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Changed dimension name R to D 

Changed N::from_x to crate::convert
This commit is contained in:
Fredrik Jansson 2020-04-12 11:46:00 +02:00
parent c7d9e415ce
commit 0a3ee99cdb
1 changed files with 111 additions and 119 deletions
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230
src/linalg/exp.rs
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@ -6,25 +6,25 @@ use crate::{
dimension::{DimMin, DimMinimum, DimName}, dimension::{DimMin, DimMinimum, DimName},
DefaultAllocator, DefaultAllocator,
}, },
try_convert, ComplexField, MatrixN, RealField, convert, try_convert, ComplexField, MatrixN, RealField,
}; };
// https://github.com/scipy/scipy/blob/c1372d8aa90a73d8a52f135529293ff4edb98fc8/scipy/sparse/linalg/matfuncs.py // https://github.com/scipy/scipy/blob/c1372d8aa90a73d8a52f135529293ff4edb98fc8/scipy/sparse/linalg/matfuncs.py
struct ExpmPadeHelper<N, R> struct ExpmPadeHelper<N, D>
where where
N: RealField, N: RealField,
R: DimName + DimMin<R>, D: DimName + DimMin<D>,
DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>, DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
{ {
use_exact_norm: bool, use_exact_norm: bool,
ident: MatrixN<N, R>, ident: MatrixN<N, D>,
a: MatrixN<N, R>, a: MatrixN<N, D>,
a2: Option<MatrixN<N, R>>, a2: Option<MatrixN<N, D>>,
a4: Option<MatrixN<N, R>>, a4: Option<MatrixN<N, D>>,
a6: Option<MatrixN<N, R>>, a6: Option<MatrixN<N, D>>,
a8: Option<MatrixN<N, R>>, a8: Option<MatrixN<N, D>>,
a10: Option<MatrixN<N, R>>, a10: Option<MatrixN<N, D>>,
d4_exact: Option<N>, d4_exact: Option<N>,
d6_exact: Option<N>, d6_exact: Option<N>,
@ -37,16 +37,16 @@ where
d10_approx: Option<N>, d10_approx: Option<N>,
} }
impl<N, R> ExpmPadeHelper<N, R> impl<N, D> ExpmPadeHelper<N, D>
where where
N: RealField, N: RealField,
R: DimName + DimMin<R>, D: DimName + DimMin<D>,
DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>, DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
{ {
fn new(a: MatrixN<N, R>, use_exact_norm: bool) -> Self { fn new(a: MatrixN<N, D>, use_exact_norm: bool) -> Self {
ExpmPadeHelper { ExpmPadeHelper {
use_exact_norm, use_exact_norm,
ident: MatrixN::<N, R>::identity(), ident: MatrixN::<N, D>::identity(),
a, a,
a2: None, a2: None,
a4: None, a4: None,
@ -64,9 +64,9 @@ where
} }
} }
fn a2(&self) -> &MatrixN<N, R> { fn a2(&self) -> &MatrixN<N, D> {
if self.a2.is_none() { if self.a2.is_none() {
let ap = &self.a2 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>; let ap = &self.a2 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
unsafe { unsafe {
*ap = Some(&self.a * &self.a); *ap = Some(&self.a * &self.a);
} }
@ -74,9 +74,9 @@ where
self.a2.as_ref().unwrap() self.a2.as_ref().unwrap()
} }
fn a4(&self) -> &MatrixN<N, R> { fn a4(&self) -> &MatrixN<N, D> {
if self.a4.is_none() { if self.a4.is_none() {
let ap = &self.a4 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>; let ap = &self.a4 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
let a2 = self.a2(); let a2 = self.a2();
unsafe { unsafe {
*ap = Some(a2 * a2); *ap = Some(a2 * a2);
@ -85,11 +85,11 @@ where
self.a4.as_ref().unwrap() self.a4.as_ref().unwrap()
} }
fn a6(&self) -> &MatrixN<N, R> { fn a6(&self) -> &MatrixN<N, D> {
if self.a6.is_none() { if self.a6.is_none() {
let a2 = self.a2(); let a2 = self.a2();
let a4 = self.a4(); let a4 = self.a4();
let ap = &self.a6 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>; let ap = &self.a6 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
