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InvokeAI/ldm/simplet2i.py
Lincoln Stein dd2af3f93c added walkthru, small code fixes
2022-09-02 17:54:55 -04:00

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# Copyright (c) 2022 Lincoln D. Stein (https://github.com/lstein)
# Derived from source code carrying the following copyrights
# Copyright (c) 2022 Machine Vision and Learning Group, LMU Munich
# Copyright (c) 2022 Robin Rombach and Patrick Esser and contributors
import torch
import numpy as np
import random
import os
import traceback
from omegaconf import OmegaConf
from PIL import Image
from tqdm import tqdm, trange
from itertools import islice
from einops import rearrange, repeat
from torchvision.utils import make_grid
from pytorch_lightning import seed_everything
from torch import autocast
from contextlib import contextmanager, nullcontext
import transformers
import time
import re
import sys
from ldm.util import instantiate_from_config
from ldm.models.diffusion.ddim import DDIMSampler
from ldm.models.diffusion.plms import PLMSSampler
from ldm.models.diffusion.ksampler import KSampler
from ldm.dream.pngwriter import PngWriter
from ldm.dream.image_util import InitImageResizer
from ldm.dream.devices import choose_autocast_device, choose_torch_device
"""Simplified text to image API for stable diffusion/latent diffusion
Example Usage:
from ldm.simplet2i import T2I
# Create an object with default values
t2i = T2I(model = <path> // models/ldm/stable-diffusion-v1/model.ckpt
config = <path> // configs/stable-diffusion/v1-inference.yaml
iterations = <integer> // how many times to run the sampling (1)
steps = <integer> // 50
seed = <integer> // current system time
sampler_name= ['ddim', 'k_dpm_2_a', 'k_dpm_2', 'k_euler_a', 'k_euler', 'k_heun', 'k_lms', 'plms'] // k_lms
grid = <boolean> // false
width = <integer> // image width, multiple of 64 (512)
height = <integer> // image height, multiple of 64 (512)
cfg_scale = <float> // unconditional guidance scale (7.5)
)
# do the slow model initialization
t2i.load_model()
# Do the fast inference & image generation. Any options passed here
# override the default values assigned during class initialization
# Will call load_model() if the model was not previously loaded and so
# may be slow at first.
# The method returns a list of images. Each row of the list is a sub-list of [filename,seed]
results = t2i.prompt2png(prompt = "an astronaut riding a horse",
outdir = "./outputs/samples",
iterations = 3)
for row in results:
print(f'filename={row[0]}')
print(f'seed ={row[1]}')
# Same thing, but using an initial image.
results = t2i.prompt2png(prompt = "an astronaut riding a horse",
outdir = "./outputs/,
iterations = 3,
init_img = "./sketches/horse+rider.png")
for row in results:
print(f'filename={row[0]}')
print(f'seed ={row[1]}')
# Same thing, but we return a series of Image objects, which lets you manipulate them,
# combine them, and save them under arbitrary names
results = t2i.prompt2image(prompt = "an astronaut riding a horse"
outdir = "./outputs/")
for row in results:
im = row[0]
seed = row[1]
im.save(f'./outputs/samples/an_astronaut_riding_a_horse-{seed}.png')
im.thumbnail(100,100).save('./outputs/samples/astronaut_thumb.jpg')
Note that the old txt2img() and img2img() calls are deprecated but will
still work.
"""
class T2I:
"""T2I class
Attributes
----------
model
config
iterations
steps
seed
sampler_name
width
height
cfg_scale
latent_channels
downsampling_factor
precision
strength
embedding_path
The vast majority of these arguments default to reasonable values.
"""
