JSMatrix

Class: Matrix

JSMatrix. Matrix

Represents 2D matrix of real (floating point) numbers

new Matrix(nRows, nCols)

Matrix implementation
This:
Parameters:
Name Type Argument Description
nRows number <optional>
 (default=0) number or rows of newly created Matrix
nCols number <optional>
 (default=0) number or columns of newly created Matrix
Properties:
Name Type Description
nRows number number of rows of receiver
nCols number number of columns of receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 119

Methods

<static> create(arry) → {JSMatrix.Matrix}

Constructs new Matrix from given 2D array
Parameters:
Name Type Description
arry Array.<Array.<number>> (default=[[]]) array containing elements of new matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4336
Returns:
new Matrix object
Type
JSMatrix.Matrix
Example
m = JSMatrix.Matrix.create([[1,2,3],[4,5,6],[7,8,9]]) // m = Matrix([[1,2,3],[4,5,6],[7,8,9]])

<static> Diagonal(arry) → {JSMatrix.Matrix}

Constructs new diagonal matrix from given 1D array
Parameters:
Name Type Description
arry Array.<number> | JSMatrix.Vector array or vector containing elements of new matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4360
Returns:
new Matrix object
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.Matrix.Diagonal([1,2,3]); // m1 = Matrix([[1,0,0],[0,2,0],[0,0,3]])
m2 = JSMatrix.Matrix.Diagonal(JSMatrix.vec([1,2,3])); // m2 = Matrix([[1,0,0],[0,2,0],[0,0,3]])

<static> Householder(vec=0, precompI) → {JSMatrix.Matrix}

Creates a Householder matrix from given vector (ret = I - 2*v*v^T/(v^T*v). Householder matrix is symmetric, orthogonal and involutary
Parameters:
Name Type Argument Description
vec=0 JSMatrix.Vector Householder vector to form Householder matrix
precompI JSMatrix.Matrix <optional>
 =undefined] precomputed identity matrix to save some time of creation
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4437
Returns:
Householder matrix
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.Matrix.Householder(JSMatrix.vec([0,1,0]))
// m1 = Matrix([[1,0,0],[0,-1,0],[0,0,1]])
b1 = m1.isSymmetric() // b1 = true
b2 = m1.isOrthogonal() // b2 = true
b3 = m1.isInvolutary() // b3 = true

<static> I()

Alias for JSMatrix.Matrix.Identity(), see {@JSMatrix.Matrix#Identity}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4386

<static> Identity(size) → {JSMatrix.Matrix}

Constructs new identity matrix of given size
Parameters:
Name Type Description
size number size of returned matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4375
Returns:
identity matri
Type
JSMatrix.Matrix
Example
m = JSMatrix.Matrix.Identity(4) // m = Matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]])

<static> Ones(nRows, nCols) → {JSMatrix.Matrix}

Creates a matrix of given size full of ones
Parameters:
Name Type Argument Description
nRows number <optional>
 =0] number of rows
nCols number <optional>
 =0] number of columns
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4411
Returns:
new vector full of zero
Type
JSMatrix.Matrix
Example
m = JSMatrix.Matrix.Ones(2,3); // m = Matrix([[1,1,1],[1,1,1]])

<static> UnitMatrix()

Alias for Matrix.Identity(), see {@JSMatrix.Matrix#Identity}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4391

<static> Zeros(nRows, nCols) → {JSMatrix.Matrix}

Creates a matrix of given size full of zeros
Parameters:
Name Type Argument Description
nRows number <optional>
 =0] number of rows
nCols number <optional>
 =0] number of columns
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4400
Returns:
new matrix full of zero
Type
JSMatrix.Matrix
Example
m = JSMatrix.Matrix.Zeros(2,3); // m = Matrix([[0,0,0],[0,0,0]])

abs() → {JSMatrix.Matrix}

Returns receiver's elementwse absolute value
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2834
Returns:
receiver's elementwise absolute value
Type
JSMatrix.Matrix
Example
a = JSMatrix.mat([[1,-2,3],[-4,5,-6],[-7,8,-9]]);
b = a.abs(); // b = Matrix([[1,2,3],[4,5,6],[7,8,9]])

add(mat) → {JSMatrix.Matrix}

Returns sum of receiver and matrix ( ret = this + mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be added
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1527
Returns:
sum of receiver and matrix
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m3 = m1.add(m2); // m3 = Matrix([[3,7],[6,6]])

antiSymmetrize()

Anti-symmetrize receiver ( this = this - .5*(this+this^T) ). Receiver must be square
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2294
Example
m = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m.antiSymmetrize(); // m = Matrix([[0,1,2],[-1,0,2],[-2,-2,0]])
b = m.isAntiSymmetric(); // b = true

antiSymmetrized()

Returns anti-symetric part of receiver ( ret = this - .5*(this+this^T) ). Receiver must be square
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2313
Example
m1 = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m2 = m1.antiSymmetrized(); // m2 = Matrix([[0,1,2],[-1,0,3],[-2,0,0]])
b = m2.isAntiSymmetric(); // b = true

appendCols(cols)

Appends vector(s)/matrix(s) as column(s) to receiver
Parameters:
Name Type Description
cols JSMatrix.Vector | JSMatrix.Matrix | Array.<JSMatrix.Vector> | Array.<JSMatrix.Matrix> new row(s) to be appended
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2774
Example
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendCols(JSMatrix.vec([7,6]));
// m = Matrix([[1,2,7],[3,4,6]])
m.appendCols(JSMatrix.mat([[1,3],[2,4]]));
// m = Matrix([[1,2,7,1,3],[3,4,6,2,4]])
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendCols([JSMatrix.vec([2,1]),JSMatrix.vec([33,44])]);
// m = Matrix([[1,2,2,33],[3,4,1,44]])
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendCols([JSMatrix.mat([[11,12],[21,22]]),JSMatrix.mat([[9,8],[7,6]])]);
// m = Matrix([[1,2,11,12,9,8],[3,4,21,22,7,6]])

appendRows(rows)

Appends vector(s)/matrix(s) as row(s) to receiver
Parameters:
Name Type Description
rows JSMatrix.Vector | JSMatrix.Matrix | Array.<JSMatrix.Vector> | Array.<JSMatrix.Matrix> new row(s) to be appended
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2735
Example
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendRows(JSMatrix.vec([7,6]));
// m = Matrix([[1,2],[3,4],[7,6]])
m.appendRows(JSMatrix.mat([[1,3],[2,4]]));
// m = Matrix([[1,2],[3,4],[7,6],[1,3],[2,4]])
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendRows([JSMatrix.vec([2,1]),JSMatrix.vec([33,44])]);
// m = Matrix([[1,2],[3,4],[2,1],[33,44]])
m = JSMatrix.mat([[1,2],[3,4]]);
m.appendRows([JSMatrix.mat([[11,12],[21,22]]),JSMatrix.mat([[5,6],[7,8]])]);
// m = Matrix([[1,2],[3,4],[11,12],[21,22],[5,6],[7,8]])

assemble(mat, rows, cols)

assemble receiver to given matrix ( mat[rows][cols] += this )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix where receiver is assembled
rows Array.<number> | JSMatrix.Vector array containing row coefficients of mat to be incremented
cols Array.<number> | JSMatrix.Vector array containing column coefficients of mat to be incremented
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2517
Example
m1 = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m2 = JSMatrix.mat([[66,77],[88,99]]);
m2.assemble(m1,[1,2],[0,2]);
// m1 = Matrix([11,12,13,14],[87,22,100,24],[119,32,132,34],[41,42,43,44]])

backwardSubstitution(vec, saveOrig) → {JSMatrix.Vector}

Returns vector x as a solution of this*ret = vec, receiver is assumed to be upper triangular matrix
Parameters:
Name Type Argument Description
vec JSMatrix.Vector right hand side
saveOrig boolean <optional>
 =true] if true, returns vec will be unchanged and new vector will be returned. If false, solution will be saved to vec and vec will be returned
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3252
Returns:
solution of this*ret = vec
Type
JSMatrix.Vector
Example
a = JSMatrix.mat([[1,2,3,4],[0,5,6,7],[0,0,8,9],[0,0,0,10]]);
y = JSMatrix.vec([20,34,25,10]);
x = a.backwardSubstitution(y);
// x = Vector([4,3,2,1])
// y = Vector([20,34,25,10])
check = a.mul(x); // check = Vector([20,34,25,10])
yy = y.copy();
// yy = Vector([20,34,25,10])
a.backwardSubstitution(yy,false);
// yy = Vector([4,3,2,1])

beAntiSymmetricPartOf(mat)

