We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on ...We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.展开更多
We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improv...We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.展开更多
Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class c...Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.展开更多
The concepts of local correlation coefficient, local canonical correlation coefficients and local canonical variables of groups of random variables are defined, which generalize the classical concepts in two groups of...The concepts of local correlation coefficient, local canonical correlation coefficients and local canonical variables of groups of random variables are defined, which generalize the classical concepts in two groups of random variables.These concepts together with total corresponding concepts clarify the correlativity among groups of random variables.展开更多
Zero correlation window （ZCW） or zero correlation zone （ZCZ） sequence can be used in quasi-synchronous code division multiple access （QS-CDMA） system to eliminate multiple access and multipath interferences. How...Zero correlation window （ZCW） or zero correlation zone （ZCZ） sequence can be used in quasi-synchronous code division multiple access （QS-CDMA） system to eliminate multiple access and multipath interferences. However, as the length of ZCW or ZCZ increases, fewer sequences are available. Recently, a new concept, sequence set with group-wise zero correlation window is introduced, which can increase the number of available sequences for a QS-CDMA system. In this article, a new method for generating sequence set with group-wise zero correlation window is presented. This method is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M. Compared with previous methods, the proposed sequence set has a group-wise zero correlation window for both periodic and aperiodic cross-correlation functions.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11834005,and 11904145)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35).
文摘We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11834005,and 11904145)the Program for Changjiang Scholars and Innovative Research Team in Universities,China(Grant No.IRT-16R35).
文摘We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.
文摘Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.
文摘The concepts of local correlation coefficient, local canonical correlation coefficients and local canonical variables of groups of random variables are defined, which generalize the classical concepts in two groups of random variables.These concepts together with total corresponding concepts clarify the correlativity among groups of random variables.
基金supported by the National Natural Science Foundation of China(60272026,60872061)the PhD Programs Foundation of Ministry of Education of China(20060216010)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China
文摘Zero correlation window （ZCW） or zero correlation zone （ZCZ） sequence can be used in quasi-synchronous code division multiple access （QS-CDMA） system to eliminate multiple access and multipath interferences. However, as the length of ZCW or ZCZ increases, fewer sequences are available. Recently, a new concept, sequence set with group-wise zero correlation window is introduced, which can increase the number of available sequences for a QS-CDMA system. In this article, a new method for generating sequence set with group-wise zero correlation window is presented. This method is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M. Compared with previous methods, the proposed sequence set has a group-wise zero correlation window for both periodic and aperiodic cross-correlation functions.
