utils

A set of utility functions and constants used for unit conversions and adding generic structure common to multiple models.

K_CMB2K_RJ(freq)

Convert from K_CMB to K_RJ.

Parameters:

Name	Type	Description	Default
freq	float	The observing frequency in Hz.	required

Returns:

Name	Type	Description
K_CMB2K_RJ	float	Conversion factor from K_CMB to K_RJ.

Source code in witch/utils.py

@partial(jax.jit, static_argnums=(0,))
def K_CMB2K_RJ(freq: float) -> float:
    """
    Convert from K_CMB to K_RJ.

    Parameters
    ----------
    freq : float
        The observing frequency in Hz.

    Returns
    -------
    K_CMB2K_RJ : float
        Conversion factor from K_CMB to K_RJ.
    """
    x = freq * h / kb / Tcmb
    return jnp.exp(x) * x * x / jnp.expm1(x) ** 2

beam_double_gauss(dr, fwhm1, amp1, fwhm2, amp2)

Helper function to generate a double gaussian beam.

Parameters:

Name	Type	Description	Default
dr	float	Pixel size.	required
fwhm1	float	Full width half max of the primary gaussian in the same units as dr.	required
amp1	float	Amplitude of the primary gaussian.	required
fwhm2	float	Full width half max of the secondairy gaussian in the same units as dr.	required
amp2	float	Amplitude of the secondairy gaussian.	required

Returns:

Type	Description
beam: Double gaussian beam.

Source code in witch/utils.py

def beam_double_gauss(
    dr: float, fwhm1: float, amp1: float, fwhm2: float, amp2: float
) -> jax.Array:
    """
    Helper function to generate a double gaussian beam.

    Parameters
    ----------
    dr : float
        Pixel size.
    fwhm1 : float
        Full width half max of the primary gaussian in the same units as `dr`.
    amp1 : float
        Amplitude of the primary gaussian.
    fwhm2 : float
        Full width half max of the secondairy gaussian in the same units as `dr`.
    amp2 : float
        Amplitude of the secondairy gaussian.

    Returns
    -------
        beam: Double gaussian beam.
    """
    x = jnp.arange(-1.5 * fwhm1 // (dr), 1.5 * fwhm1 // (dr)) * (dr)
    beam_xx, beam_yy = jnp.meshgrid(x, x)
    beam_rr = jnp.sqrt(beam_xx**2 + beam_yy**2)
    beam = amp1 * jnp.exp(-4 * jnp.log(2) * beam_rr**2 / fwhm1**2) + amp2 * jnp.exp(
        -4 * jnp.log(2) * beam_rr**2 / fwhm2**2
    )
    return beam / jnp.sum(beam)

bilinear_interp(x, y, xp, yp, fp)

JAX implementation of bilinear interpolation. Out of bounds values are set to 0. Using the repeated linear interpolation method here, see https://en.wikipedia.org/wiki/Bilinear_interpolation#Repeated_linear_interpolation.

Parameters:

Name	Type	Description	Default
x	Array	X values to return interpolated values at.	required
y	Array	Y values to return interpolated values at.	required
xp	Array	X values to interpolate with, should be 1D. Assumed to be sorted.	required
yp	Array	Y values to interpolate with, should be 1D. Assumed to be sorted.	required
fp	Array	Functon values at (xp, yp), should have shape (len(xp), len(yp)). Note that if you are using meshgrid, we assume 'ij' indexing.	required

Returns:

Name	Type	Description
f	Array	The interpolated values.

Source code in witch/utils.py

@jax.jit
def bilinear_interp(
    x: jax.Array, y: jax.Array, xp: jax.Array, yp: jax.Array, fp: jax.Array
) -> jax.Array:
    """
    JAX implementation of bilinear interpolation.
    Out of bounds values are set to 0.
    Using the repeated linear interpolation method here,
    see https://en.wikipedia.org/wiki/Bilinear_interpolation#Repeated_linear_interpolation.