def __init__(
self,
iterations=1,
steps=50,
seed=None,
cfg_scale=7.5,
weights='models/ldm/stable-diffusion-v1/model.ckpt',
config='configs/stable-diffusion/v1-inference.yaml',
grid=False,
width=512,
height=512,
sampler_name='k_lms',
latent_channels=4,
downsampling_factor=8,
ddim_eta=0.0, # deterministic
precision='autocast',
full_precision=False,
strength=0.75, # default in scripts/img2img.py
embedding_path=None,
device_type = 'cuda',
# just to keep track of this parameter when regenerating prompt
# needs to be replaced when new configuration system implemented.
latent_diffusion_weights=False,
):
self.iterations = iterations
self.width = width
self.height = height
self.steps = steps
self.cfg_scale = cfg_scale
self.weights = weights
self.config = config
self.sampler_name = sampler_name
self.latent_channels = latent_channels
self.downsampling_factor = downsampling_factor
self.grid = grid
self.ddim_eta = ddim_eta
self.precision = precision
self.full_precision = full_precision
self.strength = strength
self.embedding_path = embedding_path
self.device_type = device_type
self.model = None # empty for now
self.sampler = None
self.device = None
self.latent_diffusion_weights = latent_diffusion_weights
if device_type == 'cuda' and not torch.cuda.is_available():
device_type = choose_torch_device()
print(">> cuda not available, using device", device_type)
self.device = torch.device(device_type)
# for VRAM usage statistics
device_type = choose_torch_device()
self.session_peakmem = torch.cuda.max_memory_allocated() if device_type == 'cuda' else None
if seed is None:
self.seed = self._new_seed()
else:
self.seed = seed
transformers.logging.set_verbosity_error()
def prompt2png(self, prompt, outdir, **kwargs):
"""
Takes a prompt and an output directory, writes out the requested number
of PNG files, and returns an array of [[filename,seed],[filename,seed]...]
Optional named arguments are the same as those passed to T2I and prompt2image()
"""
results = self.prompt2image(prompt, **kwargs)
pngwriter = PngWriter(outdir)
prefix = pngwriter.unique_prefix()
outputs = []
for image, seed in results:
name = f'{prefix}.{seed}.png'
path = pngwriter.save_image_and_prompt_to_png(
image, f'{prompt} -S{seed}', name)
outputs.append([path, seed])
return outputs
def txt2img(self, prompt, **kwargs):
outdir = kwargs.pop('outdir', 'outputs/img-samples')
return self.prompt2png(prompt, outdir, **kwargs)
def img2img(self, prompt, **kwargs):
outdir = kwargs.pop('outdir', 'outputs/img-samples')
assert (
'init_img' in kwargs
), 'call to img2img() must include the init_img argument'
return self.prompt2png(prompt, outdir, **kwargs)
def prompt2image(
self,
# these are common
prompt,
iterations = None,
steps = None,
seed = None,
cfg_scale = None,
ddim_eta = None,
skip_normalize = False,
image_callback = None,
step_callback = None,
width = None,
height = None,
# these are specific to img2img
init_img = None,
fit = False,
strength = None,
gfpgan_strength= 0,
save_original = False,
upscale = None,
sampler_name = None,
log_tokenization= False,
with_variations = None,
variation_amount = 0.0,
**args,
): # eat up additional cruft
"""
ldm.prompt2image() is the common entry point for txt2img() and img2img()
It takes the following arguments:
prompt // prompt string (no default)
iterations // iterations (1); image count=iterations
steps // refinement steps per iteration
seed // seed for random number generator
width // width of image, in multiples of 64 (512)
height // height of image, in multiples of 64 (512)
cfg_scale // how strongly the prompt influences the image (7.5) (must be >1)
init_img // path to an initial image - its dimensions override width and height
strength // strength for noising/unnoising init_img. 0.0 preserves image exactly, 1.0 replaces it completely
gfpgan_strength // strength for GFPGAN. 0.0 preserves image exactly, 1.0 replaces it completely
ddim_eta // image randomness (eta=0.0 means the same seed always produces the same image)
step_callback // a function or method that will be called each step
image_callback // a function or method that will be called each time an image is generated
with_variations // a weighted list [(seed_1, weight_1), (seed_2, weight_2), ...] of variations which should be applied before doing any generation
variation_amount // optional 0-1 value to slerp from -S noise to random noise (allows variations on an image)
To use the step callback, define a function that receives two arguments:
- Image GPU data
- The step number
To use the image callback, define a function of method that receives two arguments, an Image object
and the seed. You can then do whatever you like with the image, including converting it to
different formats and manipulating it. For example:
def process_image(image,seed):
image.save(f{'images/seed.png'})
The callback used by the prompt2png() can be found in ldm/dream_util.py. It contains code
to create the requested output directory, select a unique informative name for each image, and
write the prompt into the PNG metadata.
