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Chapter 22. Numerics > Exercises
22.9. Exercises
| 1. | (*1.5) Write a function that behaves like apply() from §22.4.3, except that it is a nonmember function and accepts function objects. |
| 2. | (*1.5) Write a function that behaves like apply() from §22.4.3, except that it is a nonmember function, accepts function objects, and modifies its valarray argument. |
| 3. | (*2) Complete Slice_iter (§22.4.5). Take special care when defining the destructor. |
| 4. | (*1.5) Rewrite the program from §17.4.1.3 using accumulate(). |
| 5. | (*2) Implement I/O operators << and >> for valarray. Implement a get_array() function that creates a valarray of a size specified as part of the input itself. |
| 6. | (*2.5) Define and implement a three-dimensional matrix with suitable operations. |
| 7. | (*2.5) Define and implement an n-dimensional matrix with suitable operations. |
| 8. | (*2.5) Implement a valarray-like class and implement + and * for it. Compare its performance to the performance of your C++ implementation’s valarray. Hint: Include x=0.5*(x+y)+z among your test cases and try it with a variety of sizes for the vectors x, y, and z. |
| 9. | (*3) Implement a Fortran-style array Fort_array where indices start from 1 rather than 0. |
| 10. | (*3) Implement Matrix using a vector< vector<double> > as the representation of the elements (rather than a pointer to a valarray). |
| 11. | (*2.5) Use compositors (§22.4.7) to implement efficient multidimensional subscripting using the [] notation. For example, v1[x], v2[x][y], v2[x], v3[x][y][z], v3[x][y], and v3[x] should all yield the appropriate elements and subarrays using a simple calculation of an index. |
| 12. | (*2) Generalize the idea from the program in §22.7 into a function that, given a generator as an argument, prints a simple graphical representation of its distribution that can be used as a crude visual check of the generator’s correctness. |
| 13. | (*1) If n is an int, what is the distribution of (double(rand())/RAND_MAX)*n? |
| 14. | (*2.5) Plot points in a square output area. The coordinate pairs for the points should be generated by Urand(N), where N is the number of pixels on a side of the output area. What does the output tell you about the distribution of numbers generated by Urand? |
| 15. | (*2) Implement a Normal distribution generator, Nrand. |