unsafe { unsafe {
*ap = Some(a4 * a2); *ap = Some(a4 * a2);
} }
@ -97,11 +97,11 @@ where
self.a6.as_ref().unwrap() self.a6.as_ref().unwrap()
} }
fn a8(&self) -> &MatrixN<N, R> { fn a8(&self) -> &MatrixN<N, D> {
if self.a8.is_none() { if self.a8.is_none() {
let a2 = self.a2(); let a2 = self.a2();
let a6 = self.a6(); let a6 = self.a6();
let ap = &self.a8 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>; let ap = &self.a8 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
unsafe { unsafe {
*ap = Some(a6 * a2); *ap = Some(a6 * a2);
} }
@ -109,11 +109,11 @@ where
self.a8.as_ref().unwrap() self.a8.as_ref().unwrap()
} }
fn a10(&mut self) -> &MatrixN<N, R> { fn a10(&mut self) -> &MatrixN<N, D> {
if self.a10.is_none() { if self.a10.is_none() {
let a4 = self.a4(); let a4 = self.a4();
let a6 = self.a6(); let a6 = self.a6();
let ap = &self.a10 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>; let ap = &self.a10 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
unsafe { unsafe {
*ap = Some(a6 * a4); *ap = Some(a6 * a4);
} }
@ -123,28 +123,28 @@ where
fn d4_tight(&mut self) -> N { fn d4_tight(&mut self) -> N {
if self.d4_exact.is_none() { if self.d4_exact.is_none() {
self.d4_exact = Some(one_norm(self.a4()).powf(N::from_f64(0.25).unwrap())); self.d4_exact = Some(one_norm(self.a4()).powf(convert(0.25)));
} }
self.d4_exact.unwrap() self.d4_exact.unwrap()
} }
fn d6_tight(&mut self) -> N { fn d6_tight(&mut self) -> N {
if self.d6_exact.is_none() { if self.d6_exact.is_none() {
self.d6_exact = Some(one_norm(self.a6()).powf(N::from_f64(1.0 / 6.0).unwrap())); self.d6_exact = Some(one_norm(self.a6()).powf(convert(1.0 / 6.0)));
} }
self.d6_exact.unwrap() self.d6_exact.unwrap()
} }
fn d8_tight(&mut self) -> N { fn d8_tight(&mut self) -> N {
if self.d8_exact.is_none() { if self.d8_exact.is_none() {
self.d8_exact = Some(one_norm(self.a8()).powf(N::from_f64(1.0 / 8.0).unwrap())); self.d8_exact = Some(one_norm(self.a8()).powf(convert(1.0 / 8.0)));
} }
self.d8_exact.unwrap() self.d8_exact.unwrap()
} }
fn d10_tight(&mut self) -> N { fn d10_tight(&mut self) -> N {
if self.d10_exact.is_none() { if self.d10_exact.is_none() {
self.d10_exact = Some(one_norm(self.a10()).powf(N::from_f64(1.0 / 10.0).unwrap())); self.d10_exact = Some(one_norm(self.a10()).powf(convert(1.0 / 10.0)));
} }
self.d10_exact.unwrap() self.d10_exact.unwrap()
} }
@ -159,7 +159,7 @@ where
} }
if self.d4_approx.is_none() { if self.d4_approx.is_none() {
self.d4_approx = Some(one_norm(self.a4()).powf(N::from_f64(0.25).unwrap())); self.d4_approx = Some(one_norm(self.a4()).powf(convert(0.25)));
} }
self.d4_approx.unwrap() self.d4_approx.unwrap()
@ -175,7 +175,7 @@ where
} }
if self.d6_approx.is_none() { if self.d6_approx.is_none() {
self.d6_approx = Some(one_norm(self.a6()).powf(N::from_f64(1.0 / 6.0).unwrap())); self.d6_approx = Some(one_norm(self.a6()).powf(convert(1.0 / 6.0)));
} }
self.d6_approx.unwrap() self.d6_approx.unwrap()
@ -191,7 +191,7 @@ where
} }
if self.d8_approx.is_none() { if self.d8_approx.is_none() {
self.d8_approx = Some(one_norm(self.a8()).powf(N::from_f64(1.0 / 8.0).unwrap())); self.d8_approx = Some(one_norm(self.a8()).powf(convert(1.0 / 8.0)));
} }
self.d8_approx.unwrap() self.d8_approx.unwrap()
@ -207,48 +207,43 @@ where
} }
if self.d10_approx.is_none() { if self.d10_approx.is_none() {
self.d10_approx = Some(one_norm(self.a10()).powf(N::from_f64(1.0 / 10.0).unwrap())); self.d10_approx = Some(one_norm(self.a10()).powf(convert(1.0 / 10.0)));
