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Mathjs 参考

Formula:
Result:
点击下面表格中某函数的 Example call，可将示例自动填入上方输入框并执行。

Expression functions

FunctionDefinitionExample callParametersExpected result
compile解析并编译表达式（负责解析，不直接返回结果）。compile('2 + 3')表达式（字符串）{}
evaluate计算表达式并返回结果。evaluate('2 + 3')表达式（字符串），作用域（可选）5
help检索函数或数据类型的使用说明。help('evaluate')搜索关键字（字符串）{ "name": "evaluate", "category": "Expression", "syntax": [ "evaluate(expression)", "evaluate(expression, scope)", "evaluate([expr1, expr2, expr3, ...])", "evaluate([expr1, expr2, expr3, ...], scope)" ], "description": "Evaluate an expression or an array with expressions.", "examples": [ "evaluate(\"2 + 3\")", "evaluate(\"sqrt(16)\")", "evaluate(\"2 inch to cm\")", "evaluate(\"sin(x * pi)\", { \"x\": 1/2 })", "evaluate([\"width=2\", \"height=4\",\"width*height\"])" ], "seealso": [], "mathjs": "Help" }
parser创建自定义操作用的解析器。parser()无{}

Algebra functions

FunctionDefinitionExample callParametersExpected result
derivative对表达式进行求导，并指定变量。derivative('x^2', 'x')表达式（字符串或节点），变量（字符串）{ "mathjs": "OperatorNode", "op": "*", "fn": "multiply", "args": [ { "mathjs": "ConstantNode", "value": 2 }, { "mathjs": "SymbolNode", "name": "x" } ], "implicit": false, "isPercentage": false }
leafCount统计表达式解析树中的叶节点数量（符号或常量）。leafCount('x^2 + y')表达式（字符串或节点）3
lsolve使用前向替换法求解线性方程组的一个解。lsolve([[1,2],[3,4]], [5,6])L（数组或矩阵），b（数组或矩阵）[ [ 5 ], [ -2.25 ] ]
lsolveAll使用前向替换法求解线性方程组的所有解。lsolveAll([[1,2],[3,4]], [5,6])L（数组或矩阵），b（数组或矩阵）[ [ [ 5 ], [ -2.25 ] ] ]
lup对矩阵执行部分主元LU分解。lup([[1,2],[3,4]])A（数组或矩阵）{ "L": [ [ 1, 0 ], [ 0.3333333333333333, 1 ] ], "U": [ [ 3, 4 ], [ 0, 0.6666666666666667 ] ], "p": [ 1, 0 ] }
lusolve求解线性方程 A*x=b（A 为 n×n 矩阵）。lusolve([[1,2],[3,4]], [5,6])A（数组或矩阵），b（数组或矩阵）[ [ -3.9999999999999987 ], [ 4.499999999999999 ] ]
lyap求解连续时间李雅普诺夫方程 AP+PA’+Q=0。lyap(A, Q)A（数组或矩阵），Q（数组或矩阵）Error: A is not defined
polynomialRoot求解多项式的数值根（可包含复数）。polynomialRoot(1, 2, 3, 4)常数项，线性系数项，... 最多到三次项（可选）[ -0.605829586188268, { "mathjs": "Complex", "re": -0.07208520690586608, "im": -0.6383267351483765 }, { "mathjs": "Complex", "re": -0.07208520690586608, "im": 0.6383267351483765 } ]
qr对矩阵执行 QR 分解。qr([[1,2],[3,4]])A（数组或矩阵）{ "Q": [ [ 0.316227766016838, 0.9486832980505138 ], [ 0.9486832980505138, -0.316227766016838 ] ], "R": [ [ 3.162277660168379, 4.427188724235731 ], [ 0, 0.6324555320336751 ] ] }
rationalize将可有理化的表达式转换为有理分式。rationalize('1/(x+1)')表达式（字符串或节点）{ "mathjs": "OperatorNode", "op": "/", "fn": "divide", "args": [ { "mathjs": "ConstantNode", "value": 1 }, { "mathjs": "OperatorNode", "op": "+", "fn": "add", "args": [ { "mathjs": "SymbolNode", "name": "x" }, { "mathjs": "ConstantNode", "value": 1 } ], "implicit": false, "isPercentage": false } ], "implicit": false, "isPercentage": false }
resolve用给定作用域中的值替换表达式中的变量。resolve('x + y', {x:2, y:3})表达式（字符串或节点），作用域（对象）{ "mathjs": "OperatorNode", "op": "+", "fn": "add", "args": [ { "mathjs": "ConstantNode", "value": 2 }, { "mathjs": "ConstantNode", "value": 3 } ], "implicit": false, "isPercentage": false }
schur对实数矩阵 A 执行施尔分解 A = U T U’。schur([[1,2],[3,4]])A（数组或矩阵）{ "U": [ [ 0.41597355791928425, -0.9093767091321243 ], [ 0.9093767091321244, 0.41597355791928414 ] ], "T": [ [ 5.37228132326902, -1.0000000000000002 ], [ 5.147016547482756e-118, -0.37228132326901375 ] ] }
simplify简化表达式解析树（合并同类项等）。simplify('2x + 3x')表达式（字符串或节点）{ "mathjs": "OperatorNode", "op": "*", "fn": "multiply", "args": [ { "mathjs": "ConstantNode", "value": 5 }, { "mathjs": "SymbolNode", "name": "x" } ], "implicit": false, "isPercentage": false }
simplifyConstant对表达式中的常量子表达式进行计算替换。simplifyConstant('2+3')表达式（字符串或节点）{ "mathjs": "ConstantNode", "value": 5 }
simplifyCore单次传递（one-pass）简化表达式，多用于性能敏感场景。simplifyCore('x+x')表达式（字符串或节点）{ "mathjs": "OperatorNode", "op": "+", "fn": "add", "args": [ { "mathjs": "SymbolNode", "name": "x" }, { "mathjs": "SymbolNode", "name": "x" } ], "implicit": false, "isPercentage": false }
slu以完全主元方式计算稀疏 LU 分解。slu([[1,2],[3,4]], 'natural', 1)A（数组或矩阵），分解顺序（字符串），阈值（数字）Error: Unexpected type of argument in function slu (expected: SparseMatrix, actual: Array, index: 0)
sylvester求解实数Sylvester方程 AX + XB = C。sylvester(A, B, C)A（数组或矩阵），B（数组或矩阵），C（数组或矩阵）Error: A is not defined
symbolicEqual检测两个表达式在符号意义上是否相等。symbolicEqual('x+x', '2x')表达式1（字符串或节点），表达式2（字符串或节点）true
usolve使用回代法求解线性方程组的一个解。usolve([[1,2],[0,1]], [3,4])U（数组或矩阵），b（数组或矩阵）[ [ -5 ], [ 4 ] ]
usolveAll使用回代法求解线性方程组的所有解。usolveAll([[1,2],[0,1]], [3,4])U（数组或矩阵），b（数组或矩阵）[ [ [ -5 ], [ 4 ] ] ]

