = sp.s(2)(); // Terse syntax,
// { re: 1.8, im: -0.2 }

// sets the value at index 3 to complex: 0.11 - i0.9
//      and returns the old value: 2.3 + i0.6
let old = sp.s(3)(0.11, -0.9);

sp.toArr();
// [ { re:1.8, im: -0.2 },
//   { re:0.11, im: -0.9 } ]

Usage TypeScript:

import {
    // pure types
    Complex,
    fpArray,
    FortranArr,
    // helper
    helper
} from 'blasjs';

const { fortranArrComplex64 } = helper;

const complexArr: Complex[] [
    { re: 1.8, im: -0.2 },
    { re: 2.3, im: 0.6 }
];

// Create an object that mimics FORTRAN COMPLEX*16 SP(2:3)
//    and fill it with above data
const sp: FortranArr = fortranArrComplex64(complexArr)(2);

let re = sp.r[ 2 - sp.base ]; //fastest! direct TypedArray access
// 1.8

let  im = sp.i[ 2 - sp.base ]; //fastest! direct TypedArray access
// -0.2

// not so fast, but easier syntax
let v = sp.s(2)(); // Terse syntax,
// { re: 1.8, im: -0.2 }

// sets the value at index 3 to complex: 0.11 - i0.9
//      and returns the old value: 2.3 + i0.6
let old = sp.s(3)(0.11, -0.9);
// {re: 2.3, im: 0.6 }

`Type Complex`

Typescript definition of a complex scalar.

decl:

declare type Complex = {
   re: number;
   im?: number;
}

Usage:

import { Complex /* pure type */ } from 'blasjs';

const complexArr: Complex[] [
    { re: 1.8, im: -0.2 },
    { re: 2.3, im: 0.6 }
];

`Matrix`

The Matrix object is the input of many level-2 and level-3 blasjs functions. Matrix is created by the helpers fortranMatrixComplex32 and fortranMatrixComplex64. Matrix encapsulates objects of Float32Array or Float64Array, the blasjs.

In this section the internals of Matrix are explained in detail and how blasjs accesses the data in the JS TypesArrays.

Float32/64Array Complex number storage for Matrix.

The Matrix object has 2 properties r and i for respectively real and imaginary parts of matrix elements. These are the actual aforementioned JS TypedArrays. The imaginary property part is optional if it is not defined the Matrix represents solely an array of real elements.

declare type Matrix = { //Incomplete declaration
    .
    r: Float64Array|Float32Array;
    i: Float64Array|Float32Array;
    .
}

Handling FORTRAN matrices (multidimensional Arrays).

Contrary to languages like JavaScript. FORTRAN defines arrays ( aka DIMENSIONS in FORTRAN lingo ) as 1 based arrays by default.. This can be changed by specifying a different base in the declaration.

Some examples:

       DOUBLE PRECISION A1(4)  ! array indexes 1,2,3,4
       DOUBLE PRECISION A2(-1:3)  ! array indexes -1,0,2,3
       DOUBLE PRECISION A3(0:3) ! Javascript like Array with 4 elements

This expands to 2-dimensional arrays (matrices).

! (default) first index loops from 1 to 4(inclusive), second index loops from 1 to 5(inclusive)
       DOUBLE PRECISION A1(4,5)
! first index loops from -2 to 4(inclusive), second index loops from -5 to -7(inclusive)
       DOUBLE PRECISION A2(-2:4,-5:-7)

The values of the FORTRAN array basis are preserved as rowBase (first index) and colBase (second index).

declare type Matrix = { //SHOW PARTIAL TYPE
    .
    rowBase: number;
    colBase: number;
    .
}

JavaScript doesn't have the notion of typed 2-dimensional arrays. The Matrix objects handles this by mapping 2 dimensional arrays to single 1-dimensional array, by serializing data on a column-first basis.

For example the elements 2x2 Matrix will be mapped in a TypedArray as:

matrix A =
 *           *
 | a11  a12  |
 | a21  a22  |
 *           *

# Stored in TypedArray as
At = [a11,a21, a12, a22]

In case of complex values for A, the real part will be stored in r and the imaginary part in i each in the same column-first manner.

Performance

Direct access to TypedArrays within the Matrix object is the preferable way to get/set matrix data. Since BLAS (and therefore blasjs) functions access matrices mostly to iterate over matrix row's first . It was decided to story 2 dimensional an a column-first basis.