} }
self.d10_approx.unwrap() self.d10_approx.unwrap()
} }
fn pade3(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) { fn pade3(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
let b = [ let b: [N; 4] = [convert(120.0), convert(60.0), convert(12.0), convert(1.0)];
N::from_f64(120.0).unwrap(),
N::from_f64(60.0).unwrap(),
N::from_f64(12.0).unwrap(),
N::from_f64(1.0).unwrap(),
];
let u = &self.a * (self.a2() * b[3] + &self.ident * b[1]); let u = &self.a * (self.a2() * b[3] + &self.ident * b[1]);
let v = self.a2() * b[2] + &self.ident * b[0]; let v = self.a2() * b[2] + &self.ident * b[0];
(u, v) (u, v)
} }
fn pade5(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) { fn pade5(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
let b = [ let b: [N; 6] = [
N::from_f64(30240.0).unwrap(), convert(30240.0),
N::from_f64(15120.0).unwrap(), convert(15120.0),
N::from_f64(3360.0).unwrap(), convert(3360.0),
N::from_f64(420.0).unwrap(), convert(420.0),
N::from_f64(30.0).unwrap(), convert(30.0),
N::from_f64(1.0).unwrap(), convert(1.0),
]; ];
let u = &self.a * (self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]); let u = &self.a * (self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]);
let v = self.a4() * b[4] + self.a2() * b[2] + &self.ident * b[0]; let v = self.a4() * b[4] + self.a2() * b[2] + &self.ident * b[0];
(u, v) (u, v)
} }
fn pade7(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) { fn pade7(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
let b = [ let b: [N; 8] = [
N::from_f64(17297280.0).unwrap(), convert(17297280.0),
N::from_f64(8648640.0).unwrap(), convert(8648640.0),
N::from_f64(1995840.0).unwrap(), convert(1995840.0),
N::from_f64(277200.0).unwrap(), convert(277200.0),
N::from_f64(25200.0).unwrap(), convert(25200.0),
N::from_f64(1512.0).unwrap(), convert(1512.0),
N::from_f64(56.0).unwrap(), convert(56.0),
N::from_f64(1.0).unwrap(), convert(1.0),
]; ];
let u = let u =
&self.a * (self.a6() * b[7] + self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]); &self.a * (self.a6() * b[7] + self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]);
@ -256,18 +251,18 @@ where
(u, v) (u, v)
} }
fn pade9(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) { fn pade9(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
let b = [ let b: [N; 10] = [
N::from_f64(17643225600.0).unwrap(), convert(17643225600.0),
N::from_f64(8821612800.0).unwrap(), convert(8821612800.0),
N::from_f64(2075673600.0).unwrap(), convert(2075673600.0),
N::from_f64(302702400.0).unwrap(), convert(302702400.0),
N::from_f64(30270240.0).unwrap(), convert(30270240.0),
N::from_f64(2162160.0).unwrap(), convert(2162160.0),
N::from_f64(110880.0).unwrap(), convert(110880.0),
N::from_f64(3960.0).unwrap(), convert(3960.0),
N::from_f64(90.0).unwrap(), convert(90.0),
N::from_f64(1.0).unwrap(), convert(1.0),
]; ];
let u = &self.a let u = &self.a
* (self.a8() * b[9] * (self.a8() * b[9]
@ -283,29 +278,29 @@ where
(u, v) (u, v)
} }
fn pade13_scaled(&mut self, s: u64) -> (MatrixN<N, R>, MatrixN<N, R>) { fn pade13_scaled(&mut self, s: u64) -> (MatrixN<N, D>, MatrixN<N, D>) {
let b = [ let b: [N; 14] = [
N::from_f64(64764752532480000.0).unwrap(), convert(64764752532480000.0),
N::from_f64(32382376266240000.0).unwrap(), convert(32382376266240000.0),
N::from_f64(7771770303897600.0).unwrap(), convert(7771770303897600.0),
N::from_f64(1187353796428800.0).unwrap(), convert(1187353796428800.0),
