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torch.linalg.svd() computes the singular value decomposition (SVD) of a matrix or a batch of matrices. Singular value decomposition is represented as a named tuple (U, S, Vh).U and Vh are orthogonal for real matrix and unitary for input complex matrix.Vh is transpose of V when V is a real value and conjugate transpose when V is complex.S is always real valued even when the input is complex.SyntaxU, S, Vh = torch.linalg.svd(A, full_matrices=True)ParametersA – PyTorch tensor (matrix or batch of matrices).full_matrices – If True, the output is a full SVD, else a reduced SVD. Default is True.OutputIt returns a named tuple ... Read More
In-place operations directly change the content of a tensor without making a copy of it. Since it does not create a copy of the input, it reduces the memory usage when dealing with high-dimensional data. An in-place operation helps to utilize less GPU memory.In PyTorch, in-place operations are always post-fixed with a "_", like add_(), mul_(), etc.StepsTo perform an in-place operation, one could follow the steps given below −Import the required library. The required library is torch.Define/create tensors on which in-place operation is to be performed.Perform both normal and in-place operations to see the clear difference between them.Display the tensors ... Read More
Trigonometric Fourier SeriesA periodic function can be represented over a certain interval of time in terms of the linear combination of orthogonal functions. If these orthogonal functions are the trigonometric functions, then it is known as trigonometric Fourier series.Mathematically, the standard trigonometric Fourier series expansion of a periodic signal is, $$\mathrm{x(t)=a_{0}+ \sum_{n=1}^{\infty}a_{n}\:cos\:\omega_{0}nt+b_{n}\:sin\:\omega_{0}nt\:\:… (1)}$$Exponential Fourier SeriesA periodic function can be represented over a certain interval of time in terms of the linear combination of orthogonal functions, if these orthogonal functions are the exponential functions, then it is known as exponential Fourier series.Mathematically, the standard exponential Fourier series expansion for a periodic ... Read More
Inflation is an important parameter in investments, as it erodes the value of money. It must be included in capital budgeting so that cash flows are appropriately included in the evaluation of an investment. In doing so, the inflation targets must be forecasted accurately over a considerably longer duration.Here are some considerations that must be made while creating inflation in an investment evaluation process.The forecasts must be spread over a periodInflation is an ever-existing truth nowadays. Investors face this reality day-in and day-out. They want to gain a return that is more than the inflation rates so that the value ... Read More
Free cash flow is the capital retained by a company after it has paid all its expenses, including building, rent, tax, payroll, inventory, etc. Companies may use the free cash flow for anything it sees fit.Free cash flow is a true measure of a company’s profitability.Businesses usually calculate free cash flow to take critical business decisions, such as whether to invest the money for expansion or to invest the money in ways to reduce the costs of operations.Investors use the free cash flow metric to check the frauds in accounting, as these measures are stringent and less manipulable than net ... Read More
Product cannibalization is the process in which a new project or product eats away the cash flows earned by an already existing product. That means, when a new project or product is launched, it may take the cash flow away from an already running product or project. Business decisions must include the cannibalization effect into consideration because ignoring this may lead to huge losses sometimes.Capital budgeting decisions are taken keeping profitability and market share of products and they should include a holistic approach.A new product or project must not negatively impact an already available product or project which is running ... Read More
Financial distress is a situation in which a company cannot meet its obligations. In fact, companies borrow debts from investors for operations and growth. When the company performs badly, it may be unable to repay back the loans and funds it has borrowed from the lenders. This is called financial distress of the company.There are many costs attached to financial distress. These may include costs related to employees, managers, customers, suppliers, and shareholders.Costs Related to EmployeesThe employees of a distressed company are not confident. They are demoralized and worried about their future. This affects the quality of the products. The ... Read More
To better understand the two concepts of risk-adjusted and certainty equivalent methods, let’s understand what they mean and how they are useful for investors.What is Risk-Adjusted Discount RateThe risk-adjusted method combines an expected risk premium with a risk-free rate to calculate the present value of an investment.Risky investments include investments in real estate and other high-level risk projects. Although the market rate is considered as the discount rate, in some cases, a risk-adjusted rate for the investments becomes crucial for the investors.The risk-adjusted discount rate method correlates risks and returns while signifying the requisite returns of an investment. This means ... Read More
Sensitivity AnalysisSensitivity analysis is a financial tool to analyze the effect of a set of independent variables on a specific dependent variable under some given conditions. It is used in a wide range of applications, such as in biology and finance as well as economics.The sensitivity analysis studies numerous sources of uncertainty that contribute to the forecast’s uncertainty by using what-if queries altogether. It is used within limited boundaries that rely on one or more inputs.How Does It Work?Also known as What-if analysis or simulation analysis, sensitivity analysis helps to ascertain some decisions depending on numerous independent variables.For example, it ... Read More
Inflation is the rise of prices of daily usable goods such as food, clothing, fuel, transport, etc. Inflation increases the cost of living. It can also be considered as the change in the average price of services and commodities at regular intervals. It indicates the losing value of purchasing power of a unit of a nation’s currency as the services and products get more expensive.In general, inflation is the difference between the demand and supply of a good or service. When aggregate demand exceeds aggregate supply an increase in price level takes place.Although high levels of inflation are unwanted, a ... Read More