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/*!
* \file
* \brief Implementation of functions for solving linear equation systems
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* IT++ is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along
* with IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#ifndef _MSC_VER
# include <itpp/config.h>
#else
# include <itpp/config_msvc.h>
#endif
#if defined(HAVE_LAPACK)
# include <itpp/base/algebra/lapack.h>
#endif
#include <itpp/base/algebra/ls_solve.h>
namespace itpp {
// ----------- ls_solve_chol -----------------------------------------------------------
#if defined(HAVE_LAPACK)
bool ls_solve_chol(const mat &A, const vec &b, vec &x)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = 1;
char uplo='U';
it_assert_debug(A.cols() == n, "ls_solve_chol: System-matrix is not square");
it_assert_debug(n == b.size(), "The number of rows in A must equal the length of b!");
ivec ipiv(n);
x = b;
mat Chol = A;
dposv_(&uplo, &n, &nrhs, Chol._data(), &lda, x._data(), &ldb, &info);
return (info==0);
}
bool ls_solve_chol(const mat &A, const mat &B, mat &X)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = B.cols();
char uplo='U';
it_assert_debug(A.cols() == n, "ls_solve_chol: System-matrix is not square");
it_assert_debug(n == B.rows(), "The number of rows in A must equal the length of B!");
ivec ipiv(n);
X = B;
mat Chol = A;
dposv_(&uplo, &n, &nrhs, Chol._data(), &lda, X._data(), &ldb, &info);
return (info==0);
}
bool ls_solve_chol(const cmat &A, const cvec &b, cvec &x)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = 1;
char uplo='U';
it_assert_debug(A.cols() == n, "ls_solve_chol: System-matrix is not square");
it_assert_debug(n == b.size(), "The number of rows in A must equal the length of b!");
ivec ipiv(n);
x = b;
cmat Chol = A;
zposv_(&uplo, &n, &nrhs, Chol._data(), &lda, x._data(), &ldb, &info);
return (info==0);
}
bool ls_solve_chol(const cmat &A, const cmat &B, cmat &X)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = B.cols();
char uplo='U';
it_assert_debug(A.cols() == n, "ls_solve_chol: System-matrix is not square");
it_assert_debug(n == B.rows(), "The number of rows in A must equal the length of B!");
ivec ipiv(n);
X = B;
cmat Chol = A;
zposv_(&uplo, &n, &nrhs, Chol._data(), &lda, X._data(), &ldb, &info);
return (info==0);
}
#else
bool ls_solve_chol(const mat &A, const vec &b, vec &x)
{
it_error("LAPACK library is needed to use ls_solve_chol() function");
return false;
}
bool ls_solve_chol(const mat &A, const mat &B, mat &X)
{
it_error("LAPACK library is needed to use ls_solve_chol() function");
return false;
}
bool ls_solve_chol(const cmat &A, const cvec &b, cvec &x)
{
it_error("LAPACK library is needed to use ls_solve_chol() function");
return false;
}
bool ls_solve_chol(const cmat &A, const cmat &B, cmat &X)
{
it_error("LAPACK library is needed to use ls_solve_chol() function");
return false;
}
#endif // HAVE_LAPACK
vec ls_solve_chol(const mat &A, const vec &b)
{
vec x;
bool info;
info = ls_solve_chol(A, b, x);
it_assert_debug(info, "ls_solve_chol: Failed solving the system");
return x;
}
mat ls_solve_chol(const mat &A, const mat &B)
{
mat X;
bool info;
info = ls_solve_chol(A, B, X);
it_assert_debug(info, "ls_solve_chol: Failed solving the system");
return X;
}
cvec ls_solve_chol(const cmat &A, const cvec &b)
{
cvec x;
bool info;
info = ls_solve_chol(A, b, x);
it_assert_debug(info, "ls_solve_chol: Failed solving the system");
return x;
}
cmat ls_solve_chol(const cmat &A, const cmat &B)
