nalgebra/nalgebra-sparse/tests/unit_tests/ops.rs

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use crate::common::{csr_strategy, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ,
PROPTEST_I32_VALUE_STRATEGY};
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use nalgebra_sparse::ops::serial::{spmm_csr_dense, spadd_pattern, spmm_pattern, spadd_csr, spmm_csr};
use nalgebra_sparse::ops::{Op};
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use nalgebra_sparse::csr::CsrMatrix;
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use nalgebra_sparse::proptest::{csr, sparsity_pattern};
use nalgebra_sparse::pattern::SparsityPattern;
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use nalgebra::{DMatrix, Scalar, DMatrixSliceMut, DMatrixSlice};
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use nalgebra::proptest::matrix;
use proptest::prelude::*;
use std::panic::catch_unwind;
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use std::sync::Arc;
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/// Represents the sparsity pattern of a CSR matrix as a dense matrix with 0/1
fn dense_csr_pattern(pattern: &SparsityPattern) -> DMatrix<i32> {
let boolean_csr = CsrMatrix::try_from_pattern_and_values(
Arc::new(pattern.clone()),
vec![1; pattern.nnz()])
.unwrap();
DMatrix::from(&boolean_csr)
}
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#[derive(Debug)]
struct SpmmCsrDenseArgs<T: Scalar> {
c: DMatrix<T>,
beta: T,
alpha: T,
a: Op<CsrMatrix<T>>,
b: Op<DMatrix<T>>,
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}
/// Returns matrices C, A and B with compatible dimensions such that it can be used
/// in an `spmm` operation `C = beta * C + alpha * trans(A) * trans(B)`.
fn spmm_csr_dense_args_strategy() -> impl Strategy<Value=SpmmCsrDenseArgs<i32>> {
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let max_nnz = PROPTEST_MAX_NNZ;
let value_strategy = PROPTEST_I32_VALUE_STRATEGY;
let c_rows = PROPTEST_MATRIX_DIM;
let c_cols = PROPTEST_MATRIX_DIM;
let common_dim = PROPTEST_MATRIX_DIM;
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let trans_strategy = trans_strategy();
let c_matrix_strategy = matrix(value_strategy.clone(), c_rows, c_cols);
(c_matrix_strategy, common_dim, trans_strategy.clone(), trans_strategy.clone())
.prop_flat_map(move |(c, common_dim, trans_a, trans_b)| {
let a_shape =
if trans_a { (common_dim, c.nrows()) }
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else { (c.nrows(), common_dim) };
let b_shape =
if trans_b { (c.ncols(), common_dim) }
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else { (common_dim, c.ncols()) };
let a = csr(value_strategy.clone(), Just(a_shape.0), Just(a_shape.1), max_nnz);
let b = matrix(value_strategy.clone(), b_shape.0, b_shape.1);
// We use the same values for alpha, beta parameters as for matrix elements
let alpha = value_strategy.clone();
let beta = value_strategy.clone();
(Just(c), beta, alpha, Just(trans_a), a, Just(trans_b), b)
}).prop_map(|(c, beta, alpha, trans_a, a, trans_b, b)| {
SpmmCsrDenseArgs {
c,
beta,
alpha,
a: if trans_a { Op::Transpose(a) } else { Op::NoOp(a) },
b: if trans_b { Op::Transpose(b) } else { Op::NoOp(b) },
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}
})
}
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#[derive(Debug)]
struct SpaddCsrArgs<T> {
c: CsrMatrix<T>,
beta: T,
alpha: T,
a: Op<CsrMatrix<T>>,
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}
fn spadd_csr_args_strategy() -> impl Strategy<Value=SpaddCsrArgs<i32>> {
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let value_strategy = PROPTEST_I32_VALUE_STRATEGY;
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spadd_pattern_strategy()
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.prop_flat_map(move |(a_pattern, b_pattern)| {
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let c_pattern = spadd_pattern(&a_pattern, &b_pattern);
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let a_values = vec![value_strategy.clone(); a_pattern.nnz()];
let c_values = vec![value_strategy.clone(); c_pattern.nnz()];
let alpha = value_strategy.clone();
let beta = value_strategy.clone();
(Just(c_pattern), Just(a_pattern), c_values, a_values, alpha, beta, trans_strategy())
}).prop_map(|(c_pattern, a_pattern, c_values, a_values, alpha, beta, trans_a)| {
let c = CsrMatrix::try_from_pattern_and_values(Arc::new(c_pattern), c_values).unwrap();
let a = CsrMatrix::try_from_pattern_and_values(Arc::new(a_pattern), a_values).unwrap();
let a = if trans_a { Op::Transpose(a.transpose()) } else { Op::NoOp(a) };
SpaddCsrArgs { c, beta, alpha, a }
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})
}
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fn dense_strategy() -> impl Strategy<Value=DMatrix<i32>> {
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matrix(PROPTEST_I32_VALUE_STRATEGY, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM)
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}
fn trans_strategy() -> impl Strategy<Value=bool> + Clone {
proptest::bool::ANY
}
/// Wraps the values of the given strategy in `Op`, producing both transposed and non-transposed
/// values.
