1 Intel Mathematics Kernel Library (MKL) Quickstart COLA Lab, Department of Mathematics, Nat’l Taiwan University 2010/05/11

2 Intel MKL Quickstart Credits  Wei-Ren Chang 張為仁 (slides and codes, 2009/03/10)  Lien-Chi Lai 賴鍊奇 (slides, 2010/05/11)

3 Intel MKL Quickstart A Brief Introduction

4 Intel MKL Quickstart Intel MKL: Intel Math Kernel Library Introduction  Availability: Windows, Linux  Functionality  Dense and Sparse Linear Algebra: BLAS, LAPACK  Sparse Solvers: Direct and Iterative Solvers  Fast Fourier Transforms  Cluster Support: ScaLAPACK, Cluster FFT  Features and Benefits  Automatic parallelization  Standard APIs in C and Fortran

5 Intel MKL Quickstart User Guide  MKL User Guide  Installation  Development Environment Configuration  Performance and Memory Management  Language-specific Usage Options  Default documents directory  /opt/intel/mkl/ /doc/userguide.pdf User Guide

6 Intel MKL Quickstart Reference Manual  MKL Reference Manual  The routines and functions description  APIs in C and Fortran  Interfaces and calling syntax  Default documents directory  /opt/intel/mkl/ /doc/mklman.pdf Reference Manual

7 Intel MKL Quickstart Some Examples

8 Intel MKL Quickstart Examples  Brief examples to  Compute Inner product (sequential)  Compute the LU factorization of a matrix  Solve linear system  Solve eigen system  Compute Inner product (parallel) Examples

9 Intel MKL Quickstart Directories containing the source codes  mkl_blas_f95 (mkl_blas_c)  mkl_lapack95_f95 (mkl_lapack95_c)  mkl_linearsym_f95 (mkl_linearsym_c)  mkl_eigensym_f95 (mkl_eigensym_c)  mkl_blas_f95_p (mkl_blas_c_p) File names

10 Intel MKL Quickstart Inner product (sequential) Examples do ii = 1,n vec_a(ii) = 1.25*ii vec_b(ii) = 0.75*ii end do dot_result = ddot(n,vec_a,inca,vec_b,incb) Inner product

11 Intel MKL Quickstart Input parameters Inner product dot_result = ddot(n,vec_a,inca,vec_b,incb)  n: The length of two vectors.  inca: Specifies the increment for the elements of vec_a  incb: Specifies the increment for the elements of vec_b  vec_a: The fitsr vector  vec_b: The second vector Input parameters

12 Intel MKL Quickstart Output parameters Inner product  dot_result: The final result Output parameters

13 Intel MKL Quickstart Inner product (parallel) Examples  Makefile clips FC=mpif90 MKL_INCLUDE =/opt/intel/mkl/ /include MKL_PATH =/opt/intel/mkl/ /lib/em64t EXE=blas_f95.exe blas_f: $(FC) -o $(EXE) blas_f.f90 -I$(MKL_INCLUDE) -L$(MKL_PATH) -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core -lguide -lpthread Inner product (parallel)

14 Intel MKL Quickstart LU factorization Examples  Define the matrix a(1,1)= 1 a(1,2)= 3 a(2,1)= 2 a(2,2)= 1  Compute LU factorization call dgetrf(m,n,a,lda,ipiv,info) LU factorization

15 Intel MKL Quickstart Input parameters LU factorization call dgetrf(m,n,a,lda,ipiv,info)  a: The matrix.  m: The number of rows in the matrix a  n: The number of columns in the matrix a  lda: The fitsr dimension of a Input parameters

16 Intel MKL Quickstart Output parameters LU factorization call dgetrf(m,n,a,lda,ipiv,info)  a: overwritten by L and U. The unit diagonal elements of L are skipped  ipiv: An array, dimension at least max(1,min(m,n)). The pivot indices: row i is interchanged with row ipiv(i)  info:  info=0, the execution is successful  info=-i, the i-th parameter had an illegal value  info= i, uii is 0. The factorization has been completed, but U is exactly singular Output parameters

17 Intel MKL Quickstart Linear System (Fortran) Examples  Define the matrix a(1,1)= 1 a(1,2)= 3 a(2,1)= 2 a(2,2)= 1  Define the right-hand side rhs(1)= 1.0 rhs(2)= 1.0  Solve the linear system call dgesv(n,nrhs,a,lda,ipiv,ths,ldb,info) Linear System

18 Intel MKL Quickstart Input parameters Linear System call dgesv(n,nrhs,a,lda,ipiv,ths,ldb,info)  n: The number of linear equations, that is, the order of the matrix a  rhs: Right-hand side  lda: The leading dimension of matrix a  nrhs: The number of right-hand sides Input parameters

19 Intel MKL Quickstart Output parameters Linear System call dgesv(n,nrhs,a,lda,ipiv,ths,ldb,info)  ipiv: An array, dimension at least max(1,min(m,n)). The pivot indices: row i was interchanged with row ipiv(i)  rhs: Overwritten by the solution matrix a  info:  info=0, the execution is successful  info=-i, the i-th parameter had an illegal value  info= i, U(i,i) is 0. The factorization has been completed, but U is exactly singular, so the solution could not be computed Output parameters

20 Intel MKL Quickstart Eigensystem (symmetric) Examples  Define the matrixdsyev a(1,1)= 1.0 a(1,2)= 2.0 a(2,1)= 2.0 a(2,2)= 3.0  Call MKL function call dsyev(jobz,uplo,dim,a,lda,eigval,work,lwork,info) Eigensystem

21 Intel MKL Quickstart Input parameters Eigensystem call dsyev(jobz,uplo,dim,a,lda,eigval,work,lwork,info)  jobz: If jobz='N', then only eigenvalues are computed  jobz: If jobz='V', then eigenvalues are eigenvectors are computed  uplo: If uplo='U', a stores the upper triangular part of a  uplo: If uplo='L', a stores the lower triangular part of a  lda: The first dimension of a  work: a workspace array, its dimension max(1,lwork)  lwork: The dimension of the array work Input parameters

22 Intel MKL Quickstart Output parameters call dsyev(jobz,uplo,dim,a,lda,eigval,work,lwork,info)  wigval: contains the eigenvalues of the matrix a in ascending order  info:  info=0, the execution is successful  info=-i, the i-th parameter had an illegal value  info= i, then the algorithm failed to converge; I indicates the number of elements of an intermediate tridiagonal form which did not converge to zero Output parametersEigensystem

23 Intel MKL Quickstart References

24 Intel MKL Quickstart Reference  Intel® Math Kernel Library Reference Manual (mklman.pdf)  Intel® Math Kernel Library for the Linux OS User’s Guide (userguide.pdf)  Reference