fastmath.matrix — generateme/fastmath 3.0.0-alpha2

Fixed size (2x2, 3x3, 4x4) matrix types.

acos clj

(acos vector)

Apply acos to matrix elements.

acosh clj

(acosh vector)

Apply acosh to matrix elements.

acot clj

(acot vector)

Apply acot to matrix elements.

acoth clj

(acoth vector)

Apply acoth to matrix elements.

acsc clj

(acsc vector)

Apply acsc to matrix elements.

acsch clj

(acsch vector)

Apply acsch to matrix elements.

add clj

(add A)

(add A B)

Add matrices, C=A+B.

adds clj

(adds A s)

Add scalar to all matrix elements

asec clj

(asec vector)

Apply asec to matrix elements.

asech clj

(asech vector)

Apply asech to matrix elements.

asin clj

(asin vector)

Apply asin to matrix elements.

asinh clj

(asinh vector)

Apply asinh to matrix elements.

atan clj

(atan vector)

Apply atan to matrix elements.

atanh clj

(atanh vector)

Apply atanh to matrix elements.

cb clj

(cb vector)

Apply cb to matrix elements.

cbrt clj

(cbrt vector)

Apply cbrt to matrix elements.

ceil clj

(ceil vector)

Apply ceil to matrix elements.

cholesky clj

(cholesky A)

(cholesky A upper?)

Calculate L (lower by default) triangular for where L * L^T = A.

Checks only for symmetry, can return NaNs when A is not positive-definite.

col clj

(col A c)

Return column as a vector

cols clj

(cols A)

Return matrix columns

cols->mat clj

(cols->mat real-matrix-cols)

(cols->mat [a00 a10] [a01 a11])

(cols->mat [a00 a10 a20] [a01 a11 a21] [a02 a12 a22])

(cols->mat [a00 a10 a20 a30]
           [a01 a11 a21 a31]
           [a02 a12 a22 a32]
           [a03 a13 a23 a33])

Create nxn matrix from nd vectors (columns).

cols->mat2x2 clj

(cols->mat2x2 [a00 a10] [a01 a11])

Create 2x2 matrix from 2d vectors (columns).

cols->mat3x3 clj

(cols->mat3x3 [a00 a10 a20] [a01 a11 a21] [a02 a12 a22])

Create 3x3 matrix from 3d vectors (columns).

cols->mat4x4 clj

(cols->mat4x4 [a00 a10 a20 a30]
              [a01 a11 a21 a31]
              [a02 a12 a22 a32]
              [a03 a13 a23 a33])

Create 4x4 matrix from 4d vectors (columns).

cols->RealMatrix clj

(cols->RealMatrix cols)

Return Apache Commons Math Array2DRowMatrix from sequence of columns

condition clj

(condition A)

(condition A norm-type)

Condition number calculated for L2 norm by default (see norm for other norm types).

Cond(A) = norm(A) * norm(inv(A))

cos clj

(cos vector)

Apply cos to matrix elements.

cosh clj

(cosh vector)

Apply cosh to matrix elements.

cot clj

(cot vector)

Apply cot to matrix elements.

coth clj

(coth vector)

Apply coth to matrix elements.

csc clj

(csc vector)

Apply csc to matrix elements.

csch clj

(csch vector)

Apply csch to matrix elements.

degrees clj

(degrees vector)

Apply degrees to matrix elements.

det clj

(det A)

Return determinant of the matrix.

diag clj

(diag A)

Return diagonal of the matrix as a vector.

diagonal clj

(diagonal v)

(diagonal a11 a22)

(diagonal a11 a22 a33)

(diagonal a11 a22 a33 a44)

Create diagonal matrix

eigenvalues clj

(eigenvalues A)

Return complex eigenvalues for given matrix as a sequence

eigenvalues-matrix clj

(eigenvalues-matrix A)

Return eigenvalues for given matrix as a diagonal or block diagonal matrix

eigenvectors clj

(eigenvectors A)

(eigenvectors A normalize?)

Return eigenvectors as a matrix (columns). Vectors can be normalized.

emulm clj

(emulm A B)

Multiply two matrices element-wise, Hadamard product, C=AoB

entry clj

(entry A row col)

Get entry at given row and column

exp clj

(exp vector)

Apply exp to matrix elements.

expm1 clj

(expm1 vector)

Apply expm1 to matrix elements.

eye clj

(eye size)

Identity matrix for given size

floor clj

(floor vector)

Apply floor to matrix elements.

fmap clj

(fmap A f)

Apply a function f to each matrix element.

frac clj

(frac vector)

Apply frac to matrix elements.

inverse clj

(inverse m)

Matrix inversion.

