diagonal matrix to square matrix Post: 302351613

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Top Forums Shell Programming and Scripting diagonal matrix to square matrix Post 302351613 by rwu on Wednesday 9th of September 2009 05:47:38 AM

09-09-2009

Registered User

Something like this would probably be better done with perl, as you can put the whole matrix in memory.

If you still want to use a shell script, here is one. By the way, I think you meant a symmetric matrix, and not a diagonal matrix.

#!/bin/bash

PATH=/usr/bin:/bin
export PATH

# length of each number in the matrix
rlen=5

# Right-justify the matrix
awk '{ if (ne == "") { ne = NF; } indent = (NR - 1) * (rlen + 1); printf("%" indent "s", ""); print }' rlen="$rlen" > temp.$$

# Fill in the missing parts
cat -n temp.$$ | while read line; do
set -- $line

# Get the row number
n="$1"

# Discard the row number and the 1.000 value
shift 2

# Calculate the start and end positions of the column
# If you're using Bourne shell, you'll have to use expr or similiar.
s=$(( ( $n -1 ) * ( $rlen + 1 ) + 1 ))
e=$(( $s + $rlen - 1 ))

# Get the values of the column for the preceding rows in the matrix
head -$n temp.$$ | cut -c$s-$e | tr '\n' ' '

# Output the rest of the row from the input
echo $*
done

# Clean up
rm -f temp.$$

rwu

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spoequ

SPOEQU(l)								 )								 SPOEQU(l)

NAME

       SPOEQU  -  compute  row	and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number
       (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )

	   INTEGER	  INFO, LDA, N

	   REAL 	  AMAX, SCOND

	   REAL 	  A( LDA, * ), S( * )

PURPOSE

       SPOEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A  and  reduce  its  condition  number
       (with  respect  to  the	two-norm).  S  contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements
       B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the condition number of B within a factor N of the smallest pos-
       sible condition number over all possible diagonal scalings.

ARGUMENTS

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       A       (input) REAL array, dimension (LDA,N)
	       The N-by-N symmetric positive definite matrix whose scaling factors are to be computed.	Only the diagonal elements of A are refer-
	       enced.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       S       (output) REAL array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) REAL
	       If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i).  If SCOND >= 0.1 and AMAX is neither too large nor  too
	       small, it is not worth scaling by S.

       AMAX    (output) REAL
	       Absolute  value	of  largest  matrix  element.	If AMAX is very close to overflow or very close to underflow, the matrix should be
	       scaled.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = i, the i-th diagonal element is nonpositive.

LAPACK version 3.0						   15 June 2000 							 SPOEQU(l)