"""
# TODO: convert this into a getattr() loop
steps = steps or self.steps
width = width or self.width
height = height or self.height
cfg_scale = cfg_scale or self.cfg_scale
ddim_eta = ddim_eta or self.ddim_eta
iterations = iterations or self.iterations
strength = strength or self.strength
self.log_tokenization = log_tokenization
with_variations = [] if with_variations is None else with_variations
model = (
self.load_model()
) # will instantiate the model or return it from cache
assert cfg_scale > 1.0, 'CFG_Scale (-C) must be >1.0'
assert (
0.0 <= strength <= 1.0
), 'can only work with strength in [0.0, 1.0]'
assert (
0.0 <= variation_amount <= 1.0
), '-v --variation_amount must be in [0.0, 1.0]'
if len(with_variations) > 0:
assert seed is not None,\
'seed must be specified when using with_variations'
if variation_amount == 0.0:
assert iterations == 1,\
'when using --with_variations, multiple iterations are only possible when using --variation_amount'
assert all(0 <= weight <= 1 for _, weight in with_variations),\
f'variation weights must be in [0.0, 1.0]: got {[weight for _, weight in with_variations]}'
seed = seed or self.seed
width, height, _ = self._resolution_check(width, height, log=True)
# TODO: - Check if this is still necessary to run on M1 devices.
# - Move code into ldm.dream.devices to live alongside other
# special-hardware casing code.
if self.precision == 'autocast' and torch.cuda.is_available():
scope = autocast
else:
scope = nullcontext
if sampler_name and (sampler_name != self.sampler_name):
self.sampler_name = sampler_name
self._set_sampler()
tic = time.time()
if torch.cuda.is_available():
torch.cuda.reset_peak_memory_stats()
results = list()
try:
if init_img:
assert os.path.exists(init_img), f'{init_img}: File not found'
init_image = self._load_img(init_img, width, height, fit).to(self.device)
with scope(self.device.type):
init_latent = self.model.get_first_stage_encoding(
self.model.encode_first_stage(init_image)
) # move to latent space
make_image = self._img2img(
prompt,
steps=steps,
cfg_scale=cfg_scale,
ddim_eta=ddim_eta,
skip_normalize=skip_normalize,
init_latent=init_latent,
strength=strength,
callback=step_callback,
)
else:
make_image = self._txt2img(
prompt,
steps=steps,
cfg_scale=cfg_scale,
ddim_eta=ddim_eta,
skip_normalize=skip_normalize,
width=width,
height=height,
callback=step_callback,
)
def get_noise():
if init_img:
return torch.randn_like(init_latent, device=self.device)
else:
return torch.randn([1,
self.latent_channels,
height // self.downsampling_factor,
width // self.downsampling_factor],
device=self.device)
initial_noise = None
if variation_amount > 0 or len(with_variations) > 0:
# use fixed initial noise plus random noise per iteration
seed_everything(seed)
initial_noise = get_noise()
for v_seed, v_weight in with_variations:
seed = v_seed
seed_everything(seed)
next_noise = get_noise()
initial_noise = self.slerp(v_weight, initial_noise, next_noise)
if variation_amount > 0:
random.seed() # reset RNG to an actually random state, so we can get a random seed for variations
seed = random.randrange(0,np.iinfo(np.uint32).max)
device_type = choose_autocast_device(self.device)
with scope(device_type), self.model.ema_scope():
for n in trange(iterations, desc='Generating'):
x_T = None
if variation_amount > 0:
seed_everything(seed)
target_noise = get_noise()
x_T = self.slerp(variation_amount, initial_noise, target_noise)
elif initial_noise is not None:
# i.e. we specified particular variations
x_T = initial_noise
else:
seed_everything(seed)
# make_image will do the equivalent of get_noise itself
image = make_image(x_T)
results.append([image, seed])
if image_callback is not None:
image_callback(image, seed)
seed = self._new_seed()
if upscale is not None or gfpgan_strength > 0:
for result in results:
image, seed = result
try:
if upscale is not None:
from ldm.gfpgan.gfpgan_tools import (
real_esrgan_upscale,
)
if len(upscale) < 2:
upscale.append(0.75)
image = real_esrgan_upscale(
image,
upscale[1],
int(upscale[0]),
prompt,
seed,
)
if gfpgan_strength > 0:
from ldm.gfpgan.gfpgan_tools import _run_gfpgan
image = _run_gfpgan(
image, gfpgan_strength, prompt, seed, 1
)
except Exception as e:
print(
f'>> Error running RealESRGAN - Your image was not upscaled.\n{e}'
)
if image_callback is not None:
if save_original:
image_callback(image, seed)
else:
image_callback(image, seed, upscaled=True)
else: # no callback passed, so we simply replace old image with rescaled one
result[0] = image
except KeyboardInterrupt:
print('*interrupted*')
print(
'>> Partial results will be returned; if --grid was requested, nothing will be returned.'