Returns nil if inversion doesn't exist.

ln clj

(ln vector)

Apply ln to matrix elements.

log clj

(log vector)

Apply log to matrix elements.

log10 clj

(log10 vector)

Apply log10 to matrix elements.

log1mexp clj

(log1mexp vector)

Apply log1mexp to matrix elements.

log1p clj

(log1p vector)

Apply log1p to matrix elements.

log1pexp clj

(log1pexp vector)

Apply log1pexp to matrix elements.

log1pmx clj

(log1pmx vector)

Apply log1pmx to matrix elements.

log1psq clj

(log1psq vector)

Apply log1psq to matrix elements.

log2 clj

(log2 vector)

Apply log2 to matrix elements.

logexpm1 clj

(logexpm1 vector)

Apply logexpm1 to matrix elements.

logit clj

(logit vector)

Apply logit to matrix elements.

logmxp1 clj

(logmxp1 vector)

Apply logmxp1 to matrix elements.

mat clj

(mat real-matrix-rows)

(mat a00 a01 a10 a11)

(mat a00 a01 a02 a10 a11 a12 a20 a21 a22)

(mat a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33)

Create mat2x2, mat3x3 or mat4x4 or RealMatrix from rows

mat->array clj

(mat->array A)

Return flat double array of entries (row order)

mat->array2d clj

(mat->array2d A)

Return doubles of doubles

mat->float-array clj

(mat->float-array A)

Return flat float array of entries (row order)

mat->float-array2d clj

(mat->float-array2d A)

Return doubles of doubles

mat->RealMatrix clj

(mat->RealMatrix A)

Return Apache Commons Math Array2DRowMatrix from a 2x2, 3x3 or 4x4 matrix

mat->seq clj

(mat->seq A)

Return flat sequence of entries (row order)

mat2x2 clj

(mat2x2 v)

(mat2x2 d1 d2)

(mat2x2 a00 a01 a10 a11)

Create 2x2 matrix.

Arity:

• 1 - fills matrix with given value
• 2 - creates diagonal matrix
• 4 - creates row ordered matrix

mat3x3 clj

(mat3x3 v)

(mat3x3 d1 d2 d3)

(mat3x3 a00 a01 a02 a10 a11 a12 a20 a21 a22)

Create 3x3 matrix.

Arity:

• 1 - fills matrix with given value
• 3 - creates diagonal matrix
• 9 - creates row ordered matrix

mat4x4 clj

(mat4x4 v)

(mat4x4 d1 d2 d3 d4)

(mat4x4 a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33)

Create 4x4 matrix.

Arity:

• 1 - fills matrix with given value
• 4 - creates diagonal matrix
• 16 - creates row ordered matrix

mulm clj

(mulm A B)

(mulm A transposeA? B transposeB?)

Multiply two matrices, C=AxB.

Optionally you can request transposition of matrices.

mulmt clj

(mulmt A B)

Multiply with transposed matrix, C=AxB^T

muls clj

(muls A s)

Multply matrix by a scalar, C=sA

mulv clj

(mulv A v)

Multply matrix by vector, x=Av

ncol clj

(ncol A)

Return number of rows

negate clj

(negate A)

Negate all matrix elements, C=-A

norm clj

(norm A)

(norm A norm-type)

Calculate norm of the matrix for given type, default: 1 (maximum absolute column sum).

All norm types are:

• 1 - maximum absolute column sum
• :inf - maximum absolute row sum
• 2 - spectral norm, maximum singular value
• :max - maximum absolute value
• :frobenius - Frobenius norm
• [p,q] - generalized L_pq norm, [2,2] - Frobenius norm, [p,p] - entrywise p-norm
• [p] - Shatten p-norm, [1] - nuclear/trace norm

normalize clj

(normalize A)

(normalize A rows?)