    Parameters
    ----------
    x : jax.Array
        X values to return interpolated values at.
    y : jax.Array
        Y values to return interpolated values at.
    xp : jax.Array
        X values to interpolate with, should be 1D.
        Assumed to be sorted.
    yp : jax.Array
        Y values to interpolate with, should be 1D.
        Assumed to be sorted.
    fp : jax.Array
        Functon values at `(xp, yp)`, should have shape `(len(xp), len(yp))`.
        Note that if you are using meshgrid, we assume `'ij'` indexing.

    Returns
    -------
    f : jax.Array
        The interpolated values.
    """
    if len(xp.shape) != 1:
        raise ValueError("xp must be 1D")
    if len(yp.shape) != 1:
        raise ValueError("yp must be 1D")
    if fp.shape != xp.shape + yp.shape:
        raise ValueError(
            "Incompatible shapes for fp, xp, yp: %s, %s, %s",
            fp.shape,
            xp.shape,
            yp.shape,
        )

    # Figure out bounds and mapping
    # This breaks if xp, yp is not sorted
    ix = jnp.clip(jnp.searchsorted(xp, x, side="right"), 1, len(xp) - 1)
    iy = jnp.clip(jnp.searchsorted(yp, y, side="right"), 1, len(yp) - 1)
    q_11 = fp[ix - 1, iy - 1]
    q_21 = fp[ix, iy - 1]
    q_12 = fp[ix - 1, iy]
    q_22 = fp[ix, iy]

    # Interpolate in x to start
    denom_x = xp[ix] - xp[ix - 1]
    dx_1 = x - xp[ix - 1]
    dx_2 = xp[ix] - x
    f_xy1 = (dx_2 * q_11 + dx_1 * q_21) / denom_x
    f_xy2 = (dx_2 * q_12 + dx_1 * q_22) / denom_x

    # Now do y as well
    denom_y = yp[iy] - yp[iy - 1]
    dy_1 = y - yp[iy - 1]
    dy_2 = yp[iy] - y
    f = (dy_2 * f_xy1 + dy_1 * f_xy2) / denom_y

    # Zero out the out of bounds values
    f = jnp.where((x < xp[0]) + (x > xp[-1]) + (y < yp[0]) + (y > yp[-1]), 0.0, f)

    return f

fft_conv(image, kernel)

Perform a convolution using FFTs for speed with jax.

Parameters:

Name	Type	Description	Default
image	ArrayLike	Data to be convolved.	required
kernel	ArrayLike	Convolution kernel.	required

Returns:

Name	Type	Description
convolved_map	Array	Image convolved with kernel.

Source code in witch/utils.py

@jax.jit
def fft_conv(image: ArrayLike, kernel: ArrayLike) -> jax.Array:
    """
    Perform a convolution using FFTs for speed with jax.

    Parameters
    ----------
    image : ArrayLike
        Data to be convolved.
    kernel : ArrayLike
        Convolution kernel.

    Returns
    -------
    convolved_map : jax.Array
        Image convolved with kernel.
    """
    Fmap = jnp.fft.fft2(jnp.fft.fftshift(image))
    Fkernel = jnp.fft.fft2(jnp.fft.fftshift(kernel))
    convolved_map = jnp.fft.fftshift(jnp.real(jnp.fft.ifft2(Fmap * Fkernel)))

    return convolved_map

get_da(z)

Get factor to convert from arcseconds to MPc.

Parameters:

Name	Type	Description	Default
z	float	The redshift at which to compute the factor.	required

Returns:

Name	Type	Description
da	float	Conversion factor from arcseconds to MPc.

Source code in witch/utils.py

def get_da(z: float) -> float:
    """
    Get factor to convert from arcseconds to MPc.

    Parameters
    ----------
    z : float
        The redshift at which to compute the factor.

