This chapter discusses the differentiation of functions of two or more variables. For most of the functions, it is common to denote y = f(x). This means that the variable y can be expressed explicitly in terms of the single variable x. However, in a great variety of applications, it ...
\dotsb, x_n)in place off_i(\vec{x}), we see thatD_jf_iis the derivative off_iwith respect tox_j, keeping the other variables fixed. The notation
You can also perform differentiation of a vector function with respect to a vector argument. Consider the transformation from Cartesian coordinates(x,y,z)to spherical coordinates(r,λ,φ)as given by x=rcosλcosφ, y=rcosλsinφ, z=rsinλ. ...
Discriminant function and cluster analyses were performed on 19 morphometric variables of the head, thorax, propodeum, wing, antenna and leg to determine whether individuals of Tetramesa sp. are distinguishable from the morphologically similar Tetramesa leucospae Zerova & Madjdzadeh, 2005. The ...
on 17 selected cranial and dental variables among samples from this region were analyzed to assess the difference between the sample and the nominate subspecies N.c.confucianus.92 individuals with complete skulls from this region were then submitted to multivariate analyses.The results showed ...
constraints (2) and (3), and verified the obtained µ 's theoretically as well with the help of an earlier result in his model [6]. The application of K-conserving differentiation in the case of constraints coupling variables of the differentiated functional, like Eq.(3), however, rai...
returns the gradients ofywith respect to the variables Calldlgradientfrom inside a function passed todlfevalCompute Gradient Using Automatic DifferentiationandUse Automatic Differentiation In Deep Learning Toolbox example yx1,...,xkName,Valuereturns the gradients and specifies additional options using one...
This feature allows consumers to instantiate variables e.g., in an embedded DSL without redeclaring their names: val x by Var() // With property delegation val x = Var("x") // Without property delegation Without property delegation, users would need to repeat the property name in the cons...
our physics-embedded generative model embeds the domain knowledge that the velocity tends to increase with depth. Four key factors (latent variables) are developed to compute the increasing velocity trend with depth. The reference fields of the geological layer properties (\(\textbf{p}\)with size...
Haralick texture method26with extended measures (eHM)7,35. The Haralick method is widely cited for the GLCM texture descriptor in the field of CADx. HoG3D27—this method counts the occurrences of gradient orientation (i.e. only the angular variables of a vector) in some cropped portions of...