To help with the calculation of finding/setting an element A(i,j) in Matrix the following helper member functions have been added to Matrix.

declare type Matrix = { //SHOW PARTIAL TYPE
    .
    rowBase: number;
    colBase: number;
    nrCols: number;
    nrRows: number;
    .
    colOfEx(number): number;
    coord(col): (row) => number;
    setCol(col: number, rowStart: number, rowEnd: number, value: number): void;
    .
}

Explanation:

nrRows: The number of rows in the matrix.
nrCols: The number of columns in the matrix.
colofEx: Calculates the physical location of a column offset within the TypedArray. Taking int account the column base colBase and row base colBase. The index of A(i,j) = (j - colBase)*nrRows + i - rowBase.
coord: Curried, emulates non-zero based FORTRAN index values for 2 dimensional Arrays. The index that is iterated over the least (usually) is used as the first to create the curried function.
setCol: Uses underlying TypedArray, fill method to set multiple column elements to a single value.

See Example

Creating new transformed Matrix instances from existing ones

One can create/transform new Matrix instances form existing onces. A copy of all relevant data is made into the new Matrix instance.

`Matrix.prototype.slice`

Slices a rectangular piece of data out of an matrix into a new Matrix instance. All arguments are FORTRAN-style non-zero based indexes.

declare type Matrix = { // only "slice" is shown
   .
   slice(rowStart: number, rowEnd: number, colStart: number, colEnd: number): Matrix;
   .
}

rowStart: The row in the matrix to begin slicing.
rowEnd: The last row to include in the slice.
colStart: The column in the matrix to begin slicing.
colEnd: The last column to include in the slice.

See Example

`Matrix.prototype.setLower`

Returns a new Matrix where everything below the matrix diagonal is set to a value. Sets the real (and imaginary part, if it exist) to said value.

declare type Matrix = { // only "setLower" is shown.
  .
  setLower(value = 0): Matrix;
  .
}

See Example

`Matrix.prototype.setUpper`

Returns a new Matrix where everything below the matrix diagonal is set to a value. Sets the real (and imaginary part, if it exist) to said value.

declare type Matrix = { //only "setUpper" is shown
  .
  setUpper(value = 0): Matrix;
  .
}

See Example

`Matrix.prototype.upperBand`

Returns a new Matrix object where the k super-diagonals are retained into the new copy. The efficient storage format of BLAS band matrices is used.

declare type Matrix = { //only "upperBand" is shown
  .
  upperBand(k = nrRows - 1): Matrix;
  .
}

The default value for k is the the maximum size possible for the number of super-diagonals: ( nrRows-1 )

See Example

`Matrix.prototype.lowerBand`

Returns a new Matrix object where the k sub-diagonals are retained into the new copy. The efficient storage format of BLAS band matrices is used.

declare type Matrix = { // Only "lowerBand" is shown
  .
  lowerBand(k = nrRows-1): Matrix;
  .
}

The default value for k is the the maximum size possible for the number of sub-diagonals: ( nrRows-1 )

See Example

`Matrix.prototype.real`

Returns a new Matrix object where with only real elements (omits the imaginary part during copy).

declare type Matrix = { // Only "real" is shown
  .
  real(): Matrix;
  .
}

See Example

`Matrix.prototype.imaginary`

Returns a new Matrix object where with only imaginary part of the element (omits the real part during copy). If there were now imaginary elements

declare type Matrix = { // Only "imaginary" is shown.
  .
  imaginary(): Matrix;
  .
}

See Example

Packed Matrices

BLAS ( and therefore blasjs ) can work with upper/lower-matrices and band-matrices in the most compacted form, aka packed matrices. With packed matrices there are no unused elements in the matrix (no zeros). Packed matrices are instances of FortranArr. BLAS reference implementation in FORTRAN uses 1 dimensional arrays as an analog.

`Matrix.prototype.packedUpper`

Creates a packed array from a normal/upper Matrix only referencing the diagonal and super-diagonals.

declare type Matrix = { // Only "packedUpper" is shown.
  .
  packedUpper(k = nrRows-1): FortranArr;
  .
}

See Example

The default value for k is the the maximum size possible for the number of super-diagonals: ( nrRows-1 )

`Matrix.prototype.packedLower`

Creates a packed array from a normal/upper Matrix only referencing the diagonal and sub-diagonals.

declare type Matrix = { // Only "packedUpper" is shown.
  .
  packedLower(k = nrRows-1): FortranArr;
  .
}

See Example

The default value for k is the the maximum size possible for the number of sub-diagonals: ( nrRows-1 )

declare type Matrix = { // Only "packedUpper" is shown.
  .
  packedLower(k = nrRows - 1): FortranArr;
  .
}

The default value for k is the the maximum size possible for the number of sub-diagonals: ( nrRows - 1 )

Convert Matrix object to a JS array

The Matrix object can convert the underlying TypedArray(s) to real JavaScript arrays.

