Skip to content

API

torch algorithm utils

lm_opt 

lm_opt(f, theta0, ytrue, iters=10, batch_dims=0, f_kwargs_vec={}, f_kwargs_no_vec={}, lam0=1e-06, alpha0=1.0, lam_factors=[[1 / 2, 1, 2], [1]], alpha_factors=[[1], [1 / 2, 1, 2]], vmap_chunk_size=None, jacfwd=True, verbose=None, verbose_indent=4, quantiles_losses=[0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100], quantiles_lams=[0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100], quantiles_alphas=[0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100], verbose_quantiles_losses=[5, 25, 50, 75, 90], verbose_quantiles_lams=[5, 25, 50, 75, 90], verbose_quantiles_alphas=[5, 25, 50, 75, 90], verbose_times=True, warn=True)

Levenberg--Marquardt optimization

Parameters:

Name Type Description Default
f func

Residual function.

required
theta0 Tensor

Initial guess for parameters \(\theta\).

required
ytrue Tensor

True y values, i.e. f(theta_true).

required
iters int

Number of iterations.

10
batch_dims int

Number of batch dimension.

0
f_kwargs_vec dict

Keyword arguments to f which will be vectorized over the first dimension.

{}
f_kwargs_no_vec dict

Keyword arguments to f which will not be vectorized over the first dimension.

{}
lam0 float

Initial positive relaxation parameter \(\lambda\).

 1e-06
alpha0 float

Initial positive step size \(\alpha\).

 1.0
lam_factors Tensor

Either a 1D torch.Tensor or list of 1d torch.Tensor.

  • Passing in a float for lam_factors is equivalent to passing in torch.tensor([lam_factors]) on the correct device
  • If a 1D torch.Tensor for lam_factors will consider all lam*lam_factors options at each step.
  • If a list of 1D torch.Tensors are passed in for lam_factors, iterations will cycle through the list and then return to the start after exhausting the list.
 [[1 / 2, 1, 2], [1]]
alpha_factors Tensor

Either a 1D torch.Tensor or list of 1d torch.Tensor.

  • Passing in a float for alpha_factors is equivalent to passing in torch.tensor([alpha_factors]) on the correct device
  • If a 1D torch.Tensor for alpha_factors will consider all lam*alpha_factors options at each step.
  • If a list of 1D torch.Tensors are passed in for alpha_factors, iterations will cycle through the list and then return to the start after exhausting the list.
[[1], [1 / 2, 1, 2]]
vmap_chunk_size int

Parameter chunksize to pass to torch.vmap.

 None
jacfwd bool

If True, use torch.func.jacfwd, otherwise use torch.func.jacrev

 True
verbose int

Controls logging verbosity

  • If True, perform logging.
  • If a positive int, only log every verbose iterations.
  • If False, don't log.
None
verbose_indent int

Positive number of indentation spaces for logging.

 4
quantiles_losses list

Loss quantiles to record.

 [0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100]
quantiles_lams list

\(\lambda\) quantiles to record.

 [0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100]
quantiles_alphas list

\(\alpha\) quantiles to record.

 [0, 1, 5, 10, 25, 40, 50, 60, 75, 90, 95, 99, 100]
verbose_quantiles_losses list

Loss quantiles to show in verbose log.

 [5, 25, 50, 75, 90]
verbose_quantiles_lams list

\(\lambda\) quantiles to show in verbose log.

 [5, 25, 50, 75, 90]
verbose_quantiles_alphas list

\(\alpha\) quantiles to show in verbose log.

 [5, 25, 50, 75, 90]
verbose_times bool

If False, do not show the times in the verbose log. This is mostly for testing where timing is not reproducible.

True
warn bool

If False, then suppress warnings.

 True

Returns:

Name Type Description
theta Tensor

Optimized parameters.
data dict

Iteration data.

Examples:

>>> torch.set_default_dtype(torch.float64)
>>> rng = torch.Generator().manual_seed(7)
>>> x = torch.rand((10,4,),generator=rng)
>>> theta_true = torch.rand((4,),generator=rng)
>>> ytrue = torch.exp((x*theta_true).sum(-1)) # (10,)
>>> def f(theta):
...     yhat = torch.exp((x*theta[...,None,:]).sum(-1)) # (...,10)
...     return yhat
>>> theta_hat,data = lm_opt(
...     f = f, 
...     theta0 = torch.rand_like(theta_true,generator=rng),
...     ytrue = ytrue,
...     iters = 3,
...     batch_dims = 0,
...     verbose_times = False,
...     )
    iter i     | losses_quantiles                                          | lams_quantiles                                            | alphas_quantiles                                          
               | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    0          | 2.3e+01   | 2.3e+01   | 2.3e+01   | 2.3e+01   | 2.3e+01   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
    1          | 7.3e+00   | 7.3e+00   | 7.3e+00   | 7.3e+00   | 7.3e+00   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
    2          | 8.5e-02   | 8.5e-02   | 8.5e-02   | 8.5e-02   | 8.5e-02   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
    3          | 3.3e-05   | 3.3e-05   | 3.3e-05   | 3.3e-05   | 3.3e-05   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
>>> torch.allclose(theta_hat,theta_true,atol=5e-2)
True
>>> print_data_signatures_lm_opt(data)
    data['theta'].shape = (4,)
    data['iterrange'].shape = (4,)
    data['times'].shape = (4,)
    data['thetas'].shape = (4, 4)
    data['losses'].shape = (4,)
    data['lams'].shape = (4,)
    data['alphas'].shape = (4,)
    data['losses_quantiles']
        data['losses_quantiles']['0'].shape = (4,)
        data['losses_quantiles']['1'].shape = (4,)
        data['losses_quantiles']['5'].shape = (4,)
        data['losses_quantiles']['10'].shape = (4,)
        data['losses_quantiles']['25'].shape = (4,)
        data['losses_quantiles']['40'].shape = (4,)
        data['losses_quantiles']['50'].shape = (4,)
        data['losses_quantiles']['60'].shape = (4,)
        data['losses_quantiles']['75'].shape = (4,)
        data['losses_quantiles']['90'].shape = (4,)
        data['losses_quantiles']['95'].shape = (4,)
        data['losses_quantiles']['99'].shape = (4,)
        data['losses_quantiles']['100'].shape = (4,)
    data['lams_quantiles']
        data['lams_quantiles']['0'].shape = (4,)
        data['lams_quantiles']['1'].shape = (4,)
        data['lams_quantiles']['5'].shape = (4,)
        data['lams_quantiles']['10'].shape = (4,)
        data['lams_quantiles']['25'].shape = (4,)
        data['lams_quantiles']['40'].shape = (4,)
        data['lams_quantiles']['50'].shape = (4,)
        data['lams_quantiles']['60'].shape = (4,)
        data['lams_quantiles']['75'].shape = (4,)
        data['lams_quantiles']['90'].shape = (4,)
        data['lams_quantiles']['95'].shape = (4,)
        data['lams_quantiles']['99'].shape = (4,)
        data['lams_quantiles']['100'].shape = (4,)
    data['alphas_quantiles']
        data['alphas_quantiles']['0'].shape = (4,)
        data['alphas_quantiles']['1'].shape = (4,)
        data['alphas_quantiles']['5'].shape = (4,)
        data['alphas_quantiles']['10'].shape = (4,)
        data['alphas_quantiles']['25'].shape = (4,)
        data['alphas_quantiles']['40'].shape = (4,)
        data['alphas_quantiles']['50'].shape = (4,)
        data['alphas_quantiles']['60'].shape = (4,)
        data['alphas_quantiles']['75'].shape = (4,)
        data['alphas_quantiles']['90'].shape = (4,)
        data['alphas_quantiles']['95'].shape = (4,)
        data['alphas_quantiles']['99'].shape = (4,)
        data['alphas_quantiles']['100'].shape = (4,)