Arithmetic functions

FunctionDefinitionExample callParametersExpected result
abs计算一个数的绝对值。abs(-3.2)x（数字、复数、数组或矩阵）3.2
add将两个或更多数值相加（x + y）。add(2, 3)x、y、…（数字、数组或矩阵）5
cbrt计算一个数的立方根，可选地计算所有立方根。cbrt(8)x（数字或复数），allRoots（布尔，可选）2
ceil向正无穷方向取整（对于复数则对实部和虚部分别取整）。ceil(3.2)x（数字、复数、数组或矩阵）4
cube计算一个数的立方 (x*x*x)。cube(3)x（数字、复数、数组或矩阵）27
divide两个值相除 (x / y)。divide(6, 2)x（数字、数组或矩阵），y（数字、数组或矩阵）3
dotDivide逐元素地对两个矩阵或数组执行除法。dotDivide([6,8],[2,4])x（数组或矩阵），y（数组或矩阵）[ 3, 2 ]
dotMultiply逐元素地对两个矩阵或数组执行乘法。dotMultiply([2,3],[4,5])x（数组或矩阵），y（数组或矩阵）[ 8, 15 ]
dotPow逐元素地对 x^y 求幂。dotPow([2,3],[2,3])x（数组或矩阵），y（数组或矩阵）[ 4, 27 ]
exp计算 e^x。exp(1)x（数字、复数、数组或矩阵）2.718281828459045
expm1计算 e^x - 1。expm1(1)x（数字或复数）1.718281828459045
fix向零方向取整（截断）。fix(3.7)x（数字、复数、数组或矩阵）3
floor向负无穷方向取整。floor(3.7)x（数字、复数、数组或矩阵）3
gcd求两个或更多数的最大公约数。gcd(8, 12)a, b, ...（数字或大数）4
hypot计算多个数的平方和的平方根（如勾股定理）。hypot(3, 4)a, b, …（数字或大数）5
invmod计算 a 在模 b 意义下的乘法逆元。invmod(3, 11)a, b（数字或大数）4
lcm求两个或更多数的最小公倍数。lcm(4, 6)a, b, ...（数字或大数）12
log计算对数（可指定底）。log(100, 10)x（数字或复数），base（可选，数字或复数）2
log10计算一个数的 10 进制对数。log10(100)x（数字或复数）2
log1p计算 ln(1 + x)。log1p(1)x（数字或复数）0.6931471805599453
log2计算一个数的 2 进制对数。log2(8)x（数字或复数）3
mod计算 x ÷ y 的余数（x mod y）。mod(8,3)x, y（数字或大数）2
multiply将两个或更多数值相乘（x * y）。multiply(2, 3)x、y、…（数字、数组或矩阵）6
norm计算数字、向量或矩阵的范数，可选 p。norm([3,4])x（数组或矩阵），p（数字或字符串，可选）5
nthRoot计算一个数的 n 次方根（主根）。nthRoot(16, 4)a（数字、大数或复数），root（可选，数字）2
nthRoots计算一个数的所有 n 次方根，可能包含复数解。nthRoots(1,3)x（数字或复数），root（数字）[ { "mathjs": "Complex", "re": 1, "im": 0 }, { "mathjs": "Complex", "re": -0.4999999999999998, "im": 0.8660254037844387 }, { "mathjs": "Complex", "re": -0.5000000000000004, "im": -0.8660254037844384 } ]
pow计算 x^y。pow(2, 3)x（数字、复数、数组或矩阵），y（数字、复数、数组或矩阵）8
round四舍五入到指定的小数位数。round(3.14159, 2)x（数字、复数、数组或矩阵），n（可选，数字）3.14
sign计算数值的符号（-1、0 或 1）。sign(-3)x（数字、大数或复数）-1
sqrt计算一个数的平方根。sqrt(9)x（数字、复数、数组或矩阵）3
square计算一个数的平方 (x*x)。square(3)x（数字、复数、数组或矩阵）9
subtract两个数相减 (x - y)。subtract(8, 3)x, y（数字、数组或矩阵）5
unaryMinus对值执行一元负操作（取反）。unaryMinus(3)x（数字、复数、数组或矩阵）-3
unaryPlus对值执行一元加操作（通常无实际变化）。unaryPlus(-3)x（数字、复数、数组或矩阵）-3
xgcd计算两个数的扩展最大公约数。xgcd(8, 12)a, b（数字或大数）{ "mathjs": "DenseMatrix", "data": [ 4, -1, 1 ], "size": [ 3 ] }