    Returns
    -------
    da : float
        Conversion factor from arcseconds to MPc.
    """
    return float(jnp.interp(z, dzline, daline))

get_hz(z)

Get the dimensionless hubble constant, h, at a given redshift.

Parameters:

Name	Type	Description	Default
z	float	The redshift at which to compute h.	required

Returns:

Name	Type	Description
hz	float	h at the given z.

Source code in witch/utils.py

def get_hz(z: float) -> float:
    """
    Get the dimensionless hubble constant, h, at a given redshift.

    Parameters
    ----------
    z : float
        The redshift at which to compute h.

    Returns
    -------
    hz : float
        h at the given z.
    """
    return float(jnp.interp(z, dzline, hzline))

get_nz(z)

Get the critical density at a given redshift.

Parameters:

Name	Type	Description	Default
z	float	The redshift at which to compute the critical density.	required

Returns:

Name	Type	Description
nz	float	Critical density at the given z.

Source code in witch/utils.py

def get_nz(z: float) -> float:
    """
    Get the critical density at a given redshift.

    Parameters
    ----------
    z : float
        The redshift at which to compute the critical density.

    Returns
    -------
    nz : float
        Critical density at the given z.
    """
    return float(jnp.interp(z, dzline, nzline))

make_grid(r_map, dx, dy=None, dz=None, x0=0, y0=0)

Make coordinate grids to build models in. All grids are sparse and are int(2*r_map / dr) in each the non-sparse dimension.

Parameters:

Name	Type	Description	Default
r_map	float	Size of grid radially.	required
dx	float	Grid resolution in x, should be in same units as r_map.	required
dy	Optional[float]	Grid resolution in y, should be in same units as r_map. If None then dy is set to dx.	None
dz	Optional[float]	Grid resolution in z, should be in same units as r_map. If None then dz is set to dx.	None
x0	float	Origin of grid in RA, assumed to be in same units as r_map.	0
y0	float	Origin of grid in Dec, assumed to be in same units as r_map.	0

Returns:

Name	Type	Description
x	Array	Grid of x coordinates in same units as r_map. Has shape (`int(2*r_map / dr), 1, 1).
y	Array	Grid of y coordinates in same units as r_map. Has shape (1, `int(2*r_map / dr), 1).
z	Array	Grid of z coordinates in same units as r_map. Has shape (1, 1, int(2*r_map / dr)).
x0	float	Origin of grid in RA, in same units as r_map.
y0	float	Origin of grid in Dec, in same units as r_map.

Source code in witch/utils.py

def make_grid(
    r_map: float,
    dx: float,
    dy: Optional[float] = None,
    dz: Optional[float] = None,
    x0: float = 0,
    y0: float = 0,
) -> Grid:
    """
    Make coordinate grids to build models in.
    All grids are sparse and are `int(2*r_map / dr)` in each the non-sparse dimension.

    Parameters
    ----------
    r_map : float
        Size of grid radially.
    dx : float
        Grid resolution in x, should be in same units as r_map.
    dy : Optional[float], default: None
        Grid resolution in y, should be in same units as r_map.
        If None then dy is set to dx.
    dz : Optional[float], default: None
        Grid resolution in z, should be in same units as r_map.
        If None then dz is set to dx.
    x0 : float, default: 0
        Origin of grid in RA, assumed to be in same units as r_map.
    y0 : float, default: 0
        Origin of grid in Dec, assumed to be in same units as r_map.