{
cmat X;
bool info;
info = ls_solve_chol(A, B, X);
it_assert_debug(info, "ls_solve_chol: Failed solving the system");
return X;
}
// --------- ls_solve ---------------------------------------------------------------
#if defined(HAVE_LAPACK)
bool ls_solve(const mat &A, const vec &b, vec &x)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = 1;
it_assert_debug(A.cols() == n, "ls_solve: System-matrix is not square");
it_assert_debug(n == b.size(), "The number of rows in A must equal the length of b!");
ivec ipiv(n);
x = b;
mat LU = A;
dgesv_(&n, &nrhs, LU._data(), &lda, ipiv._data(), x._data(), &ldb, &info);
return (info==0);
}
bool ls_solve(const mat &A, const mat &B, mat &X)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = B.cols();
it_assert_debug(A.cols() == n, "ls_solve: System-matrix is not square");
it_assert_debug(n == B.rows(), "The number of rows in A must equal the length of B!");
ivec ipiv(n);
X = B;
mat LU = A;
dgesv_(&n, &nrhs, LU._data(), &lda, ipiv._data(), X._data(), &ldb, &info);
return (info==0);
}
bool ls_solve(const cmat &A, const cvec &b, cvec &x)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = 1;
it_assert_debug(A.cols() == n, "ls_solve: System-matrix is not square");
it_assert_debug(n == b.size(), "The number of rows in A must equal the length of b!");
ivec ipiv(n);
x = b;
cmat LU = A;
zgesv_(&n, &nrhs, LU._data(), &lda, ipiv._data(), x._data(), &ldb, &info);
return (info==0);
}
bool ls_solve(const cmat &A, const cmat &B, cmat &X)
{
int n, lda, ldb, nrhs, info;
n = lda = ldb = A.rows();
nrhs = B.cols();
it_assert_debug(A.cols() == n, "ls_solve: System-matrix is not square");
it_assert_debug(n == B.rows(), "The number of rows in A must equal the length of B!");
ivec ipiv(n);
X = B;
cmat LU = A;
zgesv_(&n, &nrhs, LU._data(), &lda, ipiv._data(), X._data(), &ldb, &info);
return (info==0);
}
#else
bool ls_solve(const mat &A, const vec &b, vec &x)
{
it_error("LAPACK library is needed to use ls_solve() function");
return false;
}
bool ls_solve(const mat &A, const mat &B, mat &X)
{
it_error("LAPACK library is needed to use ls_solve() function");
return false;
}
bool ls_solve(const cmat &A, const cvec &b, cvec &x)
{
it_error("LAPACK library is needed to use ls_solve() function");
return false;
}
bool ls_solve(const cmat &A, const cmat &B, cmat &X)
{
it_error("LAPACK library is needed to use ls_solve() function");
return false;
}
#endif // HAVE_LAPACK
vec ls_solve(const mat &A, const vec &b)
{
vec x;
bool info;
info = ls_solve(A, b, x);
it_assert_debug(info, "ls_solve: Failed solving the system");
return x;
}
mat ls_solve(const mat &A, const mat &B)
{
mat X;
bool info;
info = ls_solve(A, B, X);
it_assert_debug(info, "ls_solve: Failed solving the system");
return X;
}
cvec ls_solve(const cmat &A, const cvec &b)
{
cvec x;
bool info;
info = ls_solve(A, b, x);
it_assert_debug(info, "ls_solve: Failed solving the system");
return x;
}
cmat ls_solve(const cmat &A, const cmat &B)
{
cmat X;
bool info;
info = ls_solve(A, B, X);
it_assert_debug(info, "ls_solve: Failed solving the system");
return X;
}
// ----------------- ls_solve_od ------------------------------------------------------------------
#if defined(HAVE_LAPACK)
bool ls_solve_od(const mat &A, const vec &b, vec &x)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = ldb = A.rows();
n = A.cols();
nrhs = 1;
lwork = n + std::max(m,nrhs);
it_assert_debug(m >= n, "The system is under-determined!");
it_assert_debug(m == b.size(), "The number of rows in A must equal the length of b!");
