42 results about "Linear algebra" patented technology

The invention belongs to the technical field of artificial intelligence and high-performance computing, and particularly relates to a method for improving the reasoning solution and training speed of a deep operator network model. According to the method, multi-level optimization is carried out on the PI-DeepONet model, and the reasoning solving speed and the training speed of the PI-DeepONet model are improved. According to the method, the SGEMM operator is customized, and compared with the best single-precision matrix multiplication in a basic linear algebraic library of a CUDA (Compute Unified Device Architecture) computing platform, the SGEMM operator can obtain a speed-up ratio of 1.5 times at most in a common model size range of PI-DeepONet. A fusion operator is designed according to the special structure of the modified MLP used in the model, the speed-up ratio of the end-to-end reasoning speed of the model is more than two times, and the calculation time of a graphics processor can be shortened by 5.7 times at most. According to the method, data parallel is used for carrying out distributed training on the model, a communication concealment strategy is used, and the expandability is kept at 83%-85%.

The invention relates to a quantum preprocessing method based on Schrodinger, and the method comprises the steps: carrying out the finite element discrete BPX multi-level preprocessing of a to-be-solved partial differential equation, constructing a quantum block code corresponding to a preprocessing system, and obtaining a quantum preprocessing linear algebraic equation set; solving of a quantum preprocessing linear algebraic equation set is converted into steady-state solution solving of a linear ordinary differential equation set; schrodinger is adopted, and a linear ordinary differential equation set is converted into a Hamiltonian system capable of being calculated on a quantum computer through a dimension raising method; and designing a quantum circuit diagram for the Hamiltonian system by using a quantum Hamiltonian simulation algorithm, and simulating the quantum circuit diagram through a quantum computer to obtain a simulation result. The quantum preprocessing algorithm obtained through Schrodinger has the exponential acceleration advantage on the matrix order, precision and the like, the complexity influence caused by the condition number is eliminated, and the algorithm is simple and efficient.

The invention discloses a thermal performance analysis method and system of a harmonic reducer, and relates to the technical field of thermal performance analysis of harmonic reducers, and the method comprises the following steps: data collection and preprocessing: collecting basic data of structural parameters, working conditions and material attributes of the harmonic reducer, and carrying out necessary preprocessing, according to the method, a coupling equation is solved by adopting a finite element analysis (FEA) method, a solving area is divided into a limited number of units, and a global equation set is solved by utilizing a linear algebraic solver, so that the numerical calculation efficiency is greatly improved, and meanwhile, the accuracy and reliability of an analysis result are ensured by verifying and optimizing a solving result; and powerful support is provided for thermal performance evaluation of the harmonic reducer.

The invention discloses a method for solving a mechanical problem based on a hybrid finite element method. Comprising the following steps: analyzing each unit of a stress body, and constructing a coefficient matrix and a load vector; boundary conditions on the boundary units are processed, load vectors are adjusted, and a constraint equation set is obtained; analyzing each unit interface of the Lagrange element type unit and the intrinsic mixed finite element type unit to obtain a local coefficient matrix of each unit interface, and assembling the local coefficient matrixes of each unit interface to a coefficient matrix; and processing the load vector and the coefficient matrix based on the constraint equation set to obtain a linear algebraic equation set, and solving the linear algebraic equation set to obtain a stress and displacement result. According to the method, the Lagrange element method and the intrinsic mixed finite element method are combined to solve the linear elastic mechanics problem of the stress body, so that the technical problem of low precision of a result obtained by solving the linear elastic mechanics problem by adopting a traditional finite element method in related technologies is solved under the condition of ensuring the solving efficiency.

The invention belongs to the technical field of pressure vessel structure analysis, and particularly relates to an intelligent reduced basis finite element method for rapidly analyzing the deformation behavior of a pressure vessel. According to the method, a finite element method is improved by adopting a reduced basis method, an online and offline combined solution mode is developed, after design parameters such as a structure size, a load type and size, material attributes and the like are preset, a reduced basis space is obtained by adopting an offline solution mode, and then a mapping relation between a reduced basis solution and a finite element solution is established; according to the method, order reduction of a finite element model is achieved, the degree of freedom of a problem is reduced, the calculation amount needed by solving a linear algebraic equation set through a traditional finite element method is greatly reduced while the precision is guaranteed, a Gaussian process regression method is further introduced to describe the elastic-plastic deformation behavior of the pressure vessel, and therefore the deformation behavior of the pressure vessel is rapidly solved.