Bitwise functions

FunctionDefinitionExample callParametersExpected result
bitAnd对两个值进行按位与 (x & y)。bitAnd(5, 3)x, y（数字或大数）1
bitNot对值执行按位取反 (~x)。bitNot(5)x（数字或大数）-6
bitOr对两个值进行按位或 (x | y)。bitOr(5, 3)x, y（数字或大数）7
bitXor对两个值进行按位异或 (x ^ y)。bitXor(5, 3)x, y（数字或大数）6
leftShift将 x 的二进制位左移 y 位 (x << y)。leftShift(5, 1)x, y（数字或大数）10
rightArithShift对 x 的二进制位进行算术右移 (x >> y)。rightArithShift(5, 1)x, y（数字或大数）2
rightLogShift对 x 的二进制位进行逻辑右移 (x >>> y)。rightLogShift(5, 1)x, y（数字或大数）2

Combinatorics functions

FunctionDefinitionExample callParametersExpected result
bellNumbers计算 n 个互异元素的所有划分方式数量。bellNumbers(3)n（数字）5
catalan计算 n 的卡塔兰数，对应多种组合结构计数。catalan(5)n（数字）42
composition计算将 n 拆分成 k 部分的组合数。composition(5, 3)n, k（数字）6
stirlingS2计算将 n 个有标签的元素划分为 k 个非空子集的方式（第二类斯特林数）。stirlingS2(5, 3)n, k（数字）25

Complex functions

FunctionDefinitionExample callParametersExpected result
arg计算复数的幅角（相位）。arg('2 + 2i')x（复数或数字）Error: Cannot convert "2 + 2i" to a number
conj计算复数的共轭。conj('2 + 2i')x（复数或数字）Error: Cannot convert "2 + 2i" to a number
im获取复数的虚部。im('2 + 3i')x（复数或数字）Error: Cannot convert "2 + 3i" to a number
re获取复数的实部。re('2 + 3i')x（复数或数字）Error: Cannot convert "2 + 3i" to a number

Geometry functions

FunctionDefinitionExample callParametersExpected result
distance计算 N 维空间中两点之间的欧几里得距离。distance([0,0],[3,4])point1（数组），point2（数组）5
intersect求两条线（二维/三维）或一条线与一个平面（三维）的交点。intersect([0,0],[2,2],[0,2],[2,0])直线1的起点与终点，直线2的起点与终点，...[ 1, 1 ]

Logical functions

FunctionDefinitionExample callParametersExpected result
and执行逻辑与运算。and(true, false)x, y（布尔值或数字）false
not执行逻辑非运算。not(true)x（布尔值或数字）false
or执行逻辑或运算。or(true, false)x, y（布尔值或数字）true
xor执行逻辑异或运算。xor(1, 0)x, y（布尔值或数字）true