`Matrix.prototype.toArr`

Creates a normal JS Array with element of type 'number' or of type Complex

declare type Matrix = { // Only "toArr" is shown.
  .
  toArr(): number[]|Complex[];
  .
}

See Example

Summary: Full type declaration of Matrix

Putting it all together, here is the full type declaration of Matrix:

declare type Matrix = {
     rowBase: number;
     colBase: number;
     nrCols: number;
     nrRows: number;
     r: fpArray;
     i?: fpArray; //optional
     //
     // methods
     //
     colOfEx(column: number): void;
     coord(col: number): (row: number): void;
     setCol(col: number, rowStart: number, rowEnd: number, value: number): void;
     //
     slice(rowStart: number, rowEnd: number, colStart: number, colEnd: number): Matrix;
     setLower(value?: number): Matrix;
     setUpper(value?: number): Matrix;
     upperBand(k: number): Matrix;
     lowerBand(k: number): Matrix;
     real(): Matrix;
     imaginary(): Matrix;
     //
     packedUpper(value?: number): FortranArr;
     packedLower(value?: number): FortranArr;
     //
     toArr(): Complex[] | number[];
}

Matrix Examples

Common usage of the Matrix type.

const blas = require('../blasjs');
const { fortranMatrixComplex64 } = blas.helper;

// some matrix data 3x3 array  aka a_row_column

const a11 = { re: .2, im: -.11 };
const a21 = { re: .1, im: -.2 };
const a31 = { re: .3, im: .9 };
const a12 = { re: .4, im: .5 };
const a22 = { re: .9, im: -.34 };
const a32 = { re: -.2, im: .45 };
const a13 = { re: -.1, im: .89 };
const a23 = { re: .43, im: .23 };
const a33 = { re: .23, im: .56 };

//create Matrix A
const A = fortranMatrixComplex64([
    a11, a21, a31, a12, a22, a32, a13, a23, a33
])(3, 3);

// get the second column
const columnj = A.colOfEx(3); // formula: (j - colBase )* nrRows

A.r[A.coord(1, 2)] === a12.re // true

A.slice(1, 2,  2, 3);// creates new matrix with elements from A
/*[
    a12 a13
    a22 a23
]*/

A.setLower(0); // creates new Matrix object from A
/*[
    a11 a12 a13
    0   a22 a23
    0   0   a33
]*/

A.setUpper(0); //creates new Matrix object from A
/*[
    a11 0   0
    a21 a22 0
    a31 a32 a33
]*/

A.upperBand(1); // banded array storage for BLAS(js)
/*[
    0   a12   a23
    a11 a22   a33
]*/

A.lowerBand(1); // banded array storage for BLAS(js)
/*[
   a11  a22  a33
   a21  a32  0    
]*/

const Areal = A.real();
// Areal.i is undefined
// Areal.r =
/*[
    0.2 0.4  -0.1
    0.1 0.9   0.43
    0.3 -0.2, 0.23
]*/

const Aimag = A.imaginary();
// imaginary parts are copied to real side in new Matrix
// Aimag.i is undefined
// Aimag.r =
/*[
    -0.11   0.5,  0.89
     -0.2  -0.34  0.23
      0.9   0.45  0.56
]*/

A.packedUpper(1)
/* [ a11 a12 a22 a23 a 33] */

A.packedLower(1)
/* [ a11 a21 a22 a32 a33] */

A.toArr(); // returns JavaScript Array
/*[
  { re: 0.2, im: -0.11 },
  { re: 0.1, im: -0.2 },
  { re: 0.3, im: 0.9 },
  { re: 0.4, im: 0.5 },
  { re: 0.9, im: -0.34 },
  { re: -0.2, im: 0.45 },
  { re: -0.1, im: 0.89 },
  { re: 0.43, im: 0.23 },
  { re: 0.23, im: 0.56 }
]
*/

General Helpers

Collection of helper function to manipulate common JS array and object types in a functional way.

