向量本身的M乘积的外积 [英] Outer product of a vector with itself M-times

问题描述

我想根据长度为n的向量x创建一个M模式n维张量A，

I would like to create a M-mode, n-dimensional tensor A from a vector x of length n such that

A_[i_1, i_2, ... , i_M] = x[i_1] * x[i_2] * ... * x[i_M].

到目前为止，我的代码是

The code that I have so far is

A=np.multiply.outer(x,x)
for i in range(M-2):
    A=np.multiply.outer(A,x)

我对使用Python进行编码还很陌生，所以我不确定是否有更紧凑/更方便的方法来计算此张量.

I'm rather new to coding in Python so I'm not sure if there is a more compact/convenient way of computing this tensor.

推荐答案

我们可以使用

We could make use of np.ix_ to create open grid versions of input array and then feed those to np.multiply.reduce for element-wise multiplication reductions for all of those, like so -

A = np.multiply.reduce(np.ix_(*[x]*M))

---

扩展到其他支持的功能

我们可以将其扩展到其他具有reduce方法的ufunc.因此，例如要执行外部addition，它应该是-

We could extend this to other ufuncs that have the reduce method. So, for example to perform outer addition, it would be -

np.add.reduce(np.ix_(*[x]*M))

以此类推.

有关支持此功能的ufuncs的完整列表，请参考 docs .在Grep -ing之后，我得到了以下支持reduce方法的ufunc，因此可以利用早期发布的方法:

For a complete list of ufuncs that support this feature, please refer to the docs. After Grep-ing for those, I got the following ufuncs that support reduce method and hence could leverage the earlier posted approach :

加，减，乘，除，logaddexp，logaddexp2，true_divide， floor_divide，负数，正数，功率，余数，mod，fmod，divmod， 绝对，fabs，rint，符号，heaviside，conj，exp，exp2，log，log2， log10，expm1，log1p，sqrt，正方形，cbrt，倒数，gcd，lcm，sin， cos，tan，arcsin，arcos，arctan，arctan2，hypo，sinh，cosh，tanh， arcsinh，arccosh，arctanh，deg2rad，rad2deg，bitwise_and，bitwise_or， bitwise_xor，反转，left_shift，right_shift，更大，更大等于， less，less_equal，not_equal，equal，logical_and，logical_or， 逻辑异或，逻辑非，最大值，最小值，fmax，fmin，isfinite， isinf，isnan，isat，晶圆厂，signbit，copysign，nextafter，space， modf，ldexp，frexp，fmod，floor，ceil，trunc

add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, floor_divide, negative, positive, power, remainder, mod, fmod, divmod, absolute, fabs, rint, sign, heaviside, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, cbrt, reciprocal, gcd, lcm, sin, cos, tan, arcsin, arccos, arctan, arctan2, hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, greater, greater_equal, less, less_equal, not_equal, equal, logical_and, logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, isfinite, isinf, isnan, isnat, fabs, signbit, copysign, nextafter, spacing, modf, ldexp, frexp, fmod, floor, ceil, trunc

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