COSOSIMO Parameter Definitions

EDM-Modal模态分析软件的SIMO正弦扫频模态测试包括专用测试设置和使用单个激振器输出正弦波以获取FRF信号的操作过程。

源输出类型为正弦扫频信号。

扫频模式可以是线性或对数的。

在定义的参考DOF的基础上，构建测量值DOF的FRF信号。

输出驱动量级可以设定以开环控制方式或闭环控制方式工作，闭环方式时可以指定某个通道的响应为控制反馈信号。

实验模态分析过程可与SIMO单输入多输出正弦扫频模态测试集成运行。

SIMO扫频正弦测试特点：①测试操作简单易用②测点/方向支持自动/手动遍历⑤一个扫正弦激励信号(参考信号) 激励输出量级可设定，并可以开环方式扫频，或闭环方式控制量级。

⑥线性、对数扫描模式比例滤波、RMS值、平均、峰值4种测量策略固定、可变比例跟踪滤波器,用户可定义带宽⑦用户可定义扫频方向，开始/结束频率，扫描频速度★EDM Modal模态支持的功能如下：①几何模型的创建/编辑/导入/导出/动画。

②工作变形分析(ODS)③锤击法模态实验④SIMO与MIMO FRF模态测试⑤SIMO正弦扫频模态测试⑥SIMO与MIMO步进正弦模态测试⑦工作模态测试，SSI模态识别算法⑧多参考点模态分析Poly-X (p-LSCF) 模态分析杭州锐达数字技术有限公司是美国晶钻仪器公司中国总代理，专注于振动控制、数据采集、模态分析、动态信号分析、故障诊断、综合环境测试领域，产品包括手持一体化动态信号分析仪、多通道动态数据采集系统、振动控制系统、多轴振动控制系统、三综合试验系统和远程状态监测系统，解决方案包括NVH测试、新能源电池测试、结构模态分析、故障诊断监测、机械性能测试、转子动力学测试、疲劳可靠性测试、综合环境测试。

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Comsol 内置表达式：参数、变量、函数
表达式：
参数
一个参数表达式可以包含:数字、参数、常量、函数,一元、二元操作符。

参数可以有单位。

变量
个变量表达式可以包含:数字、参数、常量、变量、函数的变量表达式,一元、二元操作符。

变量可以有单位。

函数
一个函数定义可以包含:输入参数、数字参数,=常数、函数的参数表达式包括输入参数,一元和二元操作符。

注：保留函数的名称可以被用于变量和参数名，反之同样。

内置的数学常数
内置的物理常数
变量：主要有两种类型变量：内部保留变量和用户自定义变量，变量可以是标量也可以是字段，可以有单位。

有一组有趣的变量，即空间坐标变量和因变量，这些基于空间维度和所选物理场的变量有默认的名称，comsol会创建一张变量表来表示这些变量。

内置变量
T表示2D空间维度时的温度，按时间传热的模型。

X、Y是空间坐标的名称。

所以可以生产下列变量：Tx、Ty、Txx、Txy
Tyx、Tyy、Tt、Txt、Tyt、Txxt、Txyt、Tyxt、Tyyt、Ttt、Txtt、Tytt、Txxtt、Txytt、Tyxtt、Tyytt.其中Tx是T对x的导数，Ttt是T对t的二阶导数，如果空间坐标系有其他的名字，同理置换相应变量。

内置数字函数
acosh,acoth,acsch,asech,asinh,atanh,besselj,bessely,besseli,besselk,
erf,gamma,和psi。

