Mercurial > octave
view libinterp/corefcn/sparse-xpow.cc @ 31234:a1318deb4584
sparse-xpow.cc: Improve consistency between sparse and full matrices (bug #63080)
sparse-xpow.cc: Return 0x0 matrix for empty inputs of all sizes.
Return early for all-zeros matrix with positive power.
Add FIXME for all-zeros matrix with negative power.
Add BISTs.
author | Arun Giridhar <arungiridhar@gmail.com> |
---|---|
date | Tue, 20 Sep 2022 09:00:02 -0400 |
parents | a026fb2be108 |
children | b542b88ad3b6 |
line wrap: on
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1998-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cassert> #include <limits> #include "Array-util.h" #include "oct-cmplx.h" #include "quit.h" #include "error.h" #include "ovl.h" #include "utils.h" #include "dSparse.h" #include "CSparse.h" #include "ov-re-sparse.h" #include "ov-cx-sparse.h" #include "sparse-xpow.h" OCTAVE_NAMESPACE_BEGIN static inline bool xisint (double x) { return (octave::math::x_nint (x) == x && ((x >= 0 && x < std::numeric_limits<int>::max ()) || (x <= 0 && x > std::numeric_limits<int>::min ()))); } // Safer pow functions. Only two make sense for sparse matrices, the // others should all promote to full matrices. octave_value xpow (const SparseMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return SparseMatrix(); // If we are here, A is not empty ==> A needs to be square. if (nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (! xisint (b)) error ("use full(a) ^ full(b)"); int btmp = static_cast<int> (b); if (btmp == 0) { SparseMatrix tmp = SparseMatrix (nr, nr, nr); for (octave_idx_type i = 0; i < nr; i++) { tmp.data (i) = 1.0; tmp.ridx (i) = i; } for (octave_idx_type i = 0; i < nr + 1; i++) tmp.cidx (i) = i; retval = tmp; } else { SparseMatrix atmp; if (btmp < 0) { btmp = -btmp; octave_idx_type info; double rcond = 0.0; MatrixType mattyp (a); // FIXME: This causes an error if the input sparse matrix is all-zeros. // That behavior is inconsistent with A ^ b when A is a full all-zeros // matrix, which just returns Inf of the same size with a warning. atmp = a.inverse (mattyp, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; if (atmp.nnz() == 0) // Fast return for all-zeros matrix return atmp; SparseMatrix result (atmp); btmp--; // There are two approaches to the actual exponentiation. // Exponentiation by squaring uses only a logarithmic number // of multiplications but the matrices it multiplies tend to be dense // towards the end. // Linear multiplication uses a linear number of multiplications // but one of the matrices it uses will be as sparse as the original matrix. // // The time to multiply fixed-size matrices is strongly affected by their // sparsity. Denser matrices take much longer to multiply together. // See this URL for a worked-through example: // https://octave.discourse.group/t/3216/4 // // The tradeoff is between many fast multiplications or a few slow ones. // // Large exponents favor the squaring technique, and sparse matrices favor // linear multiplication. // // We calculate a threshold based on the sparsity of the input // and use squaring for exponents larger than that. // // FIXME: Improve this threshold calculation. uint64_t sparsity = atmp.numel() / atmp.nnz(); // reciprocal of density int threshold = (sparsity >= 1000) ? 40 : (sparsity >= 100) ? 20 : 3; if (btmp > threshold) // use squaring technique { while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } } else // use linear multiplication { for (int i = 0; i < btmp; i++) result = result * atmp; } retval = result; } return retval; } octave_value xpow (const SparseComplexMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return SparseMatrix(); // If we are here, A is not empty ==> A needs to be square. if (nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (! xisint (b)) error ("use full(a) ^ full(b)"); int btmp = static_cast<int> (b); if (btmp == 0) { SparseMatrix tmp = SparseMatrix (nr, nr, nr); for (octave_idx_type i = 0; i < nr; i++) { tmp.data (i) = 1.0; tmp.ridx (i) = i; } for (octave_idx_type i = 0; i < nr + 1; i++) tmp.cidx (i) = i; retval = tmp; } else { SparseComplexMatrix atmp; if (btmp < 0) { btmp = -btmp; octave_idx_type info; double rcond = 0.0; MatrixType mattyp (a); atmp = a.inverse (mattyp, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; if (atmp.nnz() == 0) // Fast return for all-zeros matrix return atmp; SparseComplexMatrix result (atmp); btmp--; // Select multiplication sequence based on sparsity of atmp. // See the long comment in xpow (const SparseMatrix& a, double b) // for more details. // // FIXME: Improve this threshold calculation. uint64_t sparsity = atmp.numel() / atmp.nnz(); // reciprocal of density int threshold = (sparsity >= 1000) ? 