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Memristive crossbar arrays have gained considerable attention from researchers to perform analog in-memory vector-matrix multiplications in machine learning accelerators with low power and constant computational time. This work introduces a comprehensive framework for co-designing the software and hardware for deep neural networks (DNN) based on memristive and memcapacitive crossbars while considering various non-idealities. The model takes into account device-level factors, including conductance variation, cycle-to-cycle variation, device-to-device variation, peripheral circuits for error/weight gradient computation, and high tolerance. The overall neural network performance is thoroughly assessed by integrating these elements into a unified DNN training process. The proposed framework is implemented using a hybrid approach with Python and PyTorch. Performance evaluation was conducted using a simplified 8-layer VGG network on a measured <inline-formula> <tex-math notation="LaTeX">$128\times 128$ </tex-math></inline-formula> array with weight resolution. Remarkably, the memristive and memcapacitive crossbar arrays achieved outstanding training accuracies of 90.02&#x0025; and 91.03&#x0025;, respectively, for the CIFAR-10 dataset. Additionally, detailed hardware estimation for both mem-elements devices is provided, enabling meaningful comparisons with prior works.