russell_lab 1.11.0

Scientific laboratory for linear algebra and numerical mathematics
Documentation 
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use super::{to_i32, MAX_DIM_FOR_NATIVE_BLAS};
use crate::Complex64;
use crate::StrError;

extern "C" {
    // real ------------------------------------------------------------------------------------------------------

    // Computes constant times a vector plus a vector.
    // <https://www.netlib.org/lapack/explore-html/d9/dcd/daxpy_8f.html>
    fn cblas_daxpy(n: i32, alpha: f64, x: *const f64, incx: i32, y: *mut f64, incy: i32);

    // Copies a vector into another
    // <https://www.netlib.org/lapack/explore-html/da/d6c/dcopy_8f.html>
    fn cblas_dcopy(n: i32, x: *const f64, incx: i32, y: *mut f64, incy: i32);

    // Scales a vector by a constant
    // <https://www.netlib.org/lapack/explore-html/d4/dd0/dscal_8f.html>
    fn cblas_dscal(n: i32, alpha: f64, x: *mut f64, incx: i32);

    // complex ---------------------------------------------------------------------------------------------------

    // Computes constant times a vector plus a vector
    // <https://www.netlib.org/lapack/explore-html/d7/db2/zaxpy_8f.html>
    fn cblas_zaxpy(n: i32, alpha: *const Complex64, x: *const Complex64, incx: i32, y: *mut Complex64, incy: i32);

    // Copies a vector into another
    // <https://www.netlib.org/lapack/explore-html/d6/d53/zcopy_8f.html>
    fn cblas_zcopy(n: i32, x: *const Complex64, incx: i32, y: *mut Complex64, incy: i32);

    // Scales a vector by a constant
    // <https://www.netlib.org/lapack/explore-html/d2/d74/zscal_8f.html>
    fn cblas_zscal(n: i32, alpha: *const Complex64, x: *mut Complex64, incx: i32);
}

/// Adds two arrays (with multipliers)
///
/// ```text
/// w := α⋅u + β⋅v
/// ```
#[inline]
pub(crate) fn array_plus_opx(w: &mut [f64], alpha: f64, u: &[f64], beta: f64, v: &[f64]) -> Result<(), StrError> {
    let n = w.len();
    if u.len() != n || v.len() != n {
        return Err("arrays are incompatible");
    }
    if n == 0 {
        return Ok(());
    }
    if n > MAX_DIM_FOR_NATIVE_BLAS {
        let n_i32 = to_i32(n);
        unsafe {
            // w := v
            cblas_dcopy(n_i32, v.as_ptr(), 1, w.as_mut_ptr(), 1);
            // w := beta * v
            cblas_dscal(n_i32, beta, w.as_mut_ptr(), 1);
            // w := alpha*u + w
            cblas_daxpy(n_i32, alpha, u.as_ptr(), 1, w.as_mut_ptr(), 1);
        }
    } else {
        if n == 1 {
            w[0] = alpha * u[0] + beta * v[0];
        } else if n == 2 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
        } else if n == 3 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
        } else if n == 4 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
        } else if n == 5 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
        } else if n == 6 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
        } else if n == 7 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
            w[6] = alpha * u[6] + beta * v[6];
        } else if n == 8 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
            w[6] = alpha * u[6] + beta * v[6];
            w[7] = alpha * u[7] + beta * v[7];
        } else {
            let m = n % 4;
            for i in 0..m {
                w[i] = alpha * u[i] + beta * v[i];
            }
            for i in (m..n).step_by(4) {
                w[i + 0] = alpha * u[i + 0] + beta * v[i + 0];
                w[i + 1] = alpha * u[i + 1] + beta * v[i + 1];
                w[i + 2] = alpha * u[i + 2] + beta * v[i + 2];
                w[i + 3] = alpha * u[i + 3] + beta * v[i + 3];
            }
        }
    }
    Ok(())
}

/// Adds two arrays (with multipliers)
///
/// ```text
/// w := α⋅u + β⋅v
/// ```
#[inline]
pub(crate) fn array_plus_opx_complex(
    w: &mut [Complex64],
    alpha: Complex64,
    u: &[Complex64],
    beta: Complex64,
    v: &[Complex64],
) -> Result<(), StrError> {
    let n = w.len();
    if u.len() != n || v.len() != n {
        return Err("arrays are incompatible");
    }
    if n == 0 {
        return Ok(());
    }
    if n > MAX_DIM_FOR_NATIVE_BLAS {
        let n_i32 = to_i32(n);
        unsafe {
            // w := v
            cblas_zcopy(n_i32, v.as_ptr(), 1, w.as_mut_ptr(), 1);
            // w := beta * v
            cblas_zscal(n_i32, &beta, w.as_mut_ptr(), 1);
            // w := alpha*u + w
            cblas_zaxpy(n_i32, &alpha, u.as_ptr(), 1, w.as_mut_ptr(), 1);
        }
    } else {
        if n == 1 {
            w[0] = alpha * u[0] + beta * v[0];
        } else if n == 2 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
        } else if n == 3 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
        } else if n == 4 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
        } else if n == 5 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
        } else if n == 6 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
        } else if n == 7 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
            w[6] = alpha * u[6] + beta * v[6];
        } else if n == 8 {
            w[0] = alpha * u[0] + beta * v[0];
            w[1] = alpha * u[1] + beta * v[1];
            w[2] = alpha * u[2] + beta * v[2];
            w[3] = alpha * u[3] + beta * v[3];
            w[4] = alpha * u[4] + beta * v[4];
            w[5] = alpha * u[5] + beta * v[5];
            w[6] = alpha * u[6] + beta * v[6];
            w[7] = alpha * u[7] + beta * v[7];
        } else {
            let m = n % 4;
            for i in 0..m {
                w[i] = alpha * u[i] + beta * v[i];
            }
            for i in (m..n).step_by(4) {
                w[i + 0] = alpha * u[i + 0] + beta * v[i + 0];
                w[i + 1] = alpha * u[i + 1] + beta * v[i + 1];
                w[i + 2] = alpha * u[i + 2] + beta * v[i + 2];
                w[i + 3] = alpha * u[i + 3] + beta * v[i + 3];
            }
        }
    }
    Ok(())
}