内置操作函数：
这些内置的函数不同于内置的数学函数，详细见用户指南。

TimeCOS_SIM标准指令参考手册TimeCOS/SIMV1.12003/3/TimeCOS/SIM Manual 10-6-29WWWTIMECOS/SIM GSM11.11 PHASE2 ......................................................... 6 1. CHANGE CHV .................................................................... ................................... 6 1). 定义和范围 ..................................................................... ........................................................... 6 2). 命令报文 ..................................................................... ............................................................... 6 3). 命令报文数据域 ..................................................................... (7)4). 响应报文数据域 ..................................................................... (7)5). 响应报文状态码 ..................................................................... (7)2. DISABLECHVCHV ................................................................. ................................. 8 1). 定义和范围 ..................................................................... ........................................................... 8 2). 命令报文 ..................................................................... ............................................................... 8 3). 命令报文数据域 ..................................................................... (8)4). 响应报文数据域 ..................................................................... (9)5). 响应报文状态码 ..................................................................... (9)3. ENABLECHVCHV ................................................................. ................................ 10 1). 定义和范围 ..................................................................... ......................................................... 10 2). 命令报文 ..................................................................... ............................................................. 10 3). 命令报文数据域 ..................................................................... . (10)4). 响应报文数据域 ..................................................................... . (11)5). 响应报文状态码 ..................................................................... . (11)4. GETRESPONSE() ............................................................. ...................................... 12 1). 定义和范围 ..................................................................... ......................................................... 12 2). 命令报文 ..................................................................... ............................................................. 12 3). 命令报文数据域 ..................................................................... . (12)4). 响应报文数据域 ..................................................................... . (12)5). 响应报文状态码 ..................................................................... . (12)5.INCREASE ............................................................... ..................................................... 14 1). 定义和范围 ..................................................................... ......................................................... 14 2). 命令报文 ..................................................................... ............................................................. 14 3). 命令报文数据域 ..................................................................... . (14)4). 响应报文数据域 ..................................................................... . (14)2TimeCOS/SIM Manual 10-6-29WWW5). 响应报文状态码 ..................................................................... . (14)6.INVALIDATE ............................................................. ...................................... 16 1). 定义和范围 ..................................................................... ......................................................... 16 2). 命令报文 ..................................................................... ............................................................. 16 3). 命令报文数据域 ..................................................................... . (16)4). 响应报文数据域 ..................................................................... . (16)5). 响应报文状态码 ..................................................................... . (16)7. READBINARY ................................................................. ........................... 18 1). 定义和范围 ..................................................................... ......................................................... 18 2). 命令报文 ..................................................................... ............................................................. 18 3). 命令报文数据域 ..................................................................... . (18)4). 响应报文数据域 ..................................................................... . (18)5). 响应报文状态码 ..................................................................... . (18)8. READRECORD ................................................................. ............................. 20 1). 定义和范围 ..................................................................... ......................................................... 20 2). 命令报文 ..................................................................... ............................................................. 20 3). 命令报文数据域 ..................................................................... . (20)4). 响应报文数据域 ..................................................................... . (21)5). 响应报文状态码 ..................................................................... . (21)9.REHABILITATE ........................................................... .................................. 22 1). 定义和范围 ..................................................................... ......................................................... 22 2). 命令报文 ..................................................................... ............................................................. 22 3). 命令报文数据域 ..................................................................... . (22)4). 响应报文数据域 ..................................................................... . (22)5). 响应报文状态码 ..................................................................... . (22)10. RUN GSMALGORITHMGSM ........................................................... ..................... 24 1). 定义和范围 ..................................................................... ......................................................... 24 2). 命令报文 ..................................................................... ............................................................. 24 3). 命令报文数据域 ..................................................................... . (24)4). 响应报文数据域 ..................................................................... . (24)5). 响应报文状态码 ..................................................................... . (24)11. SEEK.................................................................... ................................................ 26 1). 定义和范围 ..................................................................... ......................................................... 26 2). 命令报文 ..................................................................... . (26)3TimeCOS/SIM Manual 10-6-29WWW3). 命令报文数据域 ..................................................................... . (27)4). 响应报文数据域 ..................................................................... . (27)5). 响应报文状态码 ..................................................................... . (27)12. SELECTFILE ................................................................... ................................. 28 1). 定义和范围 ..................................................................... ......................................................... 28 2). 命令报文 ..................................................................... ............................................................. 28 3). 命令报文数据域 ..................................................................... . (28)4). 响应报文数据域 ..................................................................... . (28)5). 响应报文状态码 ..................................................................... . (31)13.SLEEP .......................................................................................................................... 32 1). 定义和范围 ..................................................................... ......................................................... 32 2). 命令报文 ..................................................................... ............................................................. 32 3). 命令报文数据域 ..................................................................... . (32)4). 响应报文数据域 ..................................................................... . (32)5). 响应报文状态码 ..................................................................... . (32)14.STATUS ................................................................. ................................. 34 1). 定义和范围 ..................................................................... ......................................................... 34 2). 命令报文 ..................................................................... ............................................................. 34 3). 命令报文数据域 ..................................................................... . (34)4). 响应报文数据域 ..................................................................... . (34)5). 响应报文状态码 ..................................................................... . (34)15. UNBLOCKCHV .................................................................... ............................ 36 1). 定义和范围 ..................................................................... ......................................................... 36 2). 命令报文 ..................................................................... ............................................................. 36 3). 命令报文数据域 ..................................................................... . (36)4). 响应报文数据域 ..................................................................... . (36)5). 响应报文状态码 ..................................................................... . (37)16. UPDATEBINARY ..................................................................................... 38 1). 定义和范围 ..................................................................... ......................................................... 38 2). 命令报文 ..................................................................... ............................................................. 38 3). 命令报文数据域 ..................................................................... . (38)4). 响应报文数据域 ..................................................................... . (38)5). 响应报文状态码 ..................................................................... . (38)17. UPDATERECORD ................................................................. . (40)4TimeCOS/SIM Manual 10-6-29WWW1). 定义和范围 ..................................................................... (40)2). 命令报文 ..................................................................... . (40)3). 命令报文数据域 ..................................................................... . (41)4). 响应报文数据域 ..................................................................... . (41)5). 响应报文状态码 ..................................................................... . (41)18. VERIFYCHV .................................................................... . (42)1). 定义和范围 ..................................................................... (42)2). 命令报文 ..................................................................... . (42)3). 命令报文数据域 ..................................................................... . (42)4). 响应报文数据域 ..................................................................... . (42)5). 响应报文状态码 ..................................................................... . (43)5TimeCOS/SIM Manual 10-6-29WWWTimeCOS/SIM GSM11.11 PHASE 2 1. CHANGE CHV1). 定义和范围CHANGE CHV（Card Holder Verification information）命令用于修改持卡人口令，并将安全状态寄存器设置成相应的值。

