Computational Science I

1
Computational Science I

• Lecture 12
• CAAM 420, Fall 2004
• Instructor Tim Warburton

2
Recall calling fortran subroutines from C

• Last lecture we covered how to invoke a F77
  subroutine from C.
• This is the recipe
• 1) use nm to find out if the f77 (or g77)
  compiler appends an underscore to all function
  names on the Fortran side. (i.e. foo is saved as
  foo_ in the .o file)
• 2) Fortran passes by pointer, so we need to send
  pointers to variables.
• 3) Extra If an argument to a Fortran subroutine
  represents an array in Fortran, we need to send
  the pointer to the first entry in the array (not
  the pointer to pointer)
• 4) Extra do not use _ in your Fortran function
  names, this may confuse the issue as some Fortran
  compilers will append even more extra underscores

3
C-gtF77 Example

• Note
• The _ after myfortranfn on the C side
• We send in pointers (using to obtain the
  address of variable) as arguments from the C side
• On the Fortran side, this is plain vanilla
  Fortran (i.e. nothing special is done).

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C-gtF77 Example With Array Passing

• In this example I create an array on the C side
  and pass in the pointer to the F77 side.
• The F77 function is able to access and change the
  contents of the array.
• On the F77 side notice array accesses start from
  1
• On the F77 side notice how array accesses start
  from 0

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C-gtF77 Example with array passing cont

• Compiling and running

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Leading Dimension

• The leading dimension of an array is the number
  of rows in Fortran (since Fortran is column
  major).
• In your dmat struct it depends on whether you
  chose to store your matrix in row or column
  major.
• If the matrix is row major, then the leading
  dimension is the number of columns.
• If the matrix is column major, then the leading
  dimension is the number of rows.
• In the following I am using Fortran routines to
  compute matrix algebraic operations so I set up
  my dmat to be column major.

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BLAS

• We have been building up to using
• the Basic Linear Algebra Subroutine library BLAS
• This is available for download online at
• http//www.netlib.org/blas/
• There is a nice quick guide to the subroutines
  included in BLAS at
• http//www.netlib.org/blas/blasqr.ps
• However, I already downloaded a version and
  compiled it up into a library for you
• /net/cage/timwar/libblas.a

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BLAS

• BLAS is divided into four types and three levels.
• Functions are prefixed with the type of the
  variables
• s,d,c, or z for single, double, complex, or
  double complex (z).
• Level 1 - Vector algebra routines, notably
  include
• dcopy which copies one vector of doubles to a
  different vector of doubles
• dscal which multiplies the entries of a vector of
  doubles by a scalar
• daxpy which multiples one vector of doubles by a
  scalar and adds the result to a second vector
• ddot which computes the dot product (also known
  as vector inner product) of two vectors of
  doubles.

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BLAS Level 1 Examples

• I hid prototypes for the blas functions in blas.h
• Note the BLAS function naming is not
  particularly intuitive.
• Thats why a lot of people build these calls into
  their struct interfaces.
• Also hard coding the extra underscore as done
  here is dangerous.

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BLAS Level 2

• These functions are generally matrix-vector
  multiplying routines.
• Notably
• dgemv
• For this example, I am using my own dmat which is
  indexed from 1 and column major (as determined by
  dmatget and dmatset).

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dgemv

• In this example I build a vector x, then compute
• alphax betaAx
• This code is a disaster the intent is hidden in
  all those function arguments.

12
BLAS Level 3

• These are typically matrix-matrix multiplying
  functions.
• Notably
• dgemm
• This time I have hidden some of the functionality
  of dgemm inside my dmat interface functions.

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dgemm

• What I did was to hide the nasty dgemm call
  inside my dmatmultiply function.
• The user never needs to see the horrible dgemm
  function construction.

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What happens in dmatmultiply

• As you are not the user you should see what I
  did in dmatmultiply

15
Class Exercise

• Download the BlasDemo.tar.gz tarball from the
  website and
• make sure you can do the following
• gzip d BlasDemo.tar.gz
• tar xvf BlasDemo.tar.gz
• cd BlasDemo
• make blas1
• ./myblaslevel1
• Modify the myblaslevel1.c file to compute
• c a.(alphaa b) using ddot, and daxpy
• c b.(alphaa) using ddot, and dscal