The purpose of the high-level magicl bindings is to allow for MATLAB-like multidimensional arrays in lisp.
The construction of tensors can be done with any of the given constructors. The constructors take a shape and arguments for method of construction.
Tensors are specialized on both the shape and the element type. The class of a tensor will be of the form $CLASS/$TYPE (e.g. MATRIX/DOUBLE-FLOAT).
| Number of dimensions | Tensor Class |
|---|---|
| 1 | VECTOR |
| 2 | MATRIX |
| * | TENSOR |
| Element Type | Class Suffix |
|---|---|
SINGLE-FLOAT |
SINGLE-FLOAT |
DOUBLE-FLOAT |
DOUBLE-FLOAT |
(COMPLEX SINGLE-FLOAT) |
COMPLEX-SINGLE-FLOAT |
(COMPLEX DOUBLE-FLOAT) |
COMPLEX-DOUBLE-FLOAT |
(SIGNED-BYTE 32) |
INT32 |
The type of the elements of the tensor can be specified with the :type keyword, or the constructor will attempt to find an appropriate type from the given arguments. The default element type for a tensor is DOUBLE-FLOAT.
The layout of the tensor (column-major or row-major) can be specified with the :layout keyword. This affects the underlying storage of the tensor and will affect how it carries out operations with LAPACK.
This table was adapted largely from the NumPy Equivalents Table.
| MAGICL | MATLAB | NumPy | Description |
|---|---|---|---|
(order a) |
ndims(a) |
ndim(a) or a.ndim |
Get the number of dimensions of the array. |
(size a) |
numel(a) |
size(a) or a.size |
Get the number of elements of the array. |
(shape a) |
size(a) |
shape(a) or a.shape |
Get the shape of the array. |
(tref a 1 4) |
a(2,5) |
a[1, 4] |
Get the element in the second row, fifth column of the array. |
| MAGICL | MATLAB | NumPy | Description |
|---|---|---|---|
(from-list '(1d0 2d0 3d0 4d0 5d0 6d0) '(2 3)) |
[ 1 2 3; 4 5 6 ] |
array([[1.,2.,3.], [4.,5.,6.]]) |
Create a 2x3 matrix from given elements. |
(zeros '(2 3 4)) or (const 0d0 '(2 3 4)) |
zeros(2,3,4) |
zeros((2,3,4)) |
Create a 2x3x4 dimensional array of zeroes of double-float element type. |
(ones '(3 4) or (const 1d0 '(3 4)) |
ones(3,4) |
ones((3,4)) |
Create a 3x4 dimensional array of ones of double-float element type. |
(eye 1d0 '(3 3)) |
eye(3) |
eye(3) |
Create a 3x3 identity array of double-float element type. |
(from-diag a) |
diag(a) |
diag(a) |
Create a square matrix from the diagonal entries in a with zeroes everywhere else. |
(rand '(3 4)) |
rand(3,4) |
random.rand(3,4) |
Create a random 3x4 array. |
| MAGICL | MATLAB | NumPy | Description |
|---|---|---|---|
(@ a b) |
a * b |
a @ b |
Matrix multiplication |
(.+ a b) |
a + b |
a + b |
Element-wise add |
(.- a b) |
a - b |
a - b |
Element-wise subtract |
(.* a b) |
a .* b |
a * b |
Element-wise multiply |
(./ a b) |
a./b |
a/b |
Element-wise divide |
(.^ a b) |
a.^b |
np.power(a,b) |
Element-wise exponentiation |
| MAGICL | MATLAB | NumPy | Description |
|---|---|---|---|
(det a) |
det(a) |
linalg.det(a) |
Determinant of matrix |
(trace a) |
trace(a) |
trace(a) |
Trace (sum of diagonal elements) of matrix |
(upper-triangular a) |
triu(a) |
triu(a) |
Upper triangular part of matrix |
(lower-triangular a) |
tril(a) |
tril(a) |
Lower triangular part of matrix |
(transpose a) |
a.' |
a.transpose() or a.T |
Transpose of matrix |
(conjugate-transpose a) or (dagger a) |
a' |
a.conj().transpose() or a.H |
Conjugate transpose of matrix |
(inv a) |
inv(a) |
linalg.inv(a) |
Inverse of matrix |
(svd a) (Returns (VALUES U SIGMA Vt)) |
[U,S,V]=svd(a) |
U, S, Vh = linalg.svd(a), V = Vh.T |
Singular value decomposition of matrix |
(eig a) (Returns (VALUES EIGENVALUES EIGENVECTORS)) |
[V,D]=eig(a) |
D,V = linalg.eig(a) |
Eigenvalues and eigenvectors of matrix |
(qr a) (Returns (VALUES Q R)) |
[Q,R,P]=qr(a,0) |
Q,R = scipy.linalg.qr(a) |
QR factorization of matrix |
(ql a) (Returns (VALUES Q L)) |
QL factorization of matrix | ||
(rq a) (Returns (VALUES R Q)) |
R,Q = scipy.linalg.rq(a) |
RQ factorization of matrix | |
(lq a) (Returns (VALUES L Q)) |
LQ factorization of matrix | ||
(lu a) (Returns (VALUES LU IPIV)) |
[L,U,P]=lu(a) |
L,U = scipy.linalg.lu(a) or LU,P=scipy.linalg.lu_factor(a) |
LU decomposition of matrix |
(csd a) (Returns (VALUES U SIGMA VT)) |
Cosine-sine decomposition of matrix |