>>> torch.set_default_dtype(torch.float64)
>>> rng = torch.Generator().manual_seed(7)
>>> x = torch.rand((3,3,3,2,2),generator=rng)
>>> theta_true = torch.rand((4,4,2,2),generator=rng)
>>> ytrue = torch.exp((x*theta_true[...,None,None,None,:,:]).sum((-2,-1))) # (4,4,3,3,3)
>>> def f(theta):
...     yhat = torch.exp((x*theta[...,None,None,None,:,:]).sum((-2,-1))) # (...,3,3,3)
...     return yhat
>>> theta_hat,data = lm_opt(
...     f = f, 
...     theta0 = torch.rand_like(theta_true,generator=rng),
...     ytrue = ytrue,
...     iters = 2,
...     batch_dims = 2,
...     lam_factors = [torch.tensor([1/4,1/2,1,2,4])],
...     alpha_factors = [torch.tensor([2/3,1,3/2])],
...     verbose_times = False,
...     )
    iter i     | losses_quantiles                                          | lams_quantiles                                            | alphas_quantiles                                          
               | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    0          | 1.5e+01   | 2.5e+01   | 6.3e+01   | 1.9e+02   | 3.1e+02   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
    1          | 2.2e-01   | 6.0e-01   | 1.0e+00   | 1.7e+00   | 2.0e+01   | 2.5e-07   | 2.5e-07   | 2.5e-07   | 1.2e-06   | 4.0e-06   | 6.7e-01   | 6.7e-01   | 8.3e-01   | 1.1e+00   | 1.5e+00   
    2          | 1.4e-04   | 3.0e-04   | 1.6e-03   | 2.9e-03   | 2.0e-01   | 6.2e-08   | 6.2e-08   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 6.7e-01   | 6.7e-01   | 8.3e-01   | 1.1e+00   | 1.5e+00   
>>> torch.allclose(theta_hat,theta_true,atol=5e-2)
True
>>> print_data_signatures_lm_opt(data)
    data['theta'].shape = (4, 4, 2, 2)
    data['iterrange'].shape = (3,)
    data['times'].shape = (3,)
    data['thetas'].shape = (3, 4, 4, 2, 2)
    data['losses'].shape = (3, 4, 4)
    data['lams'].shape = (3, 4, 4)
    data['alphas'].shape = (3, 4, 4)
    data['losses_quantiles']
        data['losses_quantiles']['0'].shape = (3,)
        data['losses_quantiles']['1'].shape = (3,)
        data['losses_quantiles']['5'].shape = (3,)
        data['losses_quantiles']['10'].shape = (3,)
        data['losses_quantiles']['25'].shape = (3,)
        data['losses_quantiles']['40'].shape = (3,)
        data['losses_quantiles']['50'].shape = (3,)
        data['losses_quantiles']['60'].shape = (3,)
        data['losses_quantiles']['75'].shape = (3,)
        data['losses_quantiles']['90'].shape = (3,)
        data['losses_quantiles']['95'].shape = (3,)
        data['losses_quantiles']['99'].shape = (3,)
        data['losses_quantiles']['100'].shape = (3,)
    data['lams_quantiles']
        data['lams_quantiles']['0'].shape = (3,)
        data['lams_quantiles']['1'].shape = (3,)
        data['lams_quantiles']['5'].shape = (3,)
        data['lams_quantiles']['10'].shape = (3,)
        data['lams_quantiles']['25'].shape = (3,)
        data['lams_quantiles']['40'].shape = (3,)
        data['lams_quantiles']['50'].shape = (3,)
        data['lams_quantiles']['60'].shape = (3,)
        data['lams_quantiles']['75'].shape = (3,)
        data['lams_quantiles']['90'].shape = (3,)
        data['lams_quantiles']['95'].shape = (3,)
        data['lams_quantiles']['99'].shape = (3,)
        data['lams_quantiles']['100'].shape = (3,)
    data['alphas_quantiles']
        data['alphas_quantiles']['0'].shape = (3,)
        data['alphas_quantiles']['1'].shape = (3,)
        data['alphas_quantiles']['5'].shape = (3,)
        data['alphas_quantiles']['10'].shape = (3,)
        data['alphas_quantiles']['25'].shape = (3,)
        data['alphas_quantiles']['40'].shape = (3,)
        data['alphas_quantiles']['50'].shape = (3,)
        data['alphas_quantiles']['60'].shape = (3,)
        data['alphas_quantiles']['75'].shape = (3,)
        data['alphas_quantiles']['90'].shape = (3,)
        data['alphas_quantiles']['95'].shape = (3,)
        data['alphas_quantiles']['99'].shape = (3,)
        data['alphas_quantiles']['100'].shape = (3,)
Source code in agsutil/algos.py 
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
def lm_opt(
        f,
        theta0,
        ytrue,
        iters = 10,
        batch_dims = 0, 
        f_kwargs_vec = {},
        f_kwargs_no_vec = {},
        lam0 = 1e-6,
        alpha0 = 1e0,
        lam_factors = [[1/2,1,2],[1]],
        alpha_factors = [[1],[1/2,1,2]],
        vmap_chunk_size = None,
        jacfwd = True,
        verbose = None, 
        verbose_indent = 4,
        quantiles_losses = [0,1,5,10,25,40,50,60,75,90,95,99,100],
        quantiles_lams =   [0,1,5,10,25,40,50,60,75,90,95,99,100],
        quantiles_alphas = [0,1,5,10,25,40,50,60,75,90,95,99,100],
        verbose_quantiles_losses = [5,25,50,75,90],
        verbose_quantiles_lams =   [5,25,50,75,90],
        verbose_quantiles_alphas = [5,25,50,75,90],
        verbose_times = True, 
        warn = True,
        ):
    r"""
    Levenberg--Marquardt optimization 

    Args:
        f (func): Residual function. 
        theta0 (torch.Tensor): Initial guess for parameters $\theta$. 
        ytrue (torch.Tensor): True `y` values, i.e. `f(theta_true)`. 
        iters (int): Number of iterations. 
        batch_dims (int): Number of batch dimension. 
        f_kwargs_vec (dict): Keyword arguments to `f` which will be vectorized over the first dimension. 
        f_kwargs_no_vec (dict): Keyword arguments to `f` which will not be vectorized over the first dimension. 
        lam0 (float): Initial positive relaxation parameter $\lambda$.
        alpha0 (float): Initial positive step size $\alpha$.
        lam_factors (torch.Tensor): Either a 1D `torch.Tensor` or list of 1d `torch.Tensor`. 

            - Passing in a `float` for `lam_factors` is equivalent to passing in `torch.tensor([lam_factors])` on the correct device
            - If a 1D `torch.Tensor` for `lam_factors` will consider all `lam*lam_factors` options at each step. 
            - If a list of 1D `torch.Tensor`s are passed in for `lam_factors`, iterations will cycle through the list and then return to the start after exhausting the list.

        alpha_factors (torch.Tensor): Either a 1D `torch.Tensor` or list of 1d `torch.Tensor`. 

            - Passing in a `float` for `alpha_factors` is equivalent to passing in `torch.tensor([alpha_factors])` on the correct device
            - If a 1D `torch.Tensor` for `alpha_factors` will consider all `lam*alpha_factors` options at each step. 
            - If a list of 1D `torch.Tensor`s are passed in for `alpha_factors`, iterations will cycle through the list and then return to the start after exhausting the list. 

        vmap_chunk_size (int): Parameter `chunksize` to pass to `torch.vmap`.
        jacfwd (bool): If `True`, use `torch.func.jacfwd`, otherwise use `torch.func.jacrev`
        verbose (int): Controls logging verbosity

            - If True, perform logging. 
            - If a positive int, only log every verbose iterations. 
            - If False, don't log. 

        verbose_indent (int): Positive number of indentation spaces for logging.
        quantiles_losses (list): Loss quantiles to record.
        quantiles_lams (list): $\lambda$ quantiles to record.
        quantiles_alphas (list): $\alpha$ quantiles to record.
        verbose_quantiles_losses (list): Loss quantiles to show in verbose log.
        verbose_quantiles_lams (list): $\lambda$ quantiles to show in verbose log.
        verbose_quantiles_alphas (list): $\alpha$ quantiles to show in verbose log.
        verbose_times (bool): If `False`, do not show the times in the verbose log. This is mostly for testing where timing is not reproducible. 
        warn (bool): If `False`, then suppress warnings.