The present application discloses a method for solving mechanical problems based on a hybrid finite element method. It includes: analyzing each unit of a force-bearing body, constructing a coefficient matrix and a load vector; processing the boundary conditions on the boundary units, adjusting the load vector and obtaining a set of constraint equations; analyzing each unit interface of a Lagrangian unit and an intrinsic hybrid finite element unit, obtaining a local coefficient matrix of each unit interface, and assembling the local coefficient matrix of each unit interface into a coefficient matrix; processing the load vector and the coefficient matrix based on the set of constraint equations to obtain a set of linear algebraic equations and solving them to obtain stress and displacement results. The present application combines the Lagrangian unit method and the intrinsic hybrid finite element method to solve the linear elastic mechanics problem of a force-bearing body, and solves the problem of low accuracy of the results obtained by using the traditional finite element method to solve the linear elastic mechanics problem in the related technology while ensuring the solution efficiency.

The invention provides a calculation method and system for a press riveting center positioning workpiece, and the system comprises a data obtaining module which obtains the coordinates of a positioning mark point on a plane drawing and the actual coordinates of the mark point on a machine; the vector generation module is used for generating a two-dimensional position vector; the angle comparison module is used for comparing angle changes; the coordinate rotating module is used for rotating all coordinates in the drawing coordinate system according to the angle change so as to match the direction of the machine coordinate system; the translation calculation module is used for calculating the translation amount according to the rotated drawing coordinates and machine coordinates; the transformation matrix construction module is used for constructing a rigid transformation matrix in combination with rotation and translation information; and the coordinate conversion module is used for converting coordinates of other points on the drawing into coordinates under a machine coordinate system. According to the method, the conversion relation from the drawing coordinates to the machine coordinates is obtained through a geometric method, strict requirements about matrix attributes in linear algebra do not need to be met, the situation that only two mark points exist can be processed, and the angle change of the workpiece can be directly obtained.

An algebraic modulation method for a three-phase current source converter is to transform the distribution problem of the duty cycle into the problem of solving a non-homogeneous linear equation group. The specific steps of the method are as follows: first, according to the system mathematical model, a non-homogeneous linear equation group of the duty cycle is constructed, and the general solution of the duty cycle matrix is ​​obtained by means of the relevant linear algebra theory; secondly, according to the physical constraints of the duty cycle, the feasible solution range of the free variable is obtained by means of the geometric method; then, a point is selected in the feasible solution area as the value of the free variable to determine the final duty cycle matrix; finally, according to the specific performance requirements (low loss, low common mode voltage, low DC current ripple, etc.), the switch action sequence is reasonably arranged to obtain the driving pulse of each switch. The modulation method avoids trigonometric function calculations, saves system operation costs, and has the characteristics of easy implementation, high flexibility and strong versatility.

The present invention relates to a method for quantitative analysis of a plurality of components in at least one aqueous sample comprising an active pharmaceutical ingredient (API), the method comprises the steps of (a) providing at least one aqueous sample comprising a plurality of components, wherein the sample comprises a biologic API; (b) measuring the extinction spectrum of the at least one aqueous sample using a Fourier transform infrared (FT IR) spectrometer comprising a transmission flow-through cell in a single measurement; (c) providing at least one reference extinction coefficient spectrum for each component of the plurality of components to be analyzed in the at least one aqueous sample; and (d) quantifying the concentration of each component in the plurality of components to be analyzed in the at least one aqueous sample based on the reference extinction coefficient spectra of step (c) and the extinction spectrum of the at least one aqueous sample of step (b) by solving the classical least square (CLS) problem by an algorithm using a numerical linear algebra method for finding the approximate solution to an overdetermined system of linear equations characterized by the Beer-Lambert law for the extinction spectrum of the at least one aqueous sample. The invention further relates to methods for the production of an API or determining the purity of an API comprising using said method.