Matrix functions

FunctionDefinitionExample callParametersExpected result
apply沿指定轴对矩阵或数组应用函数。apply([[1,2],[3,4]], 1, val => val * 2)A（数组或矩阵），dim（数字），callback（函数）[ null, null ]
column从矩阵中返回指定列。column([[1,2],[3,4]], 0)value（矩阵或数组），index（数字）[ [ 1 ], [ 3 ] ]
concat沿指定维度拼接多个矩阵/数组。concat([1,2], [3,4], [5,6])a, b, c, ...（数组或矩阵），dim（数字，可选）[ 1, 2, 3, 4, 5, 6 ]
count统计矩阵、数组或字符串的元素数量。count([1,2,3,'hello'])x（数组、矩阵或字符串）4
cross计算两个三维向量的叉积。cross([1,2,3], [4,5,6])x, y（长度为3的数组或矩阵）[ -3, 6, -3 ]
ctranspose对矩阵进行转置并取共轭。ctranspose([[1,2],[3,4]])x（矩阵或数组）[ [ 1, 3 ], [ 2, 4 ] ]
det计算矩阵的行列式。det([[1,2],[3,4]])x（矩阵或数组）-2
diag创建对角矩阵或提取矩阵的对角线。diag([1,2,3])X（数组或矩阵）[ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ] ]
diff计算指定维度上相邻元素之间的差值。diff([1,4,9,16])arr（数组或矩阵），dim（数字，可选）[ 3, 5, 7 ]
dot计算两个向量的点积。dot([1,2,3],[4,5,6])x, y（数组或矩阵）32
eigs计算方阵的特征值和（可选）特征向量。eigs([[1,2],[3,4]])x（矩阵或数组），prec（数值，可选）{ "values": [ -0.37228132326901653, 5.372281323269014 ], "eigenvectors": [ { "value": -0.37228132326901653, "vector": [ -4.505883335311908, 3.091669772938812 ] }, { "value": 5.372281323269014, "vector": [ 0.4438641329939267, 0.9703494293791691 ] } ] }
expm计算矩阵的指数 e^A。expm([[1,0],[0,1]])x（矩阵或数组）{ "mathjs": "DenseMatrix", "data": [ [ 2.7182818284590424, 0 ], [ 0, 2.7182818284590424 ] ], "size": [ 2, 2 ] }
fft计算 N 维快速傅里叶变换。fft([1,2,3,4])arr（数组或矩阵）[ { "mathjs": "Complex", "re": 10, "im": 0 }, { "mathjs": "Complex", "re": -2, "im": 2 }, { "mathjs": "Complex", "re": -2, "im": 0 }, { "mathjs": "Complex", "re": -1.9999999999999998, "im": -2 } ]
filter使用测试函数过滤数组或一维矩阵。filter([1,2,3,4,5], val => val > 2)x（数组或矩阵），test（函数）[ 3, 4, 5 ]
flatten将多维矩阵或数组展开为一维。flatten([[1,2],[3,4]])x（数组或矩阵）[ 1, 2, 3, 4 ]
forEach遍历矩阵/数组的每个元素并执行回调。forEach([1,2,3], val => console.log(val))x（数组或矩阵），callback（函数）undefined
getMatrixDataType查看矩阵或数组所有元素的数据类型，例如 'number' 或 'Complex'。getMatrixDataType([[1,2.2],[3,'hello']])x（数组或矩阵）mixed
identity创建 n x n（或 m x n）的单位矩阵。identity(3)n（数字）或 [m, n]（数组）{ "mathjs": "DenseMatrix", "data": [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], "size": [ 3, 3 ] }
ifft计算 N 维逆快速傅里叶变换。ifft([1,2,3,4])arr（数组或矩阵）[ { "mathjs": "Complex", "re": 2.5, "im": 0 }, { "mathjs": "Complex", "re": -0.5, "im": -0.5 }, { "mathjs": "Complex", "re": -0.5, "im": 0 }, { "mathjs": "Complex", "re": -0.49999999999999994, "im": 0.5 } ]
inv计算方阵的逆矩阵。inv([[1,2],[3,4]])x（矩阵或数组）[ [ -2, 1 ], [ 1.5, -0.5 ] ]
kron计算两个矩阵或向量的克罗内克积。kron([[1,1],[0,1]], [[2,0],[0,2]])x, y（矩阵或数组）[ [ 2, 0, 2, 0 ], [ 0, 2, 0, 2 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ]
map通过对每个元素应用回调创建新的数组/矩阵。map([1,2,3], val => val * val)x（数组或矩阵），callback（函数）[ 1, 4, 9 ]
matrixFromColumns将多个向量作为单独列组合成一个稠密矩阵。matrixFromColumns([1,4],[2,5],[3,6])...arr（数组或矩阵）[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
matrixFromFunction根据函数对矩阵每个索引进行求值来生成矩阵。matrixFromFunction([2,3], (i,j) => i + j)size（数组），fn（函数）Error: Cannot convert "0,0undefined" to a number
matrixFromRows将多个向量作为单独行组合成一个稠密矩阵。matrixFromRows([1,2,3],[4,5,6])...arr（数组或矩阵）[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
ones创建给定维度的全 1 矩阵。ones(2, 3)m, n, p...（数字）{ "mathjs": "DenseMatrix", "data": [ [ 1, 1, 1 ], [ 1, 1, 1 ] ], "size": [ 2, 3 ] }
partitionSelect基于分区选择法，从数组或一维矩阵返回第 k 小的元素。partitionSelect([3,1,4,2], 2)x（数组或矩阵），k（数字）3
pinv计算矩阵的 Moore–Penrose 伪逆。pinv([[1,2],[2,4]])x（矩阵或数组）[ [ 0.04000000000000001, 0.08000000000000002 ], [ 0.08000000000000002, 0.16000000000000003 ] ]
range从 start 到 end 生成一个数字数组（step 可选）。range(1, 5, 2)start（数字），end（数字），step（数字，可选）{ "mathjs": "DenseMatrix", "data": [ 1, 3 ], "size": [ 2 ] }
reshape将数组/矩阵重塑为指定维度。reshape([1,2,3,4,5,6], [2,3])x（数组或矩阵），sizes（数组）[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
resize将矩阵调整为新维度，可用默认值填充缺失元素。resize([1,2,3], [5], 0)x（数组或矩阵），size（数组），defaultValue（可选）[ 1, 2, 3, 0, 0 ]
rotate将 1x2 向量逆时针旋转一定角度，或对 1x3 向量绕给定轴旋转。rotate([1, 0], Math.PI / 2)w（数组或矩阵），theta（数字[, 轴]）[ 6.123233995736766e-17, 1 ]
rotationMatrix创建给定弧度的 2x2 旋转矩阵。rotationMatrix(Math.PI / 2)theta（数字）{ "mathjs": "DenseMatrix", "data": [ [ 6.123233995736766e-17, -1 ], [ 1, 6.123233995736766e-17 ] ], "size": [ 2, 2 ] }
row从矩阵中返回指定行。row([[1,2],[3,4]], 1)value（矩阵或数组），index（数字）[ [ 3, 4 ] ]
size计算矩阵、数组或标量的尺寸（维度）。size([[1,2,3],[4,5,6]])x（数组、矩阵或数字）[ 2, 3 ]
sort对矩阵或数组进行升序排序。sort([3,1,2])x（数组或矩阵）[ 1, 2, 3 ]
sqrtm计算方阵的主平方根。sqrtm([[4,0],[0,4]])A（矩阵或数组）[ [ 2.000000000000002, 0 ], [ 0, 2.000000000000002 ] ]
squeeze移除矩阵中内部和外部的单一维度。squeeze([[[1],[2],[3]]])x（矩阵或数组）[ 1, 2, 3 ]
subset获取或替换矩阵或字符串的子集。subset(['a','b','c'], 1)x（矩阵、数组或字符串），index（索引），replacement（可选）Error: Unexpected type of argument in function subset (expected: Index, actual: number, index: 1)
trace计算方阵的迹（对角线元素之和）。trace([[1,2],[3,4]])x（矩阵或数组）5
transpose对矩阵进行转置。transpose([[1,2],[3,4]])x（矩阵或数组）[ [ 1, 3 ], [ 2, 4 ] ]
zeros创建给定维度的全 0 矩阵。zeros(2, 3)m, n, p...（数字）{ "mathjs": "DenseMatrix", "data": [ [ 0, 0, 0 ], [ 0, 0, 0 ] ], "size": [ 2, 3 ] }

