Hi Matt,
thanks for your help! You're right, the dimensions didn't make sense, so
here is the fixed version for future reference.
n1, n2 = symbols('n1 n2', integer=True)
S1, S2 = symbols('S1 S2')
U1 = MatrixSymbol('U1', n1, n1+n2)
U2 = MatrixSymbol('U2', n2, n1+n2)
D = MatrixSymbol('D', n1+n2, n1+n2)
U = BlockMatrix([[U1], [U2]])
K = U * D * U.T
block = sympy.block_collapse(K)
K_inv = sympy.block_collapse(block.inverse())
Thank you!
Chris
On Friday, March 7, 2014 7:17:54 PM UTC-8, Matthew wrote:
>
> Hi Chris,
>
> In order to simplify these further you'll need to break down U1 and U2 so
> that they are of compatible shape with D1 and the 0-matrix. At the moment
> there is no way to take these larger matrices and simplify them against
> smaller ones. This mismatch would be more evident if we had size-sensitive
> printing. For example seeing the U_1^T on the right as a big solid block
> rather than a single letter would make this mismatch easier to spot.
>
> One way to cut the matrices into smaller blocks is with blockcut. The
> inputs are input matrix, desired row sizes, desired block sizes. Output is
> a blockmatrix of MatrixSlice objects
>
> U1 = blockcut(U1, (n1,), (n1, n2))
> U2 = blockcut(U2, (n2,), (n1, n2))
>
> They look like this
>
> In [13]: U1
> Out[13]: [U₁[:n₁, :n₁] U₁[:n₁, n₁:n₁ + n₂]]
>
> After you do this (and go through the rest of your pipeline) then
> block_collapse reduces things cleanly to a 2x2 block matrix. All of the
> indexing can get in the way of clean printing unfortunately. You might
> consider creating MatrixSymbols U11, U12, U21, U22 explicitly.
>
> Best,
> -Matt
>
>
> On Thu, Mar 6, 2014 at 4:19 PM, Chris <[email protected] <javascript:>>wrote:
>
>> Dear all,
>>
>>
>> I'm trying to use block matrices in the following way:
>>
>>
>> n1, n2 = symbols('n1 n2', integer=True)
>>
>> U1 = MatrixSymbol('U1', n1, n1+n2)
>> U2 = MatrixSymbol('U2', n2, n1+n2)
>>
>> D1 = MatrixSymbol('D1', n1, n1)
>> D2 = MatrixSymbol('D2', n2, n2)
>>
>> D = BlockDiagMatrix(D1, D2)
>> U = BlockMatrix([[U1], [U2]])
>> K = U * D * U.T
>>
>> Kc = sympy.block_collapse(K)
>>
>> For the record, K looks like this:
>> In [32]: K
>> Out[32]:
>> ⎡ T T⎤
>> ⎡U₁⎤⋅⎡D₁ 0 ⎤⋅⎣U₁ U₂ ⎦
>> ⎢ ⎥ ⎢ ⎥
>> ⎣U₂⎦ ⎣0 D₂⎦
>>
>>
>> Kc looks as follows:
>>
>> ⎡ T T⎤
>> ⎢⎡U₁⎤⋅⎡D₁ 0 ⎤⋅U₁ ⎡U₁⎤⋅⎡D₁ 0 ⎤⋅U₂ ⎥
>> ⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥
>> ⎣⎣U₂⎦ ⎣0 D₂⎦ ⎣U₂⎦ ⎣0 D₂⎦ ⎦
>>
>>
>> In [30]: Kc.blockshape
>> Out[30]: (1, 2)
>>
>>
>> What I'm looking for is a way to recursively break down these blocks
>> further (i.e. a blockshape of (2,2)). I tried the following, to no avail:
>>
>> In [31]: sympy.block_collapse(Kc.blocks[0])
>> Out[31]:
>>
>>
>> T
>> ⎡U₁⎤⋅⎡D₁ 0 ⎤⋅U₁
>> ⎢ ⎥ ⎢ ⎥
>> ⎣U₂⎦ ⎣0 D₂⎦
>>
>>
>>
>>
>> Any ideas on how to achieve this?
>>
>>
>> Thank you!
>> Chris
>>
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