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Commit 438ec254 authored by Davis King's avatar Davis King
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Setup the LU decomposition code to use LAPACK when available. I also removed the older 

version from numerical recipes and made everything depend on the lu_decomposition object
instead.  Finally, I added in a triangular solver that uses BLAS when available and made
the lu_decomposition object us it.

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%403833
parent 9de0a49c
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dlib/matrix/cblas_constants.h 0 → 100644
View file @ 438ec254
#ifndef DLIB_CBLAS_CONSTAnTS_H__
#define DLIB_CBLAS_CONSTAnTS_H__
namespace dlib
{
namespace blas_bindings
{
enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102};
enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113};
enum CBLAS_UPLO {CblasUpper=121, CblasLower=122};
enum CBLAS_DIAG {CblasNonUnit=131, CblasUnit=132};
enum CBLAS_SIDE {CblasLeft=141, CblasRight=142};
}
}
#endif // DLIB_CBLAS_CONSTAnTS_H__
dlib/matrix/lapack/getrf.h
View file @ 438ec254
// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_LAPACk_GETRF_H__
#define DLIB_LAPACk_GETRF_H__
......@@ -106,28 +108,16 @@ namespace dlib
>
int getrf (
matrix<T,NR1,NC1,MM,column_major_layout>& a,
matrix<long,NR2,NC2,MM,layout>& ipiv
matrix<integer,NR2,NC2,MM,layout>& ipiv
)
{
const long m = a.nr();
const long n = a.nc();
matrix<integer,NR2,NC2,MM,column_major_layout> ipiv_temp(std::min(m,n), 1);
ipiv.set_size(std::min(m,n), 1);
// compute the actual decomposition
int info = binding::getrf(m, n, &a(0,0), a.nr(), &ipiv_temp(0,0));
// Turn the P vector into a more useful form. This way we will have the identity
// a == rowm(L*U, ipiv). The permutation vector that comes out of LAPACK is somewhat
// different.
ipiv = trans(range(0, a.nr()-1));
for (long i = ipiv_temp.size()-1; i >= 0; --i)
{
// -1 because FORTRAN is indexed starting with 1 instead of 0
std::swap(ipiv(i), ipiv(ipiv_temp(i)-1));
}
return info;
return binding::getrf(m, n, &a(0,0), a.nr(), &ipiv(0,0));
}
// ------------------------------------------------------------------------------------
......
dlib/matrix/matrix_blas_bindings.h
View file @ 438ec254
......@@ -9,6 +9,7 @@
#include "matrix_assign.h"
#include "matrix_conj_trans.h"
#include "cblas_constants.h"
//#include <iostream>
//using namespace std;
......@@ -41,9 +42,6 @@ namespace dlib
{
// Here we declare the prototypes for the CBLAS calls used by the BLAS bindings below
enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102};
enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113};
void cblas_sgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_TRANSPOSE TransB, const int M, const int N,
const int K, const float alpha, const float *A,
......
dlib/matrix/matrix_la.h
View file @ 438ec254
......@@ -393,166 +393,6 @@ namespace dlib
return true;
}
template <
typename T,
long N,
long NX,
typename MM1,
typename MM2,
typename MM3,
typename L1,
typename L2,
typename L3
>
bool ludcmp (
matrix<T,N,N,MM1,L1>& a,
matrix<long,N,NX,MM2,L2>& indx,
T& d,
matrix<T,N,NX,MM3,L3>& vv
)
/*!