算符 d(f,x)f 对x 方向的微分1. 使用d 算符来计算一个变量对另一个变量的导数，如：d(T,x)指变量T 对x 求导,而d(u^2,u)=2*u 等；2. 如果模型中含有任何独立变量，建模中使用d 算符会使模型变为非线性；3. 在解的后处理上使用d 算符，可以使用一些预置的变量，如：uxx,d(ux,x),d(d(u,x),x)都是等效的；4. pd 算符与d 算符类似，但对独立变量不使用链式法则；5. d(E,TIME)求解表达式E 的时间导数；6. dtang 算符可以计算表达式在边界上的切向微分（d 算符无法计算），在求解域上使用dtang 等价于d ，dtang 只求解对坐标变量的微分，但需要注意的是并不是所有的量都有切向微分。

pd(f,x)f 对x 方向的微分 pd 和d 的区别：d(u+x,x)=ux+1，d(u,t)=ut ，u 和x,t 等有关pd(u+x,x)=1，pd(u,t)=0，u 是独立的和x,t 无关dtang(f,x)边界上f 对x 的切向微分在边界上d(u,x)不能定义，但是可以使用dtang(u,x)，dtang 付出基本的微分法则，如乘积法则和链式法则，但是需要指出的是，dtang(x,x)不一定等于1。

test(expr)试函数用于方程弱形式的算符，test(F(u,∇u))等价于：var(expr,fieldnam e1,fieldname2, ...)变异算子用于弱形式，它和test 算符功能相同，但是仅用于某些特定的场中； 如var(F(u,∇u, v,∇v),a)，变量u 是a 场的变量，而v 不是。

试函数之只作用于变量u 。

nojac(expr)对Jacobian 矩阵没有贡献将表达式排除在Jacobian 计算外，这对那些对Jacobian 贡献不大，但是计算消耗很大的变量是否有效；k -e 湍流模型就是利用 nojac 算符来提高计算性能的例子。