)
except RuntimeError as e:
print(traceback.format_exc(), file=sys.stderr)
print('>> Are you sure your system has an adequate NVIDIA GPU?')
toc = time.time()
print('>> Usage stats:')
print(
f'>> {len(results)} image(s) generated in', '%4.2fs' % (toc - tic)
)
print(
f'>> Max VRAM used for this generation:',
'%4.2fG' % (torch.cuda.max_memory_allocated() / 1e9),
)
if self.session_peakmem:
self.session_peakmem = max(
self.session_peakmem, torch.cuda.max_memory_allocated()
)
print(
f'>> Max VRAM used since script start: ',
'%4.2fG' % (self.session_peakmem / 1e9),
)
return results
@torch.no_grad()
def _txt2img(
self,
prompt,
steps,
cfg_scale,
ddim_eta,
skip_normalize,
width,
height,
callback,
):
"""
Returns a function returning an image derived from the prompt and the initial image
Return value depends on the seed at the time you call it
"""
sampler = self.sampler
def make_image(x_T):
uc, c = self._get_uc_and_c(prompt, skip_normalize)
shape = [
self.latent_channels,
height // self.downsampling_factor,
width // self.downsampling_factor,
]
samples, _ = sampler.sample(
batch_size=1,
S=steps,
x_T=x_T,
conditioning=c,
shape=shape,
verbose=False,
unconditional_guidance_scale=cfg_scale,
unconditional_conditioning=uc,
eta=ddim_eta,
img_callback=callback
)
return self._sample_to_image(samples)
return make_image
@torch.no_grad()
def _img2img(
self,
prompt,
steps,
cfg_scale,
ddim_eta,
skip_normalize,
init_latent,
strength,
callback, # Currently not implemented for img2img
):
"""
Returns a function returning an image derived from the prompt and the initial image
Return value depends on the seed at the time you call it
"""
# PLMS sampler not supported yet, so ignore previous sampler
if self.sampler_name != 'ddim':
print(
f">> sampler '{self.sampler_name}' is not yet supported. Using DDIM sampler"
)
sampler = DDIMSampler(self.model, device=self.device)
else:
sampler = self.sampler
sampler.make_schedule(
ddim_num_steps=steps, ddim_eta=ddim_eta, verbose=False
)
t_enc = int(strength * steps)
def make_image(x_T):
uc, c = self._get_uc_and_c(prompt, skip_normalize)
# encode (scaled latent)
z_enc = sampler.stochastic_encode(
init_latent,
torch.tensor([t_enc]).to(self.device),
noise=x_T
)
# decode it
samples = sampler.decode(
z_enc,
c,
t_enc,
img_callback=callback,
unconditional_guidance_scale=cfg_scale,
unconditional_conditioning=uc,
)
return self._sample_to_image(samples)