The application discloses a polar coordinate decoupling-based image mirroring and rotating unified transformation method, which comprises the following steps: S10, inputting parameters: an original image, a transformation center point coordinate, a mirroring direction parameter and a rotating angle; S20, traversing each pixel position of an output image; S30, unified mirroring and rotating transformation mapping; S40, interpolation sampling; S50, assigning to the output image; S60, traversing all pixels until completion; and S70, outputting the image. The application abandons the traditional linear algebra idea of firstly constructing a mirroring matrix and then multiplying the mirroring matrix with a rotating matrix, and instead reconsiders the combined operation of mirroring and rotating from the perspective of polar coordinate transformation. In a local polar coordinate system around an arbitrary specified center point, the mirroring operation can be regarded as a sign operation or a shift operation on a polar angle, and the rotating is an addition operation on the polar angle. The two can be combined into a simple expression in the polar angle domain.

The invention relates to the field of teaching tools and discloses a mechanical device for teaching linear algebra, comprising a demonstration frame composed of three groups of horizontal plates and a deformable soft ellipsoid, the three groups of horizontal plates being fixedly installed vertically to each other so as to form a three-dimensional coordinate system for the demonstration frame, a suspended soft ellipsoid being provided at the center of the demonstration frame through mounting members on three inner walls, multiple groups of horizontal groove tubes being installed at the centers of the three inner walls of the demonstration frame, driven push rods extending on both sides of the horizontal plates being slidably sleeved in the multiple groups of horizontal groove tubes, end face outer walls of the multiple groups of driven push rods on the three groups of horizontal plates being fitted with the outer wall of the soft ellipsoid, active push rods being fixedly installed on the end face outer wall of the multiple groups of driven push rods extending outside the demonstration frame, the multiple groups of active push rods being connected to each other through different connecting mechanisms, the device can intuitively demonstrate the concept of matrix in linear algebra, and is conducive to better learning for students.

The application provides a sound flow coupling calculation method and device based on a Galbrun equation. The method provided by the application comprises the following steps: obtaining a Galbrun equation based on Euler equations of an ideal fluid under no external force, in combination with Euler disturbance, Lagrange disturbance and mixed disturbance relationship; the Galbrun equation represents the coupling effect of a flow field and a sound field; obtaining flow field data of a non-uniform flow field based on Navier-Stokes equations, in combination with a k-ε turbulence model in a RANS model; introducing a perfect matched layer for sound wave propagation simulation in an unbounded region, and constructing boundary conditions suitable for the Galbrun equation through geometric transformation, complex variable definition and coordinate conversion; performing weak transformation on the Galbrun equation, embedding the boundary conditions, combining the flow field data, adopting triangular finite elements for discretization processing, constructing a global linear algebraic equation group and solving, and obtaining discrete solutions of sound field parameters.

The invention belongs to the technical field of underwater sound propagation, and in particular, relates to a sound field acquisition method of a two-dimensional sound field model based on a finite element method, comprising: discretizing a target area into a finite number of calculation units according to ocean environment parameters of the acquired target area; constructing a basis function of each calculation unit according to a unit shape and a number of nodes; using a standard Galerkin variation method to derive a weak form of the Helmholtz equation; integrating unit stiffness matrices of all calculation units into a total stiffness matrix according to a one-to-one correspondence between each local number of the node and each overall number; integrating unit external load vectors of all calculation units into a total external load vector according to a one-to-one correspondence between each local number of the node and each overall number; composing the above results into a linear algebraic equation group as a two-dimensional sound field model to obtain a sound field, that is, a sound pressure of each node; and obtaining a sound pressure value of each node in space by selecting a basis function and an interpolation method.

The present invention discloses an energy optimization scheduling method based on eigenspace, which includes the following steps: S1: constructing a microgrid economy and carbon emission calculation model based on eigenspace; S2: collecting microgrid input variables and input parameters, and configuring them in the microgrid economy and carbon emission calculation model; S3: in the eigenspace, based on multiple specific eigenstates and corresponding input variables, multiple corresponding output functions are obtained, and the net electricity cost of the microgrid and the carbon emissions caused by the microgrid are calculated independently according to the output functions; S4: setting optimization objectives and constraints; S5: using particle swarm algorithm to achieve energy optimization scheduling. The energy optimization scheduling method proposed by the present invention adopts the eigenstate method in the field of linear algebra in the calculation model, which can conveniently decouple multiple key outputs from each other, and then solve the energy optimization scheduling problem within and between energy sources through computer modeling.