Modifies receiver to become anti-symmetric part of given matrix (this = mat - .5*(mat+mat^T) ). mat has to be square
Parameters:
Name Type Description
mat JSMatrix.Matrix given matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2344
Example
m1 = JSMatrix.mat([[1],[3]]);
m2 = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m1.beAntiSymmetricPartOf(m2); // m1 = Matrix([[0,1,2],[-1,0,3],[-2,0,0]])
b = m1.isAntiSymmetric(); // b = true

beCopyOf(mat)

Modifies receiver to become copy of given matrix (this = mat). Receiver's size is adjusted
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be copied to receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2567
Example
m1 = JSMatrix.mat([[4],[5]]);
m2 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m1.beCopyOf(m2); // m1 = Matrix([[1,2,3],[4,5,6]])

beDifferenceOf(mat1, mat2)

Modifies receiver to become difference of two matrices ( this = mat1 - mat2 ). Receiver's size is adjusted
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of the difference
mat2 JSMatrix.Matrix 2nd matrix of the difference
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1618
Example
m = JSMatrix.mat([[5],[9]]);
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m.beDifferenceOf(m1,m2); // m = Matrix([[-1,-3],[0,2]])

beDyadicProductOf(vec1, vec2)

Modifies receiver to become dyadic product of two vectors (this = vec1*vec2^T ). Receiver's size is adjusted
Parameters:
Name Type Description
vec1 JSMatrix.Vector 1st vector of product
vec2 JSMatrix.Vector 2nd vector of product
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2021
Example
m = JSMatrix.mat([[4],[5]]);
v1 = JSMatrix.vec([1,2,3]);
v2 = JSMatrix.vec([4,5,6]);
m.beDyadicProductOf(v1,v2); // m = Matrix([[4,5,6],[8,10,12],[12,15,18]])

beFullOfOnes()

Sets all elements of receiver to 1.0
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1331
Example
m = JSMatrix.mat([[2,3,4],[5,6,7]]);
m.beFullOfOnes(); // m = Matrix([[1,1,1],[1,1,1]])

beInverseOf(mat, method, precompDecomps)

Sets receiver as an inversion of given matrix
Parameters:
Name Type Argument Description
mat JSMatrix.Matrix given matrix
method string <optional>
 ="default"] see {@JSMatrix.Matrix#inversed} for details}
precompDecomps Array.<JSMatrix.Matrix> <optional>
 =undefined] precomputed matrix decompositions if we want to use some
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4266
Example
m1 = JSMatrix.mat([[1],[2]]);
m2 = JSMatrix.mat([[1,2,2],[1,0,1],[1,2,1]]);
m1.beInverseOf(m2); // m1 = Matrix([[2.3,-1.4,-0.8],[-1.4,1.2,0.4],[-0.8,0.4,0.8]])

beNegativeOf(mat)

Modifies receiver to become negative of given matrix (this = -vec). Receiver's size is adjusted
Parameters:
Name Type Description
mat JSMatrix.Matrix given matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1669
Example
m1 = JSMatrix.mat([[2],[3]]);
m2 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m1.beNegativeOf(m2); // m1 = Matrix([[-1,-2,-3],[-4,-5,-6]])

beProductOf(mat1, mat2)

Modifies receiver to become product of two matrices (this = mat1*mat2 ). Receiver's size is adjusted
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of product
mat2 JSMatrix.Matrix 2nd matrix of product
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2042
Example
m1 = JSMatrix.mat([[1],[2]]);
m2 = JSMatrix.mat([[11,12],[21,22]]);
m3 = JSMatrix.mat([[1,2],[3,4]]);
m1.beProductOf(m2,m3); // m1 = Matrix([[47,70],[87,130]])

beProductTOf(mat1, mat2)

Modifies receiver to become product of two matrices (this = mat1*mat2^T )
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of product
mat2 JSMatrix.Matrix 2nd matrix of product
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2094
Example
m1 = JSMatrix.mat([[1],[2]]);
m2 = JSMatrix.mat([[11,12],[21,22]]);
m3 = JSMatrix.mat([[1,3],[2,4]]);
m1.beProductTOf(m2,m3); // m1 = Matrix([[47,70],[87,130]])

beSubMatrixOf(mat, rows, cols)

Sets receiver to be submatrix of given matrix ( this = mat[rows][cols] )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to get submatrix from
rows Array.<number> | JSMatrix.Vector array containing rows coefficients of desired submatrix
cols Array.<number> | JSMatrix.Vector array containing columns coefficients of desired submatrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2406
Example
m1 = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m2 = JSMatrix.mat([[1],[2]]);
m2.beSubMatrixOf(m1,[1,2],[0,2]); // m2 = Matrix([[21,23],[31,33]])

beSumOf(mat1, mat2)

Modifies receiver to become sum of two matrices ( this = mat1 + mat2 ). Receiver's size is adjusted
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of the sum
mat2 JSMatrix.Matrix 2nd matrix of the sum
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1562
Example
m = JSMatrix.mat([[5],[9]]);
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m.beSumOf(m1,m2); // m = Matrix([[3,7],[6,6]])

beSymmetricPartOf(mat)

Modifies receiver to become symmetric part of given matrix (this = .5*(mat+mat^T) ). mat has to be square
Parameters:
Name Type Description
mat JSMatrix.Matrix given matrix. Receiver's size is adjusted
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2268
Example
m1 = JSMatrix.mat([[1],[3]]);
m2 = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m1.beSymmetricPartOf(m2); // m1 = Matrix([[1,1,1],[1,-1,3],[1,3,7]])
b = m1.isSymmetric(); // b = true

beTProductOf(mat1, mat2)

Modifies receiver to become product of two matrices (this = mat1^T*mat2 )
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of product
mat2 JSMatrix.Matrix 2nd matrix of product
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2068
Example
m1 = JSMatrix.mat([[1],[2]]);
m2 = JSMatrix.mat([[11,21],[12,22]]);
m3 = JSMatrix.mat([[1,2],[3,4]]);
m1.beTProductOf(m2,m3); // m1 = Matrix([[47,70],[87,130]])

beTProductTOf(mat1, mat2)

Modifies receiver to become product of two matrices (this = mat1^T*mat2^T )
Parameters:
Name Type Description
mat1 JSMatrix.Matrix 1st matrix of product
mat2 JSMatrix.Matrix 2nd matrix of product
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2120
Example
m1 = JSMatrix.mat([[1],[2]]);
m2 = JSMatrix.mat([[11,21],[12,22]]);
m3 = JSMatrix.mat([[1,3],[2,4]]);
m1.beTProductTOf(m2,m3); // m1 = Matrix([[47,70],[87,130]])

beTranspositionOf(mat)

Modifies receiver to become transposition of given matrix (this = mat^T ). Receiver's size is adjusted
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix of transposition
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2201
Example
m1 = JSMatrix.mat([[4],[5]]);
m2 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m1.beTranspositionOf(m2) // m1 = mat([[1,4],[2,5],[3,6]])

beUnitMatrix(newSize)

Modifies receiver to be unit matrix
Parameters:
Name Type Argument Description
newSize number <optional>
 (default=0) new size or receiver. If omitted or 0, current size is considered (then required square matrix), else resized to newSize
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1352
Example
m = JSMatrix.mat([[1],[2]]);
m.beUnitMatrix(); // m = Matrix([[1],[2]])
/// nothing happened, m is not square
m.beUnitMatrix(2); // m = Matrix([[1,0],[0,1]])
m = JSMatrix.mat([[2,3],[4,5]]);
m.beUnitMatrix(); // m = Matrix([[1,0],[0,1]])

canMultiplyMat(mat) → {boolean}

Testing if receiver can multiply given matrix ( this * mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be tested
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2888
Returns:
true if the multiplication is possible, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = JSMatrix.mat([[7,8,9],[10,11,12]]);
m3 = JSMatrix.mat([[11,12],[21,22],[31,32]]);
t1 = m1.canMultiplyMat(m2); // t1 = false
t2 = m1.canMultiplyMat(m3); // t2 = true

canMultiplyVec(vec) → {boolean}

Testing if receiver can multiply given vector ( this * vec )
Parameters:
Name Type Description
vec JSMatrix.Vector vector to be tested
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2902
Returns:
true if the multiplication is possible, false otherwise
Type
boolean
Example
m = JSMatrix.mat([[1,2,3],[4,5,6]]);
v1 = JSMatrix.vec([1,2,3]);
v2 = JSMatrix.vec([4,5]);
t1 = m.canMultiplyVec(v1); // t1 = true
t2 = m.canMultiplyVec(v2); // t2 = false

chol()