fn op_strategy<S: Strategy>(strategy: S) -> impl Strategy<Value=Op<S::Value>> {
let is_transposed = proptest::bool::ANY;
(strategy, is_transposed)
.prop_map(|(obj, is_trans)| if is_trans {
Op::Transpose(obj)
} else {
Op::NoOp(obj)
})
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}
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fn pattern_strategy() -> impl Strategy<Value=SparsityPattern> {
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sparsity_pattern(PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
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}
/// Constructs pairs (a, b) where a and b have the same dimensions
fn spadd_pattern_strategy() -> impl Strategy<Value=(SparsityPattern, SparsityPattern)> {
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pattern_strategy()
.prop_flat_map(|a| {
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let b = sparsity_pattern(Just(a.major_dim()), Just(a.minor_dim()), PROPTEST_MAX_NNZ);
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(Just(a), b)
})
}
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/// Constructs pairs (a, b) where a and b have compatible dimensions for a matrix product
fn spmm_pattern_strategy() -> impl Strategy<Value=(SparsityPattern, SparsityPattern)> {
pattern_strategy()
.prop_flat_map(|a| {
let b = sparsity_pattern(Just(a.minor_dim()), PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ);
(Just(a), b)
})
}
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#[derive(Debug)]
struct SpmmCsrArgs<T> {
c: CsrMatrix<T>,
beta: T,
alpha: T,
a: Op<CsrMatrix<T>>,
b: Op<CsrMatrix<T>>,
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}
fn spmm_csr_args_strategy() -> impl Strategy<Value=SpmmCsrArgs<i32>> {
spmm_pattern_strategy()
.prop_flat_map(|(a_pattern, b_pattern)| {
let a_values = vec![PROPTEST_I32_VALUE_STRATEGY; a_pattern.nnz()];
let b_values = vec![PROPTEST_I32_VALUE_STRATEGY; b_pattern.nnz()];
let c_pattern = spmm_pattern(&a_pattern, &b_pattern);
let c_values = vec![PROPTEST_I32_VALUE_STRATEGY; c_pattern.nnz()];
let a_pattern = Arc::new(a_pattern);
let b_pattern = Arc::new(b_pattern);
let c_pattern = Arc::new(c_pattern);
let a = a_values.prop_map(move |values|
CsrMatrix::try_from_pattern_and_values(Arc::clone(&a_pattern), values).unwrap());
let b = b_values.prop_map(move |values|
CsrMatrix::try_from_pattern_and_values(Arc::clone(&b_pattern), values).unwrap());
let c = c_values.prop_map(move |values|
CsrMatrix::try_from_pattern_and_values(Arc::clone(&c_pattern), values).unwrap());
let alpha = PROPTEST_I32_VALUE_STRATEGY;
let beta = PROPTEST_I32_VALUE_STRATEGY;
(c, beta, alpha, trans_strategy(), a, trans_strategy(), b)
})
.prop_map(|(c, beta, alpha, trans_a, a, trans_b, b)| {
SpmmCsrArgs::<i32> {
c,
beta,
alpha,
a: if trans_a { Op::Transpose(a.transpose()) } else { Op::NoOp(a) },
b: if trans_b { Op::Transpose(b.transpose()) } else { Op::NoOp(b) }
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}
})
}
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/// Helper function to help us call dense GEMM with our transposition parameters
fn dense_gemm<'a>(c: impl Into<DMatrixSliceMut<'a, i32>>,
beta: i32,
alpha: i32,