( this function is derived from the one in numerical recipes in C chapter 2.3)
ensures
- #a == both the L and U matrices
- #indx == the permutation vector (see numerical recipes in C)
- #d == some other thing (see numerical recipes in C)
- #vv == some undefined value. this is just used for scratch space
- if (the matrix is singular and we can't do anything) then
- returns false
- else
- returns true
!*/
{
DLIB_ASSERT(indx.nc() == 1,"in dlib::nric::ludcmp() the indx matrix must be a column vector");
DLIB_ASSERT(vv.nc() == 1,"in dlib::nric::ludcmp() the vv matrix must be a column vector");
const long n = a.nr();
long imax = 0;
T big, dum, sum, temp;
d = 1.0;
for (long i = 0; i < n; ++i)
{
big = 0;
for (long j = 0; j < n; ++j)
{
if ((temp=std::abs(a(i,j))) > big)
big = temp;
}
if (big == 0.0)
{
return false;
}
vv(i) = 1/big;
}
for (long j = 0; j < n; ++j)
{
for (long i = 0; i < j; ++i)
{
sum = a(i,j);
for (long k = 0; k < i; ++k)
sum -= a(i,k)*a(k,j);
a(i,j) = sum;
}
big = 0;
for (long i = j; i < n; ++i)
{
sum = a(i,j);
for (long k = 0; k < j; ++k)
sum -= a(i,k)*a(k,j);
a(i,j) = sum;
if ( (dum=vv(i)*std::abs(sum)) >= big)
{
big = dum;
imax = i;
}
}
if (j != imax)
{
for (long k = 0; k < n; ++k)
{
dum = a(imax,k);
a(imax,k) = a(j,k);
a(j,k) = dum;
}
d = -d;
vv(imax) = vv(j);
}
indx(j) = imax;
if (j < n-1)
{
if (a(j,j) == 0)
return false;
dum = 1/a(j,j);
for (long i = j+1; i < n; ++i)
a(i,j) *= dum;
}
}
return true;
}
// ----------------------------------------------------------------------------------------
template <
typename T,
long N,
long NX,
typename MM1,
typename MM2,
typename MM3,
typename L1,
typename L2,
typename L3
>
void lubksb (
const matrix<T,N,N,MM1,L1>& a,
const matrix<long,N,NX,MM2,L2>& indx,
matrix<T,N,NX,MM3,L3>& b
)
/*!
( this function is derived from the one in numerical recipes in C chapter 2.3)
requires
- a == the LU decomposition you get from ludcmp()
- indx == the indx term you get out of ludcmp()
- b == the right hand side vector from the expression a*x = b
ensures
- #b == the solution vector x from the expression a*x = b
(basically, this function solves for x given b and a)
!*/
{
DLIB_ASSERT(indx.nc() == 1,"in dlib::nric::lubksb() the indx matrix must be a column vector");
DLIB_ASSERT(b.nc() == 1,"in dlib::nric::lubksb() the b matrix must be a column vector");
const long n = a.nr();
long i, ii = -1, ip, j;
T sum;
for (i = 0; i < n; ++i)
{
ip = indx(i);
sum=b(ip);
b(ip) = b(i);
if (ii != -1)
{
for (j = ii; j < i; ++j)
sum -= a(i,j)*b(j);
}
else if (sum)
{
ii = i;
}
b(i) = sum;
}
for (i = n-1; i >= 0; --i)
{
sum = b(i);
for (j = i+1; j < n; ++j)
sum -= a(i,j)*b(j);
b(i) = sum/a(i,i);
}
}
// ------------------------------------------------------------------------------------
}
......@@ -1001,31 +841,8 @@ convergence:
);
typedef typename matrix_exp<EXP>::type type;
matrix<type, N, N,MM> a(m), y(m.nr(),m.nr());
matrix<long,N,1,MM> indx(m.nr(),1);
matrix<type,N,1,MM> col(m.nr(),1);
matrix<type,N,1,MM> vv(m.nr(),1);
type d;
long i, j;
if (ludcmp(a,indx,d,vv))
{
for (j = 0; j < m.nr(); ++j)
{
for (i = 0; i < m.nr(); ++i)
col(i) = 0;
col(j) = 1;
lubksb(a,indx,col);
for (i = 0; i < m.nr(); ++i)
y(i,j) = col(i);
}
}
else
{
// m is singular so lets just set y equal to m just so that
// it has some value
y = m;
}
return y;
lu_decomposition<EXP> lu(m);
return lu.solve(identity_matrix<type>(m.nr()));
}
};
......@@ -1502,17 +1319,7 @@ convergence:
typedef typename matrix_exp<EXP>::type type;
typedef typename matrix_exp<EXP>::mem_manager_type MM;
matrix<type, N, N,MM> lu(m);
matrix<long,N,1,MM> indx(m.nr(),1);
matrix<type,N,1,MM> vv(m.nr(),1);
type d;
if (ludcmp(lu,indx,d,vv) == false)
{
// the matrix is singular so its det is 0
return 0;
}
return prod(diag(lu))*d;
return lu_decomposition<EXP>(m).det();
}
};
......
dlib/matrix/matrix_la_abstract.h
View file @ 438ec254
......@@ -255,6 +255,9 @@ namespace dlib
LU decomposition is in the solution of square systems of simultaneous
linear equations. This will fail if is_singular() returns true (or
if A is very nearly singular).
If DLIB_USE_LAPACK is defined then the LAPACK routine xGETRF
is used to compute the LU decomposition.
