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improved accuracy of the matrix determinant and matrix inversion functions (trac #431)

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This commit is contained in:
Vadim Pisarevsky
2010-07-13 14:17:49 +00:00
parent fa91788222
commit da02688429
2 changed files with 248 additions and 218 deletions
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154
modules/core/src/lapack.cpp
View File

@@ -229,11 +229,13 @@ double determinant( const Mat& mat )
size_t step = mat.step;
const uchar* m = mat.data;
CV_Assert( mat.rows == mat.cols );
CV_Assert( mat.rows == mat.cols && (type == CV_32F || type == CV_64F));
#define Mf(y, x) ((float*)(m + y*step))[x]
#define Md(y, x) ((double*)(m + y*step))[x]
if( rows <= 10 )
{
if( type == CV_32F )
{
if( rows == 2 )
@@ -244,30 +246,21 @@ double determinant( const Mat& mat )
result = Mf(0,0);
else
{
integer i, n = rows, *ipiv, info=0;
int bufSize = n*n*sizeof(float) + (n+1)*sizeof(ipiv[0]), sign=0;
size_t bufSize = rows*rows*sizeof(float);
AutoBuffer<uchar> buffer(bufSize);
Mat a(n, n, CV_32F, (uchar*)buffer);
Mat a(rows, rows, CV_32F, (uchar*)buffer);
mat.copyTo(a);
ipiv = (integer*)cvAlignPtr(a.data + a.step*a.rows, sizeof(integer));
sgetrf_(&n, &n, (float*)a.data, &n, ipiv, &info);
assert(info >= 0);
if( info == 0 )
result = LU((float*)a.data, rows, 0, 0);
if( result )
{
result = 1;
for( i = 0; i < n; i++ )
{
result *= ((float*)a.data)[i*(n+1)];
sign ^= ipiv[i] != i+1;
}
result *= sign ? -1 : 1;
for( int i = 0; i < rows; i++ )
result *= ((const float*)(a.data + a.step*i))[i];
result = 1./result;
}
}
}
else if( type == CV_64F )
else
{
if( rows == 2 )
result = det2(Md);
@@ -277,14 +270,31 @@ double determinant( const Mat& mat )
result = Md(0,0);
else
{
integer i, n = rows, *ipiv, info=0;
int bufSize = n*n*sizeof(double) + (n+1)*sizeof(ipiv[0]), sign=0;
size_t bufSize = rows*rows*sizeof(double);
AutoBuffer<uchar> buffer(bufSize);
Mat a(rows, rows, CV_64F, (uchar*)buffer);
mat.copyTo(a);
result = LU((double*)a.data, rows, 0, 0);
if( result )
{
for( int i = 0; i < rows; i++ )
result *= ((const double*)(a.data + a.step*i))[i];
result = 1./result;
}
}
}
}
else
{
integer i, n = rows, *ipiv, info=0, sign = 0;
size_t bufSize = n*n*sizeof(double) + (n+1)*sizeof(ipiv[0]);
AutoBuffer<uchar> buffer(bufSize);
Mat a(n, n, CV_64F, (uchar*)buffer);
mat.copyTo(a);
ipiv = (integer*)cvAlignPtr(a.data + a.step*a.rows, sizeof(integer));
mat.convertTo(a, CV_64F);
ipiv = (integer*)cvAlignPtr(a.data + a.step*a.rows, sizeof(integer));
dgetrf_(&n, &n, (double*)a.data, &n, ipiv, &info);
assert(info >= 0);
@@ -299,9 +309,6 @@ double determinant( const Mat& mat )
result *= sign ? -1 : 1;
}
}
}
else
CV_Error( CV_StsUnsupportedFormat, "" );
#undef Mf
#undef Md
@@ -341,8 +348,6 @@ double invert( const Mat& src, Mat& dst, int method )
CV_Assert( src.rows == src.cols && (type == CV_32F || type == CV_64F));
dst.create( src.rows, src.cols, type );
if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
{
if( src.rows <= 3 )
{
uchar* srcdata = src.data;
@@ -470,64 +475,89 @@ double invert( const Mat& src, Mat& dst, int method )
return result;
}
src.copyTo(dst);
integer n = dst.cols, lwork=-1, elem_size = CV_ELEM_SIZE(type),
lda = (int)(dst.step/elem_size), piv1=0, info=0;
if( method == DECOMP_LU )
if( dst.cols <= 10 )
{
int buf_size = (int)(n*sizeof(integer));
AutoBuffer<uchar> buf;
uchar* buffer;
int n = dst.cols, elem_size = CV_ELEM_SIZE(type);
AutoBuffer<uchar> buf(n*n*2*elem_size);
Mat src1(n, n, type, (uchar*)buf);
