Example 1 (Integration) We will introduce some fundamental MPI function calls through the computation of a simple integral by the Mid-point rule. b p 1 n 1  cos(x)dx    a i 0 j 0 ai  ( j 1)*h ai  j *h cos(x )dx   cos(aij ) * h;  h  (b  a) / p / n;  i 0   j 0 ai  a  i * n * h; aij  ai  ( j  0.5) * h p 1  n 1  p is number of partitions and n is increments per partition Example 1 - Serial fortran code Program Example1 implicit none integer n, p, i, j real h, integral_sum, a, b, integral, pi, ai pi = acos(-1.0) ! = 3.14159... a = 0.0 ! lower limit of integration b = pi/2. ! upper limit of integration p=4 ! number of partitions (processes) n = 500 ! number of increments in each partition h = (b-a)/p/n ! length of increment ai = a + i*n*h integral_sum = 0.0 ! Initialize solution to the integral do i=0,p-1 ! Integral sum over all partitions integral_sum = integral_sum + integral(ai,h,n) enddo print *,'The Integral =', integral_sum stop end . . Serial fortran code (cont’d) example1.f continues . . . real function integral(ai, h, n) ! This function computes the integral of the ith partition implicit none integer n, i, j ! i is partition index; j is increment index real h, h2, aij, ai integral = 0.0 ! initialize integral h2 = h/2. do j=0,n-1 ! sum over all "j" integrals aij = ai+ (j+0.5)*h ! lower limit of integration of “j” integral = integral + cos(aij)*h ! contribution due “j” enddo return end Example 1 - Serial C code #include #include float integral(float a, int i, float h, int n); void main() { int n, p, i, j, ierr; float h, integral_sum, a, b, pi, ai; pi = acos(-1.0); /* = 3.14159... * a = 0.; /* lower limit of integration */ b = pi/2.; /* upper limit of integration */ p = 4; /* # of partitions */ n = 500; /* increments in each process */ h = (b-a)/n/p; /* length of increment */ integral_sum = 0.0; for (i=0; i float integral(float ai, float h, int n); // prototyping void main(int argc, char* argv[]) { int n, p, myid, tag, proc, ierr; float h, integral_sum, a, b, ai, pi, my_int; int master = 0; /* processor performing total sum */ MPI_Comm comm; MPI_Status status; . . . Parallel C code (cont’d) comm = MPI_COMM_WORLD; ierr = MPI_Init(&argc,&argv); MPI_Comm_rank(comm, &myid); MPI_Comm_size(comm, &p); // starts MPI // get current process id // get number of processes pi = acos(-1.0); // = 3.14159... a = 0.; // lower limit of integration b = pi*1./2.; // upper limit of integration n = 500; // number of increment within each process tag = 123; // set the tag to identify this particular job h = (b-a)/n/p; // length of increment ai = a + myid*n*h; // lower limit of integration for partition myid my_int = integral(ai, h, n) // compute local sum due myid ... Parallel C code (cont’d) } printf("Process %d has the partial integral of %f\n", myid,my_int); MPI_Send(&my_int, 1, MPI_FLOAT, master, // message destination tag, // message tag comm); if(myid == master) { // Receives serialized integral_sum = 0.0; for (proc=0;proc { // if (!document.getElementById("doc-template-use").classList.contains("doc-template-use")) { // window.location = '/?redirect=login'; // return // } // } // // const redirectToRegister = () => { // if (!document.getElementById("doc-template-use").classList.contains("doc-template-use")) { // window.location = '/?redirect=register'; // return // } // } // const saveDocument = async () => { // if (!document.getElementById("doc-template-use").classList.contains("doc-template-use")) { // window.location = '/?redirect=login'; // return // } // // document.getElementById("save-button").classList.toggle("btn_selected") // document.getElementById("save-button-small").classList.toggle("btn_selected") // // try { // await fetch(`/api/user/saved-documents/${documentId}`, settings); // } catch (e) { // console.log(e) // } // } // // const saveReport = async () => { // let checkboxArray = [] // checkboxArray.push(document.getElementById("checkbox-1").checked) // checkboxArray.push(document.getElementById("checkbox-2").checked) // checkboxArray.push(document.getElementById("checkbox-3").checked) // checkboxArray.push(document.getElementById("checkbox-4").checked) // checkboxArray.push(document.getElementById("checkbox-5").checked) // // const reason = checkboxArray.findIndex((element) => element === true) + 1 // // try { // await fetch(`/api/reports`, {...settings, body: JSON.stringify({document: Number(documentId), reason})}); // closeReportModal() // openThankReportModal() // } catch (e) { // console.log(e) // } // } // const handleDownload = () => { // const downloadLink = JSON.parse(documentFileHash) // const url = `/download/${downloadLink}` // window.open(url, "_blank", "noreferrer"); // } const hideInfo = () => { if (window.innerWidth < 1279.98) { const button = document.querySelector(".document-details__title"); const hiddenDetailsItems = document.querySelectorAll(".hidden-details"); hiddenDetailsItems.forEach((item) => { item.classList.toggle("is-shown") }); button.classList.toggle("is-hidden"); } } const hideDescriptionPageInfo = () => { const button = document.getElementById("hide-button-des"); document.getElementById("description-block").classList.toggle("isShow") button.classList.toggle("is-hidden") button.innerText === "Hide description" ? button.innerHTML = "Show description" : button.innerHTML = "Hide description" } const hideDescriptionPage = () => { document.getElementById("description").classList.toggle("show") } const toggleSidebar = () => { document.getElementById("sidebar").classList.toggle("document-details_hidden"); document.body.classList.toggle( 'sidebar--closed' ); } const closeShareModal = () => { document.getElementById("share-modal").style.display="none" document.getElementById("share-modal2").style.display="none" document.getElementById("share-modal").classList.toggle("show") document.getElementById("share-modal2").classList.toggle("show") }

MPI Beginning Lecture - Introduction Pt 2