!*/
public:
......
dlib/matrix/matrix_lu.h
View file @ 438ec254
......@@ -8,8 +8,14 @@
#include "matrix.h"
#include "matrix_utilities.h"
#include "matrix_subexp.h"
#include "matrix_trsm.h"
#include <algorithm>
#ifdef DLIB_USE_LAPACK
#include "lapack/getrf.h"
#endif
namespace dlib
{
......@@ -72,7 +78,7 @@ namespace dlib
private:
/* Array for internal storage of decomposition. */
matrix_type LU;
matrix<type,0,0,mem_manager_type,column_major_layout> LU;
long m, n, pivsign;
pivot_column_vector_type piv;
......@@ -108,6 +114,28 @@ namespace dlib
<< "\n\tthis: " << this
);
#ifdef DLIB_USE_LAPACK
matrix<lapack::integer,0,1,mem_manager_type,layout_type> piv_temp;
lapack::getrf(LU, piv_temp);
pivsign = 1;
// Turn the piv_temp vector into a more useful form. This way we will have the identity
// rowm(A,piv) == L*U. The permutation vector that comes out of LAPACK is somewhat
// different.
piv = trans(range(0,m-1));
for (long i = 0; i < piv_temp.size(); ++i)
{
// -1 because FORTRAN is indexed starting with 1 instead of 0
if (piv(piv_temp(i)-1) != piv(i))
{
std::swap(piv(i), piv(piv_temp(i)-1));
pivsign = -pivsign;
}
}
#else
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
......@@ -170,6 +198,8 @@ namespace dlib
}
}
}
#endif
}
// ----------------------------------------------------------------------------------------
......@@ -311,67 +341,15 @@ namespace dlib
<< "\n\tthis: " << this
);
const long nx = B.nc();
// if there are multiple columns in B
if (nx > 1)
{
// Copy right hand side with pivoting
matrix_type X(rowm(B, piv));
// Copy right hand side with pivoting
matrix<type,0,0,mem_manager_type,column_major_layout> X(rowm(B, piv));
// Solve L*Y = B(piv,:)
for (long k = 0; k < n; k++)
{
for (long i = k+1; i < n; i++)
{
for (long j = 0; j < nx; j++)
{
X(i,j) -= X(k,j)*LU(i,k);
}
}
}
// Solve U*X = Y;
for (long k = n-1; k >= 0; k--)
{
for (long j = 0; j < nx; j++)
{
X(k,j) /= LU(k,k);
}
for (long i = 0; i < k; i++)
{
for (long j = 0; j < nx; j++)
{
X(i,j) -= X(k,j)*LU(i,k);
}
}
}
return X;
}
else
{
column_vector_type x(rowm(B, piv));
// Solve L*Y = B(piv)
for (long k = 0; k < n; k++)
{
for (long i = k+1; i < n; i++)
{
x(i) -= x(k)*LU(i,k);
}
}
// Solve U*X = Y;
for (long k = n-1; k >= 0; k--)
{
x(k) /= LU(k,k);
for (long i = 0; i < k; i++)
x(i) -= x(k)*LU(i,k);
}
return x;
}
using namespace blas_bindings;
// Solve L*Y = B(piv,:)
triangular_solver(CblasLeft, CblasLower, CblasNoTrans, CblasUnit, LU, X);
// Solve U*X = Y;
triangular_solver(CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, LU, X);
return X;
}
// ----------------------------------------------------------------------------------------
......
