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Full Discussion: diagonal matrix to square matrix
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
Old 09-09-2009
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.$$
 

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LEARN ABOUT REDHAT

cgeequ

CGEEQU(l)								 )								 CGEEQU(l)

NAME

       CGEEQU - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

SYNOPSIS

       SUBROUTINE CGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )

	   INTEGER	  INFO, LDA, M, N

	   REAL 	  AMAX, COLCND, ROWCND

	   REAL 	  C( * ), R( * )

	   COMPLEX	  A( LDA, * )

PURPOSE

       CGEEQU computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale
       factors and C the column scale factors, chosen to try to make the largest element in each row and column of  the  matrix  B  with  elements
       B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

       R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use of these scaling factors is
       not guaranteed to reduce the condition number of A but works well in practice.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

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

       A       (input) COMPLEX array, dimension (LDA,N)
	       The M-by-N matrix whose equilibration factors are to be computed.

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

       R       (output) REAL array, dimension (M)
	       If INFO = 0 or INFO > M, R contains the row scale factors for A.

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

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

       COLCND  (output) REAL
	       If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i).  If COLCND >= 0.1, it is not worth scaling by C.

       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,  and i is
	       <= M:  the i-th row of A is exactly zero
	       >  M:  the (i-M)-th column of A is exactly zero

LAPACK version 3.0						   15 June 2000 							 CGEEQU(l)
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