a: Op<impl Into<DMatrixSlice<'a, i32>>>,
b: Op<impl Into<DMatrixSlice<'a, i32>>>)
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{
let mut c = c.into();
let a = a.convert();
let b = b.convert();
use Op::{NoOp, Transpose};
match (a, b) {
(NoOp(a), NoOp(b)) => c.gemm(alpha, &a, &b, beta),
(Transpose(a), NoOp(b)) => c.gemm(alpha, &a.transpose(), &b, beta),
(NoOp(a), Transpose(b)) => c.gemm(alpha, &a, &b.transpose(), beta),
(Transpose(a), Transpose(b)) => c.gemm(alpha, &a.transpose(), &b.transpose(), beta)
}
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}
proptest! {
#[test]
fn spmm_csr_dense_agrees_with_dense_result(
SpmmCsrDenseArgs { c, beta, alpha, a, b }
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in spmm_csr_dense_args_strategy()
) {
let mut spmm_result = c.clone();
spmm_csr_dense(&mut spmm_result, beta, alpha, a.as_ref(), b.as_ref());
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let mut gemm_result = c.clone();
let a_dense = a.map_same_op(|a| DMatrix::from(&a));
dense_gemm(&mut gemm_result, beta, alpha, a_dense.as_ref(), b.as_ref());
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prop_assert_eq!(spmm_result, gemm_result);
}
#[test]
fn spmm_csr_dense_panics_on_dim_mismatch(
(alpha, beta, c, a, b)
in (PROPTEST_I32_VALUE_STRATEGY,
PROPTEST_I32_VALUE_STRATEGY,
dense_strategy(),
op_strategy(csr_strategy()),
op_strategy(dense_strategy()))
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) {
// We refer to `A * B` as the "product"
let product_rows = match &a {
Op::NoOp(ref a) => a.nrows(),
Op::Transpose(ref a) => a.ncols(),
};
let product_cols = match &b {
Op::NoOp(ref b) => b.ncols(),
Op::Transpose(ref b) => b.nrows(),
};
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// Determine the common dimension in the product
// from the perspective of a and b, respectively
let product_a_common = match &a {
Op::NoOp(ref a) => a.ncols(),
Op::Transpose(ref a) => a.nrows(),
};
let product_b_common = match &b {
Op::NoOp(ref b) => b.nrows(),
Op::Transpose(ref b) => b.ncols()
};
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let dims_are_compatible = product_rows == c.nrows()
&& product_cols == c.ncols()
&& product_a_common == product_b_common;
// If the dimensions randomly happen to be compatible, then of course we need to
// skip the test, so we assume that they are not.
prop_assume!(!dims_are_compatible);
let result = catch_unwind(|| {
let mut spmm_result = c.clone();
spmm_csr_dense(&mut spmm_result, beta, alpha, a.as_ref(), b.as_ref());
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});
prop_assert!(result.is_err(),
"The SPMM kernel executed successfully despite mismatch dimensions");
}
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#[test]
fn spadd_pattern_test((a, b) in spadd_pattern_strategy())
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{
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// (a, b) are dimensionally compatible patterns
let pattern_result = spadd_pattern(&a, &b);
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// To verify the pattern, we construct CSR matrices with positive integer entries
// corresponding to a and b, and convert them to dense matrices.