Alias for Cholesky decomposition, see {@JSMatrix.Matrix#choleskyDecomposition}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3486

choleskyDecomposition(saveOrig, checkSymm) → {JSMatrix.Matrix}

Returns lower triangular matrix of Cholesky decomposition of receiver. Receiver must be square, symmetric and positive definite. ( ret * ret^T = this )
Parameters:
Name Type Argument Description
saveOrig boolean <optional>
 =true] if true, receiver is not changed. If false, solution will be saved to receiver
checkSymm boolean <optional>
 =false] if true, test of receiver symmetricity is performed, otherwise not
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3440
Returns:
lower triangular Cholesky matrix
Type
JSMatrix.Matrix
Example
a = JSMatrix.mat([[1,2,4],[2,13,23],[4,23,77]]);
l = a.choleskyDecomposition(); // l = Matrix([[1,0,0],[2,3,0],[4,5,6]])
check = l.x(l.T()); // check = Matrix([[1,2,4],[2,13,23],[4,23,77]]);

containsOnlyOnes()

Alias for isOne(), see {@JSMatrix.Matrix#isOne}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3093

containsOnlyZeros()

Alias for isZero(), see {@JSMatrix.Matrix#isZero}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3071

copied() → {JSMatrix.Matrix}

Returns copy of receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2542
Returns:
copy of receiver
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[11,12],[21,22]]);
m2 = m1;
m3 = m1.copied();
m1.set(1,0,6);
// m1 = Matrix([[11,12],[6,22]])
// m2 = Matrix([[11,12],[6,22]])
// m3 = Matrix([[11,12],[21,22]])

copy()

Alias for copied(), see {@JSMatrix.Matrix#copied}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2558

decrCol(c, vec)

Decerements one column of receiver
Parameters:
Name Type Description
c number index of column to set
vec JSMatrix.Vector vector to be decremented from c-th column
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1786
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.decrCol(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,-9,3],[4,-7,6],[7,-5,9]])

decrRow(r, vec)

Decerements one row of receiver
Parameters:
Name Type Description
r number index of row to set
vec JSMatrix.Vector vector to be decremented from r-th row
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1772
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.decrRow(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,2,3],[-7,-7,-7],[7,8,9]])

decrsm()

Alias for decrSubMatrix, see {@JSMatrix.Matrix#decrSubMatrix}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2505

decrSubMatrix(rows, cols, mat)

Decrement submatrix at defined positions of receiver ( this[rows][cols] -= mat )
Parameters:
Name Type Description
rows Array.<number> | JSMatrix.Vector array containing rows coefficients to be decrementes
cols Array.<number> | JSMatrix.Vector array containing columns coefficients to be decremented
mat JSMatrix.Matrix matrix to be decremented on desired positions
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2488
Example
m = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m.decrSubMatrix([1,2],[0,2],JSMatrix.mat([[66,77],[88,99]]));
// m = Matrix([11,12,13,14],[-45,22,-54,24],[-57,32,-66,34],[41,42,43,44]])

det()

Alias for determinant, see {@JSMatrix.Matrix#determinant}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4323

determinant(method, precompDecomps) → {number|null}

Returns determinant of receiver.
Parameters:
Name Type Argument Description
method string <optional>
 ="default"] used method. Options are "default" and "lu" for using LU decomposition, "schurForm" or "schur" for using schur form, "schurDecomposition" for using schur decomposition, "eigen" or "eigenDecomposition" for using eigendecomposition
precompDecomps Object <optional>
 precomputed decomposition (consistent with method parameter)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4293
Returns:
determinant of receiver
Type
number | null
Example
a = JSMatrix.mat([[4,2,1],[2,5,3],[1,3,6]]);
d = a.determinant(); // d = 67
d = a.determinant('lu'); // d = 67
d = a.determinant('schur'); // d = 67
d = a.determinant('schurdecomposition'); // d = 67
d = a.determinant('eigen'); // d = 67

diag()

Alias for diagonalToVector(), see {@JSMatrix.Matrix#diagonalToVector}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2596

diagonalToVector() → {JSMatrix.Vector}

Returns vector containing receiver's diagonal elements
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2585
Returns:
vector containing receiver's diagonal elements
Type
JSMatrix.Vector
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
v = m.diag(); // v = Vector([1,5,9])

diagProduct() → {number|null}

Returns product of diagonal elements of the receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1403
Returns:
product of diagonal elements of the receiver
Type
number | null
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
p = m.diagProduct(); // p = 45

diagSum()

Alias for trace, see {@JSMatrix.Matrix#trace}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1395

dprod()

Alias for diagProduct, see {@JSMatrix.Matrix#diagProduct}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1416

eigenDecomposition(method, precompSchurDecomp) → {Object|null}

Returns orthogonal matrix P and diagonal matrix L of eigendecomposition of the receiver such that this=P*L*P^-1 (obtained from eigenvalue equation this*P = P*L). If receiver is symmetric, P is orthogonal. Columns of P are eigenvectors of this and diagonal elements of L are corresponding eigenvalues
Parameters:
Name Type Argument Description
method string <optional>
 (default="default") method of eigenvalues solution ["defaul","symm"]
precompSchurDecomp Object <optional>
 precomputed Schur decomposition
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4104
Returns:
{p,l} matrix P and diagonal matrix L of eigendecomposition of receiver
Type
Object | null
Example
m1 = JSMatrix.mat([[4,2,3,1],[3,6,5,7],[5,3,8,1],[2,3,4,5]]);
pl = m1.eigenDecomposition()
p = pl.p
l = pl.l
// p = Matrix([[0.287,-0.05676,-0.7041, 0.4897],[0.6779,0.7997,-1.367,-0.9794],[0.5142,-0.6248,1.294,0],[0.4398,0.2640,0.1196,0.4897]])
// l = Matrix([[15.61,0,0,0],[0,4.192,0,0],[0,0,2.201,0],[0,0,0,1]])
c = p.mulm(l).mulm(p.inv())
// c =

eigSymmetric(params) → {Object|null}

Returns eigenvalues (L) and eigenvectors (P) of symmetric receiver ( (this-lambda*mat)*phi = 0 ). Eigenvectors are normalized with respect to mat
Parameters:
Name Type Argument Description
params Object <optional>
Properties
Name Type Argument Description
mat JSMatrix.Matrix <optional>
 =JSMatrix.Matrix.Identity] mat in (this-lambda*mat)*phi = 0 ). If mat==Matrix.Identity (default), then the "classical" eigenvalue problem is solved ( (this-lambda*I)*phi = 0 -> this*phi=lambda*phi)
nEigModes number | string ='all'] number of first eigenvalues and eigenvectors to be returned. if "all" is, then all eigenvalues are returned
method string <optional>
 ="default"] method of the solution. "default" and "invit" stands for Stodola's inverse iterations methods with Gramm-Schmidt orthogonalization, "subspace" for subspace iterations
highest boolean <optional>
 =true] find params.nEigModes highest eigenvalues if true, params.nEigModes lowest eigenvalues otherwise
maxiter number <optional>
 =1000] maximum number of iterations
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3977
Returns:
[lambda1 ,lambda2,...,lambdaN],[phi1,phi2,...,phiN]], lambdai is i-th eigenvalue, phii is i-th eigenvector. N = nEigModes //
Type
Object | null
Example
k = JSMatrix.mat([[9,3,0,0],[3,8,2,0],[0,2,7,2],[0,0,2,8]]);
m = JSMatrix.Matrix.Diagonal([3,2,4,3]);
e = k.eigSymmetric({mat:m,nEigModes:2,highest:false});
ls = e.eigVals;
ps = e.eigVecs;
l1 = ls[0]; // l1 = 1.2504038497315775
l2 = ls[1]; // l2 = 2.279120228657416
p1 = ps[0]; // p1 = Vector([ 0.1288306767139194, -0.22540165581364102, 0.4265175098731745, -0.20077135620035116 ])
p2 = ps[1]; // p2 = Vector([ 0.4514687335612619, -0.32545467450354726, -0.11713473474653795, 0.2014979513549984 ])
///
e = k.eigSymmetric({mat:m,nEigModes:2,highest:true,method:'subspace'});
ls = e.eigVals;
ps = e.eigVecs;
l3 = ls[1]; // l3 = 2.948867853467429
l4 = ls[0]; // l4 = 4.938274734810245
p3 = ps[1]; // p3 = Vector([ 0.14681878659487543, -0.007507144503266177, -0.21233717286242818, -0.5016212772448967 ])
p4 = ps[0]; // p4 = Vector([ 0.3022519091588433, 0.585847242190032, 0.09630780190740544, 0.028264211960396433 ])
///
c1 = k.x(p1).sub(m.x(p1).x(l1)); // c1 = Vector([0,0,0,0])
c2 = k.x(p2).sub(m.x(p2).x(l2)); // c2 = Vector([0,0,0,0])
c3 = k.x(p3).sub(m.x(p3) .x(l3)); // c3 = Vector([0,0,0,0])
c4 = k.x(p4).sub(m.x(p4).x(l4)); // c4 = Vector([0,0,0,0])

eigVals(method) → {Array.<number>}

Returns eigenvalues of receiver (this*x = ret*x)
Parameters:
Name Type Argument Description
method string <optional>
 ="default"] method of solution. "default" and "schur" stand for similar transformation of receiver into schur form
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4081
Returns:
eigenvalues of receiver
Type
Array.<number>
Example
m1 = JSMatrix.mat([[4,2,3,1],[3,6,5,7],[5,3,8,1],[2,3,4,5]]);
v1 = m1.schurForm().diag().toArray();
// v1 = [15.6072, 4.1916, 2.2012, 1 ]
v2 = m1.eigVals();
// v2 = [15.6072, 4.1916, 2.2012, 1 ]

empty()

