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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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