Gauss6.0软件程序函数大全一、数学函数1、科学函数abs Returns absolute value of argument.arccos Computes inverse cosine.arcsin Computes inverse sine.atan Computes inverse tangent.atan2Computes angle given a point x,y.besselj Computes Bessel function, first kind.bessely Computes Bessel function, second kind.boxcox Computes the Box-Cox function.cos Computes cosine.cosh Computes hyperbolic cosine.curve Computes a one-dimensional smoothing curve.digamma Computes the digamma function.exp Computes the exponential function of x.fmod Computes the floating-point remainder of x/y.gamma Computes gamma function value.ln Computes the natural log of each element.lnfact Computes natural log of factorial function.log Computes the log10 of each element.mbesseli Computes modified and exponentially scaled modified Bessels of the first kind of the n th order.Returns allowable matrix dimensions for computing FFT’s.nextn,nextnevnoptn, optnevn Returns optimal matrix dimensions for computing FFT’s.pi Returns .polar Graphs data using polar coordinates.sin Computes sine.sinh Computes the hyperbolic sine.spline Computes a two-dimensional interpolatory spline.spline1D Computes a smoothing spline for a curve.spline2D Computes a smoothing spline for a surface.sqrt Computes the square root of each element.tan Computes tangent.tanh Computes hyperbolic tangenttocart Converts from polar to cartesian coordinates.topolar Converts from cartesian to polar coordinates.trigamma Computes trigamma function.All trigonometric functions take or return values in radian units.2、微分与积分函数Computes numerical gradient.gradMTgradMTm Computes numerical gradient with mask.gradp Computes first derivative of a function.hessMT Computes numerical Hessian.hessMTg Computes numerical Hessian using gradient procedure. hessMTgw Computes numerical Hessian using gradient procedure with weights. hessMTm Computes numerical Hessian with mask.hessMTmw Computes numerical Hessian with mask and weights.hessMTw Computes numerical Hessian with weights.hessp Computes second derivative of a function.intgrat2Integrates a 2-dimensional function over a user-defined region. intgrat3Integrates a 3-dimensional function over a user-defined region. intquad1Integrates a 1-dimensional function.intquad2Integrates a 2-dimensional function over a user-defined rectangular region.intquad3Integrates a 3-dimensional function over a user-defined rectangular region.intsimp Integrates by Simpson’s metho d.gradp and hessp use a finite difference approximation to compute the first and second derivatives. Use gradp to calculate a Jacobian.intquad1, intquad2, and intquad3 use Gaussian quadrature to calculate the integral of the user-defined function over a rectangular region.To calculate an integral over a region defined by functions of x and y, use intgrat2 and intgrat3.To get a greater degree of accuracy than that provided by intquad1, use intsimp for 1-dimensional integration.3、线性代数函数Balances a matrix.balancechol Computes Cholesky decomposition, X = Y Y.choldn Performs Cholesky downdate on an upper triangular matrix. cholsol Solves a system of equations given the Cholesky factorization of a matrix.cholup Performs Cholesky update on an upper triangular matrix.cond Computes condition number of a matrix.conj Returns the complex conjugate of a matrix.crout Computes Crout decomposition, X = LU (real matrices only). croutp Computes Crout decomposition with row pivoting (real matrices only).det Computes determinant of square matrix.detl Computes determinant of decomposed matrix.eigcg Computes the eigenvalues of a complex, general matrix. (Included for backwards compatibility — use eig instead.)eigcg2Computes eigenvalues and eigenvectors of a complex, generalmatrix. (Included for backwards compatibility — use eigv instead.) eigch Computes the eigenvalues of a complex, hermitian matrix. (Included for backwards compatibility — use eigh instead.)eigch2Computes eigenvalues and eigenvectors of a complex, hermitian matrix. (Included for backwards compatibility — use eighvinstead.)eigrg Computes the eigenvalues of a real, general matrix. (Included for backwards compatibility — use eig instead.)eigrg2Computes eigenvalues and eigenvectors of a real, general matrix.(Included for backwards compatibility — use eigv instead.)eigrs Computes the eigenvalues of a real, symmetric matrix. (Included for backwards compatibility — use eigh instead.)eigrs2Computes eigenvalues and eigenvectors of a real, symmetric matrix.(Included for backwards compatibility — use eighv instead.)hess Computes upper Hessenberg form of a matrix (real matrices only).inv Inverts a matrix.invpd Inverts a positive definite matrix.invswp Generalized sweep inverse.lapeighb Computes eigenvalues only of a real symmetric or complexHermitian matrix selected by bounds.lapeighi Computes eigenvalues only of a real symmetric or complexHermitian matrix selected by index.lapeighvb Computes eigenvalues and eigenvectors of a real symmetric orcomplex Hermitian matrix selected by bounds.lapeighvi Computes selected eigenvalues and eigenvectors of a real symmetric or complex Hermitian matrix.lapgeig Computes generalized eigenvalues for a pair of real or complexgeneral matrices.lapgeigh Computes generalized eigenvalues for a pair of real symmetric or Hermitian matrices.lapgeighv Computes generalized eigenvalues and eigenvectors for a pair of real symmetric or Hermitian matrices.lapgeigv Computes generalized eigenvalues, left eigenvectors, and righteigenvectors for a pair of real or complex general matrices.lapgsvds Compute the generalized singular value decomposition of a pair of real or complex general matrices.lapgsvdcst