Empties receiver (resizes it to size 0)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1299
Example
m = JSMatrix.mat([[1,2],[3,4]]);
m.empty(); // m = Matrix([[]])

forwardSubstitution(vec, saveOrig) → {JSMatrix.Vector}

Returns vector x as a solution of this*ret = vec, receiver is assumed to be lower triangular matrix
Parameters:
Name Type Argument Description
vec JSMatrix.Vector right hand side
saveOrig boolean <optional>
 =true] if true, returns vec will be unchanged and new vector will be returned. If false, solution will be saved to vec and vec will be returned
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3206
Returns:
solution of this*ret = vec
Type
JSMatrix.Vector
Example
a = JSMatrix.mat([[1,0,0,0],[2,3,0,0],[4,5,6,0],[7,8,9,10]]);
y = JSMatrix.vec([4,17,43,80]);
x = a.forwardSubstitution(y);
// x = Vector([4,3,2,1])
// y = Vector([4,17,43,80])
check = a.mul(x); // check = Vector([4,17,43,80])
yy = y.copy();
// yy = Vector([4,17,43,80])
a.forwardSubstitution(yy,false);
// yy = Vector([4,3,2,1])

fromArray(arry)

Sets elements of receiver form given Array object
Parameters:
Name Type Description
arry Array.<Array.<number>> 2D array containing new receiver elements
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1488
Example
m = JSMatrix.mat([[3,2],[1,1]])
m.fromArray([[1,2,3],[4,5,6],[7,8,9]]); // m = Matrix([[1,2,3],[4,5,6],[7,8,9]])

gaussianElimination(rhs, pivoting, saveOrig) → {JSMatrix.Vector}

Returns vector as a solution of system of linear equations using gaussian elimination method (this * ret = rhs --> ret )
Parameters:
Name Type Argument Description
rhs JSMatrix.Vector vector of right hand sides
pivoting string <optional>
 ="default"] what type of pivoting to use. "default" and "nopivot" stands for no pivoting, "partpivot" for implicit partial pivoting (only row interchanges)
saveOrig boolean <optional>
 =true] if true, returns vec will be unchanged and new vector will be returned. If false, solution will be saved to vec and vec will be returned
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3297
Returns:
vector of solution
Type
JSMatrix.Vector
Example
a = JSMatrix.mat([[1,2,9],[8,3,2],[3,7,3]]);
b = JSMatrix.vec([32,20,26]);
x = a.gaussianElimination(b); // x = Vector([1,2,3])
x = a.gaussianElimination(b,'partpivot'); // x = Vector([1,2,3])
a.gaussianElimination(b,'nopivot',false);
// a = Matrix([[1,2,9],[8,-13,-70],[3,1,-29.384615384615387]])
// b = Vector([1,2,3])

gaussJordanElimination(rhs, pivoting, saveOrig) → {JSMatrix.Vector|Array.<JSMatrix.Vector>|JSMatrix.Matrix}

Returns matrix, whose columns are solutions of system of equations this*ret = rhs
Parameters:
Name Type Argument Description
rhs JSMatrix.Matrix | Array.<JSMatrix.Vector> | JSMatrix.Vector matrix/vector/array of vectors representing right hand sides
pivoting string <optional>
 ="default"] what type of pivoting to use. "default" and "nopivot" stands for no pivoting, "partpivot" for implicit partial pivoting (only row interchanges)
saveOrig boolean <optional>
 =true] if true, receiver is not changed. If false, solution will be saved to rhs and rhs will be returned
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3356
Returns:
matrix, whose columns are solution for particular right hand sides
Type
JSMatrix.Vector | Array.<JSMatrix.Vector> | JSMatrix.Matrix
Example
a = JSMatrix.mat([[1,2,9],[8,3,2],[3,7,3]]);
b1 = JSMatrix.vec([32,20,26]);
b2 = JSMatrix.vec([16,32,26]);
b3 = [b1.copy(),b2.copy()];
b4 = JSMatrix.mat([b1.toArray(),b2.toArray()]).T();
x1 = a.gaussJordanElimination(b1);
// x1 = Vector([ 1, 2, 3 ])
x2 = a.gaussJordanElimination(b2);
// x2 = Vector([ 3, 2, 1 ])
x3 = a.gaussJordanElimination(b3);
// x3 = [Vector([ 1, 2, 3 ]) ,Vector([ 3, 2, 1 ])]
x4 = a.gaussJordanElimination(b4);
// x4 = Matrix([[ 1, 3 ], [ 2, 2 ], [ 3, 1 ]])
x5 = a.gaussJordanElimination(b1,'nopivot');;
// x5 = Vector([ 1, 2, 3 ])
x6 = a.gaussJordanElimination(b2,'nopivot');
// x6 = Vector([ 3, 2, 1 ])
x7 = a.gaussJordanElimination(b3,'nopivot');
// x7 = Vector([ 1, 2, 3 ]) ,Vector([ 3, 2, 1 ])
x8 = a.gaussJordanElimination(b4,'nopivot');
// x8 = Matrix([[ 1, 3 ], [ 2, 2 ], [ 3, 1 ]])
a.gaussJordanElimination(b4,'nopivot',false);
// b4 = Matrix([[ 1, 3 ], [ 2, 2 ], [ 3, 1 ]])

get(r, c) → {number|null}

Coefficient access function, returns one element of receiver ( ret = this[r][c] ). Matrix.get(r,c) is much safer than direct Matrix[r][c] access method
Parameters:
Name Type Description
r number index of row of element to be returned
c number index of column of element to be returned
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1433
Returns:
value of the element at r-th row and c-th column
Type
number | null
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
g = m.get(1,2); // g = 23
g = m[1][2]; // g = 23
/// c out of bounds
g = m.get(1,5); // g = null
g = m[1][5]; // g = undefined
/// r out of bounds
g = m.get(6,5) // g = null
/// g = m[6][5]; would be error (m[6] is not defined)

getCol(c) → {JSMatrix.Vector}

Returns one column of receiver
Parameters:
Name Type Description
c number index of column to return
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1702
Returns:
c-th column of receiver as vector
Type
JSMatrix.Vector
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
v = m.getCol(1); // v = Vector([2,5,8])

getRow(r) → {JSMatrix.Vector}

Returns one row of receiver
Parameters:
Name Type Description
r number index of row to return
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1688
Returns:
r-th row of receiver as vector
Type
JSMatrix.Vector
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
v = m.getRow(1); // v = Vector([4,5,6])

getsm()

Alias for getSubMatrix, see {@JSMatrix.Matrix#getSubMatrix}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2395

getSubMatrix(rows, cols) → {JSMatrix.Matrix}

Returns submatrix of receiver ( ret = this[rows][cols] )
Parameters:
Name Type Description
rows Array.<number> | JSMatrix.Vector array containing rows coefficients of desired submatrix
cols Array.<number> | JSMatrix.Vector array containing columns coefficients of desired submatrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2372
Returns:
desired submatrix
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m2 = m1.getSubMatrix([1,2],[0,2]); // m2 = Matrix([[21,23],[31,33]])

giveAntiSymmetricPart()

Alias for symetrized(), see {@JSMatrix.Matrix#antiSymmetrized}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2334

giveDeterminant()

Alias for determinant, see {@JSMatrix.Matrix#determinant}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4328

giveSymmetricPart()