`arrayrify`

Creates a new function from an existing one, to add the ability to accept vectorized input.

Example:

const blas = require('blasjs');

const { helper: { arrayrify } } = blas;
const PI = Math.PI;
//
const sin = arrayrify(Math.sin)

sin([PI/3, PI/4, PI/6]); // returns array aswell
// [ 0.866025, 0.7071067811, 0.5 ]

sin(PI/3); // returns scalar
sin( [ PI/3 ] ); // returns scalar
// 0.866025

sin([]) // edge case
// undefined

sin() //
//NaN  same as Math.sin()

`complex`

Mimics the GNU Fortran extension complex. Creates a JS object that represents a complex scalar number. Used by blasjs for scalar input arguments.

Example:

const blas = require('blasjs');

const { helper: { complex } } = blas;

const c1 = complex(0.1,0.3);
//c1 = { re: 0.1, im: 0.3 }

const c2 = complex();
//c2 = { re: 0, im: 0 }

const c3 = complex(0.5);
//c3 = { re: 0.5, im:0 }

`each`

Curried functional analog to Array.prototype.forEach, but takes arbitrary input.

Example:

const blas = require('blasjs');

const { helper: { each } } = blas;

//Iterates over an object like a map
const curry1 = each( {  hello: 'world', ts: new Date() })
curry1( (val, key) => console.log(`${val} ':'  ${key}`)))
//world: hello
//2018-05-10T13:57:08.923Z : ts

//Handles array also
each( ['a','b','c','d'])( (v,idx) =>console.log(v,idx, typeof idx))
//a 0 number
//b 1 number
//c 2 number
//d 3 number

//Edge cases
each()(console.log)
//nothing happens

each(null)(console.log)
//nothing happens

each([])(console.log)
//nothing happens

`map`

Curried functional analog to Array.prototype.map, but takes arbitrary input.

:warning: Forces the output to be a an array regardless of the input.

Example:

const blas = require('blasjs');

const { helper: { map } } = blas;

//trivial
map([1,2,3])(v=>v*2);
//[ 2, 4, 6 ]

//key properties
map({ a:'A', b:'B' })( (val, key) => key+'='+val);
//[ 'a=A', 'b=B' ]

map(null)( v => '/'+v);
//[]

map()( v => '/'+v);
//[]

map()()
//[]

`muxCmplx`

Creates an array of complex numbers from arrayed input. The result is always an array type.

Example:

const blas = require('blasjs');

const { helper: { muxCmplx } } = blas;

const reals = [ 0.1, -0.2, 0.3, 0.45 ];
const imaginary = [ 0.1, -0.2, 0.3, 0.45 ];

// normal usage
muxCmplx(reals, imaginary)
/*[ { re: 0.1, im: 0.1 },
    { re: -0.2, im: -0.2 },
    { re: 0.3, im: 0.3 },
    { re: 0.45, im: 0.45 } ]*/

//R recycling rule is used
muxCmplx([1,2], imaginary)
/*^[ { re: 1, im: 0.1 },
     { re: 2, im: -0.2 },
     { re: 1, im: 0.3 },
     { re: 2, im: 0.45 } ]*/

//dont care about imaginary
muxCmplx(reals)
/*[ { re: 0.1, im: undefined },
    { re: -0.2, im: undefined },
    { re: 0.3, im: undefined },
    { re: 0.45, im: undefined } ]*/

muxCmplx() //
// [ { re: undefined, im: undefined } ]

muxCmplx(1) //
// [ { re: 1, im: undefined } ]

//3 specify real and imaginary
muxCmplx(1,-2)//
//[ { re: 1, im: -2 } ]

`numberPrecision`

Enforces significant figure of a number, or on the properties of a JS object (deep search) with numeric values.

Example:

const blas = require('blasjs');

const { helper: { numberPrecision } } = blas;

const _4 = numberPrecision(4);

_4(0.123456789);
//0.1235

_4(123456789)
//123500000

//enforce significance over properties
_4( { car: 'Mazda' , aux: { priceUSD: 24.3253E+3, maxWarpSpeed:3.42111E-4 } } );
//{ car: 'Mazda', aux: { priceUSD: 24330, maxWarpSpeed: 0.0003421 } }

_4([0.123456, 0.78901234]);
//[ 0.1235, 0.789 ]

Vector Constructors

These constructors create the FortranArr object for working with single/double precision complex/real Arrays.