Compute the generalized singular value decomposition of a pair of real or complex general matrices.lapgsvdst Compute the generalized singular value decomposition of a pair of real or complex general matrices.lapschur Compute the generalized Schur form of a pair of real or complex general matrices.lapsvdcusv Computes the singular value decomposition a real or complexrectangular matrix, returns compact u and v.lapsvds Computes the singular values of a real or complex rectangular matrixlapsvdusv Computes the singular value decomposition a real or complexrectangular matrix.lu Computes LU decomposition with row pivoting (real and complex matrices).null Computes orthonormal basis for right null space.null1Computes orthonormal basis for right null space.orth Computes orthonormal basis for column space x.pinv Generalized pseudo-inverse: Moore-Penrose.polymroot Computes the roots of the determinant of a matrix polynomialqqr QR decomposition: returns Q1 and R.qqre QR decomposition: returns Q1, R, and a permutation vector, E.qqrep QR decomposition with pivot control: returns Q1, R, and E.qr QR decomposition: returns R.qre QR decomposition: returns R and E.qrep QR decomposition with pivot control: returns R and E.qrsol Solves a system of equations Rx=b given an upper triangular matrix, typically the R matrix from a QR decomposition.qrtsolSolves a system of equations given an upper triangularmatrix, typically the R matrix from a QR decomposition.qtyrQR decomposition: returns and R.qtyreQR decomposition: returns , R, and E.qtyrepQR decomposition with pivot control: returns , R, and E.qyr QR decomposition: returns QY and R.qyre QR decomposition: returns QY, R, and E.qyrep QR decomposition with pivot control: returns QY, R, and E.rank Computes rank of a matrix.rcondl Returns reciprocal of the condition number of last decomposedmatrix.rref Computes reduced row echelon form of a matrix.schur Computes Schur decomposition of a matrix (real matrices only).solpd Solves a system of positive definite linear equations.schtoc To reduce any 2x2 blocks on the diagional of the real Schur matrix returned from schur. The transformation matrix is also updated.svd Computes the singular values of a matrix.svd1Computes singular value decomposition, .svd2Computes svd1 with compact U.svdcusv Computes the singular value decomposition of a matrix so that:x = u * s * v' (compact u).svds Computes the singular values of a matrix.svdusv Computes the singular value decomposition of a matrix so that:x = u * s * v'.The decomposition routines are chol for Cholesky decomposition, crout and croutp for Crout decomposition, qqr-qyrep for QR decomposition, and svd, svd1, and svd2 for singular value decomposition.null, null1, and orth calculate orthonormal bases.inv, invpd, solpd, cholsol, qrsol, and the “/” operator can all be used to solve linear systems of equations.rank and rref will find the rank and reduced row echelon form of a matrix.det, detl, and cond will calculate the determinant and condition number of a matrix.4、特征值函数Computes eigenvalues of general matrix.eigeigh Computes eigenvalues of complex Hermitian or real symmetricmatrix.eighv Computes eigenvalues and eigenvectors of complex Hermitian or real symmetric matrix.eigv Computes eigenvalues and eigenvectors of general matrix.There are four eigenvalue-eigenvector routines. Two calculate eigenvalues only, and two calculate eigenvalues and eigenvectors. The types of matrices handled by these routines are:General: eig, eigvSymmetric or Hermitian: eigh, eighv5、多项式运算Computes characteristic polynomial of a square matrix.polycharpolyeval Evaluates polynomial with given coefficients.polyint Calculates N th order polynomial interpolation given known point pairs.polymake Computes polynomial coefficients from roots.polymat Returns sequence powers of a matrix.polymult Multiplies two polynomials together.polyroot Computes roots of polynomial from coefficients.See also recserrc, recsercp, and conv.6、傅立叶变换函数Computes discrete 1-D FFT.dfftdffti Computes inverse discrete 1-D FFT.fft Computes 1- or 2-D FFT.ffti Computes inverse 1- or 2-D FFT.fftm Computes multi-dimensional FFT.fftmi Computes inverse multi-dimensional FFT.fftn Computes 1- or 2-D FFT using prime factor algorithm.rfft Computes real 1- or 2-D FFT.rffti Computes inverse real 1- or 2-D FFT.rfftip Computes inverse real 1- or 2-D FFT from packed format FFT. rfftn Computes real 1- or 2-D FFT using prime factor algorithm.rfftnp Computes real 1- or 2-D FFT using prime factor algorithm, returns packed format FFT.rfftp Computes real 1- or 2-D FFT, returns packed format FFT.7、随机数函数Computes random numbers with beta distribution.rndbetarndcon Changes constant of the LC random number generator.rndgam Computes random numbers with gamma distribution.rndi Returns random integers, 0 <= y < 2^32.rndKMbeta Computes beta pseudo-random numbers.rndKMgam Computes gamma pseudo-random numbers.rndKMi Returns random integers, 0 <= y < 2^32.rndKMn Computes standard normal pseudo-random numbers. rndKMnb Computes negative binomial pseudo-random numbers. rndKMp Computes Poisson pseudo-random numbers.rndKMu Computes uniform pseudo-random numbers.rndKMvm Computes von Mises pseudo-random numbers.rndLCbeta Computes beta pseudo-random numbers.rndLCgam Computes gamma pseudo-random numbers.rndLCi Returns random integers, 0 <= y < 2^32.rndLCn Computres standard normal pseudo-random numbers. rndLCnb Computes negative binomial pseudo-random numbers.rndLCp Computes Poisson pseudo-random numbers.rndLCu Computes uniform pseudo-random numbers.rndLCvm Computes von Mises pseudo-random numbers.rndmult Changes multiplier of the LC random number generator.rndn Computes random numbers with Normal distribution.rndnb Computes random numbers with negative binomial distribution. rndp Computes random numbers with Poisson distribution. rndseed Changes seed of the LC random number generator.rndu Computes random numbers with uniform distribution.8、模糊条件函数Fuzzy .