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        AMATH 483代做、C++程序語言代寫

        時間:2024-06-01  來源:合肥網hfw.cc  作者:hfw.cc 我要糾錯



        AMATH 483 / 583 (roche) - HW6
        Due Friday May 31, 11:59pm PT
        May 24, 2024
        Homework 6 (80 points, 0 EC points)
        1. (+20) Complex double linear system solver. Plot both the log of the residual and the log of the
        normalized error ( kbAzk2
        kAk1 kzk2 ✏machine ) versus the square matrix dimensions 16,**,64,...,8192 for the following
        LAPACK routine. It is supported in the OpenBLAS build on Hyak. Submit your plot, and label it
        accordingly.
        l a p a c k i n t LAPACKE zgesv( int matrix orde r ,
        l a p a c k i n t n ,
        l a p a c k i n t nrhs ,
        lapack compl ex doubl e ∗ a ,
        l a p a c k i n t lda ,
        l a p a c k i n t ∗ ipiv ,
        lapack compl ex doubl e ∗ b ,
        l a p a c k i n t ldb );
        Use the following snippet code to initialize your matrices and rhs vectors and note the headers I use:
        #include <ios t ream>
        #include <complex>
        #include <c s t d l i b >
        #include <c s t r i n g >
        #include <cmath>
        #include <ve c tor>
        #include <chrono>
        #include <l i m it s >
        #include <c b l a s . h>
        #include <lapacke . h>
        . . .
        int main () {
        . . .
        a =( s td : : complex<double>∗) malloc ( s izeof ( s td : : complex<double>) ∗ ma ∗ na ) ;
        b = ( s td : : complex<double>∗) malloc ( s izeof ( s td : : complex<double>) ∗ ma ) ;
        z = ( s td : : complex<double>∗) malloc ( s izeof ( s td : : complex<double>) ∗ na ) ;
        . . .
        s rand ( 0 );
        int k =0;
        for ( int j = 0 ; j < na ; j++) {
        for ( int i = 0 ; i < ma ; i++) {
        a [ k ] = 0 . 5 − (double ) rand () / (double )RANDMAX
        + s td : : complex<double>(0 , 1)
        ∗ ( 0 . 5 − (double ) rand () / (double )RANDMAX) ;
        i f ( i==j ) a [ k]∗= s tat ic cas t<double>(ma ) ;
        k++;
        }
        }
        s rand ( 1 );
        for ( int i = 0 ; i < ma; i++) {
        b [ i ] = 0 . 5 − (double ) rand () / (double )RANDMAX
        + s td : : complex<double>(0 , 1)
        ∗ ( 0 . 5 − (double ) rand () / (double )RANDMAX) ;
        }
        . . .
        12. (+20) CPU-GPU data copy speed on HYAK. Write a C++ code to measure the data copy performance
        between the host CPU and GPU (host to device), and between the GPU and the host CPU (device to host). Copy
        8 bytes to 256MB increasing in multiples of 2. Plot the bandwidth for both directions: (bytes per second) on the
        y-axis and the bu↵er size in bytes on the x-axis. Submit your plot and test code.
        3. (+20) Compare FFTW to CUFFT on HYAK. Measure and plot the performance of calculating the gradient
        of a 3D double complex plane wave defined on cubic lattices of dimension n3 from 163 to n = 2563, stride n⇤ = 2
        for both the FFTW and CUDA FFT (CUFFT) implementations on HYAK. Let each n be measured ntrial times
        and plot the average performance for each case versus n, ntrial 3. Submit your performance plot which should
        have ’FLOPs’ on the y-axis (or some appropriate unit of FLOPs) and the dimension of the cubic lattices (n) on
        the x-axis. You will need to estimate the operation count of computing the derivative using FFT on a lattice.
        4. (+20) Fourier transforms. Evaluate the Fourier transform of the following functions by hand. Use the definitions
        I provided (includes p1
        2V**; , this is common in physics but also now the default used in WolframAlpha - a powerful
        math AI tool) as well as the definition for Dirac delta I used in lecture if needed.
        (a) f(x) = 1
        p2V**; e
        1
        22 (xµ)2
        (b) f(t) = sin(!0t) , !0 constant
        (c) f(x) = ea|x| and a > 0
        (d) (distribution) f(t) = (t)


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