    Returns
    -------
    x : jax.Array
        Grid of x coordinates in same units as r_map.
        Has shape (`int(2*r_map / dr), 1, 1).
    y : jax.Array
        Grid of y coordinates in same units as r_map.
        Has shape (1, `int(2*r_map / dr), 1).
    z : jax.Array
        Grid of z coordinates in same units as r_map.
        Has shape (1, 1, `int(2*r_map / dr)`).
    x0 : float
        Origin of grid in RA, in same units as r_map.
    y0 : float
        Origin of grid in Dec, in same units as r_map.
    """
    if dy is None:
        dy = dx
    if dz is None:
        dz = dx

    # Make grid with resolution dr and size r_map
    x = (
        jnp.linspace(-1 * r_map, r_map, 2 * int(r_map / dx))
        / jnp.cos(y0 / rad_to_arcsec)
        + x0
    )
    y = jnp.linspace(-1 * r_map, r_map, 2 * int(r_map / dy)) + y0
    z = jnp.linspace(-1 * r_map, r_map, 2 * int(r_map / dz))
    x, y, z = jnp.meshgrid(x, y, z, sparse=True, indexing="ij")

    return (x, y, z, x0, y0)

make_grid_from_skymap(skymap, z_map, dz, x0=None, y0=None)

Make coordinate grids to build models in from a minkasi skymap. All grids are sparse and match the input map and xy and have size int(2*z_map/dz) in z. Unlike make_grid here we assume things are radians.

Parameters:

Name	Type	Description	Default
skymap	Skymap	The map to base the grid off of.	required
z_map	float	Size of grid along LOS, in radians.	required
dz	float	Grid resolution along LOS, in radians.	required
x0	Optional[float]	Map x center in radians. If None, grid center is used.	None
y0	Optional[float]	Map y center in radians. If None, grid center is used.	None

Returns:

Name	Type	Description
x	Array	Grid of x coordinates in radians. Has shape (skymap.nx, 1, 1).
y	Array	Grid of y coordinates in radians. Has shape (1, skymap.ny, 1).
z	Array	Grid of z coordinates in same units as radians. Has shape (1, 1, int(2*z_map / dz)).
x0	float	Origin of grid in RA, in radians.
y0	float	Origin of grid in Dec, in radians.

Source code in witch/utils.py

def make_grid_from_skymap(
    skymap,
    z_map: float,
    dz: float,
    x0: Optional[float] = None,
    y0: Optional[float] = None,
) -> Grid:
    """
    Make coordinate grids to build models in from a minkasi skymap.
    All grids are sparse and match the input map and xy and have size `int(2*z_map/dz)` in z.
    Unlike `make_grid` here we assume things are radians.

    Parameters
    ----------
    skymap : minkasi.maps.Skymap
        The map to base the grid off of.
    z_map : float
        Size of grid along LOS, in radians.
    dz : float
        Grid resolution along LOS, in radians.
    x0 : Optional[float], default: None
        Map x center in radians.
        If None, grid center is used.
    y0 : Optional[float], default: None
        Map y center in radians. If None, grid center is used.

    Returns
    -------
    x : jax.Array
        Grid of x coordinates in radians.
        Has shape (`skymap.nx`, 1, 1).
    y : jax.Array
        Grid of y coordinates in radians.
        Has shape (1, `skymap.ny`, 1).
    z : jax.Array
        Grid of z coordinates in same units as radians.
        Has shape (1, 1, `int(2*z_map / dz)`).
    x0 : float
        Origin of grid in RA, in radians.
    y0 : float
        Origin of grid in Dec, in radians.
    """
    # make grid
    _x = jnp.arange(skymap.nx, dtype=float)
    _y = jnp.arange(skymap.ny, dtype=float)
    _z = jnp.linspace(-1 * z_map, z_map, 2 * int(z_map / dz), dtype=float)
    x, y, z = jnp.meshgrid(_x, _y, _z, sparse=True, indexing="ij")

    # Pad so we don't need to broadcast
    x_flat = x.ravel()
    y_flat = y.ravel()
    len_diff = len(x_flat) - len(y_flat)
    if len_diff > 0:
        y_flat = jnp.pad(y_flat, (0, len_diff), "edge")
    elif len_diff < 0:
        x_flat = jnp.pad(x_flat, (0, abs(len_diff)), "edge")

