Add Ideal Size node to core nodes

The Ideal Size node is useful for High-Res Optimization as it gives the optimum size for creating an initial generation with minimal artifacts (duplication and other strangeness) from today's models.

After inclusion, front end graph generation can be simplified by offloading calculations for HRO initial generation to this node.

invokeai/app/invocations/latent.py

@@ -1,5 +1,6 @@
 # Copyright (c) 2023 Kyle Schouviller (https://github.com/kyle0654)
 
+import math
 from contextlib import ExitStack
 from functools import singledispatchmethod
 from typing import List, Literal, Optional, Union
@@ -1228,3 +1229,54 @@ class CropLatentsCoreInvocation(BaseInvocation):
         context.services.latents.save(name, cropped_latents)
 
         return build_latents_output(latents_name=name, latents=cropped_latents)
+
+
+@invocation_output("ideal_size_output")
+class IdealSizeOutput(BaseInvocationOutput):
+    """Base class for invocations that output an image"""
+
+    width: int = OutputField(description="The ideal width of the image in pixels")
+    height: int = OutputField(description="The ideal height of the image in pixels")
+
+
+@invocation(
+    "ideal_size",
+    title="Ideal Size",
+    tags=["latents", "math", "ideal_size"],
+    version="1.0.2",
+)
+class IdealSizeInvocation(BaseInvocation):
+    """Calculates the ideal size for generation to avoid duplication"""
+
+    width: int = InputField(default=1024, description="Target width")
+    height: int = InputField(default=576, description="Target height")
+    unet: UNetField = InputField(default=None, description="UNet submodel")
+    multiplier: float = InputField(default=1.0, description="Dimensional multiplier")
+
+    def trim_to_multiple_of(self, *args, multiple_of=LATENT_SCALE_FACTOR):
+        return tuple((x - x % multiple_of) for x in args)
+
+    def invoke(self, context: InvocationContext) -> IdealSizeOutput:
+        aspect = self.width / self.height
+        dimension = 512
+        if self.unet.unet.base_model == BaseModelType.StableDiffusion2:
+            dimension = 768
+        elif self.unet.unet.base_model == BaseModelType.StableDiffusionXL:
+            dimension = 1024
+        dimension = dimension * self.multiplier
+        min_dimension = math.floor(dimension * 0.5)
+        model_area = dimension * dimension  # hardcoded for now since all models are trained on square images
+
+        if aspect > 1.0:
+            init_height = max(min_dimension, math.sqrt(model_area / aspect))
+            init_width = init_height * aspect
+        else:
+            init_width = max(min_dimension, math.sqrt(model_area * aspect))
+            init_height = init_width / aspect
+
+        scaled_width, scaled_height = self.trim_to_multiple_of(
+            math.floor(init_width),
+            math.floor(init_height),
+        )
+
+        return IdealSizeOutput(width=scaled_width, height=scaled_height)