Nested Loop

This generic procedure affords the powder EPR absorption spectrum, which should be differentiated to get the powder EPR spectrum. Note that the whole procedure consists of three nested loops with the computation of an exponential (Equation 4.8) within the inner loop. Coded in a higher language (C, FORTRAN95) and run on a standard PC, this program will generate the EPR spectrum of a simple S = 1/2 or an effective S = 1/2 system in a split second (of the order of 10 ms or less). It is, however, useful to think about ways to make it as fast as possible, because extending... 

As posed here, the problem is a nonlinear programming one and involves nested loops of calculations, the outer loop of which is Equation (j) subject to Equations (a) through (i), and subject to the inequality constraints. If capital costs are to be included in the objective function, refer to Frey and colleagues (1997). 

Avoid nesting control loops. Control loops are nested if the operation of the external loop depends on the operation of the internal loop. Figure 8.11 illustrates a nested loop. A vapor sidestream is drawn off a column to hold the column base level, and a temperature higher up in the column is held by heat input to the reboilcr. The base liquid level is ouly affected by the liquid stream entering and the vapor boiled off, and therefore it is not directly influenced by the amount of vapor sidestream withdrawn. Thus the base level... 

If the temperature controller is on manual, the level loop cannot work. In this process it probably would be better to reverse the pairing of the loops control temperature with vapor sidestream and control base level with heat input. Notice that if the sidestream were removed as a liquid, the control system would not be nested. Sometimes, of course, nested loops cannot be avoided. Notice that the recommended Scheme B in Fig. 8.10 is just such a nested system. DistOlate has no direct effect on tray temperature. It is only... 

Note that the makeup of liquid A to the column is set by the level controller on the reflux drum of the column. This may seem like an unusual arrangement, and it certainly involves nested loops (the reflux drum level is not directly affected by makeup feed, but only through the bottoms composition loop changing heat input). If the makeup could be added directly into the reflux drum, there would be no nesting of control loops. 

All three approaches to isomerism - formal charges, tautomers, and nitrogen configurations - and the duplicate removal are put together in a nested loop as shown in the following piece of pseudocode ... 

In order to achieve an accurate control of the internal reactor temperature, a cascade controller can be used. In this type of controller, temperature control is managed by two controllers arranged in cascade, that is, in two nested loops (Figure 9.14). The external loop, called the master, controls the temperature of the reaction mixture by delivering a set value to the slave, the inner loop, which controls the temperature of the heat carrier (Tc). 

The process includes a number of recycles that can be interpreted as 18 intersecting and nested loops of a first through fifth order. 

There are two nested loops in the program (see Figure 5) o Composition of the recycle gas o Octane number of the C5+ reformate... 

For a discussion and an example on how to program an arbitrary number of nested loops using a single loop algorithm, allowing to realize an arbitrary number of nested sums, see references [45b,c]. 

Clearly the form of the code depends on the starting point of the "walk" and the direction of circling the tree The above code can be "translated" into a set of inscribed circles, by first replacing 0, 1 labels by left and right brackets leading to "nested loops" specified as... 

Analogous R relations exist for all possible subsets of M as well as for the augmented set S in which "nested loops" and "inscribed contours" and other such possible objects may be possible ... 

As an example, we describe the parallel computation of two-electron repulsion integrals over Gaussian basis functions. These integrals are usually computed over shell blocks of integrals to make optimal reuse of intermediate quantities, where the computation of each shell block is totally independent from that of other shell blocks.2 -34 jhis is an example of an embarrassingly parallel application. The four nested loops that exist in this algorithm are ... 

This is much more convenient than the loop method, where two nested loops would be required to read or write a 2-D range. However, a problem arises when you use this method with a 1-D range, as described next. 

From a Do or For loop, control is transferred to the statement following the Loop or Next statement, or, in the case of nested loops, to the loop that is one level above the loop containing the Exit statement. From a Function or Sub procedure, control is transferred to the statement following the one that called the procedure. 

Once the lattice is created, the bonds are randomly destroyed in a proportion specified at the command line. There is a linked list of sheets in the structure, and each sheet involves a linked list of bonds thus, all bonds are processed using a double nested loop. For each bond, a random number between 0 and 1 is generated and compared to the specified probability (which is also between 0 and 1) if the random number is smaller, the bond is deleted. When a bond is deleted, it acquires the property deleted , which is used later in the program. 

To specify a parameter in a module as a design variable, you have to place a control block around the module and adjust the parameter such that design specifications are met. This arrangement creates a loop. If the values of many design variables are to be determined, you might end up with several nested loops of calculation. 

Because the workunits require a long calculation (1-2 hours), mechanisms for restarting after an interruption are essential. With the nested loop structure in the calculation, it is easy to write information to a file at the beginning of each of the two outermost iterations (lines 2, 3 in the script. Sect. 7.6). When the calculation starts. 

P.K. Dasgupta, H. Huang, Application of a nested loop system for flow injection analysis of trace aqueous peroxides, Anal. Chem. 57 (1985) 1009. 

P. K. Dasgupta and H. Hwang, Application of a Nested Loop System for the Flow Injection Analysis of Trace Aqueous Peroxides. Anal. Chem., 51 (1985) 1009. 

Difficulty to treat more complex computation sequences, as nested loops or... 

The flowsheet in Fig 3.37 consisting of three nested loops of mixers and flashes, is a standard problem in flowsheeting known as the Cavett s problem (Rosen, 1980). Table 3.9 gives the cycle matrix, where 1 marks each stream included in a recycle loop. For example, the stream Z, appears both in the loops 1 and 3, while the stream Sj only in the loop 3. The last column shows the number of loops tom by each stream, and may be used to evaluate the tearing action. An obvious choice would be to consider three tear streams for three recycles, as for example R Rj, R3, which tom each loop only one. Another choice would be R, Sj, and R3, where Sj would replace Rj. However, it is possible to solve the flowsheet only with two tear streams, as Z, and Zj, now each breaking two loops. Zj may be also replaced by R3 or S3. Hence, several tear sets are... 

In Sequential-Modular approach, the calculation sequence plays an important role in obtaining overall convergence. Transmission of information techniques may be used to untie the nested loops and simplify the calculation sequence. 

The initial CIM-CC papers [38 0] showed some promise, demonstrating that the CIM-CC methods are capable of recovering 99% or so of the correlation energy calculated at the CCD level, but the molecular systems calculated at the CCD level had to be relatively small in size due to the explicit nested loop structure used in the underlying pilot CCD codes which slows down the required CC calculations for subsystems by a large factor. No other CC methods were examined in the earlier CIM-CC work either. This chapter reviews our recent effort toward the development and efficient implementation of the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches that addresses these important issues. Thus, unlike the initial implementations of the CIM-CCD approach [38 0], which utilized pilot CCD codes with explicit loops over excitations and orbital indices that enter the molecular integrals and cluster amplitudes in the CC equations, the CIM-CC methods discussed and examined in this work are characterized by high... 

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