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174 lines
6.2 KiB
C
174 lines
6.2 KiB
C
/*************************************************************************
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Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
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Contributors:
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* Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
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pseudocode.
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See subroutines comments for additional copyrights.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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- Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer listed
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in this license in the documentation and/or other materials
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provided with the distribution.
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- Neither the name of the copyright holders nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*************************************************************************/
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#ifndef _qr_h
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#define _qr_h
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#include "alglib/ap.h"
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#include "alglib/reflections.h"
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/*************************************************************************
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QR decomposition of a rectangular matrix of size MxN
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Input parameters:
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A - matrix A whose indexes range within [0..M-1, 0..N-1].
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M - number of rows in matrix A.
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N - number of columns in matrix A.
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Output parameters:
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A - matrices Q and R in compact form (see below).
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Tau - array of scalar factors which are used to form
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matrix Q. Array whose index ranges within [0.. Min(M-1,N-1)].
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Matrix A is represented as A = QR, where Q is an orthogonal matrix of size
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MxM, R - upper triangular (or upper trapezoid) matrix of size M x N.
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The elements of matrix R are located on and above the main diagonal of
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matrix A. The elements which are located in Tau array and below the main
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diagonal of matrix A are used to form matrix Q as follows:
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Matrix Q is represented as a product of elementary reflections
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Q = H(0)*H(2)*...*H(k-1),
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where k = min(m,n), and each H(i) is in the form
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H(i) = 1 - tau * v * (v^T)
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where tau is a scalar stored in Tau[I]; v - real vector,
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so that v(0:i-1) = 0, v(i) = 1, v(i+1:m-1) stored in A(i+1:m-1,i).
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-- LAPACK routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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February 29, 1992.
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Translation from FORTRAN to pseudocode (AlgoPascal)
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by Sergey Bochkanov, ALGLIB project, 2005-2007.
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*************************************************************************/
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ALGLIB_EXPORT
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void rmatrixqr(ap::real_2d_array& a, int m, int n, ap::real_1d_array& tau);
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/*************************************************************************
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Partial unpacking of matrix Q from the QR decomposition of a matrix A
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Input parameters:
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A - matrices Q and R in compact form.
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Output of RMatrixQR subroutine.
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M - number of rows in given matrix A. M>=0.
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N - number of columns in given matrix A. N>=0.
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Tau - scalar factors which are used to form Q.
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Output of the RMatrixQR subroutine.
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QColumns - required number of columns of matrix Q. M>=QColumns>=0.
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Output parameters:
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Q - first QColumns columns of matrix Q.
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Array whose indexes range within [0..M-1, 0..QColumns-1].
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If QColumns=0, the array remains unchanged.
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-- ALGLIB --
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Copyright 2005 by Bochkanov Sergey
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*************************************************************************/
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ALGLIB_EXPORT
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void rmatrixqrunpackq(const ap::real_2d_array& a,
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int m,
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int n,
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const ap::real_1d_array& tau,
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int qcolumns,
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ap::real_2d_array& q);
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/*************************************************************************
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Unpacking of matrix R from the QR decomposition of a matrix A
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Input parameters:
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A - matrices Q and R in compact form.
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Output of RMatrixQR subroutine.
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M - number of rows in given matrix A. M>=0.
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N - number of columns in given matrix A. N>=0.
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Output parameters:
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R - matrix R, array[0..M-1, 0..N-1].
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-- ALGLIB --
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Copyright 2005 by Bochkanov Sergey
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*************************************************************************/
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ALGLIB_EXPORT
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void rmatrixqrunpackr(const ap::real_2d_array& a,
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int m,
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int n,
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ap::real_2d_array& r);
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/*************************************************************************
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Obsolete 1-based subroutine. See RMatrixQR for 0-based replacement.
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*************************************************************************/
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ALGLIB_EXPORT
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void qrdecomposition(ap::real_2d_array& a,
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int m,
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int n,
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ap::real_1d_array& tau);
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/*************************************************************************
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Obsolete 1-based subroutine. See RMatrixQRUnpackQ for 0-based replacement.
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*************************************************************************/
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ALGLIB_EXPORT
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void unpackqfromqr(const ap::real_2d_array& a,
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int m,
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int n,
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const ap::real_1d_array& tau,
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int qcolumns,
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ap::real_2d_array& q);
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/*************************************************************************
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Obsolete 1-based subroutine. See RMatrixQR for 0-based replacement.
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*************************************************************************/
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ALGLIB_EXPORT
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void qrdecompositionunpacked(ap::real_2d_array a,
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int m,
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int n,
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ap::real_2d_array& q,
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ap::real_2d_array& r);
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#endif
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