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Integration by trapezoidal rule


 
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Old 10-24-2007
Integration by trapezoidal rule

Hi everybody:
Somebody know or have a simple script which can calculate the integration from a database using the trapezoidal rule in awk.

I have a file like:

Code:
0.490 952.296 284.19 11.3169 0.002481 0.488 0.01
0.500 965.57 288.25 11.3395 2.48E-03 0.048 0.01
0.510 964.47 288.25 10.8759 0.002479 0.036 0.01
0.520 963.343 288.383 10.4918 0.002478 0.029 0.01
0.530 962.193 288.583 10.5154 0.002477 0.024 0.01
0.540 961.048 288.75 10.611 0.002476 0.020 0.01
0.550 959.91 288.817 10.6468 0.002475 0.017 0.01
0.560 958.783 288.75 10.5994 0.002474 0.015 0.01
0.570 957.644 288.798 10.6117 0.002473 0.013 0.01
0.580 956.5 288.878 10.6471 0.002472 0.012 0.01
0.590 955.366 288.95 10.6756 0.002471 0.011 0.01
0.600 954.23 288.95 10.6384 2.47E-03 0.010 0.01

and I would like to know the integration where x=$1 and f(x)=$6.

Thanks in advance. Smilie
tonet

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clantr.f(3)							      LAPACK							       clantr.f(3)

NAME
clantr.f - SYNOPSIS
Functions/Subroutines REAL function clantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK) CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. Function/Subroutine Documentation REAL function clantr (characterNORM, characterUPLO, characterDIAG, integerM, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )WORK) CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. Purpose: CLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. Returns: CLANTR CLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm' ( ( norm1(A), NORM = '1', 'O' or 'o' ( ( normI(A), NORM = 'I' or 'i' ( ( normF(A), NORM = 'F', 'f', 'E' or 'e' where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. Parameters: NORM NORM is CHARACTER*1 Specifies the value to be returned in CLANTR as described above. UPLO UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower trapezoidal. = 'U': Upper trapezoidal = 'L': Lower trapezoidal Note that A is triangular instead of trapezoidal if M = N. DIAG DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal. = 'N': Non-unit diagonal = 'U': Unit diagonal M M is INTEGER The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, CLANTR is set to zero. N N is INTEGER The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, CLANTR is set to zero. A A is COMPLEX array, dimension (LDA,N) The trapezoidal matrix A (A is triangular if M = N). If UPLO = 'U', the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1). WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Definition at line 142 of file clantr.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 clantr.f(3)

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