lambdify function with array of parameters

[Nico Schlömer]

Given the degrees in numerator and denominator I would like to represent a Padé polynomial à la

```

P(x) = (a[0] + a[1]*x + a[2]*x**2 + ...) / (1 + b[1]*x + b[2]*x**2 + ...)

```

in sympy and let it do the heavy lifting, e.g., computation of derivatives.

Operations that I'll need to do:

  * Replace a[] and b[] with actual numerical values (in both P and P')

  * Evaluate those P_{a,b} and P'_{a, b} for many x.

The first idea was to go

```

import numpy

import sympy

a = sympy.MatrixSymbol('a', 2, 1)

b = sympy.MatrixSymbol('b', 3, 1)

x = sympy.Symbol('x')

P = (a[0] + a[1]*x) / (1 + b[0]*x + b[1]*x**2 + b[2]*x**3)

val_a = numpy.random.rand(2)

P_a = P.evalf(subs={a: val_a})  

```

The last line however doesn't seem to do anything at all. Second attempt:

```

Pa = sympy.lambdify(a, P)(val_a)

```

This gives

```

IndexError: too many indices for array

```

Hm. Any hints of how to proceed here? Perhaps `MatrixSymbol` isn't what I'm looking for.

[Leonid Kovalev]

P_a = P.subs(dict(zip(a, val_a)))

returns 

(0.450033195586719*x + 0.829322314411828)/(x**3*b[2, 0] + x**2*b[1, 0] + x*b[0, 0] + 1)

You need to substitute individual MatrixElement objects like a[0], not the MatrixSymbol itself (which isn't even present in the expression P). 

[Leonid Kovalev]

Also, the conversion to dict was unnecessary, subs can take an iterator of tuples.   

P_a = P.subs(zip(a, val_a))

[Nico Schlömer]

I see!

I also noticed that I can use `DeferredVector`s instead of `MatrixSymbol`s to get avoid those dict shenanigans. This

```

import numpy

import sympy

a = sympy.DeferredVector('a')

b = sympy.DeferredVector('b')

x = sympy.Symbol('x')

P = (a[0] + a[1]*x) / (1 + b[0]*x + b[1]*x**2 + b[2]*x**3)

val_a = numpy.random.rand(2)

val_b = numpy.random.rand(3)

Pa = sympy.lambdify((a, b), P)(val_a, val_b)

print(P)

print(Pa)

```

works. It's a bit weird to create a lambdify only to call it straight away though. Also, I'm reading [1] that `DeferredVector` were once scheduled for removal? Probably outdated.

[1] https://github.com/sympy/sympy/issues/6788

[Leonid Kovalev]

lambdify should not be needed to work with or create SymPy
expressions. Its purpose is to make a SymPy expression usable by other
libraries.

As I wrote, "dict shenanigans" were not needed. A MatrixSymbol is an
iterable. `zip(MatrixSymbol, array_of_values)` creates an iterator of
tuples, indicating what element is substituted by what value. A
natural thing to do in Python, I wouldn't look to replace it with
lambdify and DeferredVector (which apparently isn't removed because
everyone forgot about it).

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[Nico Schlömer]

Alright, thanks for the explanation.

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