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use super::Matrix;
use crate::{to_i32, StrError, CBLAS_COL_MAJOR, CBLAS_NO_TRANS};
extern "C" {
// Performs the matrix-matrix multiplication
// <https://www.netlib.org/lapack/explore-html/d7/d2b/dgemm_8f.html>
fn cblas_dgemm(
layout: i32,
transa: i32,
transb: i32,
m: i32,
n: i32,
k: i32,
alpha: f64,
a: *const f64,
lda: i32,
b: *const f64,
ldb: i32,
beta: f64,
c: *mut f64,
ldc: i32,
);
}
/// (dgemm) Performs the matrix-matrix multiplication
///
/// ```text
/// c := α a ⋅ b + β c
/// (m,n) (m,k) (k,n) (m,n)
/// ```
///
/// See also: <https://www.netlib.org/lapack/explore-html/d7/d2b/dgemm_8f.html>
///
/// # Examples
///
/// ```
/// use russell_lab::{mat_mat_mul, Matrix, StrError};
///
/// fn main() -> Result<(), StrError> {
/// let a = Matrix::from(&[
/// [1.0, 2.0],
/// [3.0, 4.0],
/// [5.0, 6.0],
/// ]);
/// let b = Matrix::from(&[
/// [-1.0, -2.0, -3.0],
/// [-4.0, -5.0, -6.0],
/// ]);
/// let mut c = Matrix::new(3, 3);
/// mat_mat_mul(&mut c, 1.0, &a, &b, 0.0)?;
/// let correct = "┌ ┐\n\
/// │ -9 -12 -15 │\n\
/// │ -19 -26 -33 │\n\
/// │ -29 -40 -51 │\n\
/// └ ┘";
/// assert_eq!(format!("{}", c), correct);
/// Ok(())
/// }
/// ```
pub fn mat_mat_mul(c: &mut Matrix, alpha: f64, a: &Matrix, b: &Matrix, beta: f64) -> Result<(), StrError> {
let (m, n) = c.dims();
let k = a.ncol();
if a.nrow() != m || b.nrow() != k || b.ncol() != n {
return Err("matrices are incompatible");
}
if m == 0 || n == 0 {
return Ok(());
}
if k == 0 {
c.fill(0.0);
return Ok(());
}
let m_i32: i32 = to_i32(m);
let n_i32: i32 = to_i32(n);
let k_i32: i32 = to_i32(k);
let lda = m_i32;
let ldb = k_i32;
unsafe {
cblas_dgemm(
CBLAS_COL_MAJOR,
CBLAS_NO_TRANS,
CBLAS_NO_TRANS,
m_i32,
n_i32,
k_i32,
alpha,
a.as_data().as_ptr(),
lda,
b.as_data().as_ptr(),
ldb,
beta,
c.as_mut_data().as_mut_ptr(),
m_i32,
);
}
Ok(())
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#[cfg(test)]
mod tests {
use super::{mat_mat_mul, Matrix};
use crate::{mat_approx_eq, mat_norm, Norm};
fn naive_mat_mat_mul(c: &mut Matrix, alpha: f64, a: &Matrix, b: &Matrix) {
let (m, n) = c.dims();
let k = a.ncol();
if a.nrow() != m || b.nrow() != k || b.ncol() != n {
panic!("matrices are incompatible");
}
if m == 0 || n == 0 || k == 0 {
return;
}
for i in 0..m {
for j in 0..n {
c.set(i, j, 0.0);
for p in 0..k {
c.add(i, j, alpha * a.get(i, p) * b.get(p, j));
}
}
}
}
#[test]
#[should_panic(expected = "matrices are incompatible")]
fn naive_mat_mat_mul_capture_errors() {