40 : (sparsity >= 100) ? 20 : 3; if (btmp > threshold) // use squaring technique { while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } } else // use linear multiplication { for (int i = 0; i < btmp; i++) result = result * atmp; } retval = result; } return retval; } // Safer pow functions that work elementwise for matrices. // // op2 \ op1: s m cs cm // +-- +---+---+----+----+ // scalar | | * | 3 | * | 9 | // +---+---+----+----+ // matrix | 1 | 4 | 7 | 10 | // +---+---+----+----+ // complex_scalar | * | 5 | * | 11 | // +---+---+----+----+ // complex_matrix | 2 | 6 | 8 | 12 | // +---+---+----+----+ // // * -> not needed. // FIXME: these functions need to be fixed so that things // like // // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b // // and // // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end // // produce identical results. Also, it would be nice if -1^0.5 // produced a pure imaginary result instead of a complex number with a // small real part. But perhaps that's really a problem with the math // library... // Handle special case of scalar-sparse-matrix .^ sparse-matrix. // Forwarding to the scalar elem_xpow function and then converting the // result back to a sparse matrix is a bit wasteful but it does not // seem worth the effort to optimize -- how often does this case come up // in practice? template <typename S, typename SM> inline octave_value scalar_xpow (const S& a, const SM& b) { octave_value val = elem_xpow (a, b); if (val.iscomplex ()) return SparseComplexMatrix (val.complex_matrix_value ()); else return SparseMatrix (val.matrix_value ()); } /* %!assert (sparse (2) .^ [3, 4], sparse ([8, 16])) %!assert <47775> (sparse (2i) .^ [3, 4], sparse ([-0-8i, 16])) %!test <*63080> %! Z = sparse ([]); %! A = sparse (zeros (0, 2)); %! B = sparse (zeros (2, 0)); %! assert (Z ^ 1, Z); %! assert (Z ^ 0, Z); %! assert (Z ^ -1, Z); %! assert (A ^ 1, Z); %! assert (A ^ 0, Z); %! assert (A ^ -1, Z); %! assert (B ^ 1, Z); %! assert (B ^ 0, Z); %! assert (B ^ -1, Z); %!test <*63080> %! A = sparse (zeros (2, 2)); %! assert (A ^ 1, A); %! assert (A ^ 0, sparse (eye (2, 2))); %!test <63080> %! A = sparse (zeros (2, 2)); %! assert (A ^ -1, sparse (inf (2, 2))); */ // -*- 1 -*- octave_value elem_xpow (double a, const SparseMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); double d1, d2; if (a < 0.0 && ! b.all_integers (d1, d2)) { Complex atmp (a); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (atmp, b(i, j)); } } retval = result; } else { Matrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (a, b(i, j)); } } retval = result; } return retval; } // -*- 2 -*- octave_value elem_xpow (double a, const SparseComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); Complex atmp (a); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (atmp, b(i, j)); } } return result; } // -*- 3 -*- octave_value elem_xpow (const SparseMatrix& a, double b) { // FIXME: What should a .^ 0 give? Matlab gives a // sparse matrix with same structure as a, which is strictly // incorrect. Keep compatibility. octave_value retval; octave_idx_type nz = a.nnz (); if (b <= 0.0) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (! xisint (b) && a.any_element_is_negative ()) { ComplexMatrix result (nr, nc, Complex (std::pow (0.0, b))); // FIXME: avoid apparent GNU libm bug by // converting A and B to complex instead of just A. Complex btmp (b); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); Complex atmp (a.data (i)); result(a.ridx (i), j) = std::pow (atmp, btmp); } retval = octave_value (result); } else { Matrix result (nr, nc, (std::pow (0.0, b))); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result(a.ridx (i), j) = std::pow (a.data (i), b); } retval = octave_value (result); } } else if (! xisint (b) && a.any_element_is_negative ()) { SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); // FIXME: avoid apparent GNU libm bug by // converting A and B to complex instead of just A. Complex atmp (a.data (i)); Complex btmp (b); result.data (i) = std::pow (atmp, btmp); } result.maybe_compress (true); retval = result; } else { SparseMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 4 -*- octave_value elem_xpow (const SparseMatrix& a, const SparseMatrix& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); int convert_to_complex = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { if (a.data(i) < 0.0) { double btmp = b (a.ridx (i), j); if (! xisint (btmp)) { convert_to_complex = 1; goto done; } } } done: // This is a dumb operator for sparse matrices anyway, and there is // no sensible way to handle the 0.^0 versus the 0.^x cases. Therefore // allocate a full matrix filled for the 0.^0 case and shrink it later // as needed. if (convert_to_complex) { SparseComplexMatrix complex_result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); complex_result.xelem (a.ridx (i), j) = std::pow (Complex (a.data (i)), Complex (b(a.ridx (i), j))); } } complex_result.maybe_compress (true); retval = complex_result; } else { SparseMatrix result (nr, nc, 1.0); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx (i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const SparseMatrix& a, const Complex& b) { octave_value retval; if (b == 0.0) // Can this case ever happen, due to automatic retyping with maybe_mutate? retval = octave_value (NDArray (a.dims (), 1)); else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (Complex (a.data (i)), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 6 -*- octave_value elem_xpow (const SparseMatrix& a, const SparseComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx(i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); return result; } // -*- 7 -*- octave_value elem_xpow (const Complex& a, const SparseMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); double btmp = b (i, j); if (xisint (btmp)) result (i, j) = std::pow (a, static_cast<int> (btmp)); else result (i, j) = std::pow (a, btmp); } } return result; } // -*- 8 -*- octave_value elem_xpow (const Complex& a, const SparseComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result (i, j) = std::pow (a, b (i, j)); } return result; } // -*- 9 -*- octave_value elem_xpow (const SparseComplexMatrix& a, double b) { octave_value retval; if (b <= 0) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); ComplexMatrix result (nr, nc, Complex (std::pow (0.0, b))); if (xisint (b)) { for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result (a.ridx (i), j) = std::pow (a.data (i), static_cast<int> (b)); } } else { for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result (a.ridx (i), j) = std::pow (a.data (i), b); } } retval = result; } else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); if (xisint (b)) { for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), static_cast<int> (b)); } } else { for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } } result.maybe_compress (true); retval = result; } return retval; } // -*- 10 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const SparseMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); double btmp = b(a.ridx (i), j); if (xisint (btmp)) result.xelem (a.ridx (i), j) = std::pow (a.data (i), static_cast<int> (btmp)); else result.xelem (a.ridx (i), j) = std::pow (a.data (i), btmp); } } result.maybe_compress (true); return result; } // -*- 11 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const Complex& b) { octave_value retval; if (b == 0.0) // Can this case ever happen, due to automatic retyping with maybe_mutate? retval = octave_value (NDArray (a.dims (), 1)); else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 12 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const SparseComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx (i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); return result; } OCTAVE_NAMESPACE_END