return make_image
# TODO: does this actually need to run every loop? does anything in it vary by random seed?
def _get_uc_and_c(self, prompt, skip_normalize):
uc = self.model.get_learned_conditioning([''])
# get weighted sub-prompts
weighted_subprompts = T2I._split_weighted_subprompts(
prompt, skip_normalize)
if len(weighted_subprompts) > 1:
# i dont know if this is correct.. but it works
c = torch.zeros_like(uc)
# normalize each "sub prompt" and add it
for subprompt, weight in weighted_subprompts:
self._log_tokenization(subprompt)
c = torch.add(
c,
self.model.get_learned_conditioning([subprompt]),
alpha=weight,
)
else: # just standard 1 prompt
self._log_tokenization(prompt)
c = self.model.get_learned_conditioning([prompt])
return (uc, c)
def _sample_to_image(self, samples):
x_samples = self.model.decode_first_stage(samples)
x_samples = torch.clamp((x_samples + 1.0) / 2.0, min=0.0, max=1.0)
if len(x_samples) != 1:
raise Exception(
f'>> expected to get a single image, but got {len(x_samples)}')
x_sample = 255.0 * rearrange(
x_samples[0].cpu().numpy(), 'c h w -> h w c'
)
return Image.fromarray(x_sample.astype(np.uint8))
def _new_seed(self):
self.seed = random.randrange(0, np.iinfo(np.uint32).max)
return self.seed
def load_model(self):
"""Load and initialize the model from configuration variables passed at object creation time"""
if self.model is None:
seed_everything(self.seed)
try:
config = OmegaConf.load(self.config)
model = self._load_model_from_config(config, self.weights)
if self.embedding_path is not None:
model.embedding_manager.load(
self.embedding_path, self.full_precision
)
self.model = model.to(self.device)
# model.to doesn't change the cond_stage_model.device used to move the tokenizer output, so set it here
self.model.cond_stage_model.device = self.device
except AttributeError as e:
print(f'>> Error loading model. {str(e)}', file=sys.stderr)
print(traceback.format_exc(), file=sys.stderr)
raise SystemExit from e
self._set_sampler()
return self.model
def _set_sampler(self):
msg = f'>> Setting Sampler to {self.sampler_name}'
if self.sampler_name == 'plms':
self.sampler = PLMSSampler(self.model, device=self.device)
elif self.sampler_name == 'ddim':
self.sampler = DDIMSampler(self.model, device=self.device)
elif self.sampler_name == 'k_dpm_2_a':
self.sampler = KSampler(
self.model, 'dpm_2_ancestral', device=self.device
)
elif self.sampler_name == 'k_dpm_2':
self.sampler = KSampler(self.model, 'dpm_2', device=self.device)
elif self.sampler_name == 'k_euler_a':
self.sampler = KSampler(
self.model, 'euler_ancestral', device=self.device
)
elif self.sampler_name == 'k_euler':
self.sampler = KSampler(self.model, 'euler', device=self.device)
elif self.sampler_name == 'k_heun':
self.sampler = KSampler(self.model, 'heun', device=self.device)
elif self.sampler_name == 'k_lms':
self.sampler = KSampler(self.model, 'lms', device=self.device)
else:
msg = f'>> Unsupported Sampler: {self.sampler_name}, Defaulting to plms'
self.sampler = PLMSSampler(self.model, device=self.device)
print(msg)
def _load_model_from_config(self, config, ckpt):
print(f'>> Loading model from {ckpt}')
pl_sd = torch.load(ckpt, map_location='cpu')
# if "global_step" in pl_sd:
# print(f"Global Step: {pl_sd['global_step']}")
sd = pl_sd['state_dict']
model = instantiate_from_config(config.model)
m, u = model.load_state_dict(sd, strict=False)
model.to(self.device)
model.eval()
if self.full_precision:
print(
'Using slower but more accurate full-precision math (--full_precision)'
)
else:
print(
'>> Using half precision math. Call with --full_precision to use more accurate but VRAM-intensive full precision.'
)
model.half()
return model
def _load_img(self, path, width, height, fit=False):
with Image.open(path) as img:
image = img.convert('RGB')
print(
f'>> loaded input image of size {image.width}x{image.height} from {path}'
)
# The logic here is:
# 1. If "fit" is true, then the image will be fit into the bounding box defined
# by width and height. It will do this in a way that preserves the init image's
# aspect ratio while preventing letterboxing. This means that if there is
# leftover horizontal space after rescaling the image to fit in the bounding box,
# the generated image's width will be reduced to the rescaled init image's width.
# Similarly for the vertical space.
# 2. Otherwise, if "fit" is false, then the image will be scaled, preserving its
# aspect ratio, to the nearest multiple of 64. Large images may generate an
# unexpected OOM error.
if fit:
image = self._fit_image(image,(width,height))
else:
image = self._squeeze_image(image)
image = np.array(image).astype(np.float32) / 255.0
image = image[None].transpose(0, 3, 1, 2)
image = torch.from_numpy(image)
return 2.0 * image - 1.0
def _squeeze_image(self,image):
x,y,resize_needed = self._resolution_check(image.width,image.height)
if resize_needed:
return InitImageResizer(image).resize(x,y)
return image
def _fit_image(self,image,max_dimensions):
w,h = max_dimensions
print(
f'>> image will be resized to fit inside a box {w}x{h} in size.'
