Sine Gaussian Waveform

src/ripplegw/waveforms/SineGaussian.py

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+import jax.numpy as jnp
+from jax.lax import complex
+
+from ..constants import PI
+from ..typing import Array
+
+
+def semi_major_minor_from_e(e: Array) -> tuple[Array, Array]:
+    """
+    Calculate the semi-major and semi-minor axes of an ellipse given the
+    eccentricity of the ellipse.
+
+    Args:
+        e: Eccentricity of the ellipse
+    Returns:
+        Semi-major (a) and semi-minor (b) axes of the ellipse
+    """
+    a = 1.0 / jnp.sqrt(2.0 - (e * e))
+    b = a * jnp.sqrt(1.0 - (e * e))
+    return a, b
+
+
+def gen_SineGaussian_hphc(
+    t: Array,
+    theta: Array,
+) -> tuple[Array, Array]:
+    """
+    Generate lalinference implementation of a sine-Gaussian waveform in Jax.
+    See
+    git.ligo.org/lscsoft/lalsuite/-/blob/master/lalinference/lib/LALInferenceBurstRoutines.c#L381
+    for details on parameter definitions.
+
+    Args:
+    --------
+        t:
+            Time grid (centered at t=0) on which to evaluate the waveform.
+            Create it using `jax.numpy.arange(-duration/2, duration/2, 1/fs)`
+            where `duration` is the duration of the waveform (in seconds) and `fs`
+            is the sample rate at which the waveform is evaluated.
+        theta:
+            Array of waveform parameters [quality, frequency, hrss, phase, eccentricity]
+            quality:
+                Quality factor of the sine-Gaussian waveform
+            frequency:
+                Central frequency of the sine-Gaussian waveform
+            hrss:
+                Hrss of the sine-Gaussian waveform
+            phase:
+                Phase of the sine-Gaussian waveform
+            eccentricity:
+                Eccentricity of the sine-Gaussian waveform.
+                Controls the relative amplitudes of the
+                hplus and hcross polarizations.
+
+    Returns:
+    --------
+        Jax Arrays of plus and cross polarizations (in that order)
+    """
+
+    quality, frequency, hrss, phase, eccentricity = theta
+
+    # add dimension for calculating waveforms in batch
+    quality = quality.reshape(-1, 1)
+    frequency = frequency.reshape(-1, 1)
+    hrss = hrss.reshape(-1, 1)
+    phase = phase.reshape(-1, 1)
+    eccentricity = eccentricity.reshape(-1, 1)
+
+    pi = jnp.array([PI])
+
+    # calculate relative hplus / hcross amplitudes based on eccentricity
+    # as well as normalization factors
+    a, b = semi_major_minor_from_e(eccentricity)
+    norm_prefactor = quality / (4.0 * frequency * jnp.sqrt(pi))
+    cosine_norm = norm_prefactor * (1.0 + jnp.exp(-quality * quality))
+    sine_norm = norm_prefactor * (1.0 - jnp.exp(-quality * quality))
+
+    cos_phase, sin_phase = jnp.cos(phase), jnp.sin(phase)
+
+    h0_plus = (
+        hrss * a / jnp.sqrt(cosine_norm * (cos_phase**2) + sine_norm * (sin_phase**2))
+    )
+    h0_cross = (
+        hrss * b / jnp.sqrt(cosine_norm * (sin_phase**2) + sine_norm * (cos_phase**2))
+    )
+
+    # cast the phase to a complex number
+    phi = 2 * pi * frequency * t
+    complex_phase = complex(jnp.zeros_like(phi), (phi - phase))
+
+    # calculate the waveform and apply a tukey
+    # window to taper the waveform
+    fac = jnp.exp(phi**2 / (-2.0 * quality**2) + complex_phase)
+
+    cross = fac.imag * h0_cross
+    plus = fac.real * h0_plus
+
+    return plus, cross