


'''simple docstring'''



from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				NDArray[floataa]      ,    UpperCAmelCase_    :				NDArray[floataa]      ,    UpperCAmelCase_    :				list[int]      ,    UpperCAmelCase_    :				int      ,    )     ->		list[float]:
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[int]								=		coefficient_matrix.shape
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		constant_matrix.shape

     if rowsa != colsa:
          __lowerCamelCase   :	Union[str, Any]								=		F'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
          raise ValueError(UpperCAmelCase_							)

     if colsa != 1:
          __lowerCamelCase   :	int								=		F'Constant matrix must be nx1 but received {rowsa}x{colsa}'
          raise ValueError(UpperCAmelCase_							)

     if rowsa != rowsa:
          __lowerCamelCase   :	Tuple								=		(
              'Coefficient and constant matrices dimensions must be nxn and nx1 but '
              F'received {rowsa}x{colsa} and {rowsa}x{colsa}'
          )
          raise ValueError(UpperCAmelCase_							)

     if len(UpperCAmelCase_							) != rowsa:
          __lowerCamelCase   :	Optional[Any]								=		(
              'Number of initial values must be equal to number of rows in coefficient '
              F'matrix but received {len(UpperCAmelCase_							)} and {rowsa}'
          )
          raise ValueError(UpperCAmelCase_							)

     if iterations <= 0:
          raise ValueError('Iterations must be at least 1'							)

     __lowerCamelCase   :	NDArray[floataa]								=		np.concatenate(
         (coefficient_matrix, constant_matrix)      ,    axis=1							)

     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		table.shape

     strictly_diagonally_dominant(UpperCAmelCase_							)

     # Iterates the whole matrix for given number of times
     for _ in range(UpperCAmelCase_							):
          __lowerCamelCase   :	Optional[int]								=		[]
          for row in range(UpperCAmelCase_							):
               __lowerCamelCase   :	Any								=		0
               for col in range(UpperCAmelCase_							):
                    if col == row:
                         __lowerCamelCase   :	Union[str, Any]								=		table[row][col]
                    elif col == cols - 1:
                         __lowerCamelCase   :	Optional[int]								=		table[row][col]
                    else:
                         temp += (-1) * table[row][col] * init_val[col]
               __lowerCamelCase   :	Union[str, Any]								=		(temp + val) / denom
               new_val.append(UpperCAmelCase_							)
          __lowerCamelCase   :	Optional[Any]								=		new_val

     return [float(UpperCAmelCase_							) for i in new_val]



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				NDArray[floataa]							)     ->		bool:
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[int]								=		table.shape

     __lowerCamelCase   :	str								=		True

     for i in range(0      ,    UpperCAmelCase_							):
          __lowerCamelCase   :	int								=		0
          for j in range(0      ,    cols - 1							):
               if i == j:
                    continue
               else:
                    total += table[i][j]

          if table[i][i] <= total:
               raise ValueError('Coefficient matrix is not strictly diagonally dominant'							)

     return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
      import doctest

      doctest.testmod()










'''simple docstring'''



from . import (
    albert,
    align,
    altclip,
    audio_spectrogram_transformer,
    auto,
    autoformer,
    bark,
    bart,
    barthez,
    bartpho,
    beit,
    bert,
    bert_generation,
    bert_japanese,
    bertweet,
    big_bird,
    bigbird_pegasus,
    biogpt,
    bit,
    blenderbot,
    blenderbot_small,
    blip,
    blip_a,
    bloom,
    bridgetower,
    byta,
    camembert,
    canine,
    chinese_clip,
    clap,
    clip,
    clipseg,
    codegen,
    conditional_detr,
    convbert,
    convnext,
    convnextva,
    cpm,
    cpmant,
    ctrl,
    cvt,
    dataavec,
    deberta,
    deberta_va,
    decision_transformer,
    deformable_detr,
    deit,
    deprecated,
    deta,
    detr,
    dialogpt,
    dinat,
    distilbert,
    dit,
    donut,
    dpr,
    dpt,
    efficientformer,
    efficientnet,
    electra,
    encodec,
    encoder_decoder,
    ernie,
    ernie_m,
    esm,
    falcon,
    flaubert,
    flava,
    fnet,
    focalnet,
    fsmt,
    funnel,
    git,
    glpn,
    gpta,
    gpt_bigcode,
    gpt_neo,
    gpt_neox,
    gpt_neox_japanese,
    gpt_swa,
    gptj,
    gptsan_japanese,
    graphormer,
    groupvit,
    herbert,
    hubert,
    ibert,
    imagegpt,
    informer,
    instructblip,
    jukebox,
    layoutlm,
    layoutlmva,
    layoutlmva,
    layoutxlm,
    led,
    levit,
    lilt,
    llama,
    longformer,
    longta,
    luke,
    lxmert,
    mam_aaa,
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    maskformer,
    mbart,
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    mega,
    megatron_bert,
    megatron_gpta,
    mgp_str,
    mluke,
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    mobilenet_va,
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    mra,
    mta,
    musicgen,
    mvp,
    nat,
    nezha,
    nllb,
    nllb_moe,
    nystromformer,
    oneformer,
    open_llama,
    openai,
    opt,
    owlvit,
    pegasus,
    pegasus_x,
    perceiver,
    phobert,
    pixastruct,
    plbart,
    poolformer,
    prophetnet,
    qdqbert,
    rag,
    realm,
    reformer,
    regnet,
    rembert,
    resnet,
    roberta,
    roberta_prelayernorm,
    roc_bert,
    roformer,
    rwkv,
    sam,
    segformer,
    sew,
    sew_d,
    speech_encoder_decoder,
    speech_to_text,
    speech_to_text_a,
    speechta,
    splinter,
    squeezebert,
    swiftformer,
    swin,
    swinasr,
    swinva,
    switch_transformers,
    ta,
    table_transformer,
    tapas,
    time_series_transformer,
    timesformer,
    timm_backbone,
    transfo_xl,
    trocr,
    tvlt,
    umta,
    unispeech,
    unispeech_sat,
    upernet,
    videomae,
    vilt,
    vision_encoder_decoder,
    vision_text_dual_encoder,
    visual_bert,
    vit,
    vit_hybrid,
    vit_mae,
    vit_msn,
    vivit,
    wavaveca,
    wavaveca_conformer,
    wavaveca_phoneme,
    wavaveca_with_lm,
    wavlm,
    whisper,
    x_clip,
    xglm,
    xlm,
    xlm_prophetnet,
    xlm_roberta,
    xlm_roberta_xl,
    xlnet,
    xmod,
    yolos,
    yoso,
)