Alias for symmetrized(), see {@JSMatrix.Matrix#symmetrized}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2258

iadd(mat)

Add given matrix to receiver ( this += mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be added
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1546
Example
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m1.iadd(m2); // m1 = Matrix([[3,7],[6,6]])

implicitPartialPivotPermutation(saveOrig) → {Object|null}

Returns row permutation matrix using implicit partial pivoting (for each column find row with relatively highest element at that column and place that line to the position such that the highest element is on diagonal. Lines that are placed in this way are not considered for further steps)
Parameters:
Name Type Argument Description
saveOrig boolean <optional>
 =true] if true, returns permutated copy of receiver. If false, permutate receiver and return this
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3155
Returns:
{mat:JSMatrix.Matrix,coeffs:Array.} permutated matrix and array containing coefficients of original matrix according to position in the permutated one ( such that this.rowPermutation(coeffs) = ret )
Type
Object | null
Example
m1 = JSMatrix.mat([[1,2,4,9],[1,8,1,1],[9,4,5,3],[1,2,6,2]]);
m2 = m1.implicitPartialPivotPermutation();
// m2.mat = Matrix([[9,4,5,3],[1,8,1,1],[1,2,6,2],[1,2,4,9]])
// m2.coeffs = [2,1,3,0]
// m1 = Matrix([[1,2,4,9],[1,8,1,1],[9,4,5,3],[1,2,6,2]])
m3 = m1.rowPermutation(m2.coeffs); // m3 = Matrix([[9,4,5,3],[1,8,1,1],[1,2,6,2],[1,2,4,9]])
b = m3.isEqualTo(m2.mat); // b = true
m4 = m2.mat.rowPermutation(m2.coeffs,true); // m4 = Matrix([[1,2,4,9],[1,8,1,1],[9,4,5,3],[1,2,6,2]])
b = m4.isEqualTo(m1); // b = true
m1.implicitPartialPivotPermutation(false);
// m1 = Matrix([[9,4,5,3],[1,8,1,1],[1,2,6,2],[1,2,4,9]])

imulf(f)

Multiply receiver by float f ( this *= f )
Parameters:
Name Type Description
f number float multiplier
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1928
Example
m = JSMatrix.mat([[1,2,3],[4,5,6]]);
m.imulf(3); // m = Matrix([[3,6,9],[12,15,18]])

incr(r, c, val)

Coefficient access function, increment one element of receiver ( this[r][c] += val ). Matrix.incr(r,c,val) is much safer than direct Matrix[r][c]+=val access method
Parameters:
Name Type Description
r number index of row of element to be incremented
c number index of column of element to be incremented
val number value to be add
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1476
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m.incr(1,2,3.45); // m = Matrix([[11,12,13],[21,22,26.45],[31,32,33]])
m[1][2] += 3.45; // m = Matrix([[11,12,13],[21,22,29.9],[31,32,33]])
/// c out of bounds
m.incr(1,5,3.45); // m = Matrix([[11,12,13],[21,22,29.9],[31,32,33]])
/// m[1][5] += 3.45); would be error (m[1][5] is not defined)
/// r out of bounds
m.incr(6,5,3.45); // m = Matrix([[11,12,13],[21,22,29.9],[31,32,33]])
/// m[6][5] += 3.45; would be error (m[6] is not defined)

incrCol(c, vec)

Incerements one column of receiver
Parameters:
Name Type Description
c number index of column to set
vec JSMatrix.Vector vector to be incremented to c-th column
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1758
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.incrCol(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,13,3],[4,17,6],[7,21,9]])

incrRow(r, vec)

Incerements one row of receiver
Parameters:
Name Type Description
r number index of row to set
vec JSMatrix.Vector vector to be incremented to r-th row
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1744
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.incrRow(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,2,3],[15,17,19],[7,8,9]])

incrsm()

Alias for incrSubMatrix, see {@JSMatrix.Matrix#incrSubMatrix}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2477

incrSubMatrix(rows, cols, mat)

Increment submatrix at defined positions of receiver ( this[rows][cols] += mat )
Parameters:
Name Type Description
rows Array.<number> | JSMatrix.Vector array containing rows coefficients to be incrementes
cols Array.<number> | JSMatrix.Vector array containing columns coefficients to be incremented
mat JSMatrix.Matrix matrix to be incremented on desired positions
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2460
Example
m = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m.incrSubMatrix([1,2],[0,2],JSMatrix.mat([[66,77],[88,99]]));
// m = Matrix([11,12,13,14],[87,22,100,24],[119,32,132,34],[41,42,43,44]])

ineg()

Alias for neagete(), see {@JSMatrix.Matrix#negate}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1660

inv()

Alias for inversion, see {@JSMatrix.Matrix#inversed}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4255

inversed(method, precompDecomps) → {JSMatrix.Matrix}

Returns inversion of receiver
Parameters:
Name Type Argument Description
method string <optional>
 ="default"] method used for solution. Options are "default" and "gaussjordan" for Gauss-Jordan method, "lu" for solution with LU decomposition, "eigen" with eigen decomposition, "symmeigen" with eigen decomposition when receiver is symmetric, "svd" for SVD decomposition
precompDecomps Array.<JSMatrix.Matrix> <optional>
 =undefined] precomputed matrix decompositions if we want to use some
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4189
Returns:
inversion of receiver
Type
JSMatrix.Matrix
Example
a = JSMatrix.mat([[1,2,2],[1,0,1],[1,2,1]]);
i1 = a.inversed(); // i1 =
c = a.mulm(i1) // c = Matrix([[1,0,0],[0,1,0],[0,0,1]])
i2 = a.inversed('lu') // i2 = Matrix([[-1,1,1],[0,-0.5,0.5],[1,0,-1]])
i3 = a.inversed('eigen') // i3 = Matrix([[-1,1,1],[0,-0.5,0.5],[1,0,-1]])
i4 = a.inversed('svd') // i4 = Matrix([[-1,1,1],[0,-0.5,0.5],[1,0,-1]])
check = a.x(i1); // check = Matrix([[1,0,0],[0,1,0],[0,0,1]])

isAntiSymmetric() → {boolean}

Testing if receiver is anti-symmetric
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2944
Returns:
true if receiver is anti-symmetric, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m2 = JSMatrix.mat([[0,12,13],[-12,0,23],[-13,-23,0]]);
t1 = m1.isAntiSymmetric(); // t1 = false
t2 = m2.isAntiSymmetric(); // t2 = true

isEmpty()

Tests if receiver is empty (has size 0,0)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1311
Returns:
true if receiver is empty, false otherwise
Example
v1 = new JSMatrix.Matrix(2,3);
v2 = new JSMatrix.Matrix();
b1 = v1.isEmpty(); // b1 = false
b2 = v2.isEmpty(); // b2 = true

isEqualTo(mat) → {boolean}

Testing matrix equality
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be compared with receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2854
Returns:
true if this==mat, false otherwise
Type
boolean
Example
a = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
b = JSMatrix.mat([[1,2,2.999999999],[4.0000000000002,5,6],[7,8,8.9999999999]]);
c = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]);
t1 = a.isEqualTo(b); // t1 = true
t2 = a.isEqualTo(c); // t2 = false

isIdentity() → {boolean}

Test if receiver is identity matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3031
Returns:
true if receiver is identity, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,0,0],[0,1,0],[0,0,-1]]);
m2 = JSMatrix.mat([[1,0,0],[0,1,0],[0,0,1]]);
i1 = m1.isIdentity() // i1 = false
i2 = m2.isIdentity() // i2 = true

isInvolutary() → {boolean}

Tests receiver's involutariness (if this*this=I -> this^-1=this)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3133
Returns:
true if receiver is involutary, false otherwise
Type
boolean
Example
m = JSMatrix.mat([[1,0,0],[0,-1,0],[0,0,-1]])
t = m.isInvolutary() // t = true

isLowerTriangular() → {boolean}

Testing if receiver is lower triangular matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2983
Returns:
true if receiver is lower triangular, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m2 = JSMatrix.mat([[1,0,0],[4,5,0],[7,8,9]]);
t1 = m1.isLowerTriangular(); // t1 = false
t2 = m2.isLowerTriangular(); // t2 = true

isOne() → {boolean}

Test if receiver is matrix full of ones
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3081
Returns:
true if receiver is full of ones, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,1,1],[1,.999999999999,1],[1,1,1]]);
m2 = JSMatrix.mat([[1,0,0],[0,1,0],[0,0,1]]);
i1 = m1.isOne() // i1 = true
i2 = m2.isOne() // i2 = false