    Returns:
        theta (torch.Tensor): Optimized parameters.
        data (dict): Iteration data.

    Examples:

        >>> torch.set_default_dtype(torch.float64)
        >>> rng = torch.Generator().manual_seed(7)
        >>> x = torch.rand((10,4,),generator=rng)
        >>> theta_true = torch.rand((4,),generator=rng)
        >>> ytrue = torch.exp((x*theta_true).sum(-1)) # (10,)
        >>> def f(theta):
        ...     yhat = torch.exp((x*theta[...,None,:]).sum(-1)) # (...,10)
        ...     return yhat
        >>> theta_hat,data = lm_opt(
        ...     f = f, 
        ...     theta0 = torch.rand_like(theta_true,generator=rng),
        ...     ytrue = ytrue,
        ...     iters = 3,
        ...     batch_dims = 0,
        ...     verbose_times = False,
        ...     )
            iter i     | losses_quantiles                                          | lams_quantiles                                            | alphas_quantiles                                          
                       | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        
            ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            0          | 2.3e+01   | 2.3e+01   | 2.3e+01   | 2.3e+01   | 2.3e+01   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
            1          | 7.3e+00   | 7.3e+00   | 7.3e+00   | 7.3e+00   | 7.3e+00   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
            2          | 8.5e-02   | 8.5e-02   | 8.5e-02   | 8.5e-02   | 8.5e-02   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 2.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
            3          | 3.3e-05   | 3.3e-05   | 3.3e-05   | 3.3e-05   | 3.3e-05   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
        >>> torch.allclose(theta_hat,theta_true,atol=5e-2)
        True
        >>> print_data_signatures_lm_opt(data)
            data['theta'].shape = (4,)
            data['iterrange'].shape = (4,)
            data['times'].shape = (4,)
            data['thetas'].shape = (4, 4)
            data['losses'].shape = (4,)
            data['lams'].shape = (4,)
            data['alphas'].shape = (4,)
            data['losses_quantiles']
                data['losses_quantiles']['0'].shape = (4,)
                data['losses_quantiles']['1'].shape = (4,)
                data['losses_quantiles']['5'].shape = (4,)
                data['losses_quantiles']['10'].shape = (4,)
                data['losses_quantiles']['25'].shape = (4,)
                data['losses_quantiles']['40'].shape = (4,)
                data['losses_quantiles']['50'].shape = (4,)
                data['losses_quantiles']['60'].shape = (4,)
                data['losses_quantiles']['75'].shape = (4,)
                data['losses_quantiles']['90'].shape = (4,)
                data['losses_quantiles']['95'].shape = (4,)
                data['losses_quantiles']['99'].shape = (4,)
                data['losses_quantiles']['100'].shape = (4,)
            data['lams_quantiles']
                data['lams_quantiles']['0'].shape = (4,)
                data['lams_quantiles']['1'].shape = (4,)
                data['lams_quantiles']['5'].shape = (4,)
                data['lams_quantiles']['10'].shape = (4,)
                data['lams_quantiles']['25'].shape = (4,)
                data['lams_quantiles']['40'].shape = (4,)
                data['lams_quantiles']['50'].shape = (4,)
                data['lams_quantiles']['60'].shape = (4,)
                data['lams_quantiles']['75'].shape = (4,)
                data['lams_quantiles']['90'].shape = (4,)
                data['lams_quantiles']['95'].shape = (4,)
                data['lams_quantiles']['99'].shape = (4,)
                data['lams_quantiles']['100'].shape = (4,)
            data['alphas_quantiles']
                data['alphas_quantiles']['0'].shape = (4,)
                data['alphas_quantiles']['1'].shape = (4,)
                data['alphas_quantiles']['5'].shape = (4,)
                data['alphas_quantiles']['10'].shape = (4,)
                data['alphas_quantiles']['25'].shape = (4,)
                data['alphas_quantiles']['40'].shape = (4,)
                data['alphas_quantiles']['50'].shape = (4,)
                data['alphas_quantiles']['60'].shape = (4,)
                data['alphas_quantiles']['75'].shape = (4,)
                data['alphas_quantiles']['90'].shape = (4,)
                data['alphas_quantiles']['95'].shape = (4,)
                data['alphas_quantiles']['99'].shape = (4,)
                data['alphas_quantiles']['100'].shape = (4,)