`fortranArrComplex32`

Constructs a FortranArr object using Float32Array as the underlying array(s) (plural in the case of complex) elements.

declare function fortranArrComplex32(
    ...rest: (number | number[] | Complex | Complex[])[]
    ): (offset = 1) => FortranArr;

Argument list:

rest: takes as input.
- A single numeric value.
- A single Complex object.
- An array of Complex objects.
- An array of number values.
offset: the Fortran dimension offset (defaults to 1)

See Examples

`fortranArrComplex64`

Constructs a FortranArr object using Float64Array as the underlying array(s) (plural in the case of complex) elements.

declare function fortranArrComplex64(
    ...rest: (number | number[] | Complex | Complex[])[]
    ): (offset = 1) => FortranArr;

Argument list:

rest: takes as input.
- A single numeric value.
- A single Complex object.
- An array of Complex objects.
- An array of number values.
offset: the Fortran dimension offset (defaults to 1)

Vector creation examples

const blas = require('blasjs');

const { fortranArrComplex64, fortranArrComplex32 } = blas.helper;

const complexDataArr = [
    { re: 1.8, im: -0.2 },
    { re: 2.3, im: 0.6 }
];

const realData = [ 0.1, 2, 0.34, .56 ];

const sp1 = fortranArrComplex32(complexDataArr)();
//sp1.r = [ 1.7999999523162842, 2.299999952316284 ],
//sp1.i = [ -0.20000000298023224, 0.6000000238418579 ],

const sp2 = fortranArrComplex32(realData)();
//sp2.r =  [ 0.10000000149011612, 2, 0.3400000035762787, 0.5600000023841858 ]
//sp2.i = undefined

const sp3 = fortranArrComplex32({re:0.2, im:-0.3})();
//[ 0.20000000298023224 ]
//[ -0.30000001192092896 ]

const sp4 = fortranArrComplex32(123)(4);
/*{
  base: 4,
  r: Float32Array [ 123 ],
  i: undefined,
}*/

const sdp1 = fortranArrComplex64(complexDataArr)();
//sp1.r = [ 1.8, 2.3 ],
//sp1.i = [ -0.2, 0.6 ],

const sdp2 = fortranArrComplex64(realData)();
//sp2.r =  [ 0.1, 2, 0.34, 0.56 ]
//sp2.i = undefined

const sp3 = fortranArrComplex64({re:0.2, im:-0.3})();
//[ 0.2 ]
//[ -0.3 ]

const sp4 = fortranArrComplex64(123)(4);
/*{
  base: 4,
  r: Float32Array [ 123 ],
  i: undefined,
}*/

Matrix Constructors

These constructors create the Matrix object for working with single/double precision complex/real Matrices.

`fortranMatrixComplex32`

Constructs a Matrix object using Float32Array as the underlying array(s) (plural in the case of complex) elements.

declare function fortranMatrixComplex32(...rest: (Complex | Complex[])[]):
    (nrRows: number, nrCols: number, rowBase?: number, colBase?: number) => Matrix

Argument list:

rest: takes as input.
- A single numeric value.
- A single Complex object.
- An array of Complex objects.
- An array of number values.
nrRows: where nrRows is equal to n in the matrix A(m,n).
nrCols: where nrCols is equal to m in the matrix A(m,n).
rowBase: FORTRAN offset for the first dimension (rows) as explained in Language differences.
rowBase: FORTRAN offset for the second dimension (columns) as explained in Language differences.

See Examples

`fortranMatrixComplex64`

Constructs a Matrix object using Float64Array as the underlying array(s) (plural in the case of complex) elements.

declare function fortranMatrixComplex64(...rest: (Complex | Complex[])[]):
    (nrRows: number, nrCols: number, rowBase?: number, colBase?: number) => Matrix

Argument list:

rest: takes as input.
- A single numeric value.
- A single Complex object.
- An array of Complex objects.
- An array of number values.
nrRows: where rnRows is equal to n in the matrix A(m,n).
nrCols: where nrCols is equal to m in the matrix A(m,n).
rowBase: FORTRAN offset for the first dimension (rows) as explained in Language differences.
rowBase: FORTRAN offset for the second dimension (columns) as explained in Language differences.