The present invention discloses a method for calculating an affine power flow of an electric power system based on full-morphic embedding. First, an embedded affine power flow model describing the uncertainty of load and new energy output is established. Then, a definite initial solution of the affine power flow is obtained, and the problem that the convergence of the affine power flow algorithm is affected by the initial value is solved. Thereafter, a mathematical relationship between the affine reactive power and the affine voltage of a PV node is established, and the affine reactive power of the PV node can be directly solved by using the affine node voltage obtained by each calculation. Finally, the problem of solving the affine power flow is converted into the problem of solving the Taylor power series coefficients, and the recursive relationship of the power series coefficients of the affine state quantity is derived. Only the linear algebra operation of the affine equation group is involved in the calculation process.

The application belongs to the technical field of pressure vessel structure analysis, and specifically relates to an intelligent reduced basis finite element method for fast analysis of pressure vessel deformation behavior. The application improves the finite element method by using the reduced basis method, and develops an online and offline combined solving mode. After design parameters such as structure size, load type and size, material properties and the like are preset, the reduced basis space is obtained by using the offline solving mode, and then a mapping relationship between the reduced basis solution and the finite element solution is established, so that the finite element model is reduced, the degree of freedom of the problem is reduced, the calculation amount required for solving the linear algebraic equation set by the traditional finite element method is greatly reduced while the accuracy is ensured, and further, the Gaussian process regression method is introduced to describe the elastic-plastic deformation behavior of the pressure vessel, so that the fast solution of the pressure vessel deformation behavior is realized.

The present invention relates to a method for computing a linear algebra operation of two operands or arrays comprising one or more narrow bit width elements with a digital circuit. The method uses the principle of binary segmentation to reduce the computation overhead of linear algebra operations like linear convolution and inner product of operands such as vectors with narrow bit width components. The invention is also directed to a digital circuit configured to execute the method.

The present application relates to the technical field of numerical linear algebra and scientific computing, in particular to a residual-driven adaptive momentum average block Karmarkar method and system. The method steps include: inputting parameters and matrices; initializing the linear feasibility problem estimation solution and inequality, equality part residual; in each iteration, through the residual-driven switching mechanism, when t, the row index set is selected from the inequality row profile with a probability, and when t, the row index set is selected from the equality row profile with a probability; the selected row index is given a convex combination weight; the optimal step size and the optimal momentum coefficient are calculated; the new iteration point combined with the momentum term is generated and the residual is updated; the iteration is repeated until the error limit is met, and the estimation solution is output. Through the residual-driven block switching mechanism, the optimal step size and the optimal momentum parameter setting, the convergence speed and the calculation efficiency of solving large-scale linear feasibility problems are significantly improved.

The invention discloses an aquifer hydraulic diffusion coefficient solving method based on a semi-analytical collocation method, belongs to the technical field of groundwater seepage analysis, and aims to solve the problems that an existing finite element method is tedious and time-consuming in grid division when processing is complex, and a finite difference method depends on regular grids and is difficult to adapt to irregular boundaries and the like. The method comprises the following steps: constructing a mathematical model of a two-dimensional seepage problem under a polar coordinate system, solving a groundwater seepage control equation through a variable separation method under a space-time coordinate system to obtain a complete primary function, establishing a space-time collocation constraint system, forming a linear algebraic equation set about an unknown coefficient, and solving the linear algebraic equation set. Establishing an objective function taking a hydraulic diffusion coefficient as an unknown parameter, and combining boundary conditions to form a mathematical expression of a nonlinear optimization problem; according to the method, point collocation calculation is directly carried out in a time-space domain through a Trefftz time-space point collocation method, and the calculation process is remarkably simplified. The method is suitable for complex geometric boundary problems, and the application range of numerical simulation is expanded.