isOrthogonal() → {boolean}

Tests receiver's orthogonality (i.e. this*this^T = I => this^-1 = this^T)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3108
Returns:
true if receiver is orthogonal, false otherwise
Type
boolean
Example
m1 = JSMatrix.Matrix.Householder(JSMatrix.vec([0,1,0]))
// m1 = Matrix([[1,0,0],[0,-1,0],[0,0,1]]);
m2 = JSMatrix.mat([[0,0,1],[1,0,0],[0,1,0]])
m3 = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]])
m4 = JSMatrix.mat([[0.8,0,0.6],[0,1,0],[-0.8,0,0.6]]);
b1 = m1.isOrthogonal() // b1 = true
b2 = m2.isOrthogonal() // b2 = true
b3 = m3.isOrthogonal() // b3 = false
b4 = m4.isOrthogonal() // b4 = true

isPositiveDefinite() → {boolean}

Tests receiver's positive definitness
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3122
Returns:
true if receiver is positive definite (if Cholesky decomposition can be performed), false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[9,2,1],[2,8,3],[1,3,7]])
m2 = JSMatrix.mat([[-9,2,1],[2,8,3],[1,3,7]])
b1 = m1.isPositiveDefinite() // b1 = true
b2 = m2.isPositiveDefinite() // b2 = false

isSameSizeAs(mat) → {boolean}

Testing matrix size equality
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be tested
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2874
Returns:
true if mat and receiver has same size, false otherwise
Type
boolean
Example
a = JSMatrix.mat([[1,2,3],[4,5,6]]);
b = JSMatrix.mat([[5,6,7],[8,9,10],[11,12,13]]);
c = JSMatrix.mat([[14,15,16],[17,18,19]]);
t1 = a.isSameSizeAs(b); // t1 = false
t2 = a.isSameSizeAs(c); // t2 = true

isSingular() → {boolean}

Test receiver's singularity
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3017
Returns:
true if receiver is singular (if abs(this.det()) < JSMatrix.TOL), false otherwise
Type
boolean
Example
a = JSMatrix.mat([[1,2,3],[2,4,6],[4,5,6]]);
b = JSMatrix.mat([[4,2,1],[2,5,3],[1,3,6]]);
s1 = a.isSingular(); // s1 = true
s2 = b.isSingular(); // s2 = false

isSquare() → {boolean}

Testing if receiver is square
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2914
Returns:
true if receiver is square matrix, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
t1 = m1.isSquare(); // t1 = false
t2 = m2.isSquare(); // t2 = true

isSymmetric() → {boolean}

Testing if receiver is symmetric
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2926
Returns:
true if receiver is symmetric, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m2 = JSMatrix.mat([[11,12,13],[12,22,23],[13,23,33]]);
t1 = m1.isSymmetric(); // t1 = false
t2 = m2.isSymmetric(); // t2 = true

isTranspositionOf(mat) → {boolean}

Testing if receiver is transposition of given matrix
Parameters:
Name Type Description
mat JSMatrix.Matrix given matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2964
Returns:
true if this==mat^T, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = JSMatrix.mat([[1,4],[2,5],[3,6]]);
m3 = JSMatrix.mat([[1,2],[4,5]]);
b1 = m1.isTranspositionOf(m2); // b1 = true
b2 = m1.isTranspositionOf(m3); // b2 = false

isub(mat)

Subtract given matrix to receiver ( this -= mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be added
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1602
Example
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m1.isub(m2); // m1 = Matrix([[-1,-3],[0,2]])

isUnitMatrix()

Alias for isIdentity, see {@JSMatrix.Matrix#isIdentity}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3049

isUpperTriangular() → {boolean}

Testing if receiver is upper triangular matrix
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3000
Returns:
true if receiver is upper triangular, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m2 = JSMatrix.mat([[1,2,3],[0,5,6],[0,0,9]]);
t1 = m1.isUpperTriangular(); // t1 = false
t2 = m2.isUpperTriangular(); // t2 = true

isZero() → {boolean}

Test if receiver is zero matrix (full of zeroes)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3059
Returns:
true if receiver is zero, false otherwise
Type
boolean
Example
m1 = JSMatrix.mat([[0,0,0],[0,1e-16,0],[0,0,0]]);
m2 = JSMatrix.mat([[1,0,0],[0,1,0],[0,0,1]]);
i1 = m1.isZero() // i1 = true
i2 = m2.isZero() // i2 = false

lduDecomposition(pivoting) → {Object|null}

Returns lower triangular (L), diagonal (D) and upper triangular (U) matrix of the receiver such that L*D*U=this. Diagonal elements of both L and U are all 1. Receiver must be square.
Parameters:
Name Type Argument Description
pivoting string <optional>
 ="default"] what type of pivoting to use. "default" and "nopivot" stands for no pivoting, "partpivot" for implicit partial pivoting (only row interchanges)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3574
Returns:
{l,d,u}, lower, diagonal and upper triangular matrices
Type
Object | null
Example
a = JSMatrix.mat([[2,10,8],[4,23,22],[6,42,52]]);
ldu = a.lduDecomposition();
l = ldu.l; // l = Matrix([[1,0,0],[2,1,0],[3,4,1]])
d = ldu.d; // d = Vector([2,3,4])
u = ldu.u; // u = Matrix([[1,5,4],[0,1,2],[0,0,1]])
check = l.x(d.diag()).x(u) // check = Matrix([[2,10,8],[4,23,22],[6,42,52]]);

linSolve(rhs, method, saveOrig, precompDecomps) → {JSMatrix.Vector|Array.<JSMatrix.Vector>|JSMatrix.Matrix}

Returns vector/array of vectors/matrix as a solution of system of linear equations (this*ret=rhs --> ret). Receiver must be square. TODO: solution with LU decomposition with permutation
Parameters:
Name Type Argument Description
rhs JSMatrix.Vector | Array.<JSMatrix.Vector> | JSMatrix.Matrix vector of right hand sides. Array of vectors or Matrix as rhs is supported only with "gaussjordan" method
method string <optional>
 ="default"] method of the solution. Implemented methods are "default" and "gauss" for gaussian elimination, "gaussjordan" for Gauss-Jordan elimination (supporting more than one right hand sides in form of array of vectors or matrix with columns as rhs), "lu" for using LU decomposition, "ldu" for using LDU decomposition, "cholesky" for using Cholesky decomposition, "qr" for using QR decomposition
saveOrig boolean <optional>
 =true] if true, receiver and rhs is not changed. If false, solution will be saved to rhs and rhs will be returned and receiver will be changed
precompDecomps Array.<JSMatrix.Matrix> <optional>
 =undefined] array of Matrices objects, used for solution using matrix decomposition as precomputed values (the decomposition is performed within linSolve function if args parameter is not specified)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3702
Returns:
vector/array of vectors/matrix of solution
Type
JSMatrix.Vector | Array.<JSMatrix.Vector> | JSMatrix.Matrix
Example
a = JSMatrix.mat([[1,2,9],[8,3,2],[3,7,3]]);
b = JSMatrix.vec([32,20,26]);
x1 = a.linSolve(b); // x1 = Vector([1,2,3])
x2 = a.linSolve(b,'gauss'); // x2 = Vector([1,2,3])
x3 = a.linSolve(b,'gaussjordan'); // x3 = Vector([1,2,3])
x4 = a.linSolve(b,'lu'); // x4 = Vector([1,2,3])
x5 = a.linSolve(b,'ldu'); // x5 = Vector([1,2,3])
x7 = a.linSolve(b,'qr'); // x7 = Vector([1,2,3])
a2 = JSMatrix.mat([[1,2,4],[2,13,23],[4,23,77]]);
b2 = JSMatrix.vec([17,97,281]);
x6 = a2.linSolve(b2,'cholesky'); // x6 = Vector([1,2,3])

lltDecomposition()

