Module: Ignis::Solver::SVD

Defined in:
lib/nvruby/solver/svd.rb

Overview

Singular Value Decomposition (SVD) operations using cuSOLVER Computes A = U * Σ * V^T decomposition

Constant Summary collapse

JOB_ALL =

Job types for SVD computation

"A".ord
JOB_SLIM =

Compute all m columns of U / all n rows of V^T

"S".ord
JOB_OVERWRITE =

Compute min(m,n) columns of U / rows of V^T

"O".ord
JOB_NONE =

Overwrite A with U or V^T

"N".ord

Class Method Summary collapse

Class Method Details

.cond(matrix) ⇒ Float

Compute condition number using SVD

Parameters:

  • matrix (NvArray) —

    Input matrix

Returns:

  • (Float) —

    Condition number (ratio of largest to smallest singular value)



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# File 'lib/nvruby/solver/svd.rb', line 127

def cond(matrix)
  s = singular_values(matrix)
  s_host = s.to_a

  return Float::INFINITY if s_host.empty? || s_host.last.zero?

  s_host.first / s_host.last
end

.gesvd(matrix, full_matrices: false, compute_uv: true) ⇒ Hash

Compute SVD of a matrix

Parameters:

  • matrix (NvArray) —

    Input matrix (m x n)

  • full_matrices (Boolean) (defaults to: false) —

    If true, compute full U (m x m) and Vt (n x n)

  • compute_uv (Boolean) (defaults to: true) —

    If true, compute U and Vt matrices

Returns:

  • (Hash) —

    Contains :u, :s (singular values), :vt

Raises:

  • (CuSolverError) —

    If computation fails



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# File 'lib/nvruby/solver/svd.rb', line 23

def gesvd(matrix, full_matrices: false, compute_uv: true)
  CuSolverBindings.ensure_loaded!

  validate_matrix!(matrix)
  m, n = matrix.shape
  lda = m
  min_mn = [m, n].min

  # Determine job type
  if compute_uv
    jobu = full_matrices ? JOB_ALL : JOB_SLIM
    jobvt = full_matrices ? JOB_ALL : JOB_SLIM
  else
    jobu = JOB_NONE
    jobvt = JOB_NONE
  end

  # Allocate output arrays
  s = allocate_singular_values(min_mn, matrix.dtype)
  u = allocate_u_matrix(m, min_mn, full_matrices, compute_uv, matrix.dtype)
  vt = allocate_vt_matrix(n, min_mn, full_matrices, compute_uv, matrix.dtype)

  # Dimensions
  ldu = compute_uv ? (full_matrices ? m : m) : 1
  ldvt = compute_uv ? (full_matrices ? n : min_mn) : 1

  # Get workspace size
  lwork_ptr = FFI::MemoryPointer.new(:int)
  get_gesvd_buffer_size(m, n, lwork_ptr, matrix.dtype)
  lwork = lwork_ptr.read_int

  # Allocate workspace
  workspace = CUDA::Memory.new(lwork * dtype_size(matrix.dtype))
  rwork = CUDA::Memory.new(min_mn * dtype_size(real_dtype(matrix.dtype)))
  info = CUDA::Memory.new(4)

  # Copy matrix to avoid overwriting original
  work_matrix = matrix.dup

  # Perform SVD
  perform_gesvd(
    jobu, jobvt, m, n,
    work_matrix.device_ptr, lda,
    s, u, ldu, vt, ldvt,
    workspace, lwork, rwork, info,
    matrix.dtype
  )

  # Check info
  info_value = read_device_int(info)
  if info_value < 0
    raise CuSolverError.new("SVD: parameter #{-info_value} had an illegal value",
                            cusolver_code: CuSolverBindings::CUSOLVER_STATUS_INVALID_VALUE)
  elsif info_value > 0
    raise CuSolverError.new("SVD: #{info_value} superdiagonals did not converge",
                            cusolver_code: CuSolverBindings::CUSOLVER_STATUS_EXECUTION_FAILED)
  end

  CUDA::RuntimeAPI.cudaDeviceSynchronize

  # Create result arrays
  result = {
    s: create_singular_values_array(s, min_mn, matrix.dtype)
  }

  if compute_uv
    result[:u] = create_u_array(u, m, min_mn, full_matrices, matrix.dtype)
    result[:vt] = create_vt_array(vt, n, min_mn, full_matrices, matrix.dtype)
  end

  result
ensure
  workspace&.free! if defined?(workspace) && workspace
  rwork&.free! if defined?(rwork) && rwork
  info&.free! if defined?(info) && info
end

.rank(matrix, tol: nil) ⇒ Integer

Compute matrix rank using SVD

Parameters:

  • matrix (NvArray) —

    Input matrix

  • tol (Float, nil) (defaults to: nil) —

    Tolerance (defaults to max(m,n) * eps * largest_singular_value)

Returns:

  • (Integer) —

    Numerical rank



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# File 'lib/nvruby/solver/svd.rb', line 112

def rank(matrix, tol: nil)
  s = singular_values(matrix)
  s_host = s.to_a

  return 0 if s_host.empty?

  max_sv = s_host.first
  tol ||= [matrix.shape[0], matrix.shape[1]].max * Float::EPSILON * max_sv

  s_host.count { |sv| sv > tol }
end

.singular_values(matrix) ⇒ NvArray

Compute only singular values (faster than full SVD)

Parameters:

  • matrix (NvArray) —

    Input matrix (m x n)

Returns:

  • (NvArray) —

    Singular values in descending order



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# File 'lib/nvruby/solver/svd.rb', line 103

def singular_values(matrix)
  result = gesvd(matrix, compute_uv: false)
  result[:s]
end