Files
Baysian_Canonical_Identific…/__pycache__/models_and_mcmc.cpython-311.pyc
T

108 lines
10 KiB
Plaintext
Raw Normal View History

§
2025-11-02 20:47:28 +08:00
ú�ûhð&ã
ó8—ddlZddlZddlmZddlmZddlZddlm Z
ddl m Z m
Z
mZddlmcmZddlmZddlmZddlmZeejd¬¦«d „¦«Zd
„Zd „Zdd „Zed
k�r*ejd¦«ej  !d¦«Z"e#d¦«ej  $e"d¦«\Z%Z&Z'ee(e%d¦«¬¦«\Z)Z*Z+Z,e#d¦«dZ-dZ.dZ/ee)e*e+e,e-e.e/e(e&d¦«¬¦«\Z0Z1ej2e0¦«Z3ej2e1¦«Z4ej  $e'¦«\Z5Z6eee5e3e4e.e/¦«Z7eee6e3e4e.e/¦«Z8e#d¦«e#d¦«e#d¦«dSdS)éN)Úmultivariate_normal)ÚMCMCÚNUTSÚ
Predictive)Úpartial)Úgenerate_ground_truth_system)Úsimulate_lti_data)rééé)Ústatic_argnumsc 󶇇‡‡‡‡‡‡ ‡
‡ ‡—tj‰¦«} tj‰¦«dz}
tj‰¦«Š‰
 ||df¦«Š
‰  |‰df¦«Š ˆˆˆˆˆˆˆ ˆˆˆ
ˆ f d„}| |
f}tj ||tj|¦«¦«\\}}}tj|¦«S)uv
使用�尔曼滤波器计算 LTI 系统的对数似然。
�数:
dx, du, dy, T: 系统的维度和时间
A, B, C, D: LTI 系统矩阵 (JAX 数组)
2025-11-02 20:47:28 +08:00
Q, R: 过程噪声和测�噪声的�方差 (JAX 数组)
u_data, y_data: 输入和输出数� (T x du) 和 (T x dy)
返回:
float: 总的对数似然
çð?r
cóš• —|\}}‰|}‰|}| ‰df¦«}|‰|zz
‰|zz
}‰|z‰jz‰z}tj |¦«\} }
tj ||¦«} |j| z ¦«} tjdtjz¦«}
d‰z|
zd|
zz
d| zz
}tj |‰|z¦«j}|||zz}‰|‰zz
|z}‰|z‰|zz  ¦«}‰|z‰jz‰z}||f|fS)Nr
g@gà¿gà?)
ÚreshapeÚTÚjnpÚlinalgÚslogdetÚsolveÚsqueezeÚlogÚpiÚflatten)ÚcarryÚtÚx_t_tm1ÚP_t_tm1Úu_tÚy_tÚ x_t_tm1_colÚnu_tÚS_tÚsignÚ
logdet_S_tÚS_inv_nuÚ quad_termÚlog_2piÚ log_lik_tÚK_tÚx_t_tÚP_t_tÚx_tp1_tÚP_tp1_tÚAÚBÚCÚDÚI_dxÚQÚRÚdxÚdyÚu_dataÚy_datas €€€€€€€€€€€ú.f:\Papers\Baysian_Inference\models_and_mcmc.pyÚ kalman_stepz&kalman_likelihood.<locals>.kalman_step,swø€ð!ш�ð�QŒiˆØ�QŒiˆð —o’o r¨1 gÑ.Ô.ˆ ð�a˜+‘oÑ&¨!¨c©'Ñ2ˆð�'‰k˜AœCÑ !Ñ#ˆõœ:×-Ò-¨cÑ2Ô2шˆjÝ”:×#Ò# C¨Ñ.Ô.ˆØ”V˜hÑ&×/Ò/Ñ1Ô1ˆ Ý”'˜#¥¤™,Ñ'Ô'ˆØ˜2‘I Ñ'¨#°
Ñ*:Ñ:¸SÀ9¹_ÑLˆ õŒj×Ò˜s A¨¡KÑ0Ô0Ô2ˆð˜c D™jÑ(ˆð˜˜a™‘ 7Ñ*ˆð �u‘9˜q 3™wÑ&×/Ò/Ñ1Ô1ˆð�e‘)˜aœc‘/ AÑ%ˆð˜Ð! 9Ð,Ð,ó) rÚzerosÚeyerÚjaxÚlaxÚscanÚarangeÚsum)r6Údur7rr/r0r1r2r4r5r8r9Úx_0_m1ÚP_0_m1r;Ú
2025-11-02 20:47:28 +08:00
initial_carryÚ_Úlog_likelihoodsr3s` ` ```````` @r:Úkalman_likelihoodrJsøøøøøøøøøøø€õ ŒY�r‰]Œ]€FÝ
ŒW�R‰[Œ[˜3Ñ
€FÝ Œ7�2‰;Œ;€Dð�^Š^˜Q  A˜JÑ
2025-11-02 20:47:28 +08:00
'Ô
'€FØ
�^Š^˜Q  A˜JÑ
'Ô
'€Fð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ð/-ðf˜VÐ$€Mõ"œgŸlšl¨;¸
ÅsÄzÐRSÁ}Ä}ÑUÔUÑ�F€QˆˆOõ Œ7�?Ñ #Ô #Ð#r<có—d\}}d}|jd}tjdtjdd¦«¦«}tjdtjd|z
2025-11-02 20:47:28 +08:00