N::from_f64(129060195264000.0).unwrap(), convert(129060195264000.0),
N::from_f64(10559470521600.0).unwrap(), convert(10559470521600.0),
N::from_f64(670442572800.0).unwrap(), convert(670442572800.0),
N::from_f64(33522128640.0).unwrap(), convert(33522128640.0),
N::from_f64(1323241920.0).unwrap(), convert(1323241920.0),
N::from_f64(40840800.0).unwrap(), convert(40840800.0),
N::from_f64(960960.0).unwrap(), convert(960960.0),
N::from_f64(16380.0).unwrap(), convert(16380.0),
N::from_f64(182.0).unwrap(), convert(182.0),
N::from_f64(1.0).unwrap(), convert(1.0),
]; ];
let s = s as f64; let s = s as f64;
let mb = &self.a * N::from_f64(2.0.powf(-s)).unwrap(); let mb = &self.a * convert::<f64, N>(2.0_f64.powf(-s));
let mb2 = self.a2() * N::from_f64(2.0.powf(-2.0 * s)).unwrap(); let mb2 = self.a2() * convert::<f64, N>(2.0_f64.powf(-2.0 * s));
let mb4 = self.a4() * N::from_f64(2.0.powf(-4.0 * s)).unwrap(); let mb4 = self.a4() * convert::<f64, N>(2.0.powf(-4.0 * s));
let mb6 = self.a6() * N::from_f64(2.0.powf(-6.0 * s)).unwrap(); let mb6 = self.a6() * convert::<f64, N>(2.0.powf(-6.0 * s));
let u2 = &mb6 * (&mb6 * b[13] + &mb4 * b[11] + &mb2 * b[9]); let u2 = &mb6 * (&mb6 * b[13] + &mb4 * b[11] + &mb2 * b[9]);
let u = &mb * (&u2 + &mb6 * b[7] + &mb4 * b[5] + &mb2 * b[3] + &self.ident * b[1]); let u = &mb * (&u2 + &mb6 * b[7] + &mb4 * b[5] + &mb2 * b[3] + &self.ident * b[1]);
@ -323,13 +318,13 @@ fn factorial(n: u128) -> u128 {
} }
/// Compute the 1-norm of a non-negative integer power of a non-negative matrix. /// Compute the 1-norm of a non-negative integer power of a non-negative matrix.
fn onenorm_matrix_power_nonm<N, R>(a: &MatrixN<N, R>, p: u64) -> N fn onenorm_matrix_power_nonm<N, D>(a: &MatrixN<N, D>, p: u64) -> N
where where
N: RealField, N: RealField,
R: DimName, D: DimName,
DefaultAllocator: Allocator<N, R, R> + Allocator<N, R>, DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{ {
let mut v = crate::VectorN::<N, R>::repeat(N::from_f64(1.0).unwrap()); let mut v = crate::VectorN::<N, D>::repeat(convert(1.0));
let m = a.transpose(); let m = a.transpose();
for _ in 0..p { for _ in 0..p {
@ -339,11 +334,11 @@ where
v.max() v.max()
} }
fn ell<N, R>(a: &MatrixN<N, R>, m: u64) -> u64 fn ell<N, D>(a: &MatrixN<N, D>, m: u64) -> u64
where where
N: RealField, N: RealField,
R: DimName, D: DimName,
DefaultAllocator: Allocator<N, R, R> + Allocator<N, R>, DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{ {
// 2m choose m = (2m)!/(m! * (2m-m)!) // 2m choose m = (2m)!/(m! * (2m-m)!)
@ -357,10 +352,10 @@ where
factorial(2 * m as u128) / (factorial(m as u128) * factorial(2 * m as u128 - m as u128)); factorial(2 * m as u128) / (factorial(m as u128) * factorial(2 * m as u128 - m as u128));
let abs_c_recip = choose_2m_m * factorial(2 * m as u128 + 1); let abs_c_recip = choose_2m_m * factorial(2 * m as u128 + 1);
let alpha = a_abs_onenorm / one_norm(a); let alpha = a_abs_onenorm / one_norm(a);
let alpha = alpha / N::from_u128(abs_c_recip).unwrap(); let alpha: f64 = try_convert(alpha).unwrap() / abs_c_recip as f64;
let u = N::from_f64(2_f64.powf(-53.0)).unwrap(); let u = 2_f64.powf(-53.0);
let log2_alpha_div_u = try_convert((alpha / u).log2()).unwrap(); let log2_alpha_div_u = (alpha / u).log2();
let value = (log2_alpha_div_u / (2.0 * m as f64)).ceil(); let value = (log2_alpha_div_u / (2.0 * m as f64)).ceil();
if value > 0.0 { if value > 0.0 {
value as u64 value as u64
@ -369,11 +364,11 @@ where
