18 results about "Linear algebra" patented technology

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 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 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 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.

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 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.

The invention discloses an asymmetric topological key manufacturing method based on an odd graceful topological coding graph. An asymmetric topological key is composed of two essentially different mathematical branches, namely a topological structure and a mathematical code. Wherein the theory of the topological structure is based on a graph theory and topology; the theory of mathematical coding is based on combinatorial mathematics, linear algebra, number theory, set theory, algebra, computer science and other subjects. Giving a coding mirror image from the odd topology to the odd topology, and a mirror image or inverse substitution operation from one odd topology (private key) to another odd topology (public key); establishing a odd extension graph group and a topological graph group signature thereof; a set ordered odd topology graph W-operation graph lattice is constructed by using topological coding point superposition operation and edge addition operation, and a topological graph lattice signature and infinite'one-time pad 'keys are obtained; a generic topological coding matrix and a Fibonacci key sequence are defined so as to be suitable for wider information security application scenarios.

The application discloses a special section stiffness accurate calculation method based on feature adaptive sampling and a general analytic operator, and comprises the following steps: feature adaptive sampling and data semanticization; solving of an explicit spline equation based on topological decoupling; normalized parameter mapping and coefficient vector construction; general analytic calculation based on polynomial algebra; global assembly and stiffness matrix generation; the method retains topological sharp points through feature semantic sampling, unifies an integral domain through a normalized parameter equation, and converts a calculus problem into a linear algebra problem through polynomial algebra operation, so that fast and accurate solving of special section stiffness characteristics is realized.

The invention provides a velocity body conversion method and device based on matrix calculation, a medium and equipment, and belongs to the field of seismic exploration. The method comprises the following steps: step 1, acquiring original velocity volume data; 2, generating an initial velocity model corresponding to the three-dimensional grid of the work area according to the original velocity volume data; 3, constructing a thinning matrix or an encryption matrix according to seismic data processing requirements; and 4, performing matrix calculation to obtain a converted velocity body. According to the method, aiming at the conversion problem of the geophysical velocity body, the velocity body data is effectively processed by constructing a specific thinning matrix and an encryption matrix by utilizing a linear algebraic principle so as to adapt to different resolution ratios and data processing requirements, the flexibility and efficiency of geophysical data processing are improved, and the speed body data processing efficiency is improved. The method is of great significance in improving the overall efficiency of seismic exploration.

The invention relates to the technical field of robot motion control and heterogeneous calculation acceleration, in particular to an optimal control Riccati equation solving method based on TPU heterogeneous parallelism, which is characterized in that heterogeneous division of labor is carried out on a host side and a TPU equipment side, the host side is only responsible for input issuing and result recovery, and the equipment side is used for managing and controlling an iterative process and operator scheduling by a coprocessor; the multiple neural network processing units execute intensive linear algebraic calculation in parallel; designing a general matrix multiplication parallel acceleration operator and a parallel Gaussian elimination inversion operator, optimizing a storage layout of an on-chip local memory and a working area reuse strategy, completing Riccati equation solution based on Hamiltonian matrix sign function iteration, recovering a stable solution matrix and calculating an optimal feedback gain; for a multi-independent system scene, a system dimension parallel or batch rotation strategy is adopted to improve the batch processing throughput rate. The method solves the problems that in the prior art, intermediate data carrying overhead is large, and parallel support of key links is insufficient.

This invention discloses a personalized webpage ranking method and system based on linear algebra. It represents the graph as an adjacency matrix and performs algebraic calculations, achieving good parallelism for efficient personalized webpage ranking. Specifically, it uses the original graph data corresponding to a set of webpages as the input webpage set, with the initial webpage set being a subset of the input webpage set. A graph adjacency matrix is ​​constructed based on the original graph data. The algebraic Trim-1 method is used on the graph adjacency matrix to discover strongly connected components with one node, and the adjacency matrix is ​​reconstructed to obtain a graph represented using the reconstructed adjacency matrix. An algebraic FW-BW algorithm based on algebraic breadth-first search is used to find the largest strongly connected component in the graph. An algebraic label propagation algorithm based on matrix multiplication is used to find strongly connected components in the graph represented using the adjacency matrix. The PM algorithm is used on the reconstructed directed acyclic graph to calculate personalized webpage rankings, indicating the degree of association between the webpage and the initial webpage set.

This invention discloses a method and system for monitoring the performance of nuclear power heat exchangers based on manifold learning. The method includes: calculating an isotropic adjacent data subset of high-dimensional process measurement data of the nuclear power heat exchanger based on the finite-time nearest neighbor algorithm; eliminating the isotropic global structure shared by multiple submanifolds in the adjacent data subset using the PCA algorithm to obtain the local coordinates of the adjacent data subset; transforming the local coordinates into normal vector space coordinates using discrete differential geometry theory; based on the normal vector space coordinates, performing discriminative optimization on the features using the LDA method to obtain the optimal projection matrix; and obtaining the dimensionality-reduced data according to the projection theory of linear algebra; inputting the dimensionality-reduced data into an SVM model to achieve fault classification and performance monitoring of the nuclear power heat exchanger's operating status. This invention can effectively discriminate and monitor the performance of nuclear power heat exchangers under multiple operating conditions, and has been verified using a condenser as an example.