        >>> torch.set_default_dtype(torch.float64)
        >>> rng = torch.Generator().manual_seed(7)
        >>> x = torch.rand((3,3,3,2,2),generator=rng)
        >>> theta_true = torch.rand((4,4,2,2),generator=rng)
        >>> ytrue = torch.exp((x*theta_true[...,None,None,None,:,:]).sum((-2,-1))) # (4,4,3,3,3)
        >>> def f(theta):
        ...     yhat = torch.exp((x*theta[...,None,None,None,:,:]).sum((-2,-1))) # (...,3,3,3)
        ...     return yhat
        >>> theta_hat,data = lm_opt(
        ...     f = f, 
        ...     theta0 = torch.rand_like(theta_true,generator=rng),
        ...     ytrue = ytrue,
        ...     iters = 2,
        ...     batch_dims = 2,
        ...     lam_factors = [torch.tensor([1/4,1/2,1,2,4])],
        ...     alpha_factors = [torch.tensor([2/3,1,3/2])],
        ...     verbose_times = False,
        ...     )
            iter i     | losses_quantiles                                          | lams_quantiles                                            | alphas_quantiles                                          
                       | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        | 5         | 25        | 50        | 75        | 90        
            ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            0          | 1.5e+01   | 2.5e+01   | 6.3e+01   | 1.9e+02   | 3.1e+02   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   | 1.0e+00   
            1          | 2.2e-01   | 6.0e-01   | 1.0e+00   | 1.7e+00   | 2.0e+01   | 2.5e-07   | 2.5e-07   | 2.5e-07   | 1.2e-06   | 4.0e-06   | 6.7e-01   | 6.7e-01   | 8.3e-01   | 1.1e+00   | 1.5e+00   
            2          | 1.4e-04   | 3.0e-04   | 1.6e-03   | 2.9e-03   | 2.0e-01   | 6.2e-08   | 6.2e-08   | 1.0e-06   | 1.0e-06   | 1.0e-06   | 6.7e-01   | 6.7e-01   | 8.3e-01   | 1.1e+00   | 1.5e+00   
        >>> torch.allclose(theta_hat,theta_true,atol=5e-2)
        True
        >>> print_data_signatures_lm_opt(data)
            data['theta'].shape = (4, 4, 2, 2)
            data['iterrange'].shape = (3,)
            data['times'].shape = (3,)
            data['thetas'].shape = (3, 4, 4, 2, 2)
            data['losses'].shape = (3, 4, 4)
            data['lams'].shape = (3, 4, 4)
            data['alphas'].shape = (3, 4, 4)
            data['losses_quantiles']
                data['losses_quantiles']['0'].shape = (3,)
                data['losses_quantiles']['1'].shape = (3,)
                data['losses_quantiles']['5'].shape = (3,)
                data['losses_quantiles']['10'].shape = (3,)
                data['losses_quantiles']['25'].shape = (3,)
                data['losses_quantiles']['40'].shape = (3,)
                data['losses_quantiles']['50'].shape = (3,)
                data['losses_quantiles']['60'].shape = (3,)
                data['losses_quantiles']['75'].shape = (3,)
                data['losses_quantiles']['90'].shape = (3,)
                data['losses_quantiles']['95'].shape = (3,)
                data['losses_quantiles']['99'].shape = (3,)
                data['losses_quantiles']['100'].shape = (3,)
            data['lams_quantiles']
                data['lams_quantiles']['0'].shape = (3,)
                data['lams_quantiles']['1'].shape = (3,)
                data['lams_quantiles']['5'].shape = (3,)
                data['lams_quantiles']['10'].shape = (3,)
                data['lams_quantiles']['25'].shape = (3,)
                data['lams_quantiles']['40'].shape = (3,)
                data['lams_quantiles']['50'].shape = (3,)
                data['lams_quantiles']['60'].shape = (3,)
                data['lams_quantiles']['75'].shape = (3,)
                data['lams_quantiles']['90'].shape = (3,)
                data['lams_quantiles']['95'].shape = (3,)
                data['lams_quantiles']['99'].shape = (3,)
                data['lams_quantiles']['100'].shape = (3,)
            data['alphas_quantiles']
                data['alphas_quantiles']['0'].shape = (3,)
                data['alphas_quantiles']['1'].shape = (3,)
                data['alphas_quantiles']['5'].shape = (3,)
                data['alphas_quantiles']['10'].shape = (3,)
                data['alphas_quantiles']['25'].shape = (3,)
                data['alphas_quantiles']['40'].shape = (3,)
                data['alphas_quantiles']['50'].shape = (3,)
                data['alphas_quantiles']['60'].shape = (3,)
                data['alphas_quantiles']['75'].shape = (3,)
                data['alphas_quantiles']['90'].shape = (3,)
                data['alphas_quantiles']['95'].shape = (3,)
                data['alphas_quantiles']['99'].shape = (3,)
                data['alphas_quantiles']['100'].shape = (3,)
    """
    if warn and (not torch.get_default_dtype()==torch.float64): warnings.warn('''
            torch.get_default_dtype() = %s, but lm_opt often requires high precision updates. We recommend using:
                torch.set_default_dtype(torch.float64)'''%str(torch.get_default_dtype()))
    device = str(theta0.device)
    default_device = str(torch.get_default_device())
    assert iters%1==0, "iters should be an int"
    assert iters>=0
    assert callable(f) 
    assert batch_dims>=0
    assert isinstance(theta0,torch.Tensor)
    batch_shape = tuple(theta0.shape[:batch_dims])
    R = int(torch.tensor(batch_shape).prod())
    nonbatch_theta_dims = theta0.ndim-batch_dims
    nonbatch_theta_shape = tuple(theta0.shape[batch_dims:])
    nonbatch_y_dims = ytrue.ndim-batch_dims
    nonbatch_y_shape = tuple(ytrue.shape[batch_dims:])
    K = int(torch.tensor(nonbatch_y_shape).prod())