==dotfeqdotfge Fuzzy .>=dotfgt Fuzzy .>dotfle Fuzzy .<=dotflt Fuzzy .<dotfne Fuzzy ./=feq Fuzzy ==fge Fuzzy >=fgt Fuzzy >fle Fuzzy <=flt Fuzzy <fne Fuzzy /=The global variable _fcomptol controls the tolerance used for comparison. By default, this is 1e-15. The default can be changed by editing the filefcompare.dec.9、统计函数acf Computes sample autocorrelations.combinate Computes combinations of n things taken k at a time.combinated Writes combinations of n things taken k at a time to a GAUSSdata set.conv Computes convolution of two vectors.corrm Computes correlation matrix of a moment matrix.corrvc Computes correlation matrix from a variance-covariancematrix.corrx Computes correlation matrix.crossprd Computes cross product.design Creates a design matrix of 0’s and 1’s.dstat Computes descriptive statistics of a data set or matrix.loess Computes coefficients of locally weighted regression.meanc Computes mean value of each column of a matrix.median Computes medians of the columns of a matrix.momentComputes moment matrixmissing values.momentd Computes moment matrix from a data set.movingave Computes moving average of a series.movingaveExpwgt Computes exponentially weighted moving average of a series. movingaveWgt computes weighted moving average of a series numCombinations Computes number of combinations of N things taken K at atime.ols Computes least squares regression of data set or matrix. olsqr Computes OLS coefficients using QR decomposition.olsqr2Computes OLS coefficients, residuals, and predicted valuesusing QR decomposition.pacf Computes sample partial autocorrelations.princomp Computes principal components of a data matrix.quantile Computes quantiles from data in a matrix, given specifiedprobabilities.quantiled Computes quantiles from data in a data set, given specifiedprobabilities.rndvm Computes von Mises pseudo-random numbers.stdc Computes standard deviation of the columns of a matrix. toeplitz Computes Toeplitz matrix from column vector.varmall Computes the log-likelihood of a Vector ARMA model. varmares Computes the residuals of a Vector ARMA model.vcm Computes a variance-covariance matrix from a momentmatrix.vcx Computes a variance-covariance matrix from a data matrix. Advanced statistics and optimization routines are available in the GAUSS Applications programs. (Contact Aptech Systems for more information.)10、优化与求解函数eqsolve Solves a system of nonlinear equations. eqSolvemt Solves a system of nonlinear equations.eqSolvemtControlCreate Creates default eqSolvemtControlstructure.eqSolvemtOutCreate Creates default eqSolvemtOut structure.eqSolveset Sets global input used by eqSolve to defaultvalues.linsolve Solves Ax = b using the inverse function.ltrisol Computes the solution of Lx = b where L is alower triangular matrix.lusol Computes the solution of LUx = b where L is alower triangular matrix and U is an uppertriangular matrix.QNewton Optimizes a function using the BFGS descentalgorithm.QNewtonmt Minimize an arbitrary function.QNewtonmtControlCreate Creates default QNewtonmtControl structure.QNewtonmtOutCreate Creates default QNewtonmtOut structure. QProg Solves the quadratic programming problem.sqpSolve Solves the nonlinear programming problemusing a sequential quadratic programmingmethod.sqpSolveMT Solve the nonlinear programming problem.sqpSolveMTcontrolCreate Creates an instance of a structure of typesqpSolveMTcontrol set to default values.sqpSolveMTlagrangeCreate Creates an instance of a structure of typesqpSolveMTlagrange set to default values.sqpSolveMToutCreate Creates an instance of a structure of typesqpSolveMTout set to default values.utrisolComputes the solution of where U isan upper triangular matrix.11、统计分布函数Computes integral of beta function.cdfbetacdfbvn Computes lower tail of bivariate Normal cdf.cdfbvn2Returns cdfbvn of a bounded rectangle.cdfbvn2e Returns cdfbvn of a bounded rectangle.cdfchicComputes complement of cdf of 2.cdfchiiComputes 2 abscissae values given probability and degrees offreedom.cdfchincComputes integral of noncentral 2.cdffc Computes complement of cdf of F.cdffnc Computes integral of noncentral F.cdfgamComputes integral of incomplete function.cdfmvn Computes multivariate Normal cdf.cdfn Computes integral of Normal distribution: lower tail, or cdf.cdfn2Computes interval of Normal cdf.cdfnc Computes complement of cdf of Normal distribution (upper tail). cdfni Computes the inverse of the cdf of the Normal distribution.cdftc Computes complement of cdf of t-distribution.cdftnc Computes integral of noncentral t-distribution.cdftvn Computes lower tail of trivariate Normal cdf.erf Computes Gaussian error function.erfc Computes complement of Gaussian error function.lncdfbvn Computes natural log of bivariate Normal cdf.lncdfbvn2Returns log of cdfbvn of a bounded rectangle.lncdfmvn Computes natural log of multivariate Normal cdf.lncdfn Computes natural log of Normal cdf.lncdfn2Computes natural log of interval of Normal cdf.lncdfnc Computes natural log of complement of Normal cdf.lnpdfmvn Computes multivariate Normal log-probabilities.lnpdfmvt Computes multivariate Student’s t log-probabilities.lnpdfn Computes Normal log-probabilities.lnpdft Computes Student’s t log-probabilities.pdfn Computes standard Normal probability density function.12、序列函数Computes autoregressive recursive