Numeric functions

FunctionDefinitionExample callParametersExpected result
solveODE对常微分方程进行数值积分（默认使用RK45）。solveODE((t, y) => -0.5 * y, [0, 10], [1])函数（func），时间范围（tspan，数组），初始值（y0，数组）Error: Unexpected type of argument in function map (expected: Array or Matrix, actual: number, index: 0)

Probability functions

FunctionDefinitionExample callParametersExpected result
combinations计算从 n 个元素中取 k 个无序组合的数量。combinations(5, 2)n（数值），k（数值）10
combinationsWithRep计算可重复元素的组合数量。combinationsWithRep(5, 2)n（数值），k（数值）15
factorial计算整数 n 的阶乘。factorial(5)n（整数）120
gamma使用近似算法计算 gamma 函数值。gamma(5)n（数值）24
kldivergence计算两个分布的 KL 散度。kldivergence([0.1, 0.9], [0.2, 0.8])x（数组或矩阵），y（数组或矩阵）0.036690014034750584
lgamma计算 gamma 函数的对数（扩展近似）。lgamma(5)n（数值）3.178053830347945
multinomial根据一组计数计算多项式系数。multinomial([1, 2, 3])a（数组）60
permutations计算 n 个元素中，取 k 个有序排列的数量。permutations(5, 2)n（数值），k（数值，可选）20
pickRandom从一维数组中随机选取一个或多个值。pickRandom([10, 20, 30])数组20
random获取一个均匀分布的随机数。random(1, 10)最小值（可选），最大值（可选）3.6099423753668143
randomInt获取一个均匀分布的随机整数。randomInt(1, 10)最小值（可选），最大值（可选）5

Relational functions

FunctionDefinitionExample callParametersExpected result
compare比较两个值，可返回 -1、0 或 1。compare(2, 3)x，y（任意类型）-1
compareNatural以自然、可重复的方式比较任意类型的值。compareNatural('2', '10')x，y（任意类型）-1
compareText以字典序方式比较两个字符串。compareText('apple', 'banana')x（字符串），y（字符串）-1
deepEqual逐元素比较两个矩阵/数组是否相同。deepEqual([[1, 2]], [[1, 2]])x（数组/矩阵），y（数组/矩阵）true
equal判断两个值是否相等。equal(2, 2)x，y（任意类型）true
equalText判断两个字符串是否相同。equalText('hello', 'hello')x（字符串），y（字符串）true
larger判断 x 是否大于 y。larger(3, 2)x，y（数字或大数）true
largerEq判断 x 是否大于等于 y。largerEq(3, 3)x，y（数字或大数）true
smaller判断 x 是否小于 y。smaller(2, 3)x，y（数字或大数）true
smallerEq判断 x 是否小于等于 y。smallerEq(2, 2)x，y（数字或大数）true
unequal判断两个值是否不相等。unequal(2, 3)x，y（任意类型）true

Set functions

FunctionDefinitionExample callParametersExpected result
setCartesian生成两个（多）集合的笛卡尔积。setCartesian([1, 2], [3, 4])第一个集合（数组），第二个集合（数组）[ [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ] ]
setDifference生成两个（多）集合的差集（set1 中有但 set2 中没有的元素）。setDifference([1, 2, 3], [2])第一个集合（数组），第二个集合（数组）[ 1, 3 ]
setDistinct获取（多）集合中的唯一元素。setDistinct([1, 2, 2, 3])集合（数组）[ 1, 2, 3 ]
setIntersect生成两个（多）集合的交集。setIntersect([1, 2], [2, 3])第一个集合（数组），第二个集合（数组）[ 2 ]
setIsSubset判断 set1 是否是 set2 的子集。setIsSubset([1, 2], [1, 2, 3])第一个集合（数组），第二个集合（数组）true
setMultiplicity统计在多重集合中某个元素出现的次数。setMultiplicity(2, [1, 2, 2, 3])元素（任意类型），集合（数组）2
setPowerset生成一个（多）集合的所有子集，即幂集。setPowerset([1, 2])集合（数组）[ [], [ 1 ], [ 2 ], [ 1, 2 ] ]
setSize统计（多）集合中所有元素的数量。setSize([1, 2, 3])集合（数组）3
setSymDifference生成两个（多）集合的对称差（只在其中一个集合中的元素）。setSymDifference([1, 2], [2, 3])第一个集合（数组），第二个集合（数组）[ 1, 3 ]
setUnion生成两个（多）集合的并集。setUnion([1, 2], [2, 3])第一个集合（数组），第二个集合（数组）[ 1, 3, 2 ]