    T = int(torch.tensor(nonbatch_theta_shape).prod())
    if batch_dims==0:
        theta = theta0[None,...]
    else: # batch_dims>0:
        theta = theta0.flatten(end_dim=batch_dims-1)
    if batch_dims==0:
        ytrue = ytrue[None,...]
    else: # batch_dims>0:
        ytrue = ytrue.flatten(end_dim=batch_dims-1)
    assert isinstance(f_kwargs_vec,dict)
    assert isinstance(f_kwargs_no_vec,dict)
    f_kwargs_vec_names = list(f_kwargs_vec.keys())
    f_kwargs_vec_vals = []
    for key in f_kwargs_vec_names:
        assert f_kwargs_vec[key].shape[:batch_dims]==batch_shape, "f_kwargs_vec['%s'].shape[:%d] = %s but bs = %s"%(key,batch_dims,f_kwargs_vec[key].shape[:batch_dims])
        if batch_dims==0:
            f_kwargs_vec_vals.append(f_kwargs_vec[key][None,...])
        else: # batch_dims>0
            f_kwargs_vec_vals.append(f_kwargs_vec[key].flatten(end_dim=batch_dims-1))
    f_kwargs_vec_names = ["ytrue"]+f_kwargs_vec_names
    f_kwargs_vec_vals = [ytrue]+f_kwargs_vec_vals
    if verbose is None: 
        verbose = max(1,iters//20)
    assert lam0>0
    assert alpha0>0
    if np.isscalar(lam_factors):
        lam_factors = [torch.tensor([lam_factors],device=device)]
    elif isinstance(lam_factors,torch.Tensor):
        lam_factors = [lam_factors.to(device)]
    lam_factors = [torch.tensor(list(lam_factors[i])).to(device) for i in range(len(lam_factors))]
    assert isinstance(lam_factors,list)
    assert all(isinstance(lam_factors[i],torch.Tensor) for i in range(len(lam_factors)))
    assert all(lam_factors[i].ndim==1 for i in range(len(lam_factors)))
    if np.isscalar(alpha_factors):
        alpha_factors = [torch.tensor([alpha_factors],device=device)]
    elif isinstance(alpha_factors,torch.Tensor):
        alpha_factors = [alpha_factors.to(device)]
    alpha_factors = [torch.tensor(list(alpha_factors[i])).to(device) for i in range(len(alpha_factors))]
    assert isinstance(alpha_factors,list)
    assert all(isinstance(alpha_factors[i],torch.Tensor) for i in range(len(alpha_factors)))
    assert all(alpha_factors[i].ndim==1 for i in range(len(alpha_factors)))
    if len(alpha_factors)==1:
        alpha_factors = alpha_factors*len(lam_factors)
    if len(lam_factors)==1:
        lam_factors = lam_factors*len(alpha_factors)
    assert len(lam_factors)==len(alpha_factors)
    assert isinstance(quantiles_losses,list)
    assert all(0<=qt<=100 for qt in quantiles_losses)
    assert isinstance(quantiles_lams,list)
    assert all(0<=qt<=100 for qt in quantiles_lams)
    assert isinstance(quantiles_alphas,list)
    assert all(0<=qt<=100 for qt in quantiles_alphas)
    assert isinstance(verbose_quantiles_losses,list)
    assert all(qt in quantiles_losses for qt in verbose_quantiles_losses)
    assert isinstance(verbose_quantiles_lams,list)
    assert all(qt in quantiles_lams for qt in verbose_quantiles_lams)
    assert isinstance(verbose_quantiles_alphas,list)
    assert all(qt in quantiles_alphas for qt in verbose_quantiles_alphas)
    assert verbose%1==0
    assert verbose>=0 
    assert verbose_indent%1==0 
    assert verbose_indent>=0
    assert isinstance(verbose_times,bool)
    thetas = torch.nan*torch.ones((iters+1,*batch_shape,*nonbatch_theta_shape),device=default_device)
    times = torch.nan*torch.ones(iters+1,device=default_device)
    losses = torch.nan*torch.ones((iters+1,*batch_shape),device=default_device)
    lams = torch.nan*torch.ones((iters+1,*batch_shape),device=default_device)
    alphas = torch.nan*torch.ones((iters+1,*batch_shape),device=default_device)
    losses_quantiles = {str(qt):torch.nan*torch.ones(iters+1,device=default_device) for qt in quantiles_losses}
    lams_quantiles = {str(qt):torch.nan*torch.ones(iters+1,device=default_device) for qt in quantiles_lams}
    alphas_quantiles = {str(qt):torch.nan*torch.ones(iters+1,device=default_device) for qt in quantiles_alphas}
    def f_resid(theta, *f_kwargs_vec_vals):
        assert len(f_kwargs_vec_vals)==len(f_kwargs_vec_names)
        ytrue = f_kwargs_vec_vals[0]
        f_kwargs_vec = {f_kwargs_vec_names[i]:f_kwargs_vec_vals[i] for i in range(1,len(f_kwargs_vec_names))}
        yhat = f(theta,**f_kwargs_vec,**f_kwargs_no_vec)
        resid = yhat-ytrue
        return resid,(resid,yhat)
    assert isinstance(jacfwd,bool)
    if jacfwd:
        jac_ftilde = torch.func.jacfwd(f_resid,argnums=(0,),has_aux=True)
    else:
        jac_ftilde = torch.func.jacrev(f_resid,argnums=(0,),has_aux=True)
    vjac_ftilde = torch.func.vmap(jac_ftilde,in_dims=(0,)+(0,)*len(f_kwargs_vec_names),chunk_size=vmap_chunk_size)
    if warn and jacfwd and T>K: warnings.warn('''
        For T the number of inputs and K the number of outputs:
            torch.func.jacfwd performs best when T << K. 
            torch.func.jacrev performs best when K << T.
        You are using torch.func.jacfwd but T = %d > %d = K. 
        Try using torch.func.jacrev by setting jacfwd = False.'''%(T,K))
    if warn and (not jacfwd) and T<K: warnings.warn('''
        For T the number of inputs and K the number of outputs:
            torch.func.jacfwd performs best when T << K. 
            torch.func.jacrev performs best when K << T.
        You are using torch.func.jacrev but T = %d < %d = K. 
        Try using torch.func.jacrev by setting jacfwd = True.'''%(T,K))
    eyeT = torch.eye(T,device=device)
    Rrange = torch.arange(R,device=device)
    lam = lam0*torch.ones(R,device=device)
    alpha = alpha0*torch.ones(R,device=device)
    if verbose:
        _h_iter = "%-10s "%"iter i"
        _h_times = "| %-10s"%"times" if verbose_times else ""