Matrix Creation Examples

const blas = require('blasjs');
const {
    fortranMatrixComplex64,
    fortranMatrixComplex32
} = blas.helper;

// some matrix data 3x3 array  aka a_row_column

const a11 = { re: .2, im: -.11 };
const a21 = { re: .1, im: -.2 };
const a31 = { re: .3, im: .9 };
const a12 = { re: .4, im: .5 };
const a22 = { re: .9, im: -.34 };
const a32 = { re: -.2, im: .45 };
const a13 = { re: -.1, im: .89 };
const a23 = { re: .43, im: .23 };
const a33 = { re: .23, im: .56 };

const {
    fortranMatrixComplex64,
    fortranMatrixComplex32
} = blas.helper;

// Some matrix data 3x3 array  aka a_row_column

const a11 = { re: .2, im: -.11 };
const a21 = { re: .1, im: -.2 };
const a31 = { re: .3, im: .9 };
const a12 = { re: .4, im: .5 };
const a22 = { re: .9, im: -.34 };
const a32 = { re: -.2, im: .45 };
const a13 = { re: -.1, im: .89 };
const a23 = { re: .43, im: .23 };
const a33 = { re: .23, im: .56 };

//functional curry to prepare for different mappings of A()
const A32 = fortranMatrixComplex64([
    a11, a21, a31, a12, a22, a32, a13, a23, a33
]);

//matrix 1
const m1 = A32(3, 3); // 3x3 matrix with rowBase=1, colBase=1

// mimic FORTRAN  "COMPLEX*8  A(-2:1, -3:0)"
const m2 = A32(3, 3, -2, -3);

//same as FORTRAN default COMPLEX*8 A(3,3) !aka A(1:3,1:3)
const m3 = A32(3, 3, 1, 1)

/* double precision */
/* double precision */
/* double precision */

const A64 = fortranMatrixComplex64([
    a11, a21, a31, a12, a22, a32, a13, a23, a33
]);

// matrix 1 FORTRAN "COMPLEX*16  A(-2:1, -3:0).
const m1 = A64(3, 3); // 3x3 matrix with rowBase=1, colBase=1

// mimic FORTRAN  "COMPLEX*16  A(-2:1, -3:0)"
const m2 = A64(3, 3, -2, -3);

// same as FORTRAN default COMPLEX*16 A(3,3) !aka A(1:3,1:3)
const m3 = A64(3, 3, 1, 1);

A note on numeric precision

In blasjs, contrary to the FORTRAN reference implementation, the numeric precision of a routine, is not determined by its name but by how its arguments like FortranArr and Matrix are constructed before used as arguments in blasjs routines. The original FORTRAN names are kept for backwards compatibility to ease the porting of FORTRAN code toward blasjs.

Mimicking FORTRAN OUT Arguments

In FORTRAN a subroutine can have IN, OUT and IN/OUT scalar arguments. In JavaScript only arguments of type object are passed by reference. To mimic OUT and IN/OUT FORTRAN arguments, scalars are wrapped in a JS object. See Construct a Givens plane rotation for an example.

Level 1 routines

Routines categorized as Level 1 perform scalar-vector and vector-vector operations.

Euclidean norm: √(xᴴ·x) or √(xᵀ·x)

Calculates the norm of a (complex) vector.

xᴴ is the conjugate of x

xᵀ is the transpose of x

scrnm2/dznrm2, snrm2/dnrm2

scrnm2: complex, single or double precision. See blas ref.
dznrm2: complex, (alias for scrnm2). See blas ref.
snrm2: real, single or double precision. See blas ref.
dnrm2: real, (alias for dnrm2). See blas ref.

decl

function scnrm2(n: number, x: FortranArr, incx: number): number;
function dznrm2(n: number, x: FortranArr, incx: number): number;
function snrm2(n: number, x: FortranArr, incx: number): number;
function dnrm2(n: number, x: FortranArr, incx: number): number;

