[petsc-users] Orthogonalization of a (sparse) PETSc matrix

[Jose E. Roman]

Thanasis:

I have finished the change that I mentioned in my previous email, the details are here https://gitlab.com/slepc/slepc/-/merge_requests/586

The change has been already merged into the main branch, and thus will be included in version 3.20, to be released on Friday this week.

You should now be able to do
   bv = SLEPc.BV().createFromMat(A))
instead of
   bv = SLEPc.BV().createFromMat(A.convert('dense'))
 without error or cost penalty.

Thanks.
Jose


> El 30 ago 2023, a las 9:17, Jose E. Roman <jroman at dsic.upv.es> escribió:
> 
> The conversion from MATAIJ to MATDENSE should be very cheap, see https://gitlab.com/petsc/petsc/-/blob/main/src/mat/impls/dense/seq/dense.c?ref_type=heads#L172
> 
> The matrix copy hidden inside createFromMat() is likely more expensive. I am currently working on a modification of BV that will be included in version 3.20 if everything goes well - then I think I can allow passing a sparse matrix to createFromMat() and do the conversion internally, avoiding the matrix copy.
> 
> Jose
> 
> 
>> El 29 ago 2023, a las 22:46, Thanasis Boutsikakis <thanasis.boutsikakis at corintis.com> escribió:
>> 
>> Thanks Jose, 
>> 
>> This works indeed. However, I was under the impression that this conversion might be very costly for big matrices with low sparsity and it would scale with the number of non-zero values.
>> 
>> Do you have any idea of the efficiency of this operation?
>> 
>> Thanks
>> 
>>> On 29 Aug 2023, at 19:13, Jose E. Roman <jroman at dsic.upv.es> wrote:
>>> 
>>> The result of bv.orthogonalize() is most probably a dense matrix, and the result replaces the input matrix, that's why the input matrix is required to be dense.
>>> 
>>> You can simply do this:
>>> 
>>> bv = SLEPc.BV().createFromMat(A.convert('dense'))
>>> 
>>> Jose
>>> 
>>>> El 29 ago 2023, a las 18:50, Thanasis Boutsikakis <thanasis.boutsikakis at corintis.com> escribió:
>>>> 
>>>> Hi all, I have the following code that orthogonalizes a PETSc matrix. The problem is that this implementation requires that the PETSc matrix is dense, otherwise, it fails at bv.SetFromOptions(). Hence the assert in orthogonality().
>>>> 
>>>> What could I do in order to be able to orthogonalize sparse matrices as well? Could I convert it efficiently? (I tried to no avail)
>>>> 
>>>> Thanks!
>>>> 
>>>> """Experimenting with matrix orthogonalization"""
>>>> 
>>>> import contextlib
>>>> import sys
>>>> import time
>>>> import numpy as np
>>>> from firedrake import COMM_WORLD
>>>> from firedrake.petsc import PETSc
>>>> 
>>>> import slepc4py
>>>> 
>>>> slepc4py.init(sys.argv)
>>>> from slepc4py import SLEPc
>>>> 
>>>> from numpy.testing import assert_array_almost_equal
>>>> 
>>>> EPSILON_USER = 1e-4
>>>> EPS = sys.float_info.epsilon
>>>> 
>>>> 
>>>> def Print(message: str):
>>>>  """Print function that prints only on rank 0 with color
>>>> 
>>>>  Args:
>>>>      message (str): message to be printed
>>>>  """
>>>>  PETSc.Sys.Print(message)
>>>> 
>>>> 
>>>> def create_petsc_matrix(input_array, sparse=True):
>>>>  """Create a PETSc matrix from an input_array
>>>> 
>>>>  Args:
>>>>      input_array (np array): Input array
>>>>      partition_like (PETSc mat, optional): Petsc matrix. Defaults to None.
>>>>      sparse (bool, optional): Toggle for sparese or dense. Defaults to True.
>>>> 
>>>>  Returns:
>>>>      PETSc mat: PETSc matrix
>>>>  """
>>>>  # Check if input_array is 1D and reshape if necessary