dlib/matrix/matrix_trsm.h 0 → 100644
View file @ 438ec254
// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#include "lapack/fortran_id.h"
#include "cblas_constants.h"
namespace dlib
{
namespace blas_bindings
{
extern "C"
{
void cblas_strsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const float alpha, const float *A, const int lda,
float *B, const int ldb);
void cblas_dtrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const double alpha, const double *A, const int lda,
double *B, const int ldb);
}
// ------------------------------------------------------------------------------------
/* Purpose */
/* ======= */
/* DTRSM solves one of the matrix equations */
/* op( A )*X = alpha*B, or X*op( A ) = alpha*B, */
/* where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
/* non-unit, upper or lower triangular matrix and op( A ) is one of */
/* op( A ) = A or op( A ) = A'. */
/* The matrix X is overwritten on B. */
/* Arguments */
/* ========== */
/* SIDE - CHARACTER*1. */
/* On entry, SIDE specifies whether op( A ) appears on the left */
/* or right of X as follows: */
/* SIDE = 'L' or 'l' op( A )*X = alpha*B. */
/* SIDE = 'R' or 'r' X*op( A ) = alpha*B. */
/* Unchanged on exit. */
/* UPLO - CHARACTER*1. */
/* On entry, UPLO specifies whether the matrix A is an upper or */
/* lower triangular matrix as follows: */
/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
/* Unchanged on exit. */
/* TRANSA - CHARACTER*1. */
/* On entry, TRANSA specifies the form of op( A ) to be used in */
/* the matrix multiplication as follows: */
/* TRANSA = 'N' or 'n' op( A ) = A. */
/* TRANSA = 'T' or 't' op( A ) = A'. */
/* TRANSA = 'C' or 'c' op( A ) = A'. */
/* Unchanged on exit. */
/* DIAG - CHARACTER*1. */
/* On entry, DIAG specifies whether or not A is unit triangular */
/* as follows: */
/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
/* DIAG = 'N' or 'n' A is not assumed to be unit */
/* triangular. */
/* Unchanged on exit. */
/* M - INTEGER. */
/* On entry, M specifies the number of rows of B. M must be at */
/* least zero. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the number of columns of B. N must be */
/* at least zero. */
/* Unchanged on exit. */
/* ALPHA - DOUBLE PRECISION. */
/* On entry, ALPHA specifies the scalar alpha. When alpha is */
/* zero then A is not referenced and B need not be set before */
/* entry. */
/* Unchanged on exit. */
/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
/* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */
/* Before entry with UPLO = 'U' or 'u', the leading k by k */
/* upper triangular part of the array A must contain the upper */
/* triangular matrix and the strictly lower triangular part of */
/* A is not referenced. */
/* Before entry with UPLO = 'L' or 'l', the leading k by k */
/* lower triangular part of the array A must contain the lower */
/* triangular matrix and the strictly upper triangular part of */
/* A is not referenced. */
/* Note that when DIAG = 'U' or 'u', the diagonal elements of */
/* A are not referenced either, but are assumed to be unity. */
/* Unchanged on exit. */
/* LDA - INTEGER. */
/* On entry, LDA specifies the first dimension of A as declared */
/* in the calling (sub) program. When SIDE = 'L' or 'l' then */
/* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */
/* then LDA must be at least max( 1, n ). */
/* Unchanged on exit. */
/* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
/* Before entry, the leading m by n part of the array B must */
/* contain the right-hand side matrix B, and on exit is */
/* overwritten by the solution matrix X. */
/* LDB - INTEGER. */
/* On entry, LDB specifies the first dimension of B as declared */
/* in the calling (sub) program. LDB must be at least */
/* max( 1, m ). */
/* Unchanged on exit. */
/* Level 3 Blas routine. */
/* -- Written on 8-February-1989. */
/* Jack Dongarra, Argonne National Laboratory. */
/* Iain Duff, AERE Harwell. */
/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */
/* Sven Hammarling, Numerical Algorithms Group Ltd. */
template <typename T>
void local_trsm(
const enum CBLAS_ORDER Order,
enum CBLAS_SIDE Side,
enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
long m,
long n,
T alpha,
const T *a,
long lda,
T *b,
long ldb
)
/*!
This is a copy of the dtrsm routine from the netlib.org BLAS which was run though
f2c and converted into this form for use when a BLAS library is not available.
!*/
{
if (Order == CblasRowMajor)
{
// since row major ordering looks like transposition to FORTRAN we need to flip a
// few things.
if (Side == CblasLeft)
Side = CblasRight;
else
Side = CblasLeft;
if (Uplo == CblasUpper)
Uplo = CblasLower;
else
Uplo = CblasUpper;
std::swap(m,n);
}
/* System generated locals */
long a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
long i__, j, k, info;
T temp;
bool lside;
long nrowa;
bool upper;
bool nounit;
/* Parameter adjustments */
a_dim1 = lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = (Side == CblasLeft);
if (lside)
{
nrowa = m;
} else
{
nrowa = n;
}
nounit = (Diag == CblasNonUnit);
upper = (Uplo == CblasUpper);
info = 0;
if (! lside && ! (Side == CblasRight)) {
info = 1;
} else if (! upper && !(Uplo == CblasLower) ) {
info = 2;
} else if (!(TransA == CblasNoTrans) &&