    # Convert x and y to ra/dec
    ra_dec = skymap.wcs.wcs_pix2world(
        jnp.column_stack((x_flat, y_flat)), 0, ra_dec_order=True
    )
    ra_dec = np.deg2rad(ra_dec)
    ra = ra_dec[:, 0]
    dec = ra_dec[:, 1]

    # Remove padding
    if len_diff > 0:
        dec = dec[: (-1 * len_diff)]
    elif len_diff < 0:
        ra = ra[:len_diff]

    if not x0:
        x0 = (skymap.lims[1] + skymap.lims[0]) / 2
    if not y0:
        y0 = (skymap.lims[3] + skymap.lims[2]) / 2

    if x0 is None or y0 is None:
        raise TypeError("Origin still None")

    ra -= x0
    dec -= y0

    # Sparse indexing to save mem
    x = x.at[:, 0, 0].set(ra)
    y = y.at[0, :, 0].set(dec)

    return x, y, z, float(x0), float(y0)

tod_hi_pass(tod, N_filt)

High pass a tod with a tophat

Parameters:

Name	Type	Description	Default
tod	Array	TOD to high pass.	required
N_filt	int	N_filt of tophat.	required

Returns:

Name	Type	Description
tod_filtered	Array	High pass filtered TOD

Source code in witch/utils.py

@partial(jax.jit, static_argnums=(1,))
def tod_hi_pass(tod: jax.Array, N_filt: int) -> jax.Array:
    """
    High pass a tod with a tophat

    Parameters
    ----------
    tod : jax.Array
        TOD to high pass.
    N_filt : int
        N_filt of tophat.

    Returns
    -------
    tod_filtered : jax.Array
        High pass filtered TOD
    """
    mask = jnp.ones(tod.shape)
    mask = mask.at[..., :N_filt].set(0.0)

    ## apply the filter in fourier space
    Ftod = jnp.fft.fft(tod)
    Ftod_filtered = Ftod * mask
    tod_filtered = jnp.fft.ifft(Ftod_filtered).real
    return tod_filtered

tod_to_index(xi, yi, x0, y0, grid, conv_factor=1.0)

Convert RA/Dec TODs to index space.

Parameters:

Name	Type	Description	Default
xi	NDArray[floating]	RA TOD, usually in radians	required
yi	NDArray[floating]	Dec TOD, usually in radians	required
grid	Grid	The grid to index on.	required
conv_factor	float	Conversion factor to put RA and Dec in same units as the grid.	1.

Returns:

Name	Type	Description
idx	Array	The RA TOD in index space
idy	Array	The Dec TOD in index space.

Source code in witch/utils.py

def tod_to_index(
    xi: NDArray[np.floating],
    yi: NDArray[np.floating],
    x0: float,
    y0: float,
    grid: Grid,
    conv_factor: float = 1.0,
) -> tuple[jax.Array, jax.Array]:
    """
    Convert RA/Dec TODs to index space.

    Parameters
    ----------
    xi : NDArray[np.floating]
        RA TOD, usually in radians
    yi : NDArray[np.floating]
        Dec TOD, usually in radians
    grid : Grid
        The grid to index on.
    conv_factor : float, default: 1.
        Conversion factor to put RA and Dec in same units as the grid.

    Returns
    -------
    idx : jax.Array
        The RA TOD in index space
    idy : jax.Array
        The Dec TOD in index space.
    """
    x0, y0 = grid[-2:]
    dx = (xi - x0) * jnp.cos(yi)
    dy = yi - y0

    dx *= conv_factor
    dy *= conv_factor

    # Assuming sparse indexing here
    idx = np.digitize(dx, grid[0].ravel())
    idy = np.digitize(dy, grid[1].ravel())

    idx = np.rint(idx).astype(int)
    idy = np.rint(idy).astype(int)

    # Ensure out of bounds for stuff not in grid
    idx = jnp.where((idx < 0) + (idx >= grid[0].shape[0]), 2 * grid[0].shape[0], idx)
    idy = jnp.where((idy < 0) + (idy >= grid[1].shape[1]), 2 * grid[1].shape[1], idy)

    return idx, idy

transform_grid(dx, dy, dz, r_1, r_2, r_3, theta, xyz)

Shift, rotate, and apply ellipticity to coordinate grid. Note that the Grid type is an alias for tuple[jax.Array, jax.Array, jax.Array, float, float].