let a = Matrix::new(1, 0);
let b = Matrix::new(0, 0);
let mut c = Matrix::new(0, 0);
naive_mat_mat_mul(&mut c, 1.0, &a, &b);
}
#[test]
fn mat_mat_mul_fails_on_wrong_dims() {
let a_2x1 = Matrix::new(2, 1);
let a_1x2 = Matrix::new(1, 2);
let b_2x1 = Matrix::new(2, 1);
let b_1x3 = Matrix::new(1, 3);
let mut c_2x2 = Matrix::new(2, 2);
assert_eq!(
mat_mat_mul(&mut c_2x2, 1.0, &a_2x1, &b_2x1, 0.0),
Err("matrices are incompatible")
);
assert_eq!(
mat_mat_mul(&mut c_2x2, 1.0, &a_1x2, &b_2x1, 0.0),
Err("matrices are incompatible")
);
assert_eq!(
mat_mat_mul(&mut c_2x2, 1.0, &a_2x1, &b_1x3, 0.0),
Err("matrices are incompatible")
);
}
#[test]
fn mat_mat_mul_0x0_works() {
let a = Matrix::new(0, 0);
let b = Matrix::new(0, 0);
let mut c = Matrix::new(0, 0);
mat_mat_mul(&mut c, 2.0, &a, &b, 0.0).unwrap();
let a = Matrix::new(1, 0);
let b = Matrix::new(0, 1);
let mut c = Matrix::from(&[[123.0]]);
mat_mat_mul(&mut c, 2.0, &a, &b, 0.0).unwrap();
let correct = &[
[0.0], //
];
mat_approx_eq(&c, correct, 1e-15);
}
#[test]
fn mat_mat_mul_works_1() {
let a = Matrix::from(&[
// 2 x 3
[1.0, 2.00, 3.0],
[0.5, 0.75, 1.5],
]);
let b = Matrix::from(&[
// 3 x 4
[0.1, 0.5, 0.5, 0.75],
[0.2, 2.0, 2.0, 2.00],
[0.3, 0.5, 0.5, 0.50],
]);
let mut c = Matrix::new(2, 4);
// c := 2⋅a⋅b
mat_mat_mul(&mut c, 2.0, &a, &b, 0.0).unwrap();
#[rustfmt::skip]
let correct = &[
[2.80, 12.0, 12.0, 12.50],
[1.30, 5.0, 5.0, 5.25],
];
mat_approx_eq(&c, correct, 1e-15);
}
#[test]
fn mat_mat_mul_works_2() {
let a = Matrix::from(&[
// 2 x 3
[1.0, 2.00, 3.0],
[0.5, 0.75, 1.5],
]);
let b = Matrix::from(&[
// 3 x 4
[0.1, 0.5, 0.5, 0.75],
[0.2, 2.0, 2.0, 2.00],
[0.3, 0.5, 0.5, 0.50],
]);
let mut c = Matrix::filled(2, 4, 100.0);
// c := 2 a⋅b + 10 c
mat_mat_mul(&mut c, 2.0, &a, &b, 10.0).unwrap();
#[rustfmt::skip]
let correct = &[
[1002.80, 1012.0, 1012.0, 1012.50],
[1001.30, 1005.0, 1005.0, 1005.25],
];
mat_approx_eq(&c, correct, 1e-15);
}
#[test]
fn mat_mat_mul_works_range() {
// c := a ⋅ b
// (m,n) (m,k) (k,n)
for m in [0, 5, 7_usize] {
for n in [0, 6, 12_usize] {
let mut c = Matrix::new(m, n);
let mut c_local = Matrix::new(m, n);
for k in [0, 5, 10, 15_usize] {
let a = Matrix::filled(m, k, 1.0);
let b = Matrix::filled(k, n, 1.0);
mat_mat_mul(&mut c, 1.0, &a, &b, 0.0).unwrap();
naive_mat_mat_mul(&mut c_local, 1.0, &a, &b);
if m == 0 || n == 0 {
assert_eq!(mat_norm(&c, Norm::Max), 0.0);
} else {
assert_eq!(mat_norm(&c, Norm::Max), k as f64);
}
mat_approx_eq(&c, &c_local, 1e-15);
}
}
}
}
}