Signal functions

FunctionDefinitionExample callParametersExpected result
freqz根据滤波器系数计算频率响应。freqz([1, -0.5], [1])分子系数数组 b，分母系数数组 a{ "h": [ { "mathjs": "Complex", "re": 0.5, "im": 0 }, { "mathjs": "Complex", "re": 0.5000094123586994, "im": 0.0030679423245772376 }, { "mathjs": "Complex", "re": 0.5000376490804277, "im": 0.006135769142859963 }, { "mathjs": "Complex", "re": 0.5000847091020884, "im": 0.00920336495290241 }, { "mathjs": "Complex", "re": 0.5001505906518979, "im": 0.012270614261456144 }, { "mathjs": "Complex", "re": 0.5002352912494534, "im": 0.015337401588318313 }, { "mathjs": "Complex", "re": 0.5003388077058253, "im": 0.018403611470679416 }, { "mathjs": "Complex", "re": 0.5004611361236773, "im": 0.02146912846747041 }, { "mathjs": "Complex", "re": 0.5006022718974138, "im": 0.024533837163709007 }, { "mathjs": "Complex", "re": 0.5007622097133526, "im": 0.027597622174844967 }, { "mathjs": "Complex", "re": 0.5009409435499255, "im": 0.03066036815110429 }, { "mathjs": "Complex", "re": 0.5011384666779042, "im": 0.033721959781832025 }, { "mathjs": "Complex", "re": 0.5013547716606549, "im": 0.03678228179983371 }, { "mathjs": "Complex", "re": 0.5015898503544172, "im": 0.03984121898571506 }, { "mathjs": "Complex", "re": 0.501843693908611, "im": 0.04289865617221995 }, { "mathjs": "Complex", "re": 0.5021162927661701, "im": 0.04595447824856636 }, { "mathjs": "Complex", "re": 0.5024076366639015, "im": 0.0490085701647803 }, { "mathjs": "Complex", "re": 0.5027177146328723, "im": 0.05206081693602729 }, { "mathjs": "Complex", "re": 0.5030465149988219, "im": 0.05511110364694153 }, { "mathjs": "Complex", "re": 0.5033940253826028, "im": 0.058159315455952376 }, { "mathjs": "Complex", "re": 0.503760232700645, "im": 0.0612053375996081 }, { "mathjs": "Complex", "re": 0.5041451231654502, "im": 0.06424905539689658 }, { "mathjs": "Complex", "re": 0.50454868228611, "im": 0.06729035425356308 }, { "mathjs": "Complex", "re": 0.5049708948688514, "im": 0.0703291196664246 }, { "mathjs": "Complex", "re": 0.5054117450176094, "im": 0.07336523722768087 }, { "mathjs": "Complex", "re": 0.5058712161346253, "im": 0.07639859262922172 }, { "mathjs": "Complex", "re": 0.5063492909210707, "im": 0.07942907166693072 }, { "mathjs": "Complex", "re": 0.5068459513777006, "im": 0.08245656024498496 }, { "mathjs": "Complex", "re": 0.5073611788055294, "im": 0.08548094438015061 }, { "mathjs": "Complex", "re": 0.5078949538065355, "im": 0.08850211020607437 }, { "mathjs": "Complex", "re": 0.5084472562843918, "im": 0.09151994397757048 }, { "mathjs": "Complex", "re": 0.5090180654452223, "im": 0.0945343320749031 }, { "mathjs": "Complex", "re": 0.5096073597983848, "im": 0.09754516100806412 }, { "mathjs": "Complex", "re": 0.5102151171572797, "im": 0.10055231742104595 }, { "mathjs": "Complex", "re": 0.5108413146401862, "im": 0.10355568809610928 }, { "mathjs": "Complex", "re": 0.5114859286711229, "im": 0.10655515995804568 }, { "mathjs": "Complex", "re": 0.5121489349807358, "im": 0.1095506200784349 }, { "mathjs": "Complex", "re": 0.5128303086072121, "im": 0.11254195567989642 }, { "mathjs": "Complex", "re": 0.5135300238972199, "im": 0.11552905414033555 }, { "mathjs": "Complex", "re": 0.5142480545068742, "im": 0.1185118029971836 }, { "mathjs": "Complex", "re": 0.514984373402728, "im": 0.12149008995163194 }, { "mathjs": "Complex", "re": 0.5157389528627914, "im": 0.12446380287286007 }, { "mathjs": "Complex", "re": 0.516511764477574, "im": 0.12743282980225729 }, { "mathjs": "Complex", "re": 0.5173027791511553, "im": 0.13039705895763776 }, { "mathjs": "Complex", "re": 0.51811196710228, "im": 0.13335637873744918 }, { "mathjs": "Complex", "re": 0.5189392978654792, "im": 0.1363106777249745 }, { "mathjs": "Complex", "re": 0.5197847402922171, "im": 0.13925984469252653 }, { "mathjs": "Complex", "re": 0.5206482625520642, "im": 0.14220376860563594 }, { "mathjs": "Complex", "re": 0.5215298321338956, "im": 0.14514233862723117 }, { "mathjs": "Complex", "re": 0.5224294158471146, "im": 0.1480754441218119 }, { "mathjs": "Complex", "re": 0.5233469798229031, "im": 0.15100297465961404 }, { "mathjs": "Complex", "re": 0.5242824895154958, "im": 0.15392482002076743 }, { "mathjs": "Complex", "re": 0.5252359097034817, "im": 0.15684087019944576 }, { "mathjs": "Complex", "re": 0.5262072044911295, "im": 0.15975101540800785 }, { "mathjs": "Complex", "re": 0.5271963373097394, "im": 0.16265514608113146 }, { "mathjs": "Complex", "re": 0.5282032709190199, "im": 0.16555315287993821 }, { "mathjs": "Complex", "re": 0.5292279674084897, "im": 0.16844492669611003 }, { "mathjs": "Complex", "re": 0.530270388198905, "im": 0.1713303586559972 }, { "mathjs": "Complex", "re": 0.5313304940437125, "im": 0.17420934012471728 }, { "mathjs": "Complex", "re": 0.5324082450305262, "im": 0.17708176271024517 }, { "mathjs": "Complex", "re": 0.5335036005826306, "im": 0.17994751826749406 }, { "mathjs": "Complex", "re": 0.5346165194605081, "im": 0.18280649890238693 }, { "mathjs": "Complex", "re": 0.5357469597633921, "im": 0.18565859697591877 }, { "mathjs": "Complex", "re": 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1.8714565612204823, 1.8775924843720249, 1.8837284075235674, 1.88986433067511, 1.8960002538266525, 1.902136176978195, 1.9082721001297376, 1.9144080232812801, 1.9205439464328227, 1.9266798695843652, 1.932815792735908, 1.9389517158874505, 1.945087639038993, 1.9512235621905356, 1.9573594853420782, 1.9634954084936207, 1.9696313316451632, 1.9757672547967058, 1.9819031779482483, 1.9880391010997909, 1.9941750242513334, 2.000310947402876, 2.0064468705544187, 2.012582793705961, 2.018718716857504, 2.024854640009046, 2.030990563160589, 2.0371264863121317, 2.043262409463674, 2.0493983326152168, 2.055534255766759, 2.061670178918302, 2.067806102069844, 2.073942025221387, 2.0800779483729293, 2.086213871524472, 2.0923497946760143, 2.098485717827557, 2.1046216409791, 2.110757564130642, 2.116893487282185, 2.1230294104337273, 2.12916533358527, 2.1353012567368124, 2.141437179888355, 2.1475731030398975, 2.1537090261914402, 2.1598449493429825, 2.1659808724945253, 2.172116795646068, 2.1782527187976104, 2.184388641949153, 2.1905245651006955, 2.1966604882522383, 2.2027964114037806, 2.2089323345553233, 2.2150682577068657, 2.2212041808584084, 2.227340104009951, 2.2334760271614935, 2.2396119503130363, 2.2457478734645786, 2.2518837966161214, 2.2580197197676637, 2.2641556429192065, 2.270291566070749, 2.2764274892222915, 2.282563412373834, 2.2886993355253766, 2.2948352586769194, 2.3009711818284617, 2.3071071049800045, 2.313243028131547, 2.3193789512830896, 2.325514874434632, 2.3316507975861747, 2.337786720737717, 2.3439226438892597, 2.350058567040802, 2.356194490192345, 2.3623304133438876, 2.36846633649543, 2.3746022596469727, 2.380738182798515, 2.386874105950058, 2.3930100291016, 2.399145952253143, 2.405281875404685, 2.411417798556228, 2.4175537217077703, 2.423689644859313, 2.429825568010856, 2.435961491162398, 2.442097414313941, 2.448233337465483, 2.454369260617026, 2.4605051837685683, 2.466641106920111, 2.4727770300716534, 2.478912953223196, 2.4850488763747385, 2.4911847995262812, 2.497320722677824, 2.5034566458293663, 2.509592568980909, 2.5157284921324514, 2.521864415283994, 2.5280003384355365, 2.5341362615870793, 2.5402721847386216, 2.5464081078901644, 2.552544031041707, 2.5586799541932495, 2.564815877344792, 2.5709518004963345, 2.5770877236478773, 2.5832236467994196, 2.5893595699509624, 2.5954954931025047, 2.6016314162540475, 2.60776733940559, 2.6139032625571326, 2.6200391857086753, 2.6261751088602177, 2.6323110320117604, 2.6384469551633027, 2.6445828783148455, 2.650718801466388, 2.6568547246179306, 2.662990647769473, 2.6691265709210157, 2.675262494072558, 2.6813984172241008, 2.6875343403756435, 2.693670263527186, 2.6998061866787286, 2.705942109830271, 2.7120780329818137, 2.718213956133356, 2.724349879284899, 2.730485802436441, 2.736621725587984, 2.742757648739526, 2.748893571891069, 2.7550294950426117, 2.761165418194154, 2.767301341345697, 2.773437264497239, 2.779573187648782, 2.7857091108003242, 2.791845033951867, 2.7979809571034093, 2.804116880254952, 2.8102528034064944, 2.816388726558037, 2.82252464970958, 2.8286605728611223, 2.834796496012665, 2.8409324191642074, 2.84706834231575, 2.8532042654672924, 2.859340188618835, 2.8654761117703775, 2.8716120349219203, 2.8777479580734626, 2.8838838812250054, 2.890019804376548, 2.8961557275280905, 2.9022916506796332, 2.9084275738311756, 2.9145634969827183, 2.9206994201342606, 2.9268353432858034, 2.9329712664373457, 2.9391071895888885, 2.945243112740431, 2.9513790358919736, 2.9575149590435164, 2.9636508821950587, 2.9697868053466014, 2.9759227284981438, 2.9820586516496865, 2.988194574801229, 2.9943304979527716, 3.000466421104314, 3.0066023442558567, 3.0127382674073995, 3.018874190558942, 3.0250101137104846, 3.031146036862027, 3.0372819600135696, 3.043417883165112, 3.0495538063166547, 3.055689729468197, 3.06182565261974, 3.067961575771282, 3.074097498922825, 3.0802334220743677, 3.08636934522591, 3.0925052683774528, 3.098641191528995, 3.104777114680538, 3.11091303783208, 3.117048960983623, 3.1231848841351653, 3.129320807286708, 3.1354567304382504 ] }
zpk2tf根据零点、极点及增益计算传递函数。zpk2tf([-0.5], [1], 1)零点数组 z，极点数组 p，增益 k[ [ { "mathjs": "Complex", "re": 1, "im": 0 }, { "mathjs": "Complex", "re": 0.5, "im": 0 } ], [ { "mathjs": "Complex", "re": 1, "im": 0 }, { "mathjs": "Complex", "re": -1, "im": 0 } ] ]