Mat dst1(n, n, type, dst.isContinuous() ? dst.data : src1.data + n*n*elem_size);
src.copyTo(src1);
setIdentity(dst1);
if( type == CV_32F )
{
real work1 = 0;
sgetri_(&n, (float*)dst.data, &lda, &piv1, &work1, &lwork, &info);
lwork = cvRound(work1);
if( method == DECOMP_LU && type == CV_32F )
result = LU((float*)src1.data, n, (float*)dst1.data, n);
else if( method == DECOMP_LU && type == CV_64F )
result = LU((double*)src1.data, n, (double*)dst1.data, n);
else if( method == DECOMP_LU && type == CV_32F )
result = Cholesky((float*)src1.data, n, (float*)dst1.data, n);
else
result = Cholesky((double*)src1.data, n, (double*)dst1.data, n);
dst1.copyTo(dst);
result = std::abs(result);
}
else
{
integer n = dst.cols, lwork=-1, lda = n, piv1=0, info=0;
int t_size = type == CV_32F ? n*n*sizeof(double) : 0;
int buf_size = t_size;
AutoBuffer<uchar> buf;
if( method == DECOMP_LU )
{
double work1 = 0;
dgetri_(&n, (double*)dst.data, &lda, &piv1, &work1, &lwork, &info);
lwork = cvRound(work1);
}
buf_size += (int)((lwork + 1)*elem_size);
buf_size += (int)(n*sizeof(integer) + (lwork + 1)*sizeof(double));
buf.allocate(buf_size);
buffer = (uchar*)buf;
uchar* buffer = (uchar*)buf;
Mat arr = dst;
if( type == CV_32F )
{
sgetrf_(&n, &n, (float*)dst.data, &lda, (integer*)buffer, &info);
if(info==0)
sgetri_(&n, (float*)dst.data, &lda, (integer*)buffer,
(float*)(buffer + n*sizeof(integer)), &lwork, &info);
arr = Mat(n, n, CV_64F, buffer);
src.convertTo(arr, CV_64F);
buffer += t_size;
}
else
{
dgetrf_(&n, &n, (double*)dst.data, &lda, (integer*)buffer, &info);
src.copyTo(arr);
lda = arr.step/sizeof(double);
}
dgetrf_(&n, &n, (double*)arr.data, &lda, (integer*)buffer, &info);
if(info==0)
dgetri_(&n, (double*)dst.data, &lda, (integer*)buffer,
(double*)cvAlignPtr(buffer + n*sizeof(integer), elem_size), &lwork, &info);
dgetri_(&n, (double*)arr.data, &lda, (integer*)buffer,
(double*)cvAlignPtr(buffer + n*sizeof(integer), sizeof(double)),
&lwork, &info);
if(info==0 && arr.data != dst.data)
arr.convertTo(dst, dst.type());
}
}
else if( method == CV_CHOLESKY )
else if( method == DECOMP_CHOLESKY )
{
Mat arr = dst;
if( type == CV_32F )
{
buf.allocate(buf_size);
arr = Mat(n, n, CV_64F, (uchar*)buf);
src.convertTo(arr, CV_64F);
}
else
{
src.copyTo(arr);
lda = arr.step/sizeof(double);
}
char L[] = {'L', '\0'};
if( type == CV_32F )
{
spotrf_(L, &n, (float*)dst.data, &lda, &info);
dpotrf_(L, &n, (double*)arr.data, &lda, &info);
if(info==0)
spotri_(L, &n, (float*)dst.data, &lda, &info);
}
else
{
dpotrf_(L, &n, (double*)dst.data, &lda, &info);
dpotri_(L, &n, (double*)arr.data, &lda, &info);
if(info==0)
dpotri_(L, &n, (double*)dst.data, &lda, &info);
{
completeSymm(arr);
if( arr.data != dst.data )
arr.convertTo(dst, dst.type());
}
completeSymm(dst);
}
result = info == 0;
}

8
tests/cxcore/src/amath.cpp
View File

@@ -2420,7 +2420,7 @@ void CxCore_DetTest::prepare_to_validation( int )
*((CvScalar*)(test_mat[REF_OUTPUT][0].data.db)) = cvRealScalar(cvTsLU(&test_mat[TEMP][0], 0, 0));
}
//CxCore_DetTest det_test;
CxCore_DetTest det_test;
@@ -2475,8 +2475,8 @@ void CxCore_InvertTest::get_test_array_types_and_sizes( int test_case_idx, CvSiz
if( bits & 4 )
{
sizes[INPUT][0] = cvSize(min_size, min_size);
if( bits & 8 )
method = CV_SVD_SYM;
if( bits & 16 )
method = CV_CHOLESKY;
}
}
else
@@ -2536,7 +2536,7 @@ int CxCore_InvertTest::prepare_test_case( int test_case_idx )
{
cvTsFloodWithZeros( &test_mat[INPUT][0], ts->get_rng() );
if( method == CV_SVD_SYM )
if( method == CV_CHOLESKY )
{
cvTsGEMM( &test_mat[INPUT][0], &test_mat[INPUT][0], 1.,
0, 0., &test_mat[TEMP][0], CV_GEMM_B_T );