Parameters:

Name	Type	Description	Default
dx	float	Amount to move grid origin in x	required
dy	float	Amount to move grid origin in y	required
dz	float	Amount to move grid origin in z	required
r_1	float	Amount to scale along x-axis	required
r_2	float	Amount to scale along y-axis	required
r_3	float	Amount to scale along z-axis	required
theta	float	Angle to rotate in xy-plane in radians	required
xyz	Grid	Coordinte grid to transform	required

Returns:

Name	Type	Description
trasnformed	Grid	Transformed coordinate grid.

Source code in witch/utils.py

@jax.jit
def transform_grid(
    dx: float,
    dy: float,
    dz: float,
    r_1: float,
    r_2: float,
    r_3: float,
    theta: float,
    xyz: Grid,
):
    """
    Shift, rotate, and apply ellipticity to coordinate grid.
    Note that the `Grid` type is an alias for `tuple[jax.Array, jax.Array, jax.Array, float, float]`.

    Parameters
    ----------
    dx : float
        Amount to move grid origin in x
    dy : float
        Amount to move grid origin in y
    dz : float
        Amount to move grid origin in z
    r_1 : float
        Amount to scale along x-axis
    r_2 : float
        Amount to scale along y-axis
    r_3 : float
        Amount to scale along z-axis
    theta : float
        Angle to rotate in xy-plane in radians
    xyz : Grid
        Coordinte grid to transform

    Returns
    -------
    trasnformed : Grid
        Transformed coordinate grid.
    """
    # Get origin
    x0, y0 = xyz[3], xyz[4]
    # Shift origin
    x = (xyz[0] - (x0 + dx / jnp.cos(y0 / rad_to_arcsec))) * jnp.cos(
        (y0 + dy) / rad_to_arcsec
    )
    y = xyz[1] - (y0 + dy)
    z = xyz[2] - dz

    # Rotate
    xx = x * jnp.cos(theta) + y * jnp.sin(theta)
    yy = y * jnp.cos(theta) - x * jnp.sin(theta)

    # Apply ellipticity
    x = xx / r_1
    y = yy / r_2
    z = z / r_3

    return x, y, z, x0 - dx, y0 - dy

y2K_CMB(freq, Te)

Convert from compton y to K_CMB.

Parameters:

Name	Type	Description	Default
freq	float	The observing frequency in Hz.	required
Te	float	Electron temperature	required

Returns:

Name	Type	Description
y2K_CMB	float	Conversion factor from compton y to K_CMB.

Source code in witch/utils.py

@partial(jax.jit, static_argnums=(0, 1))
def y2K_CMB(freq: float, Te: float) -> float:
    """
    Convert from compton y to K_CMB.

    Parameters
    ----------
    freq : float
        The observing frequency in Hz.
    Te : float
        Electron temperature