vec work(lwork);
x = b;
mat QR = A;
dgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, x._data(), &ldb, work._data(), &lwork, &info);
x.set_size(n, true);
return (info==0);
}
bool ls_solve_od(const mat &A, const mat &B, mat &X)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = ldb = A.rows();
n = A.cols();
nrhs = B.cols();
lwork = n + std::max(m,nrhs);
it_assert_debug(m >= n, "The system is under-determined!");
it_assert_debug(m == B.rows(), "The number of rows in A must equal the length of b!");
vec work(lwork);
X = B;
mat QR = A;
dgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, X._data(), &ldb, work._data(), &lwork, &info);
X.set_size(n, nrhs, true);
return (info==0);
}
bool ls_solve_od(const cmat &A, const cvec &b, cvec &x)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = ldb = A.rows();
n = A.cols();
nrhs = 1;
lwork = n + std::max(m,nrhs);
it_assert_debug(m >= n, "The system is under-determined!");
it_assert_debug(m == b.size(), "The number of rows in A must equal the length of b!");
cvec work(lwork);
x = b;
cmat QR = A;
zgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, x._data(), &ldb, work._data(), &lwork, &info);
x.set_size(n, true);
return (info==0);
}
bool ls_solve_od(const cmat &A, const cmat &B, cmat &X)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = ldb = A.rows();
n = A.cols();
nrhs = B.cols();
lwork = n + std::max(m,nrhs);
it_assert_debug(m >= n, "The system is under-determined!");
it_assert_debug(m == B.rows(), "The number of rows in A must equal the length of b!");
cvec work(lwork);
X = B;
cmat QR = A;
zgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, X._data(), &ldb, work._data(), &lwork, &info);
X.set_size(n, nrhs, true);
return (info==0);
}
#else
bool ls_solve_od(const mat &A, const vec &b, vec &x)
{
it_error("LAPACK library is needed to use ls_solve_od() function");
return false;
}
bool ls_solve_od(const mat &A, const mat &B, mat &X)
{
it_error("LAPACK library is needed to use ls_solve_od() function");
return false;
}
bool ls_solve_od(const cmat &A, const cvec &b, cvec &x)
{
it_error("LAPACK library is needed to use ls_solve_od() function");
return false;
}
bool ls_solve_od(const cmat &A, const cmat &B, cmat &X)
{
it_error("LAPACK library is needed to use ls_solve_od() function");
return false;
}
#endif // HAVE_LAPACK
vec ls_solve_od(const mat &A, const vec &b)
{
vec x;
bool info;
info = ls_solve_od(A, b, x);
it_assert_debug(info, "ls_solve_od: Failed solving the system");
return x;
}
mat ls_solve_od(const mat &A, const mat &B)
{
mat X;
bool info;
info = ls_solve_od(A, B, X);
it_assert_debug(info, "ls_solve_od: Failed solving the system");
return X;
}
cvec ls_solve_od(const cmat &A, const cvec &b)
{
cvec x;
bool info;
info = ls_solve_od(A, b, x);
it_assert_debug(info, "ls_solve_od: Failed solving the system");
return x;
}
cmat ls_solve_od(const cmat &A, const cmat &B)
{
cmat X;
bool info;
info = ls_solve_od(A, B, X);
it_assert_debug(info, "ls_solve_od: Failed solving the system");
return X;
}
// ------------------- ls_solve_ud -----------------------------------------------------------
#if defined(HAVE_LAPACK)
bool ls_solve_ud(const mat &A, const vec &b, vec &x)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = A.rows();
n = A.cols();
ldb = n;
nrhs = 1;
lwork = m + std::max(n,nrhs);
it_assert_debug(m < n, "The system is over-determined!");
it_assert_debug(m == b.size(), "The number of rows in A must equal the length of b!");
vec work(lwork);
x = b;
x.set_size(n, true);
mat QR = A;
dgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, x._data(), &ldb, work._data(), &lwork, &info);
return (info==0);
}
bool ls_solve_ud(const mat &A, const mat &B, mat &X)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = A.rows();
n = A.cols();
ldb = n;
nrhs = B.cols();
lwork = m + std::max(n,nrhs);
it_assert_debug(m < n, "The system is over-determined!");
it_assert_debug(m == B.rows(), "The number of rows in A must equal the length of b!");
vec work(lwork);
X = B;
X.set_size(n, std::max(m, nrhs), true);
mat QR = A;
dgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, X._data(), &ldb, work._data(), &lwork, &info);
X.set_size(n, nrhs, true);
return (info==0);
}
bool ls_solve_ud(const cmat &A, const cvec &b, cvec &x)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = A.rows();
n = A.cols();
ldb = n;
nrhs = 1;
lwork = m + std::max(n,nrhs);
it_assert_debug(m < n, "The system is over-determined!");
it_assert_debug(m == b.size(), "The number of rows in A must equal the length of b!");
cvec work(lwork);
x = b;
x.set_size(n, true);
cmat QR = A;
zgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, x._data(), &ldb, work._data(), &lwork, &info);
return (info==0);
}
bool ls_solve_ud(const cmat &A, const cmat &B, cmat &X)
{
int m, n, lda, ldb, nrhs, lwork, info;
char trans='N';
m = lda = A.rows();
n = A.cols();
ldb = n;
nrhs = B.cols();
lwork = m + std::max(n,nrhs);
it_assert_debug(m < n, "The system is over-determined!");
it_assert_debug(m == B.rows(), "The number of rows in A must equal the length of b!");
cvec work(lwork);
X = B;
X.set_size(n, std::max(m, nrhs), true);
cmat QR = A;
zgels_(&trans, &m, &n, &nrhs, QR._data(), &lda, X._data(), &ldb, work._data(), &lwork, &info);
X.set_size(n, nrhs, true);
return (info==0);
}
#else
bool ls_solve_ud(const mat &A, const vec &b, vec &x)
{
it_error("LAPACK library is needed to use ls_solve_ud() function");
return false;
}
bool ls_solve_ud(const mat &A, const mat &B, mat &X)
{
it_error("LAPACK library is needed to use ls_solve_ud() function");
return false;
}
bool ls_solve_ud(const cmat &A, const cvec &b, cvec &x)
{
it_error("LAPACK library is needed to use ls_solve_ud() function");
return false;
}
bool ls_solve_ud(const cmat &A, const cmat &B, cmat &X)
{
it_error("LAPACK library is needed to use ls_solve_ud() function");
return false;
}
#endif // HAVE_LAPACK
vec ls_solve_ud(const mat &A, const vec &b)
{
vec x;
bool info;
info = ls_solve_ud(A, b, x);
it_assert_debug(info, "ls_solve_ud: Failed solving the system");
return x;
}
mat ls_solve_ud(const mat &A, const mat &B)
{
mat X;
bool info;
info = ls_solve_ud(A, B, X);
it_assert_debug(info, "ls_solve_ud: Failed solving the system");
return X;
}
cvec ls_solve_ud(const cmat &A, const cvec &b)
{
cvec x;
bool info;
info = ls_solve_ud(A, b, x);
it_assert_debug(info, "ls_solve_ud: Failed solving the system");
return x;
}
cmat ls_solve_ud(const cmat &A, const cmat &B)
{
cmat X;
bool info;
info = ls_solve_ud(A, B, X);
it_assert_debug(info, "ls_solve_ud: Failed solving the system");
return X;
}
// ---------------------- backslash -----------------------------------------
bool backslash(const mat &A, const vec &b, vec &x)
{
int m=A.rows(), n=A.cols();
bool info;
if (m == n)
info = ls_solve(A,b,x);
else if (m > n)
info = ls_solve_od(A,b,x);
else
info = ls_solve_ud(A,b,x);
return info;
}
vec backslash(const mat &A, const vec &b)
{
vec x;
bool info;
info = backslash(A, b, x);
it_assert_debug(info, "backslash(): solution was not found");
return x;
}
bool backslash(const mat &A, const mat &B, mat &X)