d|z¦«¦«} tjdtjdd¦«¦«}
tjd tjdd¦«¦«} t
jd
d g| | gg¦«} t
jd
gd gg¦«}
t
j|
| gg¦«}t
j||f¦«}t
j |¦«|dzz}t
j |¦«|dzz}t||||| |
||||||¦ « }tj d |¦«d
S)u5
NumPyro 模型 - 规范型 (Canonical Form)
2025-11-02 20:47:28 +08:00
©r r
r
rÚa0éÿÿÿÿÚa1Úb0r Úb1çrÚlog_likelihoodN) ÚshapeÚnumpyroÚsampleÚdistÚUniformÚNormalrÚarrayr=r>rJÚfactor)r8r9Ú
sigma_processÚ
sigma_measurer6rDr7rrMrOrPrQr/r0r1r2r4r5Ú
log_lik_totals r:Úmodel_canonicalr_jsn€ð�F€BˆØ
€BØŒ �QŒ€Aõ
2025-11-02 20:47:28 +08:00
Œ˜�dœl¨2¨qÑ1Ô1Ñ 2Ô 2€Bå Œ˜�dœl¨2°©7°A¸±FÑ;Ô;Ñ <Ô <€Bõ
Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€BÝ Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€Bõ Œ �C˜�:   b S˜zÐ*Ñ+Ô+€AÝ Œ �C�5˜3˜%�.Ñ!Ô!€AÝ Œ �B˜�8�*ÑÔ€AÝ Œ �2�r�(ÑÔ€Aõ Œ�‰ Œ �}¨Ñ)Ñ*€AÝ Œ�‰ Œ �}¨Ñ)Ñ*€Aõ& b¨"¨b°!°Q¸¸1¸aÀÀAÀvÈvÑVÔV€Mõ „NÐ# ]Ñ3Ô3Ð3Ð3Ð3r<có2—d\}}d}|jd}tjdtjdd¦«¦«}tjdtjdd¦«¦«} tjdtjdd¦«¦«}
tjdtjdd¦«¦«} tjd tjdd¦«¦«} tjd
tjdd¦«¦«}
tjd tjdd¦«¦«}tjd tjdd¦«¦«}t j|| g|
| gg¦«}t j| g|
gg¦«}t j||gg¦«}t j||f¦«}t j|¦«|dzz}t j|¦«|dzz}t||||||||||||¦ « }tj
2025-11-02 20:47:28 +08:00
d
|¦«dS)u4
NumPyro 模型 - 标准型 (Standard Form)
rLr
rÚA11r ÚA12ÚA21ÚA22ÚB1ÚB2ÚC1ÚC2rSN) rTrUrVrWrYrrZr=r>rJr[)r8r9r\r]r6rDr7rrarbrcrdrerfrgrhr/r0r1r2r4r5r^s r:Úmodel_standardri’sØ€ð�F€BˆØ
2025-11-02 20:47:28 +08:00
€BØŒ �QŒ€Aõ Œ.˜¥¤ ¨A¨qÑ 1Ô 1Ñ
2Ô
2€CÝ
Œ.˜¥¤ ¨A¨qÑ 1Ô 1Ñ
2Ô
2€CÝ
Œ.˜¥¤ ¨A¨qÑ 1Ô 1Ñ
2025-11-02 20:47:28 +08:00
2Ô
2€CÝ
Œ.˜¥¤ ¨A¨qÑ 1Ô 1Ñ
2Ô
2025-11-02 20:47:28 +08:00
2€Cõ
Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€BÝ Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€Bõ
Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€BÝ Œ˜�dœk¨!¨QÑ/Ô/Ñ 0Ô 0€Bõ Œ �C˜�:  S˜zÐ*Ñ+Ô+€AÝ Œ �B�4˜"˜�,ÑÔ€AÝ Œ �B˜�8�*ÑÔ€AÝ Œ �2�r�(ÑÔ€Aõ Œ�‰ Œ �}¨Ñ)Ñ*€AÝ Œ�‰ Œ �}¨Ñ)Ñ*€Aõ& b¨"¨b°!°Q¸¸1¸aÀÀAÀvÈvÑVÔV€Mõ „NÐ# ]Ñ3Ô3Ð3Ð3Ð3r<cóÞ—td|j›d�¦«d}d}d} |rTtd¦«d„| ¦«D¦«}
tj|
¬¦«} t || ¬ ¦«} ntd
¦«t |¦«} t
| ||| d ¬ ¦«}
|
 |||||¬
2025-11-02 20:47:28 +08:00
¦«td|j›d�¦«|
 ¦«|
S)u*辅助函数,用于�行 NUTS 采样器u
--- 开始为模型 u è¿�行 MCMC ---i Ni@œéuE--- MCMC 正在使用 'init_to_value' ç­–ç•¥ (从真实值开始) ---có>—i|]\}}|tj|¦«“ŒS©)rrZ)Ú.0ÚkÚvs r:ú
2025-11-02 20:47:28 +08:00
<dictcomp>zrun_mcmc.<locals>.<dictcomp>Ìs&€ÐGÐGÐG©4¨1¨a�q�#œ) A™,œ,ÐGÐGÐGr<)Úvalues)Ú