Matrix to be used in pure computations, uses column major memory layout, features copy-free FFI with C++ Eigen library.

Alias for single precision matrix

Alias for double precision matrix

Alias for single previsiom matrix of complex numbers

Alias for double prevision matrix of complex numbers

Complex number for FFI with the same memory layout as std::complex<T>

Verify matrix dimensions and memory layout

Construct matrix from a list of rows, column count is detected as maximum row length. Missing values are filled with 0

Convert matrix to a list of rows

Build matrix of given dimensions and values from given list split on rows. Invalid list length results in error.

Convert matrix to a list by concatenating rows

generate rows cols (λ row col -> val)

Create matrix using generator function λ row col -> val

Empty 0x0 matrix

Is matrix empty?

Is matrix square?

Matrix where all coeff are 0

Matrix where all coeff are 1

The identity matrix (not necessarily square).

Matrix where all coeffs are filled with given value

The random matrix of a given size

Number of columns for the matrix

Number of rows for the matrix

Mtrix size as (rows, cols) pair

Matrix coefficient at specific row and col

Matrix coefficient at specific row and col

Unsafe version of coeff function. No bounds check performed so SEGFAULT possible

List of coefficients for the given col

List of coefficients for the given row

Extract rectangular block from matrix defined by startRow startCol blockRows blockCols

Top N rows of matrix

Bottom N rows of matrix

Left N columns of matrix

Right N columns of matrix

The sum of all coefficients of the matrix

The product of all coefficients of the matrix

The mean of all coefficients of the matrix

The minimum coefficient of the matrix

The maximum coefficient of the matrix

The trace of a matrix is the sum of the diagonal coefficients and can also be computed as sum (diagonal m)

For vectors, the l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of this with itself.

For vectors, the squared l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of this with itself.

The l2 norm of the matrix using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

The l2 norm of the matrix avoiding undeflow and overflow. This version use a concatenation of hypot calls, and it is very slow.

The determinant of the matrix

Reduce matrix using user provided function applied to each element.

Reduce matrix using user provided function applied to each element. This is strict version of fold

Reduce matrix using user provided function applied to each element and it's index

Reduce matrix using user provided function applied to each element and it's index. This is strict version of ifold

Reduce matrix using user provided function applied to each element.

Reduce matrix using user provided function applied to each element. This is strict version of fold

Applied to a predicate and a matrix, all determines if all elements of the matrix satisfies the predicate

Applied to a predicate and a matrix, any determines if any element of the matrix satisfies the predicate

Returns the number of coefficients in a given matrix that evaluate to true

Adding two matrices by adding the corresponding entries together. You can use (+) function as well.

Subtracting two matrices by subtracting the corresponding entries together. You can use (-) function as well.

Matrix multiplication. You can use (*) function as well.

Apply a given function to each element of the matrix.

Here is an example how to implement scalar matrix multiplication:

>>> let a = fromList [[1,2],[3,4]] :: MatrixXf

>>> a
Matrix 2x2
1.0 2.0
3.0 4.0

>>> map (*10) a
Matrix 2x2
10.0    20.0
30.0    40.0

Apply a given function to each element of the matrix.

Here is an example how upper triangular matrix can be implemented:

>>> let a = fromList [[1,2,3],[4,5,6],[7,8,9]] :: MatrixXf

>>> a
Matrix 3x3
1.0 2.0 3.0
4.0 5.0 6.0
7.0 8.0 9.0

>>> imap (\row col val -> if row <= col then val else 0) a
Matrix 3x3
1.0 2.0 3.0
0.0 5.0 6.0
0.0 0.0 9.0

Filter elements in the matrix. Filtered elements will be replaced by 0

Filter elements in the matrix. Filtered elements will be replaced by 0

Diagonal of the matrix

Transpose of the matrix

Inverse of the matrix

For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses PartialPivLU decomposition

Adjoint of the matrix

Conjugate of the matrix

Nomalize the matrix by deviding it on its norm

Apply a destructive operation to a matrix. The operation will be performed in place if it is safe to do so and will modify a copy of the matrix otherwise.

Convert matrix to different type using user provided element converter

Triangular view extracted from the current matrix

Lower trinagle of the matrix. Shortcut for triangularView Lower

Upper trinagle of the matrix. Shortcut for triangularView Upper

Encode the matrix as a lazy byte string

Decode matrix from the lazy byte string

Yield a mutable copy of the immutable matrix

Yield an immutable copy of the mutable matrix

Unsafely convert an immutable matrix to a mutable one without copying. The immutable matrix may not be used after this operation.

Unsafe convert a mutable matrix to an immutable one without copying. The mutable matrix may not be used after this operation.

Pass a pointer to the matrix's data to the IO action. The data may not be modified through the pointer.