{
int m=A.rows(), n=A.cols();
bool info;
if (m == n)
info = ls_solve(A, B, X);
else if (m > n)
info = ls_solve_od(A, B, X);
else
info = ls_solve_ud(A, B, X);
return info;
}
mat backslash(const mat &A, const mat &B)
{
mat X;
bool info;
info = backslash(A, B, X);
it_assert_debug(info, "backslash(): solution was not found");
return X;
}
bool backslash(const cmat &A, const cvec &b, cvec &x)
{
int m=A.rows(), n=A.cols();
bool info;
if (m == n)
info = ls_solve(A,b,x);
else if (m > n)
info = ls_solve_od(A,b,x);
else
info = ls_solve_ud(A,b,x);
return info;
}
cvec backslash(const cmat &A, const cvec &b)
{
cvec x;
bool info;
info = backslash(A, b, x);
it_assert_debug(info, "backslash(): solution was not found");
return x;
}
bool backslash(const cmat &A, const cmat &B, cmat &X)
{
int m=A.rows(), n=A.cols();
bool info;
if (m == n)
info = ls_solve(A, B, X);
else if (m > n)
info = ls_solve_od(A, B, X);
else
info = ls_solve_ud(A, B, X);
return info;
}
cmat backslash(const cmat &A, const cmat &B)
{
cmat X;
bool info;
info = backslash(A, B, X);
it_assert_debug(info, "backslash(): solution was not found");
return X;
}
// --------------------------------------------------------------------------
vec forward_substitution(const mat &L, const vec &b)
{
int n = L.rows();
vec x(n);
forward_substitution(L, b, x);
return x;
}
void forward_substitution(const mat &L, const vec &b, vec &x)
{
it_assert( L.rows() == L.cols() && L.cols() == b.size() && b.size() == x.size(),
"forward_substitution: dimension mismatch" );
int n = L.rows(), i, j;
double temp;
x(0)=b(0)/L(0,0);
for (i=1;i<n;i++) {
// Should be: x(i)=((b(i)-L(i,i,0,i-1)*x(0,i-1))/L(i,i))(0); but this is to slow.
//i_pos=i*L._row_offset();
temp=0;
for (j=0; j<i; j++) {
temp += L._elem(i,j) * x(j);
//temp+=L._data()[i_pos+j]*x(j);
}
x(i) = (b(i)-temp)/L._elem(i,i);
//x(i)=(b(i)-temp)/L._data()[i_pos+i];
}
}
vec forward_substitution(const mat &L, int p, const vec &b)
{
int n = L.rows();
vec x(n);
forward_substitution(L, p, b, x);
return x;
}
void forward_substitution(const mat &L, int p, const vec &b, vec &x)
{
it_assert( L.rows() == L.cols() && L.cols() == b.size() && b.size() == x.size() && p <= L.rows()/2,
"forward_substitution: dimension mismatch");
int n = L.rows(), i, j;
x=b;
for (j=0;j<n;j++) {
x(j)/=L(j,j);
for (i=j+1;i<std::min(j+p+1,n);i++) {
x(i)-=L(i,j)*x(j);
}
}
}
vec backward_substitution(const mat &U, const vec &b)
{
vec x(U.rows());
backward_substitution(U, b, x);
return x;
}
void backward_substitution(const mat &U, const vec &b, vec &x)
{
it_assert( U.rows() == U.cols() && U.cols() == b.size() && b.size() == x.size(),
"backward_substitution: dimension mismatch" );
int n = U.rows(), i, j;
double temp;
x(n-1)=b(n-1)/U(n-1,n-1);
for (i=n-2; i>=0; i--) {
// Should be: x(i)=((b(i)-U(i,i,i+1,n-1)*x(i+1,n-1))/U(i,i))(0); but this is too slow.
temp=0;
//i_pos=i*U._row_offset();
for (j=i+1; j<n; j++) {
temp += U._elem(i,j) * x(j);
//temp+=U._data()[i_pos+j]*x(j);
}
x(i) = (b(i)-temp)/U._elem(i,i);
//x(i)=(b(i)-temp)/U._data()[i_pos+i];
}
}
vec backward_substitution(const mat &U, int q, const vec &b)
{
vec x(U.rows());
backward_substitution(U, q, b, x);
return x;
}
void backward_substitution(const mat &U, int q, const vec &b, vec &x)
{
it_assert( U.rows() == U.cols() && U.cols() == b.size() && b.size() == x.size() && q <= U.rows()/2,
"backward_substitution: dimension mismatch" );
int n = U.rows(), i, j;
x=b;
for (j=n-1; j>=0; j--) {
x(j) /= U(j,j);
for (i=std::max(0,j-q); i<j; i++) {
x(i)-=U(i,j)*x(j);
}
}
}
} // namespace itpp