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
slaqge
SLAQGE(l) ) SLAQGE(l)
NAME
SLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
SYNOPSIS
SUBROUTINE SLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED )
CHARACTER EQUED
INTEGER LDA, M, N
REAL AMAX, COLCND, ROWCND
REAL A( LDA, * ), C( * ), R( * )
PURPOSE
SLAQGE equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C.
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/output) REAL array, dimension (LDA,N)
On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).
R (input) REAL array, dimension (M)
The row scale factors for A.
C (input) REAL array, dimension (N)
The column scale factors for A.
ROWCND (input) REAL
Ratio of the smallest R(i) to the largest R(i).
COLCND (input) REAL
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) REAL
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies the form of equilibration that was done. = 'N': No equilibration
= 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmulti-
plied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).
PARAMETERS
THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors.
If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done.
LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, row scaling is done.
LAPACK version 3.0 15 June 2000 SLAQGE(l)