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need help-matrix inverse (awk)
Post 302151325 by vesyyr on Friday 14th of December 2007 01:44:21 PM
12-14-2007
need help-matrix inverse (awk)
I have few days to complete my awk homework. But I'm stucked. i hope some1 will help me out.
I have to inverse n x n matrix, but I have problems with finding the determinant of the matrix.
I found the algoritm, how to find a determinant of n x n matrix:
http://www.es.ucsc.edu/~eart111/lecture12.pdf
same text here:
a11 a12 a13
a21 a22 a23
a31 a32 a33
= a11(a22a33 − a23a32) − a12(a21a33 − a23a31) + a13(a21a32 − a22a31)
Note the pattern of + and − signs.
The general formula is compact, but tedious to compute. Here it is for an n by n matrix A:
detA = ai1Ci1 + ai2Ci2 + · · · + ainCin
where Cij are referred to as the cofactors and are computed from
Cij = (−1)i+j detMij
The term Mij is known as the ”minor matrix” and is the matrix you get if you eliminate row
i and column j from matrix A. So to find the determinant of e.g. a 4×4 matrix, you end up
calculating a bunch of 3 × 3 matrix determinants (much easier). Obviously you can apply this
technique recursively (probably using a computer).
****************************
Can some1 please write this matrix determinant algoritm into my code or if you have time, complete the full inverse?
I'm reading the matrix from a text file into an array "row"
--------------------
#!/usr/bin/awk -f
BEGIN{}
{
m=1
while (m <= NF){
row[NR,m] = $m
m++
}
}
END{}
-------------------
thank you
I have to inverse n x n matrix, but I have problems with finding the determinant of the matrix.
I found the algoritm, how to find a determinant of n x n matrix:
http://www.es.ucsc.edu/~eart111/lecture12.pdf
same text here:
a11 a12 a13
a21 a22 a23
a31 a32 a33
= a11(a22a33 − a23a32) − a12(a21a33 − a23a31) + a13(a21a32 − a22a31)
Note the pattern of + and − signs.
The general formula is compact, but tedious to compute. Here it is for an n by n matrix A:
detA = ai1Ci1 + ai2Ci2 + · · · + ainCin
where Cij are referred to as the cofactors and are computed from
Cij = (−1)i+j detMij
The term Mij is known as the ”minor matrix” and is the matrix you get if you eliminate row
i and column j from matrix A. So to find the determinant of e.g. a 4×4 matrix, you end up
calculating a bunch of 3 × 3 matrix determinants (much easier). Obviously you can apply this
technique recursively (probably using a computer).
****************************
Can some1 please write this matrix determinant algoritm into my code or if you have time, complete the full inverse?
I'm reading the matrix from a text file into an array "row"
--------------------
#!/usr/bin/awk -f
BEGIN{}
{
m=1
while (m <= NF){
row[NR,m] = $m
m++
}
}
END{}
-------------------
thank you
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LEARN ABOUT REDHAT
zhetri
ZHETRI(l) ) ZHETRI(l) NAME
ZHETRI - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF SYNOPSIS
SUBROUTINE ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, N INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), WORK( * ) PURPOSE
ZHETRI computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. ARGUMENTS
UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF. On exit, if INFO = 0, the (Hermitian) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF. WORK (workspace) COMPLEX*16 array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. LAPACK version 3.0 15 June 2000 ZHETRI(l)