3 column .csv --> correlation matrix; awk, perl? Post: 302669315

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Top Forums Shell Programming and Scripting 3 column .csv --> correlation matrix; awk, perl? Post 302669315 by bakunin on Tuesday 10th of July 2012 11:20:20 PM

07-11-2012

Registered User

Quote:

Originally Posted by R3353

I have a 3 column csv file with ~13 million rows and I would like to generate a correlation matrix.

Let us first have some rough estimations about sizes:

How many rows/columns will this matrix have? Will there be empty matrix elements? The background is: there are some limitations which may or may not affect the solution: Unix files have maximum line lengths because text processing utilities like "sed", "awk", etc. can't handle longer ones (see MAXLINE in sys/limits.h. Shell arrays cannot have more than 1024 elements.

Then some questions: How to deal with multiple entries with the same indexes - add together, generate error, other?

My take would be to first put the lines in "normal form": the lines are of the form

Code:

keyA, keyB, value

As all keys are interchangeable, so that the following two entries would in effect be the same

Code:

x, y, value
y, x, value

and the matrix you are constructing is symetrical along the main diagonal the first step should be to sort the keys within the lines by some criteria, so that the first key in the line is consistently "lower or equal" or "higher or equal" than the second key in the line.

Than a simple sort over the first two fields will reduce the problem to a simple sort-of group-change: all lines with a given keyA will represent one row AND - because the matrix is symetrical - also one column.

I hope this helps.

bakunin

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dlar1v

DLAR1V(l)								 )								 DLAR1V(l)

NAME

       DLAR1V  - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma
       I

SYNOPSIS

       SUBROUTINE DLAR1V( N, B1, BN, SIGMA, D, L, LD, LLD, GERSCH, Z, ZTZ, MINGMA, R, ISUPPZ, WORK )

	   INTEGER	  B1, BN, N, R

	   DOUBLE	  PRECISION MINGMA, SIGMA, ZTZ

	   INTEGER	  ISUPPZ( * )

	   DOUBLE	  PRECISION D( * ), GERSCH( * ), L( * ), LD( * ), LLD( * ), WORK( * ), Z( * )

PURPOSE

       DLAR1V computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T  -  sigma
       I. The following steps accomplish this computation : (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T, (b) Progressive qd
       transform, L D L^T - sigma I = U(-) D(-) U(-)^T, (c) Computation of the diagonal elements of the inverse of
	   L D L^T - sigma I by combining the above transforms, and choosing
	   r as the index where the diagonal of the inverse is (one of the)
	   largest in magnitude.
       (d) Computation of the (scaled) r-th column of the inverse using the
	   twisted factorization obtained by combining the top part of the
	   the stationary and the bottom part of the progressive transform.

ARGUMENTS

       N	(input) INTEGER
		The order of the matrix L D L^T.

       B1	(input) INTEGER
		First index of the submatrix of L D L^T.

       BN	(input) INTEGER
		Last index of the submatrix of L D L^T.

       SIGMA	(input) DOUBLE PRECISION
		The shift. Initially, when R = 0, SIGMA should be a good approximation to an eigenvalue of L D L^T.

       L	(input) DOUBLE PRECISION array, dimension (N-1)
		The (n-1) subdiagonal elements of the unit bidiagonal matrix L, in elements 1 to N-1.

       D	(input) DOUBLE PRECISION array, dimension (N)
		The n diagonal elements of the diagonal matrix D.

       LD	(input) DOUBLE PRECISION array, dimension (N-1)
		The n-1 elements L(i)*D(i).

       LLD	(input) DOUBLE PRECISION array, dimension (N-1)
		The n-1 elements L(i)*L(i)*D(i).

       GERSCH	(input) DOUBLE PRECISION array, dimension (2*N)
		The n Gerschgorin intervals. These are used to restrict the initial search for R, when R is input as 0.

       Z	(output) DOUBLE PRECISION array, dimension (N)
		The (scaled) r-th column of the inverse. Z(R) is returned to be 1.

       ZTZ	(output) DOUBLE PRECISION
		The square of the norm of Z.

       MINGMA	(output) DOUBLE PRECISION
		The reciprocal of the largest (in magnitude) diagonal element of the inverse of L D L^T - sigma I.

       R	(input/output) INTEGER
		Initially, R should be input to be 0 and is then output as the index where the diagonal element of the inverse is largest in  mag-
		nitude. In later iterations, this same value of R should be input.

       ISUPPZ	(output) INTEGER array, dimension (2)
		The support of the vector in Z, i.e., the vector Z is nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ).

       WORK	(workspace) DOUBLE PRECISION array, dimension (4*N)

FURTHER DETAILS

       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0						   15 June 2000 							 DLAR1V(l)