The present invention discloses a quantum classifier based on a support vector machine, comprising: converting the optimization problem of an SVM into an equivalent linear algebra problem; utilizing quantum feature mapping to store data in a quantum state, thereby allowing a quantum computer to process data analysis; proposing a quantum matrix inversion algorithm to solve the linear algebra problem, constructing a quantum classifier, and realizing data classification; the present invention combines traditional solutions with quantum algorithms, leveraging the advantages of quantum computing, improving the training speed of the support vector machine in processing complex problems and ensuring computational accuracy, thereby breaking through the bottleneck problem of traditional solutions.

A processing unit includes a plurality of processing cores and is configured to arrange a sparse matrix for parallel performance by the cores on different rows of the matrix at least in part by calculating a respective quantity of non-zero elements in each row, assigning each row to a respective collection according to the respective quantity of non-zero elements for the row, wherein the processing unit is configured to assign at least one first row of the sparse matrix to respective collections of in parallel with assigning at least one second row of the sparse matrix to respective collections, and performing at least one mathematical operation on at least a first collection of the plurality of collections in parallel with performing the at least one mathematical operation on at least a second collection of the plurality of collections.

1. Name of the product in this design: Mathematical Teaching Aid (Mathematical Formula Finder). 2. Purpose of this design: An electronic device for finding formulas in linear algebra. 3. The key design feature of this product is its shape. 4. The image or photograph that best illustrates the design's key points: a 3D model.

The present application discloses a post-processing method for improving the displacement solution accuracy of the intrinsic hybrid finite element method, and relates to the technical field of structural mechanics. Among them, the method includes: determining the values ​​of the stress tensor and displacement vector of the current unit at the integration point respectively by solving the linear algebraic equations by the intrinsic hybrid finite element method, and combining the values ​​of the k-1-order discontinuous Lagrangian element basis function at the integration point, the values ​​of the k+1-order discontinuous Lagrangian element basis function at the integration point and their derivative values ​​to reconstruct the unit coefficient matrix and unit load vector of the current unit, and solve the unit linear equations composed of the unit coefficient matrix and the unit load vector to obtain the post-processing displacement solution of the current unit, and the above post-processing process is repeated for each unit to finally obtain the overall post-processing displacement solution of the linear algebraic equations. The present application solves the technical problem of low displacement accuracy in the relevant intrinsic hybrid finite element method.

The present invention relates to a quantum preprocessing method based on Schrödingerization. The method includes: performing finite element discretization of the BPX multilevel preprocessing on the partial differential equation to be solved, constructing a quantum block encoding corresponding to the preprocessing system to obtain a quantum preprocessed linear algebraic equation set; transforming the solution of the quantum preprocessed linear algebraic equation set into the solution of the steady state of a linear ordinary differential equation set; adopting Schrödingerization, and using the dimension elevation method to transform the linear ordinary differential equation set into a Hamiltonian system that can be calculated on a quantum computer; designing a quantum circuit diagram for the Hamiltonian system by using a quantum Hamiltonian simulation algorithm, and obtaining a simulation result by simulating the quantum circuit diagram on a quantum computer. The quantum preprocessing algorithm obtained by using Schrödingerization not only has an exponential acceleration advantage in terms of matrix order and accuracy, etc., but also eliminates the complexity influence brought by the condition number, and the algorithm is simple and efficient.

The invention discloses a lightweight design method of an ICA-R algorithm and related components, and relates to the field of signal processing. According to the method, prior information of a target signal is introduced to construct a reference signal, a separation vector is initialized based on a minimum mean square error criterion, iterative optimization of an ICA-R algorithm is realized on an FPGA, dependence on complex linear algebraic operations such as pseudo-inverse, matrix product and Cholesky decomposition is not needed, and occupation of computing resources and logic resources of the FPGA is reduced. Meanwhile, the initialization mode under the guidance of the prior information avoids the problem of local optimum caused by random initialization, and improves the precision and convergence speed of target signal extraction. Visibly, occupation of computing resources and logic resources of the FPGA can be reduced, the FPGA can extract the target signal from the observation signal more quickly, and the parallel processing advantage of the FPGA is combined, so that the signal processing capacity of the wireless communication equipment and the signal transmission reliability in a wireless communication scene are improved.