Alias for Cholesky decomposition, see {@JSMatrix.Matrix#choleskyDecomposition}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3491

luDecomposition(pivoting) → {Object|null}

Returns lower (L) and upper (U) triangular matrix of the receiver such that L*U=this. Diagonal elements of L are all 1. Receiver must be square.
Parameters:
Name Type Argument Description
pivoting string <optional>
 ="default"] what type of pivoting to use. "default" and "nopivot" stands for no pivoting, "partpivot" for implicit partial pivoting (only row interchanges)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3503
Returns:
{l,u}, lower and upper triangular matrices
Type
Object | null
Example
a = JSMatrix.mat([[6,5,4],[12,13,10],[18,27,21]]);
lu = a.luDecomposition();
l = lu.l; // l = Matrix([[1,0,0],[2,1,0],[3,4,1]])
u = lu.u; // u = Matrix([[6,5,4],[0,3,2],[0,0,1]])
check = l.x(u); // check = Matrix([[6,5,4],[12,13,10],[18,27,21]])

max() → {number}

Returns receiver's maximal element
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2802
Returns:
receiver's maximal element
Type
number
Example
a = JSMatrix.mat([[1,-2,3],[-4,5,-6],[-7,8,-9]]);
b = a.max(); // b = 8

min() → {number}

Returns receiver's minimal element
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2818
Returns:
receiver's minimal element
Type
number
Example
a = JSMatrix.mat([[1,-2,3],[-4,5,-6],[-7,8,-9]]);
b = a.min(); // b = -9

mul(what) → {JSMatrix.Matrix|JSMatrix.Vector}

Returns product of receiver and given multiplier (Matrix, Vector or float)
Parameters:
Name Type Description
what JSMatrix.Matrix | JSMatrix.Vector | number matrix, vector or float to multiply
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1999
Returns:
copy of receiver multiplied by what
Type
JSMatrix.Matrix | JSMatrix.Vector
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = m1.mul(3); // m2 = Matrix([[3,6,9],[12,15,18]])
//
m3 = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
v1 = JSMatrix.vec([1,2,3]);
v2 = m3.mul(v1) // v2 = Vector([74,134,194]);
//
m4 = JSMatrix.mat([[11,12],[21,22]]);
m5 = JSMatrix.mat([[1,2],[3,4]]);
m6 = m4.mul(m5); // m6 = Matrix([[47,70],[87,130]])

mulf(f) → {JSMatrix.Matrix}

Returns receiver multiplied by float f ( ret = this * f )
Parameters:
Name Type Description
f number float multiplier
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1909
Returns:
copy of receiver multiplied by f
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = m1.mulf(3); // m2 = Matrix([[3,6,9],[12,15,18]])

mulm(mat) → {JSMatrix.Matrix}

Returns product of receiver and given matrix ( ret = this * mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to multiply
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1965
Returns:
copy of receiver multiplied by mat
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[11,12],[21,22]]);
m2 = JSMatrix.mat([[1,2],[3,4]]);
m3 = m1.mulm(m2); // m3 = Matrix([[47,70],[87,130]])

mulv(vec) → {JSMatrix.Vector}

Returns product of receiver and given vector ( ret = this * vec )
Parameters:
Name Type Description
vec JSMatrix.Vector vector to multiply
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1942
Returns:
copy of receiver multiplied by vec
Type
JSMatrix.Vector
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
v1 = JSMatrix.vec([1,2,3]);
v2 = m.mulv(v1); // v2 = Vector([74,134,194])

neg()

Alias for neageted(), see {@JSMatrix.Matrix#negated}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1644

negate()

Negate receiver ( ret *= -1., ret = -ret )
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1651
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m1.negate(); // m1 = Matrix([[-1,-2,-3],[-4,-5,-6]])

negated() → {JSMatrix.Matrix}

Returns negative of receiver ( ret = -this )
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1637
Returns:
negative of receiver
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = m1.negated(); // m2 = Matrix([[-1,-2,-3],[-4,-5,-6]])

one()

Alias for beFullOfOnes(), see {@JSMatrix.Matrix#beFullOfOnes}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1340

permuteRows(coeffs, backward)

Permute rows of receiver according to given coefficients
Parameters:
Name Type Argument Description
coeffs Array.<number> | JSMatrix.Vector coefficients of row permutation
backward boolean <optional>
 =false] if false, receiver's rows is permutated to given coefficients (forward). If true, from given coefficients (backward)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1834
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m.permuteRows([1,2,0]); // m = Matrix([[21,22,23],[31,32,33],[11,12,13]])
m.permuteRows([1,2,0],true); // m = mat([[11,12,13],[21,22,23],[31,32,33]])

polarDecomposition(precompSvd) → {Object|null}

Returns orthogonal matrix R and symmetric matrix U of polar decomposition of the receiver such that this=R*U. The decomposition is computed from SVD decomposition (this = U*S*V^T -> R = U*V^T, U = V*S*V^T
Parameters:
Name Type Argument Description
precompSvd Object <optional>
 =undefined] precomputed SVD decomposition
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3930
Returns:
{r,u} orthogonal matrix R and symmetric matrix U of polar decomposition of receiver
Type
Object | null
Example
m = JSMatrix.mat([[1.6,.6,0],[-1.2,0.8,0],[0,0,3]])
ru = m.polarDecomposition();
r = ru.r; // r = Matrix([[0.8,0.6,0],[-0.6,0.8,0],[0,0,1]])
u = ru.u; // u = Matrix([[2,0,0],[0,1,0],[0,0,3]])
b1 = r.isOrthogonal(); // b1 = true
b2 = u.isSymmetric(); // b2 = true
c = r.mulm(u); // c = Matrix([[1.6,.6,0],[-1.2,0.8,0],[0,0,3]])

resize(nRows, nCols)

Resize receiver according to given size (delete extra elements or add zero elements)
Parameters:
Name Type Description
nRows number new number of rows
nCols number new number of columns
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2642
Example
m1 = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m2 = JSMatrix.mat([[11,12],[21,22]]);
m1.resize(3,3); // m1 = Matrix([[11,12,13],[21,22,23],[31,32,33]])
m2.resize(3,3); // m2 = Matrix([[11,12,0],[21,22,0],[0,0,0]])

resized(nRows, nCols) → {JSMatrix.Matrix}

Returns resized copy of receiver according to given size (delete extra elements or add zero elements)
Parameters:
Name Type Description
nRows number new number of rows
nCols number new number of columns
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2683
Returns:
resized copy of receiver
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m2 = m1.resized(2,4); // m2 = Matrix([[11,12,13,0],[21,22,23,0]])
m3 = m1.resized(4,2); // m3 = Matrix([[11,12],[21,22],[31,32],[0,0]])

rowPermutation(coeffs, backward) → {JSMatrix.Matrix}

Returns copy of receiver with rows permutated according to given coefficients
Parameters:
Name Type Argument Description
coeffs Array.<number> | JSMatrix.Vector coefficients of permutation.
backward boolean <optional>
 =false] if false, receiver is permutated to given coefficients (forward). If true, from given coefficients (backward)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1877
Returns:
copy of receiver with permutated rows
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m2 = m1.rowPermutation([1,2,0]); // m2 = Matrix([[21,22,23],[31,32,33],[11,12,13]])
m3 = m1.rowPermutation([1,2,0],true); // m3 = mat([[31,32,33],[11,12,13],[21,22,23]])

schurDecomposition(saveOrig, maxiter) → {Object|null}

returns orthogonal matrix Q and upper triangular matrix S as Schur decomposition of receiver such that this=Q*S*Q^-1. Columns of Q are eigenvectors of receiver and diagonal elements of S are eigenvalues of receiver
Parameters:
Name Type Argument Description
saveOrig boolean <optional>
 =true] if true, returns new matrices, if false, S is formed into original matrix
maxiter number <optional>
 =1000] maximum number of iterations
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3812
Returns:
{q,s} - Scur decomposition of receiver
Type
Object | null
Example
m1 = JSMatrix.mat([[4,2,3,1],[3,6,5,7],[5,3,8,1],[2,3,4,5]]);
qs = m1.schurDecomposition();
q = qs.q; s = qs.s;
// s = Matrix([[ 15.6072, -3.6605, -0.7006, 2.3149 ], [ 0, 4.1916, 3.3807, 2.0775 ], [ 0, 0, 2.2012, 0.0769 ], [ 0, 0, 0, 1 ]])
qr = s.qrDecomposition();
q1 = qr.q; r = qr.r;
// q1 = Matrix([[ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ]])
// r = Matrix([[ 15.6072, -3.6605, -0.7006, 2.3149 ], [ 0, 4.1916, 3.3807, 2.0775 ], [ 0, 0, 2.2012, 0.0769 ], [ 0, 0, 0, 1 ]])
b1 = q.isOrthogonal() // b1 = true
b2 = s.isUpperTriangular() // b2 = true
c = q.mulm(s).mulm(q.inv()); // c = Matrix([[4,2,3,1],[3,6,5,7],[5,3,8,1],[2,3,4,5]])

schurForm(saveOrig, maxiter) → {JSMatrix.Matrix}

returns Schur form of receiver (upper triangular matrix with eigenvalues of the receiver on the diagonal). QR algorithm is used for calculation
Parameters:
Name Type Argument Description
saveOrig boolean <optional>
 =true] if true, returns new matrix, if false the Schur form is formed on original matrix
maxiter number <optional>
 =1000] maximum number of iterations
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3765
Returns:
Schur form of receiver (upper triangular matrix with eigenvalues on diagonal)
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[4,2,3,1],[3,6,5,7],[5,3,8,1],[2,3,4,5]]);
m2 = m1.schurForm(); // m2 = Matrix([[ 15.6072, -3.6605, -0.7006, 2.3149 ], [ 0, 4.1916, 3.3807, 2.0775 ], [ 0, 0, 2.2012, 0.0769 ], [ 0, 0, 0, 1 ]])
b = m2.isUpperTriangular(); // b = true

set(r, c, val)