Special functions

FunctionDefinitionExample callParametersExpected result
erf使用有理切比雪夫近似来计算误差函数。erf(0.5)输入值 x（数字）0.5204998778130465
zeta利用级数展开来计算黎曼ζ函数。zeta(2)输入值 n（数字）1.6449340668482526

Statistics functions

FunctionDefinitionExample callParametersExpected result
corr计算两个列表或矩阵之间的相关系数。corr([2, 3, 4], [5, 6, 7])A，B可为数组或矩阵1
cumsum计算列表或矩阵的累加和。cumsum([1, 2, 3, 4])[ 1, 3, 6, 10 ]
mad计算数据的中位绝对偏差。mad([1, 2, 3, 4])1
max返回列表或矩阵的最大值。max([1, 2, 3])3
mean计算平均值。mean([2, 4, 6])4
median计算中位数。median([1, 2, 3, 4, 5])3
min返回列表或矩阵的最小值。min([1, 2, 3])1
mode计算众数（最常出现的值）。mode([1, 2, 2, 3])[ 2 ]
prod计算列表或矩阵中所有数的乘积。prod([1, 2, 3, 4])24
quantileSeq计算列表或矩阵在 prob 位置上的分位数。quantileSeq([1, 2, 3, 4], 0.25)1.75
std计算数据的标准差。std([1, 2, 3, 4])1.2909944487358056
sum计算列表或矩阵所有数的和。sum([1, 2, 3])6
variance计算数据的方差。variance([1, 2, 3, 4])1.6666666666666667

String functions

FunctionDefinitionExample callParametersExpected result
bin将数字格式化为二进制。bin(13)0b1101
format将任意类型的值转为指定精度的字符串。format(123.456, 2)120
hex将数字格式化为十六进制。hex(255)0xff
oct将数字格式化为八进制。oct(64)0o100
print将多个数值插入到字符串模板中。print('x = $x, y = $y', {x: 3, y: 4}, 2)x = 3, y = 4

Trigonometry functions

FunctionDefinitionExample callParametersExpected result
acos计算反余弦值。acos(0.5)1.0471975511965979
acosh计算双曲反余弦值。acosh(2)1.3169578969248166
acot计算反余切值。acot(1)0.7853981633974483
acoth计算双曲反余切值。acoth(2)0.5493061443340548
acsc计算反余割值。acsc(2)0.5235987755982989
acsch计算双曲反余割值。acsch(2)0.48121182505960347
asec计算反正割值。asec(2)1.0471975511965979
asech计算双曲反正割值。asech(0.5)1.3169578969248166
asin计算反正弦值。asin(0.5)0.5235987755982989
asinh计算双曲反正弦值。asinh(1.5)1.1947632172871094
atan计算反正切值。atan(1)0.7853981633974483
atan2计算具有两个参数的反正切值。atan2(1, 2)0.4636476090008061
atanh计算双曲反正切值。atanh(0.5)0.5493061443340548
cos计算 x 的余弦值。cos(0.5)0.8775825618903728
cosh计算 x 的双曲余弦值。cosh(0.5)1.1276259652063807
cot计算 x 的余切值。cot(0.5)1.830487721712452
coth计算 x 的双曲余切值。coth(0.5)2.163953413738653
csc计算 x 的余割值。csc(0.5)2.085829642933488
csch计算 x 的双曲余割值。csch(0.5)1.9190347513349437
sec计算 x 的正割值。sec(0.5)1.139493927324549
sech计算 x 的双曲正割值。sech(0.5)0.886818883970074
sin计算 x 的正弦值。sin(0.5)0.479425538604203
sinh计算 x 的双曲正弦值。sinh(0.5)0.5210953054937474
tan计算 x 的正切值。tan(0.5)0.5463024898437905
tanh计算 x 的双曲正切值。tanh(0.5)0.46211715726000974

Unit functions

FunctionDefinitionExample callParametersExpected result
to将一个数值转换为指定单位。to(5, 'cm')Error: Unexpected type of argument in function to (expected: Array or DenseMatrix or Matrix, actual: identifier | string, index: 1)

Utils functions

FunctionDefinitionExample callParametersExpected result
clone对输入值进行深拷贝。clone([1, 2, 3])[ 1, 2, 3 ]
hasNumericValue检测输入是否包含数值。hasNumericValue('123')true
isInteger检测输入是否是整数。isInteger(3.0)true
isNaN检测输入是否为 NaN。isNaN(NaN)true
isNegative检测输入是否为负数。isNegative(-5)true
isNumeric检测输入是否为数值。isNumeric('123')false
isPositive检测输入是否为正数。isPositive(2)true
isPrime检测输入是否为质数。isPrime(7)true
isZero检测输入是否为 0。isZero(0)true
numeric将输入值转换为特定的数值类型（如 number、BigNumber 等）。numeric('123')123
typeOf返回输入值的类型名称。typeOf([1, 2, 3])Array
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