} }
} }
fn solve_p_q<N, R>(u: MatrixN<N, R>, v: MatrixN<N, R>) -> MatrixN<N, R> fn solve_p_q<N, D>(u: MatrixN<N, D>, v: MatrixN<N, D>) -> MatrixN<N, D>
where where
N: ComplexField, N: ComplexField,
R: DimMin<R, Output = R> + DimName, D: DimMin<D, Output = D> + DimName,
DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>, DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
{ {
let p = &u + &v; let p = &u + &v;
let q = &v - &u; let q = &v - &u;
@ -381,11 +376,11 @@ where
q.lu().solve(&p).unwrap() q.lu().solve(&p).unwrap()
} }
fn one_norm<N, R>(m: &MatrixN<N, R>) -> N fn one_norm<N, D>(m: &MatrixN<N, D>) -> N
where where
N: RealField, N: RealField,
R: DimName, D: DimName,
DefaultAllocator: Allocator<N, R, R>, DefaultAllocator: Allocator<N, D, D>,
{ {
let mut col_sums = vec![N::zero(); m.ncols()]; let mut col_sums = vec![N::zero(); m.ncols()];
for i in 0..m.ncols() { for i in 0..m.ncols() {
@ -399,11 +394,11 @@ where
max max
} }
impl<N: RealField, R> MatrixN<N, R> impl<N: RealField, D> MatrixN<N, D>
where where
R: DimMin<R, Output = R> + DimName, D: DimMin<D, Output = D> + DimName,
DefaultAllocator: DefaultAllocator:
Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>> + Allocator<N, R>, Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>> + Allocator<N, D>,
{ {
/// Computes exponential of this matrix /// Computes exponential of this matrix
pub fn exp(&self) -> Self { pub fn exp(&self) -> Self {
@ -415,30 +410,30 @@ where
let mut h = ExpmPadeHelper::new(self.clone(), true); let mut h = ExpmPadeHelper::new(self.clone(), true);
let eta_1 = N::max(h.d4_loose(), h.d6_loose()); let eta_1 = N::max(h.d4_loose(), h.d6_loose());
if eta_1 < N::from_f64(1.495585217958292e-002).unwrap() && ell(&h.a, 3) == 0 { if eta_1 < convert(1.495585217958292e-002) && ell(&h.a, 3) == 0 {
let (u, v) = h.pade3(); let (u, v) = h.pade3();
return solve_p_q(u, v); return solve_p_q(u, v);
} }
let eta_2 = N::max(h.d4_tight(), h.d6_loose()); let eta_2 = N::max(h.d4_tight(), h.d6_loose());
if eta_2 < N::from_f64(2.539398330063230e-001).unwrap() && ell(&h.a, 5) == 0 { if eta_2 < convert(2.539398330063230e-001) && ell(&h.a, 5) == 0 {
let (u, v) = h.pade5(); let (u, v) = h.pade5();
return solve_p_q(u, v); return solve_p_q(u, v);
} }
let eta_3 = N::max(h.d6_tight(), h.d8_loose()); let eta_3 = N::max(h.d6_tight(), h.d8_loose());
if eta_3 < N::from_f64(9.504178996162932e-001).unwrap() && ell(&h.a, 7) == 0 { if eta_3 < convert(9.504178996162932e-001) && ell(&h.a, 7) == 0 {
let (u, v) = h.pade7(); let (u, v) = h.pade7();
return solve_p_q(u, v); return solve_p_q(u, v);
} }
if eta_3 < N::from_f64(2.097847961257068e+000).unwrap() && ell(&h.a, 9) == 0 { if eta_3 < convert(2.097847961257068e+000) && ell(&h.a, 9) == 0 {
let (u, v) = h.pade9(); let (u, v) = h.pade9();
return solve_p_q(u, v); return solve_p_q(u, v);
} }
let eta_4 = N::max(h.d8_loose(), h.d10_loose()); let eta_4 = N::max(h.d8_loose(), h.d10_loose());
let eta_5 = N::min(eta_3, eta_4); let eta_5 = N::min(eta_3, eta_4);
let theta_13 = N::from_f64(4.25).unwrap(); let theta_13 = convert(4.25);
let mut s = if eta_5 == N::zero() { let mut s = if eta_5 == N::zero() {
0 0
@ -452,10 +447,7 @@ where
} }
}; };
s += ell( s += ell(&(&h.a * convert::<f64, N>(2.0_f64.powf(-(s as f64)))), 13);
&(&h.a * N::from_f64(2.0_f64.powf(-(s as f64))).unwrap()),
13,
);
let (u, v) = h.pade13_scaled(s); let (u, v) = h.pade13_scaled(s);
let mut x = solve_p_q(u, v); let mut x = solve_p_q(u, v);