Coefficient access function, sets one element of receiver ( this[r][c] = val ). Matrix.set(r,c,val) is much safer than direct Matrix[r][c]=val access method
Parameters:
Name Type Description
r number index of row of element to be set
c number index of column of element to be set
val number value to be set
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1455
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m.set(1,2,3.45); // m = Matrix([[11,12,13],[21,22,3.45],[31,32,33]])
m[1][2] = 3.45; // m = Matrix([[11,12,13],[21,22,3.45],[31,32,33]])
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
/// c out of bounds (nothing is done by both appraches)
m.set(1,5,8.45); // m = Matrix([[11,12,13],[21,22,3.45],[31,32,33]])
m[1][5] = 8.45; // m = Matrix([[11,12,13],[21,22,3.45],[31,32,33]])
/// r out of bounds
m.set(6,5,8.45); // m = Matrix([[11,12,13],[21,22,3.45],[31,32,33]])
/// m[6][5] = 8.45; would be error (m[6] is not defined)

setCol(c, vec)

Sets one column of receiver
Parameters:
Name Type Description
c number index of column to set
vec JSMatrix.Vector vector to be set as new c-th column
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1730
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.setCol(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,11,3],[4,12,6],[7,13,9]])

setRow(r, vec)

Sets one row of receiver
Parameters:
Name Type Description
r number index of row to set
vec JSMatrix.Vector vector to be set as new r-th row
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1716
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.setRow(1,JSMatrix.vec([11,12,13])); // m = Matrix([[1,2,3],[11,12,13],[7,8,9]])

setsm()

Alias for setSubMatrix, see {@JSMatrix.Matrix#setSubMatrix}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2449

setSubMatrix(rows, cols, mat)

Sets submatrix at defined positions of receiver ( this[rows][cols] = mat )
Parameters:
Name Type Description
rows Array.<number> | JSMatrix.Vector array containing rows coefficients to be set
cols Array.<number> | JSMatrix.Vector array containing columns coefficients to be set
mat JSMatrix.Matrix matrix to be set on desired positions
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2432
Example
m = JSMatrix.mat([[11,12,13,14],[21,22,23,24],[31,32,33,34],[41,42,43,44]]);
m.setSubMatrix([1,2],[0,2],JSMatrix.mat([[66,77],[88,99]]));
// m = Matrix([[11,12,13,14],[66,22,77,24],[88,32,99,34],[41,42,43,44]])

singularValueDecomposition() → {Object|null}

Returns orthogonal matrix U, diagonal matrix S and orthogonal matrix V of singular value decomposition (SVD) of receiver such that this = U*S*V^T. U is computed as orthonormalized iegenvectors of this^T*this, V as orhonormalized eigenvectors of this*this^T and diagonal components of S as square roots of eigenvalues of this^T*this (TODO faster algorithm). this*V = U*S, A^T*U = V*S. Current implementation allows only square matrices (TODO gegeral-shaped matrices)
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3859
Returns:
{u,s,v} orthogonal matrix U, diagonal of matrix S and orthogonal matrix V of svd decomposition of receiver
Type
Object | null
Example
m1 = JSMatrix.mat([[1.6,0.6,0.],[-1.2,0.8,0.],[0.,0.,3.]])
svd = m1.singularValueDecomposition();
u = svd.u; // u = Matrix([[0.6,0.8,0],[0.8,-0.6,0],[0,0,1]])
s = svd.s; // s = Vector([1,2,3])
v = svd.v; // v = Matrix([[0,1,0],[1,0,0],[0,0,1]])
b1 = u.isOrthogonal() // b1 = true
b2 = v.isOrthogonal() // b2 = true
c = u.mulm(s.diag()).mulm(v.transposed());
// c = JSMatrix.mat([[1.6,0.6,0.],[-1.2,0.8,0.],[0.,0.,3.]])

size() → {Object}

Returns size of receiver as [nRows,nCols]
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1373
Returns:
{nRows:number,nCols:number} size of receiver
Type
Object
Example
m = JSMatrix.mat([[1,2,3],[4,5,6]]);
s = m.size(); // s = {nRows:2,nCols:3}
nRows = s.nRows; // nRows = 2
nCols = s.nCols; // nCols = 3

spectralDecomposition()

Returns spectral decomposition of receiver, identical to {@JSMatrix.Matrix#eigenDecomposition}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 4153

sub(mat) → {JSMatrix.Matrix}

Returns difference of receiver and matrix ( ret = this - mat )
Parameters:
Name Type Description
mat JSMatrix.Matrix matrix to be added
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1583
Returns:
sum of receiver and matrix
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[1,2],[3,4]]);
m2 = JSMatrix.mat([[2,5],[3,2]]);
m3 = m1.sub(m2); // m3 = Matrix([[-1,-3],[0,2]])

svd()

Alias for singular value decomposition, see JSMatrix.Matrix.singularValueDecomposition
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 3879

swapCols(c1, c2)

Swaps two columns of receiver
Parameters:
Name Type Description
c1 number index of first row to swap
c2 number index of second row to swap
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1815
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m.swapCols(0,2); // m = Matrix([[13,12,11],[23,22,21],[33,32,31]])

swapRows(r1, r2)

Swaps two rows of receiver
Parameters:
Name Type Description
r1 number index of first row to swap
r2 number index of second row to swap
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1800
Example
m = JSMatrix.mat([[11,12,13],[21,22,23],[31,32,33]]);
m.swapRows(0,2); // m = Matrix([[31,32,33],[21,22,23],[11,12,13]])

symmetrize()

Symmetrize receiver ( this = .5*(this+this^T) ). Receiver must be square
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2219
Example
m = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m.symmetrize(); // m = Matrix([[1,1,1],[1,-1,3],[1,3,7]])
b = m.isSymmetric(); // b = true

symmetrized()

Returns symmetric part of receiver ( ret = .5*(this+this^T) ). Receiver must be square
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2237
Example
m1 = JSMatrix.mat([[1,2,3],[0,-1,5],[-1,1,7]])
m2 = m1.symmetrized(); // m2 = Matrix([[1,1,1],[1,-1,3],[1,3,7]])
b = m2.isSymmetric(); // b = true

T()

Alias for transposed(), see {@JSMatrix.Matrix#transposed}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2157

toArray() → {Array.<Array.<number>>}

Returns elements of receiver as an Array object
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1508
Returns:
2D array containing receiver's elements
Type
Array.<Array.<number>>
Example
m =JSMatrix.mat([[11,12],[21,22]]);
a = m.toArray(); // a = [[11,12],[21,22]]

toString() → {string}

Returns string representation of receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2604
Returns:
string representation of receiver
Type
string
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
s = m.toString(); // s = 'Matrix([[1,2,3],[4,5,6],[7,8,9]])'

trace() → {number|null}

Returns trace (sum of diagonal elements) of the receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1383
Returns:
trace of the receiver
Type
number | null
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]])
tr = m.trace() // tr = 15

transpose()

Modifies receiver to become transposition of itself ( this = this^T )
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2165
Example
m = JSMatrix.mat([[1,2,3],[4,5,6]]);
m.transpose(); // m = Matrix([[1,4],[2,5],[3,6]])
m.transpose(); // m = Matrix([[1,2,3],[4,5,6]])

transposed() → {JSMatrix.Matrix}

Returns transposition of receiver ( ret = this^T )
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2143
Returns:
transposed copy of receiver
Type
JSMatrix.Matrix
Example
m1 = JSMatrix.mat([[1,2,3],[4,5,6]]);
m2 = m1.transposed(); // m2 = Matrix([[1,4],[2,5],[3,6]])

x()

Alias for mul(), see {@JSMatrix.Matrix#mul}
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 2010

zero()

Zeroes all elements of receiver
Source:
  • /var/www/html/software/jsmatrix/jsmatrix.src.js, line 1320
Example
m = JSMatrix.mat([[1,2,3],[4,5,6],[7,8,9]]);
m.zero(); // m = Matrix([[0,0,0],[0,0,0],[0,0,0]])