Corso2020-2021 < CI

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<font color="#3F467A" size="+1"><b>Lectures 2020-2021</b></font><br /> <br />  

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*Lecture 1, February 24th, 2021* Introduction to the course. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture1-IntensiveComputationIntro.pdf][Lecture 1 - Introduction]]

 
*Lecture 2, February 26th, 2021* Introduction to Matlab - Part 1 -  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture2-Matlab.pdf][Lecture 2 - Matlab]]<br>
*Laboratory, February 26th, 2021*    [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Homework0-Intro-1.pdf][Laboratory: Introductory exercises - Part 1]]<br>


*Lecture 3, March 3rd, 2021* Introduction to Matlab - Part 2 -  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture3-Matlab.pdf][Lecture 3 - Matlab]]<br>
*Laboratory, March 3rd, 2021*   [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Homework0-Intro-1bis.pdf][Laboratory: Introductory exercises - Part 2]]<br>

*Lecture 4, March 5th, 2021* Sparse matrices: definitions and motivation of compact formats. Compact storage methods for sparse matrix: Coordinate, Skyline, Compact Sparse Row CSR, Compact Sparse Column CSC, Modified Sparse Row  MSR. 
[[http://twiki.di.uniroma1.it/pub/CI/WebHome//2021-Lecture4-SparseMatrices.pdf][Lecture 4 - SparseMatrices.pdf]]
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/Appendix-SolvingNumericalPDEs-FormaggiaSaleriVeneziani-2012.pdf][Appendix]] of book Solving Numerical PDEs: Problems, Applications, Exercises - Formaggia, Saleri, Veneziani - 2012 - *read pp. 395-409* <br>

*Lecture 5, March 10th, 2021*   [[%ATTACHURL%/2021-03-10-Esercitazione-SparseMatrices.pdf][Exercises on Sparse matrices.]]
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Homework1-SparseMatrices.pdf][Homework 1 - Sparse Matrices]] - *Deadline: 25 March 2021* <br>

*Lecture 6, March 12th, 2021* Lecture by Dr. Viviana Arrigoni.  Linear systems. Gaussian elimination for solving systems of linear equations. Pivoting. Methods to avoid pivoting.  Random Butterfly Transformations and Transpose methods.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture6-ICLinSys1_21-Viviana.pdf][Lecture 7 - Linear Systems Part 1]]


*Lecture 7, March 17th, 2021* Lecture by Dr. Viviana Arrigoni. Linear systems. Cholesky factorization. Jacobi iterative method. Gauss-Seidel iterative method. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture7-ICLinSys2_21-Viviana.pdf][Lecture 7 - Linear Systems Part 2]]<br>
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/homework2IC.pdf][Homework 2 - Direct and iterative methods]] - *Deadline: 2 April 2021* <br>

*Lecture 8, March 19th, 2021* Errors: Computational errors, Data errors, Truncation errors, Rounding errors. Forward error and backward error. Sensitivity and condition number. Stability and accuracy. Errors in floating-point representation. Uncertainty in measurements.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture8-Errors.pdf][Lecture 8 - Errors]]<br> 
Exercises on linear systems: Exercise 3 from Midterm exam 18 April 2018 (to be continued). <br>

*Lecture 9, March 24th, 2021* Discussion on Homework 1: student's solutions. Exercises on linear systems and errors: Exercise 3 from Midterm exam 18 April 2018 (continued);  Exercise 3 from Midterm exam 17 April 2019. <br>

*Lecture 10, March 26th, 2021* Eigenvalues and eigenvectors. The Power method. The Deflation methods. 
Applications: Gould Index - Eigenvector Centrality in a Graph; the Fiedler Eigenvector and the Graph Partitioning; the Steady State of a Markov Chain using eigenvalues and eigenvectors; covariance matrix and eigenvectors. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture10-Eigenvalues.pdf][Lecture 10 - Eigenvalues, Eigenvectors and applications]]<br>
 