// The sum of these dense matrices will then have non-zeros in exactly the same locations
// as the result of "adding" the sparsity patterns
let a_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(a.clone()), vec![1; a.nnz()])
.unwrap();
let a_dense = DMatrix::from(&a_csr);
let b_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(b.clone()), vec![1; b.nnz()])
.unwrap();
let b_dense = DMatrix::from(&b_csr);
let c_dense = a_dense + b_dense;
let c_csr = CsrMatrix::from(&c_dense);
prop_assert_eq!(&pattern_result, c_csr.pattern().as_ref());
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}
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#[test]
fn spadd_csr_test(SpaddCsrArgs { c, beta, alpha, a } in spadd_csr_args_strategy()) {
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// Test that we get the expected result by comparing to an equivalent dense operation
// (here we give in the C matrix, so the sparsity pattern is essentially fixed)
let mut c_sparse = c.clone();
spadd_csr(&mut c_sparse, beta, alpha, a.as_ref()).unwrap();
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let mut c_dense = DMatrix::from(&c);
let op_a_dense = match a {
Op::NoOp(a) => DMatrix::from(&a),
Op::Transpose(a) => DMatrix::from(&a).transpose(),
};
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c_dense = beta * c_dense + alpha * &op_a_dense;
prop_assert_eq!(&DMatrix::from(&c_sparse), &c_dense);
}
#[test]
fn csr_add_csr(
// a and b have the same dimensions
(a, b)
in csr_strategy()
.prop_flat_map(|a| {
let b = csr(PROPTEST_I32_VALUE_STRATEGY, Just(a.nrows()), Just(a.ncols()), 40);
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(Just(a), b)
}))
{
// We use the dense result as the ground truth for the arithmetic result
let c_dense = DMatrix::from(&a) + DMatrix::from(&b);
// However, it's not enough only to cover the dense result, we also need to verify the
// sparsity pattern. We can determine the exact sparsity pattern by using
// dense arithmetic with positive integer values and extracting positive entries.
let c_dense_pattern = dense_csr_pattern(a.pattern()) + dense_csr_pattern(b.pattern());
let c_pattern = CsrMatrix::from(&c_dense_pattern).pattern().clone();
// Check each combination of owned matrices and references
let c_owned_owned = a.clone() + b.clone();
prop_assert_eq!(&DMatrix::from(&c_owned_owned), &c_dense);
prop_assert_eq!(c_owned_owned.pattern(), &c_pattern);
let c_owned_ref = a.clone() + &b;
prop_assert_eq!(&DMatrix::from(&c_owned_ref), &c_dense);
prop_assert_eq!(c_owned_ref.pattern(), &c_pattern);
let c_ref_owned = &a + b.clone();
prop_assert_eq!(&DMatrix::from(&c_ref_owned), &c_dense);
prop_assert_eq!(c_ref_owned.pattern(), &c_pattern);
let c_ref_ref = &a + &b;
prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
}
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#[test]
fn spmm_pattern_test((a, b) in spmm_pattern_strategy())
{
// (a, b) are multiplication-wise dimensionally compatible patterns
let c_pattern = spmm_pattern(&a, &b);
// To verify the pattern, we construct CSR matrices with positive integer entries
// corresponding to a and b, and convert them to dense matrices.
// The product of these dense matrices will then have non-zeros in exactly the same locations
// as the result of "multiplying" the sparsity patterns
let a_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(a.clone()), vec![1; a.nnz()])
.unwrap();
let a_dense = DMatrix::from(&a_csr);
let b_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(b.clone()), vec![1; b.nnz()])
.unwrap();
let b_dense = DMatrix::from(&b_csr);
let c_dense = a_dense * b_dense;
let c_csr = CsrMatrix::from(&c_dense);
prop_assert_eq!(&c_pattern, c_csr.pattern().as_ref());
}
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#[test]
fn spmm_csr_test(SpmmCsrArgs { c, beta, alpha, a, b }
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in spmm_csr_args_strategy()
) {
// Test that we get the expected result by comparing to an equivalent dense operation
// (here we give in the C matrix, so the sparsity pattern is essentially fixed)
let mut c_sparse = c.clone();
spmm_csr(&mut c_sparse, beta, alpha, a.as_ref(), b.as_ref()).unwrap();
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let mut c_dense = DMatrix::from(&c);
let op_a_dense = match a {
Op::NoOp(ref a) => DMatrix::from(a),
Op::Transpose(ref a) => DMatrix::from(a).transpose(),
};
let op_b_dense = match b {
Op::NoOp(ref b) => DMatrix::from(b),
Op::Transpose(ref b) => DMatrix::from(b).transpose(),
};
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c_dense = beta * c_dense + alpha * &op_a_dense * op_b_dense;
prop_assert_eq!(&DMatrix::from(&c_sparse), &c_dense);
}
#[test]
fn spmm_csr_panics_on_dim_mismatch(
(alpha, beta, c, a, b)
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in (PROPTEST_I32_VALUE_STRATEGY,
PROPTEST_I32_VALUE_STRATEGY,
csr_strategy(),
op_strategy(csr_strategy()),
op_strategy(csr_strategy()))
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) {
// We refer to `A * B` as the "product"
let product_rows = match &a {
Op::NoOp(ref a) => a.nrows(),
Op::Transpose(ref a) => a.ncols(),
};
let product_cols = match &b {
Op::NoOp(ref b) => b.ncols(),
Op::Transpose(ref b) => b.nrows(),
};
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// Determine the common dimension in the product
// from the perspective of a and b, respectively
let product_a_common = match &a {
Op::NoOp(ref a) => a.ncols(),
Op::Transpose(ref a) => a.nrows(),
};
let product_b_common = match &b {
Op::NoOp(ref b) => b.nrows(),
Op::Transpose(ref b) => b.ncols(),
};
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let dims_are_compatible = product_rows == c.nrows()
&& product_cols == c.ncols()
&& product_a_common == product_b_common;
// If the dimensions randomly happen to be compatible, then of course we need to
// skip the test, so we assume that they are not.