subroutine	operation	complex	real	type of matrix A	blas ref link
cgbmv/zgbmv	y ⟵ α·A·x + β·y , y ⟵ α·Aᵀ·x + β·y, y ⟵ α·Aᴴ·x + β·y	α, A, β	none	upper/lower band	cgbmv/zgbmv
chbmv/zhbmv	y ⟵ α·A·x + β·y	α, A, β	none	upper/lower band	chbmv/zhbmv
ssbmv/dsbmv	y ⟵ α·A·x + β·y	none	α, A, β	upper/lower band	chbmv/zhbmv
sgbmv/dgbmv	y ⟵ α·A·x + β·y , y ⟵ α·Aᵀ·x + β·y	none	α, A, β	upper/lower band	sgbmv/dgbmv
stbmv/dtbmv	y ⟵ α·A·x + β·y	none	α, A, β	upper/lower band	stbmv/dtbmv
chemv/zhemv	y ⟵ α·A·x + β·y	α, A, β	none	triangular upper/lower	chemv/zhemv
sgemv/dgemv	y ⟵ α·A·x + β·y , y ⟵ α·Aᵀ·x + β·y	none	α, A, β	full m x n	sgemv/dgemv
cgemv/zgemv	y ⟵ α·A·x + β·y , y ⟵ α·Aᵀ·x + β·y, y ⟵ α·Aᴴ·x + β·y	α, A, β	none	full m x n	cgemv/zgemv
chpmv/zhpmv	y ⟵ α·A·x + β·y	α, A, β	none	packed upper/lower triangular	cgemv/zgemv
sspmv/dspmv	y ⟵ α·A·x + β·y	none	α, A, β	packed upper/lower triangular	sspmv/dspmv
ssymv/dsymv	y ⟵ α·A·x + β·y	α, A, β	none	upper/lower triangular	ssymv/dsymv

BLASjs (Basic Linear Algebra Subprograms)

summary

Node and Web

Installation

node

web

Table of Contents

Language differences with FORTRAN/BLAS

Helper functions

Types

fpArray

FortranArr

Type Complex

Matrix

Float32/64Array Complex number storage for Matrix.

Handling FORTRAN matrices (multidimensional Arrays).

Performance

Creating new transformed Matrix instances from existing ones

Matrix.prototype.slice

Matrix.prototype.setLower

Matrix.prototype.setUpper

Matrix.prototype.upperBand

Matrix.prototype.lowerBand

Matrix.prototype.real

Matrix.prototype.imaginary

Packed Matrices

Matrix.prototype.packedUpper

Matrix.prototype.packedLower

Convert Matrix object to a JS array

Matrix.prototype.toArr

Summary: Full type declaration of Matrix

Matrix Examples

General Helpers

arrayrify

complex

each

map

muxCmplx

numberPrecision

Vector Constructors

fortranArrComplex32

fortranArrComplex64

Vector creation examples

Matrix Constructors

fortranMatrixComplex32

fortranMatrixComplex64

Matrix Creation Examples

A note on numeric precision

Mimicking FORTRAN OUT Arguments

Level 1 routines

Euclidean norm: √(xᴴ·x) or √(xᵀ·x)

scrnm2/dznrm2, snrm2/dnrm2

Construct a Givens plane rotation

srotg/drotg, crotg/zrotg

Construct the modified Givens rotation matrix H

srotmg/drotmg

Apply the modified Givens Transformation

srotm/drotm

Applies a plane rotation

srot/drot, csrot/zdrot

Scale a vector by a constant

sscal/dscal, cscal/zscal, csscal/zdscal

Takes the sum of the absolute values of the components of vector

sasum/dasum, scasum/dzasum

Interchanges 2 vectors

sswap/dswap, cswap/zswap

Dot product of two complex vectors

cdotu/cdotc, zdotu/zdotc

Dot product of two non complex vectors

sdot/ddot, sdsdot/dsdot

Finds the index of the first element having maximum absolut value.

isamax/idamax, icamax/izamax

Copy a vector x to a vector y

scopy/dcopy, ccopy/zcopy

Constant times a vector plus a vector

saxpy/daxpy, caxpy/zaxpy

Level 2 Routines

The hermitian rank 2 operation A ⟵ α·x·yᴴ + conjg( α )·y·xᴴ + A

cher2/zher2, chpr2|zhpr2

The symmetric rank 2 operation A ⟵ α·x·yᵀ + α·y·xᵀ + A

`fpArray`

`FortranArr`

`Type Complex`

`Matrix`

`Matrix.prototype.slice`

`Matrix.prototype.setLower`

`Matrix.prototype.setUpper`

`Matrix.prototype.upperBand`

`Matrix.prototype.lowerBand`

`Matrix.prototype.real`

`Matrix.prototype.imaginary`

`Matrix.prototype.packedUpper`

`Matrix.prototype.packedLower`

`Matrix.prototype.toArr`

`arrayrify`

`complex`

`each`

`map`

`muxCmplx`

`numberPrecision`

`fortranArrComplex32`

`fortranArrComplex64`

`fortranMatrixComplex32`

`fortranMatrixComplex64`

Construct the modified Givens rotation matrix `H`