Normalize columns (or rows)

nrow clj

(nrow A)

Return number of rows

outer clj

(outer v1 v2)

Outer project for two vectors.

radians clj

(radians vector)

Apply radians to matrix elements.

rint clj

(rint vector)

Apply rint to matrix elements.

rotation-matrix-2d clj

(rotation-matrix-2d theta)

Create rotation matrix for a plane

rotation-matrix-3d clj

(rotation-matrix-3d [x y z])

(rotation-matrix-3d x y z)

Create rotation matrix for a 3d space. Tait–Bryan angles z-y′-x″

rotation-matrix-3d-x clj

(rotation-matrix-3d-x a)

Create rotation matrix for a 3d space, x-axis, right hand rule.

rotation-matrix-3d-y clj

(rotation-matrix-3d-y a)

Create rotation matrix for a 3d space, y-axis, right hand rule.

rotation-matrix-3d-z clj

(rotation-matrix-3d-z a)

Create rotation matrix for a 3d space, z-axis, right hand rule.

rotation-matrix-axis-3d clj

(rotation-matrix-axis-3d angle axis)

Create 3d rotation matrix for axis ratation.

round clj

(round vector)

Apply round to matrix elements.

row clj

(row A r)

Return row as a vector

rows clj

(rows A)

Return matrix rows

rows->mat clj

(rows->mat real-matrix-rows)

(rows->mat [a00 a01] [a10 a11])

(rows->mat [a00 a01 a02] [a10 a11 a12] [a20 a21 a22])

(rows->mat [a00 a01 a02 a03]
           [a10 a11 a12 a13]
           [a20 a21 a22 a23]
           [a30 a31 a32 a33])

Create nxn matrix from nd vectors (rows).

rows->mat2x2 clj

(rows->mat2x2 [a00 a01] [a10 a11])

Create 2x2 matrix from 2d vectors (rows).

rows->mat3x3 clj

(rows->mat3x3 [a00 a01 a02] [a10 a11 a12] [a20 a21 a22])

Create 3x3 matrix from 3d vectors (rows).

rows->mat4x4 clj

(rows->mat4x4 [a00 a01 a02 a03]
              [a10 a11 a12 a13]
              [a20 a21 a22 a23]
              [a30 a31 a32 a33])

Create 4x4 matrix from 4d vectors (rows).

rows->RealMatrix clj

(rows->RealMatrix rows)

Return Apache Commons Math Array2DRowMatrix from sequence of rows

safe-sqrt clj

(safe-sqrt vector)

Apply safe-sqrt to matrix elements.

scale-cols clj

(scale-cols A)

(scale-cols A scale)

Shift columns by a value (default: sqrt(sum(x^2)/(n-1))) or a result of the function

scale-rows clj

(scale-rows A)

(scale-rows A scale)

Shift rows by a value (default: sqrt(sum(x^2)/(n-1))) or a result of the function

sec clj

(sec vector)

Apply sec to matrix elements.

sech clj

(sech vector)

Apply sech to matrix elements.

sfrac clj

(sfrac vector)

Apply sfrac to matrix elements.

sgn clj

(sgn vector)

Apply sgn to matrix elements.

shift-cols clj

(shift-cols A)

(shift-cols A shift)

Shift columns by a value or a result of the function (mean by default)

shift-rows clj

(shift-rows A)

(shift-rows A shift)

Shift rows by a value or a result of the function (mean by default)

sigmoid clj

(sigmoid vector)

Apply sigmoid to matrix elements.

signum clj

(signum vector)

Apply signum to matrix elements.

sin clj

(sin vector)

Apply sin to matrix elements.

sinc clj

(sinc vector)

Apply sinc to matrix elements.

singular-values clj

(singular-values A)

Returun singular values of the matrix as sqrt of eigenvalues of A^T * A matrix.

sinh clj

(sinh vector)

Apply sinh to matrix elements.

solve clj

(solve A b)

Solve linear equation Ax=b

sq clj

(sq vector)

Apply sq to matrix elements.

sqrt clj

(sqrt vector)

Apply sqrt to matrix elements.

sub clj

(sub A)

(sub A B)

Subract matrices, C=A-B.

symmetric? clj

(symmetric? A)

Check if matrix is symmetric

tan clj

(tan vector)

Apply tan to matrix elements.

tanh clj

(tanh vector)

Apply tanh to matrix elements.

tmulm clj

(tmulm A B)

Transpose and multiply, C=A^TxB

tmulmt clj

(tmulmt A B)

Transpose both and multiply, C=A^TxB^T

trace clj

(trace A)

Return trace of the matrix (sum of diagonal elements)

transpose clj

(transpose A)

Transpose matrix, C=A^T

trunc clj

(trunc vector)

Apply trunc to matrix elements.

vtmul clj

(vtmul A v)

Multiply transposed vector by matrix, C=v^T A

xlogx clj

(xlogx vector)

Apply xlogx to matrix elements.

zero clj

(zero size)

Zero matrix for given size