>>>>  assert len(input_array.shape) == 2, "Input array should be 2-dimensional"
>>>>  global_rows, global_cols = input_array.shape
>>>> 
>>>>  size = ((None, global_rows), (global_cols, global_cols))
>>>> 
>>>>  # Create a sparse or dense matrix based on the 'sparse' argument
>>>>  if sparse:
>>>>      matrix = PETSc.Mat().createAIJ(size=size, comm=COMM_WORLD)
>>>>  else:
>>>>      matrix = PETSc.Mat().createDense(size=size, comm=COMM_WORLD)
>>>>  matrix.setUp()
>>>> 
>>>>  local_rows_start, local_rows_end = matrix.getOwnershipRange()
>>>> 
>>>>  for counter, i in enumerate(range(local_rows_start, local_rows_end)):
>>>>      # Calculate the correct row in the array for the current process
>>>>      row_in_array = counter + local_rows_start
>>>>      matrix.setValues(
>>>>          i, range(global_cols), input_array[row_in_array, :], addv=False
>>>>      )
>>>> 
>>>>  # Assembly the matrix to compute the final structure
>>>>  matrix.assemblyBegin()
>>>>  matrix.assemblyEnd()
>>>> 
>>>>  return matrix
>>>> 
>>>> 
>>>> def orthogonality(A):  # sourcery skip: avoid-builtin-shadow
>>>>  """Checking and correcting orthogonality
>>>> 
>>>>  Args:
>>>>      A (PETSc.Mat): Matrix of size [m x k].
>>>> 
>>>>  Returns:
>>>>      PETSc.Mat: Matrix of size [m x k].
>>>>  """
>>>>  # Check if the matrix is dense
>>>>  mat_type = A.getType()
>>>>  assert mat_type in (
>>>>      "seqdense",
>>>>      "mpidense",
>>>>  ), "A must be a dense matrix. SLEPc.BV().createFromMat() requires a dense matrix."
>>>> 
>>>>  m, k = A.getSize()
>>>> 
>>>>  Phi1 = A.getColumnVector(0)
>>>>  Phi2 = A.getColumnVector(k - 1)
>>>> 
>>>>  # Compute dot product using PETSc function
>>>>  dot_product = Phi1.dot(Phi2)
>>>> 
>>>>  if abs(dot_product) > min(EPSILON_USER, EPS * m):
>>>>      Print("    Matrix is not orthogonal")
>>>> 
>>>>      # Type can be CHOL, GS, mro(), SVQB, TSQR, TSQRCHOL
>>>>      _type = SLEPc.BV().OrthogBlockType.GS
>>>> 
>>>>      bv = SLEPc.BV().createFromMat(A)
>>>>      bv.setFromOptions()
>>>>      bv.setOrthogonalization(_type)
>>>>      bv.orthogonalize()
>>>> 
>>>>      A = bv.createMat()
>>>> 
>>>>      Print("    Matrix successfully orthogonalized")
>>>> 
>>>>      # # Assembly the matrix to compute the final structure
>>>>      if not A.assembled:
>>>>          A.assemblyBegin()
>>>>          A.assemblyEnd()
>>>>  else:
>>>>      Print("    Matrix is orthogonal")
>>>> 
>>>>  return A
>>>> 
>>>> 
>>>> # --------------------------------------------
>>>> # EXP: Orthogonalization of an mpi PETSc matrix
>>>> # --------------------------------------------
>>>> 
>>>> m, k = 11, 7
>>>> # Generate the random numpy matrices
>>>> np.random.seed(0)  # sets the seed to 0
>>>> A_np = np.random.randint(low=0, high=6, size=(m, k))
>>>> 
>>>> A = create_petsc_matrix(A_np, sparse=False)
>>>> 
>>>> A_orthogonal = orthogonality(A)
>>>> 
>>>> # --------------------------------------------
>>>> # TEST: Orthogonalization of a numpy matrix
>>>> # --------------------------------------------
>>>> # Generate A_np_orthogonal
>>>> A_np_orthogonal, _ = np.linalg.qr(A_np)
>>>> 
>>>> # Get the local values from A_orthogonal
>>>> local_rows_start, local_rows_end = A_orthogonal.getOwnershipRange()
>>>> A_orthogonal_local = A_orthogonal.getValues(
>>>>  range(local_rows_start, local_rows_end), range(k)
>>>> )
>>>> 
>>>> # Assert the correctness of the multiplication for the local subset
>>>> assert_array_almost_equal(
>>>>  np.abs(A_orthogonal_local),
>>>>  np.abs(A_np_orthogonal[local_rows_start:local_rows_end, :]),
>>>>  decimal=5,
>>>> )
>>> 
>> 
>