series.recserarrecsercp Computes recursive series involving products.recserrc Computes recursive series involving division.seqa Creates an additive sequence.seqm Creates a multiplicative sequence.13、精度控制函数Converts number to x.xxx and a power of 10.base10ceilRounds up towards + .floorRounds down towards - .machEpsilon Returns the smallest number such that 1+ eps > 1.prcsn Sets computational precision for matrix operations.round Rounds to the nearest integer.trunc Truncates toward 0.All calculations in GAUSS are done in double precision, with the exception of some of the intrinsic functions on OS/2 and DOS. These may use extended precision (18-19 digits of accuracy). Use prcsn to change the internal accuracy used in these cases. round, trunc, ceil, and floor convert floating point numbers into integers. The internal representation for the converted integer is double precision (64 bits).Each matrix element in memory requires 8 bytes of memory.14、财务函数AmericanBinomCall American binomial method Call. AmericanBinomCall_Greeks American binomial method call Delta, Gamma,Theta, Vega, and Rho.AmericanBinomCall_ImpVol Implied volatilities for American binomialmethod calls.AmericanBinomPut American binomial method Put. AmericanBinomPut_Greeks American binomial method put Delta, Gamma,Theta, Vega, and Rho.AmericanBinomPut_ImpVol Implied volatilities for American binomialmethod puts.AmericanBSCall American Black and Scholes Call. AmericanBSCall_Greeks American Black and Scholes call Delta,Gamma, Omega, Theta, and Vega. AmericanBSCall_ImpVol Implied volatilities for American Black andScholes calls.AmericanBSPut American Black and Scholes Put. AmericanBSPut_Greeks American Black and Scholes put Delta, Gamma,Omega, Theta, and Vega.AmericanBSPut_ImpVol Implied volatilities for American Black andScholes puts.annualTradingDays Compute number of trading days in a givenyear.elapsedTradingDays Compute number of trading days between twodates inclusively.EuropeanBinomCall European binomial method call.EuropeanBinomCall_Greeks European binomial method call Delta, Gamma,Theta, Vega and Rho.EuropeanBinomCall_ImpVol Implied volatilities for European binomialmethod calls.EuropeanBinomPut European binomial method Put.EuropeanBinomPut_Greeks European binomial method put Delta, Gamma,Theta, Vega, and Rho.EuropeanBinomPut_ImpVol Implied volatilities for European binomialmethod puts.EuropeanBSCall European Black and Scholes Call.EuropeanBSCall_Greeks European Black and Scholes call Delta, Gamma,Omega, Theta, and Vega.EuropeanBSCall_ImpVol Implied volatilities for European Black andScholes calls.EuropeanBSPut European Black and Scholes Put.EuropeanBSPut_Greeks European Black and Scholes put Delta, Gamma,Omega, Theta, and Vega.EuropeanBSPut_ImpVol Implied volatilities for European Black andScholes puts.getNextTradingDay Returns the next trading day. getNextWeekDay Returns the next day that is not on a weekend. getPreviousTradingDay Returns the previous trading day.getPreviousWeekDay Returns the previous day that is not on aweekend.二、矩阵处理函数1、向量和矩阵创建函数aeye Creates an N-dimensional array in which the planes described by the two trailing dimensions of the array are equal to the identity.eye Creates identity matrix.let Creates matrix from list of constants. matalloc Allocates a matrix with unspecified contents.matinit Allocates a matrix with unspecified contents.ones Creates a matrix of ones.zeros Creates a matrix of zeros.Use zeros or ones to create a constant vector or matrix.medit is a full-screen editor that can be used to create matrices to be stored in memory, or to edit matrices that already exist.Matrices can also be loaded from an ASCII file, from a GAUSS matrix file, or from a GAUSS data set. (See “Procedures and Keywords” in the User Guide for more information.)2、矩阵载入存储函数load,loadf,loadkLoads from a disk file.loadd Loads matrix from data set.loadm Loads matrix from ASCII or matrix file.save Saves matrix to matrix file.saved Saves matrix to data set.3、矩阵大小、秩和范围函数amax Moves across one dimension of an N-dimensional array and finds the largest element.amin Moves across one dimension of an N-dimensional array and finds the smallest element.cols Returns number of columns in a matrix.colsf Returns number of columns in an open data set.counts Returns number of elements of a vector falling in specified ranges.countwts Returns weighted count of elements of a vector falling in specified ranges.cumprodc Computes cumulative products of each column of a matrix. cumsumc Computes cumulative sums of each column of a matrix.indexcat Returns indices of elements falling within a specified range.maxc Returns largest element in each column of a matrix.maxindc Returns row number of largest element in each column of a matrix.minc Returns smallest element in each column of a matrix.minindc Returns row number of smallest element in each column of a matrix.prodc Computes the product of each column of a matrix.rankindx Returns rank index of N x1 vector. (Rank order of elements in vector.) rows Returns number of rows in a matrix.rowsf Returns number of rows in an open data set.sumc Computes the sum of each column of a matrix.sumr Computes sum of rows of matrix or rows of the last two dimensions of an L-dimensional array.These functions are used to find the minimum, maximum and frequency counts of elements in matrices.Use rows and cols to find the number of rows or columns in a matrix. Use rowsf and colsf to find the numbers of rows or columns in an open GAUSS data set.4、稀疏矩阵函数band Extracts bands from a symmetric banded matrix.bandchol Computes the Cholesky decomposition of a positive definitebanded