prop_assume!(!dims_are_compatible);
let result = catch_unwind(|| {
let mut spmm_result = c.clone();
spmm_csr(&mut spmm_result, beta, alpha, a.as_ref(), b.as_ref()).unwrap();
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});
prop_assert!(result.is_err(),
"The SPMM kernel executed successfully despite mismatch dimensions");
}
#[test]
fn spadd_csr_panics_on_dim_mismatch(
(alpha, beta, c, op_a)
in (PROPTEST_I32_VALUE_STRATEGY,
PROPTEST_I32_VALUE_STRATEGY,
csr_strategy(),
op_strategy(csr_strategy()))
) {
let op_a_rows = match &op_a {
&Op::NoOp(ref a) => a.nrows(),
&Op::Transpose(ref a) => a.ncols()
};
let op_a_cols = match &op_a {
&Op::NoOp(ref a) => a.ncols(),
&Op::Transpose(ref a) => a.nrows()
};
let dims_are_compatible = c.nrows() == op_a_rows && c.ncols() == op_a_cols;
// If the dimensions randomly happen to be compatible, then of course we need to
// skip the test, so we assume that they are not.
prop_assume!(!dims_are_compatible);
let result = catch_unwind(|| {
let mut spmm_result = c.clone();
spadd_csr(&mut spmm_result, beta, alpha, op_a.as_ref()).unwrap();
});
prop_assert!(result.is_err(),
"The SPMM kernel executed successfully despite mismatch dimensions");
}
#[test]
fn csr_mul_csr(
// a and b have dimensions compatible for multiplication
(a, b)
in csr_strategy()
.prop_flat_map(|a| {
let max_nnz = PROPTEST_MAX_NNZ;
let cols = PROPTEST_MATRIX_DIM;
let b = csr(PROPTEST_I32_VALUE_STRATEGY, Just(a.ncols()), cols, max_nnz);
(Just(a), b)
}))
{
// We use the dense result as the ground truth for the arithmetic result
let c_dense = DMatrix::from(&a) * DMatrix::from(&b);
// However, it's not enough only to cover the dense result, we also need to verify the
// sparsity pattern. We can determine the exact sparsity pattern by using
// dense arithmetic with positive integer values and extracting positive entries.
let c_dense_pattern = dense_csr_pattern(a.pattern()) * dense_csr_pattern(b.pattern());
let c_pattern = CsrMatrix::from(&c_dense_pattern).pattern().clone();
// Check each combination of owned matrices and references
let c_owned_owned = a.clone() * b.clone();
prop_assert_eq!(&DMatrix::from(&c_owned_owned), &c_dense);
prop_assert_eq!(c_owned_owned.pattern(), &c_pattern);
let c_owned_ref = a.clone() * &b;
prop_assert_eq!(&DMatrix::from(&c_owned_ref), &c_dense);
prop_assert_eq!(c_owned_ref.pattern(), &c_pattern);
let c_ref_owned = &a * b.clone();
prop_assert_eq!(&DMatrix::from(&c_ref_owned), &c_dense);
prop_assert_eq!(c_ref_owned.pattern(), &c_pattern);
let c_ref_ref = &a * &b;
prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
}
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}