!(TransA == CblasTrans) &&
!(TransA == CblasConjTrans)) {
info = 3;
} else if (!(Diag == CblasUnit) &&
!(Diag == CblasNonUnit) ) {
info = 4;
} else if (m < 0) {
info = 5;
} else if (n < 0) {
info = 6;
} else if (lda < std::max<long>(1,nrowa)) {
info = 9;
} else if (ldb < std::max<long>(1,m)) {
info = 11;
}
DLIB_CASSERT( info == 0, "Invalid inputs given to local_trsm");
/* Quick return if possible. */
if (m == 0 || n == 0) {
return;
}
/* And when alpha.eq.zero. */
if (alpha == 0.) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.;
/* L10: */
}
/* L20: */
}
return;
}
/* Start the operations. */
if (lside) {
if (TransA == CblasNoTrans) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L30: */
}
}
for (k = m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L70: */
}
}
i__2 = m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__3 = m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = alpha * b[i__ + j * b_dim1];
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L110: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
for (i__ = m; i__ >= 1; --i__) {
temp = alpha * b[i__ + j * b_dim1];
i__2 = m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L140: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (TransA == CblasNoTrans) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__3 = m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L200: */
}
}
/* L210: */
}
} else {
for (j = n; j >= 1; --j) {
if (alpha != 1.) {
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L220: */
}
}
i__1 = n;
for (k = j + 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = n; k >= 1; --k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L280: */
}
}
/* L290: */
}
if (alpha != 1.) {
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
;
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L320: */
}
}
i__2 = n;
for (j = k + 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__3 = m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L330: */
}
}
/* L340: */
}
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
;
/* L350: */
}
}
/* L360: */
}
}
}
}
}
// ------------------------------------------------------------------------------------
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const float alpha, const float *A, const int lda,
float *B, const int ldb)
{
#ifdef DLIB_USE_BLAS
cblas_strsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
#else
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
#endif
}
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const double alpha, const double *A, const int lda,
double *B, const int ldb)
{
#ifdef DLIB_USE_BLAS
cblas_dtrsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
#else
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
#endif
}
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const long double alpha, const long double *A, const int lda,
long double *B, const int ldb)
{
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,row_major_layout>& A,
const T alpha,
matrix<T,NR2,NC2,MM,row_major_layout>& B
)
{
cblas_trsm(CblasRowMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
alpha, &A(0,0), A.nc(), &B(0,0), B.nc());
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,column_major_layout>& A,
const T alpha,
matrix<T,NR2,NC2,MM,column_major_layout>& B
)
{
cblas_trsm(CblasColMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM,
typename layout
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,layout>& A,
matrix<T,NR2,NC2,MM,layout>& B
)
{
const T alpha = 1;
triangular_solver(Side, Uplo, TransA, Diag, A, alpha, B);
}
// ------------------------------------------------------------------------------------
}
}
dlib/test/matrix2.cpp
View file @ 438ec254
......@@ -25,6 +25,8 @@ namespace
logger dlog("test.matrix2");
dlib::rand::float_1a rnd;
void matrix_test (
)
/*!
......@@ -370,16 +372,11 @@ namespace
matrix<double, 7, 7,MM,column_major_layout> m7;
matrix<double> dm7(7,7);
for (long r= 0; r< dm7.nr(); ++r)
{
for (long c = 0; c < dm7.nc(); ++c)
{
dm7(r,c) = r*c/3.3;
}
}
dm7 = randm(7,7, rnd);
m7 = dm7;
DLIB_TEST(inv(dm7) == inv(m7));
DLIB_TEST_MSG(max(abs(dm7*inv(dm7) - identity_matrix<double>(7))) < 1e-12, max(abs(dm7*inv(dm7) - identity_matrix<double>(7))));
DLIB_TEST(equal(inv(dm7), inv(m7)));
DLIB_TEST(det(dm7) == det(m7));
DLIB_TEST(min(dm7) == min(m7));
DLIB_TEST(max(dm7) == max(m7));
......
dlib/test/matrix_eig.cpp
View file @ 438ec254
......@@ -110,6 +110,17 @@ namespace
DLIB_TEST(max(abs(test.get_imag_eigenvalues())) < eps);
DLIB_TEST(diagm(diag(D)) == D);
// only check the determinant against the eigenvalues for small matrices
// because for huge ones the determinant might be so big it overflows a floating point number.
if (m.nr() < 50)
{
const type mdet = det(m);
DLIB_TEST_MSG(std::abs(prod(test.get_real_eigenvalues()) - mdet) < std::abs(mdet)*sqrt(std::numeric_limits<type>::epsilon()),
std::abs(prod(test.get_real_eigenvalues()) - mdet) <<" eps: " << std::abs(mdet)*sqrt(std::numeric_limits<type>::epsilon())
<< " mdet: "<< mdet << " prod(eig): " << prod(test.get_real_eigenvalues())
);
}
// V is orthogonal
DLIB_TEST(equal(V*trans(V), identity_matrix<type>(test.dim()), eps));
DLIB_TEST(equal(m , V*D*trans(V), eps));
......
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