matrix.bandcholsol Solves the system of equations Ax = b for x, given the lowertriangle of the Cholesky decomposition of a positive definitebanded matrix A.bandltsol Solves the system of equations Ax = b for x, where A is a lowertriangular banded matrix.bandrv Creates a symmetric banded matrix, given its compact form.bandsolpd Solves the system of equations Ax = b for x, where A is a positive definite banded matrix.denseSubmat Returns dense submatrix of sparse matrix.isSparse Tests whether a matrix is a sparse matrix.sparseCols Returns number of columns in sparse matrix.sparseEye Creates sparse identity matrix.sparseFD Converts dense matrix to sparse matrix.sparseFP Converts packed matrix to sparse matrix.sparseHConcat Horizontally concatenates sparse matrices.sparseNZE Returns the number of nonzero elements in sparse matrix. sparseOnes Generates sparse matrix of ones and zeros.sparseRows Returns number of rows in sparse matrix.sparseSet Resets sparse library globals.sparseSolve Solves Ax = B for x where A is a sparse matrix. sparseSubmat Returns sparse submatrix of sparse matrix. sparseTD Multiplies sparse matrix by dense matrix. sparseTrTD Multiplies sparse matrix transposed by dense matrix. sparseVConcat Vertically concatenates sparse matrices.5、各种矩阵处理函数amult Performs matrix multiplication on the planes described by the two trailing dimensions of N-dimensional arrays.complex Creates a complex matrix from two real matrices.delif Deletes rows from a matrix using a logical expression.diag Extracts the diagonal of a matrix.diagrv Puts a column vector into the diagonal of a matrix.exctsmpl Creates a random subsample of data set, with replacement.imag Returns the imaginary part of a complex matrix.indcv Checks one character vector against another and returns the indices of the elements of the first vector in the second vector.indnv Checks one numeric vector against another and returns the indices of the elements of the first vector in the second vector.indsav Checks one string array against another and returns the indices of the first string array in the second string array.intrsect Returns the intersection of two vectors.lowmat Returns the main diagonal and lower triangle.lowmat1Returns a main diagonal of 1’s and the lower triangle.real Returns the real part of a complex matrix.reshape Reshapes a matrix to new dimensions.rev Reverses the order of rows of a matrix.rotater Rotates the rows of a matrix, wrapping elements as necessary.selif Selects rows from a matrix using a logical expression.setdif Returns elements of one vector that are not in another.shiftr Shifts rows of a matrix, filling in holes with a specified value.submat Extracts a submatrix from a matrix.subvec Extracts an N x1 vector of elements from an N x K matrix.trimr Trims rows from top or bottom of a matrix.union Returns the union of two vectors.upmat Returns the main diagonal and upper triangle.upmat1Returns a main diagonal of 1’s and the upper triangle.vec Stacks columns of a matrix to form a single column.vech Reshapes the lower triangular portion of a symmetric matrix into a column vector.vecr Stacks rows of a matrix to form a single column.vget Extracts a matrix or string from a data buffer constructed with vput. vlist Lists the contents of a data buffer constructed with vput.vnamecv Returns the names of the elements of a data buffer constructed with vput.vput Inserts a matrix or string into a data buffer.vread Reads a string or matrix from a data buffer constructed with vput.vtypecv Returns the types of the elements of a data buffer constructed with vput.xpnd Expands a column vector into a symmetric matrix.vech and xpnd are complementary functions. vech provides an efficient way to store a symmetric matrix; xpnd expands the stored vector back to its original symmetric matrix.delif and selif are complementary functions. delif deletes rows of a matrix based on a logical comparison; selif selects rows based on a logical comparison. lowmat, lowmat1, upmat, and upmat1 extract triangular portions of a matrix. To delete rows that contain missing values from a matrix in memory, see packr. 6、矩阵结构函数dsCreate Creates an instance of a structure of type DS set to defaultvalues.loadstruct Loads a structure into memory from a file on the disk.pvCreate Returns an initialized an instance of structure of type PV.pvGetIndex Gets row indices of a matrix in a parameter vector.pvGetParNames Generates names for parameter vector stored in structure oftype PV.。

COMSOL_Multiphysics中各常⽤内置参量Summary of Built-In Variables With Reserved NamesThis section is an overview of the built-in elements of the following categories as defined by the underlying COMSOL language:C onstantsV ariablesF unctionsThese language elements are built-in or user-defined. In addition there are operators that cannot be user-defined, and expressions, which are always user-defined.具有保留名称的内置变量摘要本节概述了由基础COMSOL语⾔定义的以下类别的内置元素：常量?变量?功能这些语⾔元素是内置的或⽤户定义的。

此外，还有不能由⽤户定义的运算符，以及始终由⽤户定义的表达式。

ABOUT RESERVED NAMES关于预留名称Built-in variables have reserved names, names that cannot be redefined by the user. It is not recommended to use a reserved variable name for a user-defined variable, parameter, or function. For some of the most common reserved variable names, such as pi, i, and j, the text where you enter the name turns orange and you get a tooltip message if you select the text string. Reserved function names are reserved only for function names, which means that such names can be used for variable and parameter names, and vice versa. The following tables list most built-in elements and hence those reserved names.内置变量具有保留名称，⽤户⽆法重新定义。