        _s_losses_qt = ("| %-9s "*len(verbose_quantiles_losses))%tuple(str(qt) for qt in verbose_quantiles_losses)
        _s_lams_qt = ("| %-9s "*len(verbose_quantiles_lams))%tuple(str(qt) for qt in verbose_quantiles_lams)
        _s_alphas_qt = ("| %-9s "*len(verbose_quantiles_alphas))%tuple(str(qt) for qt in verbose_quantiles_alphas)
        _h_losses_qt = "| losses_quantiles"+" "*(len(_s_losses_qt)-len("| losses_quantiles"))
        _h_lams_qt   = "| lams_quantiles"  +" "*(len(_s_lams_qt)  -len("| lams_quantiles"))
        _h_alphas_qt = "| alphas_quantiles"+" "*(len(_s_alphas_qt)-len("| alphas_quantiles"))
        _h = _h_iter+_h_losses_qt+_h_lams_qt+_h_alphas_qt+_h_times
        _s = " "*len(_h_iter)+_s_losses_qt+_s_lams_qt+_s_alphas_qt+" "*len(_h_times)
        print(" "*verbose_indent+_h)
        print(" "*verbose_indent+_s)
        print(" "*verbose_indent+"~"*len(_s))
    timer = Timer(device=device)
    timer.tic()
    for i in range(iters+1):
        if i==iters:
            _,(resid,yhat) = f_resid(theta,*f_kwargs_vec_vals)
        else:
            (Jfull,),(resid,yhat) = vjac_ftilde(theta,*f_kwargs_vec_vals)
        assert Jfull.shape==(R,*nonbatch_y_shape,*nonbatch_theta_shape)
        loss = (resid**2).flatten(start_dim=1).sum(-1)
        losses[i] = loss.reshape(batch_shape).to(default_device)
        lams[i] = lam.reshape(batch_shape).to(default_device)
        alphas[i] = alpha.reshape(batch_shape).to(default_device)
        for qt in quantiles_losses:
            losses_quantiles[str(qt)][i] = loss.nanquantile(qt/100).to(default_device)
        for qt in quantiles_lams:
            lams_quantiles[str(qt)][i] = lam.nanquantile(qt/100).to(default_device)
        for qt in quantiles_alphas:
            alphas_quantiles[str(qt)][i] = alpha.nanquantile(qt/100).to(default_device)
        times[i] = timer.toc()
        if verbose and (i%verbose==0 or i==iters):
            _s_iter = "%-10d "%i
            _s_losses_qt = ("| %-9.1e "*len(verbose_quantiles_losses))%tuple(losses_quantiles[str(qt)][i] for qt in verbose_quantiles_losses)
            _s_lams_qt = ("| %-9.1e "*len(verbose_quantiles_lams))%tuple(lams_quantiles[str(qt)][i] for qt in verbose_quantiles_lams)
            _s_alphas_qt = ("| %-9.1e "*len(verbose_quantiles_alphas))%tuple(alphas_quantiles[str(qt)][i] for qt in verbose_quantiles_alphas)
            _s_times = "| %-10.1f "%(times[i]) if verbose_times else ""
            print(" "*verbose_indent+_s_iter+_s_losses_qt+_s_lams_qt+_s_alphas_qt+_s_times)
        if i==iters: break
        J = Jfull.reshape((R,K,T))
        residf = resid.reshape((R,K))
        gamma = torch.einsum("rij,ri->rj",J,residf)
        JtJ = torch.einsum("rij,ril->rjl",J,J) # (R,T,T)
        lam_factors_i = lam_factors[i%len(lam_factors)]
        alpha_factors_i = alpha_factors[i%len(alpha_factors)]
        Q_lams = len(lam_factors_i)
        Q_alphas = len(alpha_factors_i)
        lams_try = lam_factors_i[:,None]*lam # (Q_lams,R)
        alphas_try = alpha_factors_i[:,None]*alpha # (Q_alphas,R)
        JtJplam = JtJ[None,:,:,:]+lams_try[:,:,None,None]*eyeT # (Q_lams,R,T,T)
        L,fails = torch.linalg.cholesky_ex(JtJplam,upper=False) # L.shape==(Q_lams,R,T,T) and fails.shape==(Q_lams,R)
        success = ~fails.to(bool) # (Q_lams,R)
        deltaf = torch.nan*torch.ones((Q_lams,R,T),device=device)
        gammas = torch.ones((Q_lams,1,1),device=device)*gamma[None,:,:] # (Q_lams,R,T)
        deltaf[success] = torch.linalg.solve_triangular(L[success].transpose(dim0=-2,dim1=-1),torch.linalg.solve_triangular(L[success],gammas[success,...,None],upper=False),upper=True)[...,0] # (Q_lam,R,T)
        thetasf = torch.ones((Q_lams,1,1),device=device)*theta.reshape((1,R,T)) # (Q_lam,R,T)
        thetasf_new = torch.nan*torch.ones((Q_alphas,Q_lams,R,T),device=device)
        thetasf_new[:,success] = thetasf[success]-alpha_factors_i[:,None,None]*deltaf[success]
        thetas_new = thetasf_new.reshape((Q_alphas,Q_lams,R,*nonbatch_theta_shape))
        f_kwargs_vec_vals_success = [(torch.ones((Q_alphas,Q_lams)+(1,)*f_kwargs_vec_vals[l].ndim,device=device)*f_kwargs_vec_vals[l][None,None,...])[:,success] for l in range(len(f_kwargs_vec_vals))]
        residf_new = torch.inf*torch.ones((Q_alphas,Q_lams,R,K),device=device)
        _,(resid_new_success,_) = f_resid(thetas_new[:,success],*f_kwargs_vec_vals_success)
        residf_new[:,success] = resid_new_success.reshape((Q_alphas,resid_new_success.size(1),K))
        losses_new = (residf_new**2).sum(-1)
        imin = losses_new.reshape((Q_alphas*Q_lams,R)).argmin(0) # (R,)
        imin_alpha,imin_lam = imin//Q_lams,imin%Q_lams
        lam_best_new = lams_try[imin_lam,Rrange] # (R,)
        alpha_best_new = alphas_try[imin_alpha,Rrange] # (R,)
        loss_best_new = losses_new[imin_alpha,imin_lam,Rrange] # (R,)
        thetas_best_new = thetas_new[imin_alpha,imin_lam,Rrange] # (R,*nonbatch_theta_shape)
        improved = loss_best_new<loss # (R,)
        lam[improved] = lam_best_new[improved]
        alpha[improved] = alpha_best_new[improved]
        theta[improved] = thetas_best_new[improved]
    theta = theta.reshape((*batch_shape,*nonbatch_theta_shape))
    data = {
        "theta": theta.to(default_device), 
        "iterrange": torch.arange(iters+1), 
        "times": times, 
        "thetas": thetas,
        "losses": losses,
        "lams": lams, 
        "alphas": alphas,
        "losses_quantiles": losses_quantiles,
        "lams_quantiles": lams_quantiles,
        "alphas_quantiles": alphas_quantiles,
        }
    return theta,data