*Lecture 11, March 31st, 2021* Molecular Dynamics: Introduction, Hooke's Law Model, Lennard-Jones Model, Motion Equations.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture11-MolecularDynamics.pdf][Lecture11 - MolecularDynamics]][[http://twiki.di.uniroma1.it/pub/CI/WebHome/FosdickMolecDynamic.pdf][Molecular Dynamics - L. Fosdick]].<br>

*Lecture 12, April 7th, 2021* Molecular Dynamics: Euler's method and Verlet's method for Hooke's Law Model and Lennard-Jones Model. Solution of motion equations for the 1D Hard Sphere Model.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture11-MolecularDynamics-bis.pdf][Lecture12 - Molecular Dynamics Part 2 - slide 1-37]]
Exact solution for Hooke's Law Model. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/FosdickMolecDynamic.pdf][Molecular Dynamics - L. Fosdick]].<br>

*Lecture 13, April 9th, 2021* Molecular dynamics: Solution of motion equations for the 1D Hard Sphere Model. Exact solution of motion equations for Hooke's Law Model.   [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture11-MolecularDynamics-bis.pdf][Lecture12 - Molecular Dynamics Part 2 - slide 38-65]]<br>
Discussion on Homework 2: student's solutions.<br>

*Midterm test - April 16th, 2021*  <br>



*Lecture 15, April 23rd, 2021* Circuits for arithmetic operations. Pipeline of arithmetic operations. Circuit evaluation: delay and area.
[[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture15-Computer-arithmetic.pdf][Lecture15 - Computer arithmetic]] <br>
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome//2021-Homework3-Eigs-MolecularDynamics.pdf][Homework3 - Eigenpairs and Molecular Dynamics]] - *Deadline: 7 May 2021* <br>

*Lecture 16, April 28th, 2021* Representations for Fast Arithmetic. Redundant number representations for carry-free addition. Modified Signed Digit (MSB) and Redundant Binary.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture16-RepresentationsFastArithmetic.pdf][Lecture16 - Representations for Fast Arithmetic - Slides 1-31]] <br>

*Lecture 17, April 30th, 2021* Representations for Fast Arithmetic: Residue number system. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture16-RepresentationsFastArithmetic.pdf][Lecture17 - Representations for Fast Arithmetic - Slides 32-55]] <br>
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-04-30-Eser-circuit-pipeline-representations.pdf][Text of exercises on circuit evaluation and number representations]]

*Lecture 18, May 5th, 2021* SIMD class: vector architecture. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture18-VectorArchitectures.pdf][Lecture 18 - Vector Architectures]] <br>

*Lecture 19, May 7th, 2021* Graphics Processing Units. Matrix multiplication on GPUs. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture19-GPU.pdf][Lecture19 - GPUs]]<br>

*Lecture 20, May 12th, 2021* Interconnection networks. [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture20-IntNetworks.pdf][Lecture 20 - Interconnection networks - Slides 1 - 39]]  <br>

*Lecture 21, May 14th, 2021* Interconnection networks: Equivalence of log N stage and (2log N -1) stage MINs; all-to-all personalized communication on log N stage and (2log N -1) stage MINs -  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lecture20-IntNetworks.pdf][Lecture 20 - Interconnection networks - Slides 40 - 102]]  
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2004-EquivalenceJPDC.pdf][Paper on equivalence of MINs]] 
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2003-All-to-allDAM.pdf][Paper on All-to-all personalized communication on log N stage MINs]]
   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2020-All-to-All-HPCC.pdf][Paper on All-to-all personalized communication on (2 log N -1) stage MINs]] <br>

   * [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Homework4-NumberRepresentations-and-MINs.pdf][Homework4 - NumberRepresentations and Multistage Interconnection Networks]] - *Deadline: 31 May 2021* <br>

*Lecture 22, May 19th, 2021* Exercises on Interconnection networks and GPUs.  <br>

*Lecture 23, May 21st, 2021* Performance evaluation of computer architectures. Amdahl law. Performance equation.  [[http://twiki.di.uniroma1.it/pub/CI/WebHome/2021-Lesson23-Performance.pdf][Lesson 23 - Performance]] <br>

*Lecture 24, May 26th, 2021* Exercises on  GPUs, Amdahl law, and Performance equation.  Discussion on Projects and Homework.  <br>



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