    Returns
    -------
    y2K_CMB : float
        Conversion factor from compton y to K_CMB.
    """
    x = freq * h / kb / Tcmb
    xt = x / jnp.tanh(0.5 * x)
    st = x / jnp.sinh(0.5 * x)
    # fmt:off
    Y0 = -4.0 + xt
    Y1 = (-10.0
        + ((47.0 / 2.0) + (-(42.0 / 5.0) + (7.0 / 10.0) * xt) * xt) * xt
        + st * st * (-(21.0 / 5.0) + (7.0 / 5.0) * xt)
    )
    Y2 = ((-15.0 / 2.0)
        + ((1023.0 / 8.0) + ((-868.0 / 5.0) + ((329.0 / 5.0) + ((-44.0 / 5.0) + (11.0 / 30.0) * xt) * xt) * xt) * xt) * xt
        + ((-434.0 / 5.0) + ((658.0 / 5.0) + ((-242.0 / 5.0) + (143.0 / 30.0) * xt) * xt) * xt
        + (-(44.0 / 5.0) + (187.0 / 60.0) * xt) * (st * st)) * st * st
    )
    Y3 = ((15.0 / 2.0)
        + ((2505.0 / 8.0) + ((-7098.0 / 5.0) + ((14253.0 / 10.0) + ((-18594.0 / 35.0) 
         + ((12059.0 / 140.0) + ((-128.0 / 21.0) + (16.0 / 105.0) * xt) * xt) * xt) * xt) * xt) * xt) * xt
        + (((-7098.0 / 10.0) + ((14253.0 / 5.0) + ((-102267.0 / 35.0) + ((156767.0 / 140.0)
         + ((-1216.0 / 7.0) + (64.0 / 7.0) * xt) * xt) * xt) * xt) * xt)
         + (((-18594.0 / 35.0) + ((205003.0 / 280.0) + ((-1920.0 / 7.0) + (1024.0 / 35.0) * xt) * xt) * xt)
          + ((-544.0 / 21.0) + (992.0 / 105.0) * xt) * st * st) * st * st) * st * st
    )
    Y4 = ((-135.0 / 32.0)
        + ((30375.0 / 128.0) + ((-62391.0 / 10.0) + ((614727.0 / 40.0) + ((-124389.0 / 10.0) + ((355703.0 / 80.0) + ((-16568.0 / 21.0)
         + ((7516.0 / 105.0) + ((-22.0 / 7.0) + (11.0 / 210.0) * xt) * xt) * xt) * xt) * xt) * xt) * xt) * xt) * xt
        + ((-62391.0 / 20.0) + ((614727.0 / 20.0) + ((-1368279.0 / 20.0) + ((4624139.0 / 80.0) + ((-157396.0 / 7.0) + ((30064.0 / 7.0)
         + ((-2717.0 / 7.0) + (2761.0 / 210.0) * xt) * xt) * xt) * xt) * xt) * xt) * xt
         + ((-124389.0 / 10.0)
          + ((6046951.0 / 160.0) + ((-248520.0 / 7.0) + ((481024.0 / 35.0) + ((-15972.0 / 7.0) + (18689.0 / 140.0) * xt) * xt) * xt) * xt) * xt
          + ((-70414.0 / 21.0) + ((465992.0 / 105.0) + ((-11792.0 / 7.0) + (19778.0 / 105.0) * xt) * xt) * xt
           + ((-682.0 / 7.0) + (7601.0 / 210.0) * xt) * st * st) * st * st) * st * st) * st * st
    )
    # fmt:on
    factor = Y0 + (Te / me) * (
        Y1 + (Te / me) * (Y2 + (Te / me) * (Y3 + (Te / me) * Y4))
    )
    return factor * Tcmb

y2K_RJ(freq, Te)

Convert from compton y to K_RJ.

Parameters:

Name	Type	Description	Default
freq	float	The observing frequency in Hz.	required
Te	float	Electron temperature	required

Returns:

Name	Type	Description
y2K_RJ	float	Conversion factor from compton y to K_RJ.

Source code in witch/utils.py

@partial(jax.jit, static_argnums=(0, 1))
def y2K_RJ(freq: float, Te: float) -> float:
    """
    Convert from compton y to K_RJ.

    Parameters
    ----------
    freq : float
        The observing frequency in Hz.
    Te : float
        Electron temperature

    Returns
    -------
    y2K_RJ : float
        Conversion factor from compton y to K_RJ.
    """
    factor = y2K_CMB(freq, Te)
    return factor * K_CMB2K_RJ(freq)