matplotlib plotting utils

mpl_setup 

mpl_setup()

Setup matplotlib default parameters

Returns:

Name Type Description
mplparams dict

matplotlib helpful parameters
Source code in agsutil/plots.py 
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
def mpl_setup():
    r""" 
    Setup matplotlib default parameters

    Returns:
        mplparams (dict): matplotlib helpful parameters"""
    from matplotlib import pyplot 
    pyplot.style.use("seaborn-v0_8-whitegrid")
    PW = 30 # page width in inches
    FW = 30 # font size
    COLORS = ["xkcd:purple","xkcd:blue","xkcd:green","xkcd:red","xkcd:orange","xkcd:cyan","xkcd:brown","xkcd:yellow"]
    LINESTYLES = ['solid','dotted','dashed','dashdot',(0, (1, 1))]
    pyplot.rcParams['xtick.labelsize'] = FS
    pyplot.rcParams['ytick.labelsize'] = FS
    pyplot.rcParams['ytick.labelsize'] = FS
    pyplot.rcParams['axes.titlesize'] = FS
    pyplot.rcParams['figure.titlesize'] = FS
    pyplot.rcParams["axes.labelsize"] = FS
    pyplot.rcParams['legend.fontsize'] = FS
    pyplot.rcParams['font.size'] = FS
    pyplot.rcParams['lines.linewidth'] = 5
    pyplot.rcParams['lines.markersize'] = 15
    mplparams = {
        "PW": PW,
        "FS": FS,
        "COLORS": COLORS,
        "LINESTYLES": LINESTYLES,
    }
    return mplparams

set_aspects 

set_aspects(ax, ratio=1)

Set aspect ratio of the ax.

Parameters:

Name Type Description Default
ax Axes

axes to set the aspect ratio of.

required
ratio float

positive aspect ratio for the axis

 1
Source code in agsutil/plots.py 
33
34
35
36
37
38
39
40
41
42
43
44
45
def set_aspects(ax, ratio=1):
    r"""
    Set aspect ratio of the ax. 

    Args:
        ax (Axes): axes to set the aspect ratio of. 
        ratio (float): positive aspect ratio for the axis
    """
    assert ratio>0
    xmin,xmax = ax.get_xlim()
    ymin,ymax = ax.get_ylim()
    aspect = ratio*(xmax-xmin)/(ymax-ymin)
    ax.set_aspect(aspect)