Outline

1
Outline

• Announcements
• Add/drop by Monday
• HWI on the web
• Principal Components Analysis (PCA)
• Linking to libraries

2
PCA

• Many scientific problems are complicated
• High-dimensional (lots of interesting parameters)
• Observations from mulitple instruments/locations
• PCA is a method for reducing the dimensionality
  of a system by exploiting covariance among
  variables
• PCA identifies linear combinations (vectors) that
  represent interesting features common to the
  data sets

3
PCA

• Example Temperature in NW Atlantic

4
PCA
5
PCA
n

• Matrix of data

Rgn 1 Rgn 2 Rgn 8
C




m
Cov1/(m-1)CTC Cov is n-by-n
6
PCA

• Let
• v1, v2, , vN be the eigenvectors of Cov
• ?1, ? 2, , ? N be the corresponding eigenvalues
• Assume ?1gt? 2gt gt ? N
• Then,
• C v1 is a new time-series representing
• ?1/(?1 ? 2 ? N ) percent of the total
  variance
• If youre lucky, v1 v2 will represent a lot of
  the variance and can be used instead of the
  entire system

7
PCA
8
PCA Summary

• Load m-by-n data matrix C
• Compute Cov1/(m-1)CTC
• BLAS Level 3 routine SSYRK computes
• aAATbv
• aATAbv
• Compute eigenvalues and eigenvectors of Cov
• LAPACK routine SSYEV computes eigenvectors and
  eigenvalues for symmetric matrices

9
Accessing Libraries

• We could download code for BLAS and LAPACK and
  compile with our code
• Slow (BLAS and LAPACK are big)
• Ideally, we would compile BLAS LAPACK once to
  object code (.o) and link
• Saves compile time, easier to maintain

10
UNIX Libraries

• Pre-built libraries (commercial or otherwise) are
  stored as archives on UNIX machines
• libltNAMEgt.a
• libblas.a -- BLAS routines
• liblapack.a--LAPACK routines
• System libraries are in directories like /lib and
  /usr/lib
• archives are actually collections of object code
  (.o)
• How do we access routines in libraries?

11
Compiling Linking
cc prog.c -oprog
Transnslation
Link
12
Building with libraries

• 1) Compile the code you have (use -c)
• 2) Link your code together and link to the
  libraries you need
• g77 ltYOUR OBJECTSgt -LltLIBPATHgt -lname
• -L sets directory where linker will look for
  libraries
• System libraries (/usr/lib, etc.) automatically
  included, so -L not necessary
• -lname links to libname.a system libraries (or
  LIBPATH)