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Top Forums Shell Programming and Scripting how to do decimal arithmetic in shell script Post 302686317 by RudiC on Tuesday 14th of August 2012 09:56:56 AM
Old 08-14-2012
If b22 is properly formatted (right now there is a 12K in there; how to interpret?) this is reasonably fast:
Code:
tr ' ' '+' <b22|bc

 

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SLAGV2(l)								 )								 SLAGV2(l)

NAME
SLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular SYNOPSIS
SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR ) INTEGER LDA, LDB REAL CSL, CSR, SNL, SNR REAL A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 ) PURPOSE
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 types), then [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ], 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues, then [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ] where b11 >= b22 > 0. ARGUMENTS
A (input/output) REAL array, dimension (LDA, 2) On entry, the 2 x 2 matrix A. On exit, A is overwritten by the ``A-part'' of the generalized Schur form. LDA (input) INTEGER THe leading dimension of the array A. LDA >= 2. B (input/output) REAL array, dimension (LDB, 2) On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the ``B-part'' of the generalized Schur form. LDB (input) INTEGER THe leading dimension of the array B. LDB >= 2. ALPHAR (output) REAL array, dimension (2) ALPHAI (output) REAL array, dimension (2) BETA (output) REAL array, dimension (2) (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the ei- genvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. CSL (output) REAL The cosine of the left rotation matrix. SNL (output) REAL The sine of the left rotation matrix. CSR (output) REAL The cosine of the right rotation matrix. SNR (output) REAL The sine of the right rotation matrix. FURTHER DETAILS
Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA LAPACK version 3.0 15 June 2000 SLAGV2(l)
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