)
if image.width > image.height:
h = None # by setting h to none, we tell InitImageResizer to fit into the width and calculate height
elif image.height > image.width:
w = None # ditto for w
else:
pass
image = InitImageResizer(image).resize(w,h) # note that InitImageResizer does the multiple of 64 truncation internally
print(
f'>> after adjusting image dimensions to be multiples of 64, init image is {image.width}x{image.height}'
)
return image
# TO DO: Move this and related weighted subprompt code into its own module.
def _split_weighted_subprompts(text, skip_normalize=False):
"""
grabs all text up to the first occurrence of ':'
uses the grabbed text as a sub-prompt, and takes the value following ':' as weight
if ':' has no value defined, defaults to 1.0
repeats until no text remaining
"""
prompt_parser = re.compile("""
(?P<prompt> # capture group for 'prompt'
(?:\\\:|[^:])+ # match one or more non ':' characters or escaped colons '\:'
) # end 'prompt'
(?: # non-capture group
:+ # match one or more ':' characters
(?P<weight> # capture group for 'weight'
-?\d+(?:\.\d+)? # match positive or negative integer or decimal number
)? # end weight capture group, make optional
\s* # strip spaces after weight
| # OR
$ # else, if no ':' then match end of line
) # end non-capture group
""", re.VERBOSE)
parsed_prompts = [(match.group("prompt").replace("\\:", ":"), float(
match.group("weight") or 1)) for match in re.finditer(prompt_parser, text)]
if skip_normalize:
return parsed_prompts
weight_sum = sum(map(lambda x: x[1], parsed_prompts))
if weight_sum == 0:
print(
"Warning: Subprompt weights add up to zero. Discarding and using even weights instead.")
equal_weight = 1 / len(parsed_prompts)
return [(x[0], equal_weight) for x in parsed_prompts]
return [(x[0], x[1] / weight_sum) for x in parsed_prompts]
# shows how the prompt is tokenized
# usually tokens have '</w>' to indicate end-of-word,
# but for readability it has been replaced with ' '
def _log_tokenization(self, text):
if not self.log_tokenization:
return
tokens = self.model.cond_stage_model.tokenizer._tokenize(text)
tokenized = ""
discarded = ""
usedTokens = 0
totalTokens = len(tokens)
for i in range(0, totalTokens):
token = tokens[i].replace('</w>', ' ')
# alternate color
s = (usedTokens % 6) + 1
if i < self.model.cond_stage_model.max_length:
tokenized = tokenized + f"\x1b[0;3{s};40m{token}"
usedTokens += 1
else: # over max token length
discarded = discarded + f"\x1b[0;3{s};40m{token}"
print(f"\nTokens ({usedTokens}):\n{tokenized}\x1b[0m")
if discarded != "":
print(
f"Tokens Discarded ({totalTokens-usedTokens}):\n{discarded}\x1b[0m")
def _resolution_check(self, width, height, log=False):
resize_needed = False
w, h = map(
lambda x: x - x % 64, (width, height)
) # resize to integer multiple of 64
if h != height or w != width:
if log:
print(
f'>> Provided width and height must be multiples of 64. Auto-resizing to {w}x{h}'
)
height = h
width = w
resize_needed = True
if (width * height) > (self.width * self.height):
print(">> This input is larger than your defaults. If you run out of memory, please use a smaller image.")
return width, height, resize_needed
def slerp(self, t, v0, v1, DOT_THRESHOLD=0.9995):
'''
Spherical linear interpolation
Args:
t (float/np.ndarray): Float value between 0.0 and 1.0
v0 (np.ndarray): Starting vector
v1 (np.ndarray): Final vector
DOT_THRESHOLD (float): Threshold for considering the two vectors as
colineal. Not recommended to alter this.
Returns:
v2 (np.ndarray): Interpolation vector between v0 and v1
'''
inputs_are_torch = False
if not isinstance(v0, np.ndarray):
inputs_are_torch = True
v0 = v0.detach().cpu().numpy()
if not isinstance(v1, np.ndarray):
inputs_are_torch = True
v1 = v1.detach().cpu().numpy()
dot = np.sum(v0 * v1 / (np.linalg.norm(v0) * np.linalg.norm(v1)))
if np.abs(dot) > DOT_THRESHOLD:
v2 = (1 - t) * v0 + t * v1
else:
theta_0 = np.arccos(dot)
sin_theta_0 = np.sin(theta_0)
theta_t = theta_0 * t
sin_theta_t = np.sin(theta_t)
s0 = np.sin(theta_0 - theta_t) / sin_theta_0
s1 = sin_theta_t / sin_theta_0
v2 = s0 * v0 + s1 * v1
if inputs_are_torch:
v2 = torch.from_numpy(v2).to(self.device)
return v2
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