The invention provides an acoustic streaming coupling calculation method and device based on a Galbrun equation. The method provided by the invention comprises the steps of obtaining a Galbrun equation based on an Euler equation of ideal fluid under the condition of no external force and in combination with Euler disturbance, Lagrange disturbance and a mixed disturbance relation; the Galbrun equation represents the coupling effect of the flow field and the sound field; based on a Navier-Stokes equation, in combination with a k-epsilon turbulence model in the RANS model, solving to obtain flow field data of the non-uniform flow field; a perfect matching layer is introduced for sound wave propagation simulation of an unbounded region, and boundary conditions suitable for the Galbrun equation are constructed through geometric transformation, complex variable definition and coordinate transformation; and carrying out weak transformation on the Galbrun equation, embedding the boundary condition, combining the flow field data, carrying out discretization processing by adopting a triangular finite element, constructing a global linear algebraic equation set, and solving to obtain a discrete solution of sound field parameters.

The application discloses a kind of inland lake ecological water supplement amount prediction analysis method, comprising: obtaining the underwater topographic map of target lake, constructs the plane two-dimensional water flow movement basic equation of lake wind lake current and the plane two-dimensional water quality equation describing salt transport in lake conversion;Obtain the ecological water supplement flow and salt concentration of target lake, fit the plane two-dimensional water quality equation;To the finite difference discrete of continuity equation, momentum equation, the plane two-dimensional water flow movement basic equation is converted into linear algebra equation group;Linear algebra equation group is solved by ADI row-by-row method in time period, direction, and the water level, water depth and salt concentration of output prediction are exported;The water depth of each grid ecological water supplement is calculated, and then the comprehensive water depth of target lake ecological water supplement in future time is calculated, and the ecological water supplement amount of target lake prediction is obtained.

The utility model discloses an adjustable demonstration device based on linear algebra teaching, which comprises four suckers, a left sucker and a right sucker form a group, a first slide rail is fixedly arranged between each group of suckers, an auxiliary demonstration mechanism used for assisting a teacher in matrix writing is arranged on the outer side surface of the first slide rail, and the auxiliary demonstration mechanism is used for assisting the teacher in matrix writing. The auxiliary demonstration mechanism comprises a second sliding rail, a second sliding block 5 and a U-shaped writing frame, the second sliding rail is fixedly arranged between the first sliding blocks, and the outer side surface of the second sliding rail is movably sleeved with the second sliding block 5. According to the utility model, the teaching work of linear algebra is improved, when a teacher demonstrates addition and multiplication of a matrix, the device can be used for writing a regular matrix easily and quickly, wrong rows and columns are avoided, the aesthetic degree is improved, the teaching effect can be improved, and students are prevented from reading wrongly.

This invention relates to the field of capacitance calculation technology and discloses a fast algorithm for extracting parasitic capacitance in large-scale integrated circuits. This method combines the method of moments (MoM), a fast multipole algorithm for layered dielectrics, and overlapping region decomposition preprocessing techniques to construct a complete parasitic capacitance extraction solution. By directly introducing the Green's function for the layered dielectric, the numerical solution strictly satisfies the electric field transport conditions at the dielectric interface, and the electrostatic problem in the layered dielectric is transformed into boundary integral equations defined on the interconnect surface. Subsequently, the MoM is used to discretize these boundary integral equations, resulting in a large-scale dense system of linear algebraic equations. To improve solution efficiency, an efficient preprocessing strategy based on overlapping region decomposition is further designed, and combined with the matrix-free minimum residual iteration method and the layered fast multipole algorithm, achieving efficient solution with low computational and storage overhead.

Quantum-secure, multiparty computation enables the joint evaluation of multivariate functions across distributed users while ensuring the privacy of their local inputs. It uses a linear algebra engine that leverages the quantum nature of light for information-theoretically secure multiparty inference using telecommunication components. This linear algebra engine can perform deep learning inference with rigorous upper bounds on the information leakage of both the deep learning model weights and the client's data, enabling double-blind operations. Applied to the MNIST classification task, it performs with classification accuracies exceeding 95% and a leakage of less than 0.1 bit per weight and data symbols. This leakage is an order of magnitude below the minimum bit precision for accurate deep learning using state-of-the- art quantization techniques. Our quantum-secure, multiparty computation lays the foundation for practical quantum-secure computation and unlocks secure cloud deep learning.