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Corrected inverse_exact (attempt 2) #569

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6595e8a
corrected inverse_exact
Jan 29, 2016
4c5e00e
Merge branch 'master' of https://github.com/shahsaurabh0605/nmatrix i…
npriyadarshi Feb 26, 2017
2730d1e
Removing temporary variables
npriyadarshi Feb 26, 2017
e8f1513
added the alias for inverse
npriyadarshi Feb 27, 2017
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36 changes: 18 additions & 18 deletions ext/nmatrix/math.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -188,7 +188,7 @@ extern "C" {
// Math Functions //
////////////////////

namespace nm {
namespace nm {
namespace math {

/*
Expand Down Expand Up @@ -246,18 +246,18 @@ namespace nm {
for (int row = k + 1; row < M; ++row) {
typename MagnitudeDType<DType>::type big;
big = magnitude( matrix[M*row + k] ); // element below the temp pivot

if ( big > akk ) {
interchange = row;
akk = big;
akk = big;
}
}
}

if (interchange != k) { // check if rows need flipping
DType temp;

for (int col = 0; col < M; ++col) {
NM_SWAP(matrix[interchange*M + col], matrix[k*M + col], temp);
NM_SWAP(matrix[interchange*M + col], matrix[k*M + col], temp);
}
}

Expand All @@ -271,7 +271,7 @@ namespace nm {
DType pivot = matrix[k * (M + 1)];
matrix[k * (M + 1)] = (DType)(1); // set diagonal as 1 for in-place inversion

for (int col = 0; col < M; ++col) {
for (int col = 0; col < M; ++col) {
// divide each element in the kth row with the pivot
matrix[k*M + col] = matrix[k*M + col] / pivot;
}
Expand All @@ -280,7 +280,7 @@ namespace nm {
if (kk == k) continue;

DType dum = matrix[k + M*kk];
matrix[k + M*kk] = (DType)(0); // prepare for inplace inversion
matrix[k + M*kk] = (DType)(0); // prepare for inplace inversion
for (int col = 0; col < M; ++col) {
matrix[M*kk + col] = matrix[M*kk + col] - matrix[M*k + col] * dum;
}
Expand All @@ -295,7 +295,7 @@ namespace nm {

for (int row = 0; row < M; ++row) {
NM_SWAP(matrix[row * M + row_index[k]], matrix[row * M + col_index[k]],
temp);
temp);
}
}
}
Expand All @@ -321,14 +321,14 @@ namespace nm {
DType sum_of_squares, *p_row, *psubdiag, *p_a, scale, innerproduct;
int i, k, col;

// For each column use a Householder transformation to zero all entries
// For each column use a Householder transformation to zero all entries
// below the subdiagonal.
for (psubdiag = a + nrows, col = 0; col < nrows - 2; psubdiag += nrows + 1,
for (psubdiag = a + nrows, col = 0; col < nrows - 2; psubdiag += nrows + 1,
col++) {
// Calculate the signed square root of the sum of squares of the
// elements below the diagonal.

for (p_a = psubdiag, sum_of_squares = 0.0, i = col + 1; i < nrows;
for (p_a = psubdiag, sum_of_squares = 0.0, i = col + 1; i < nrows;
p_a += nrows, i++) {
sum_of_squares += *p_a * *p_a;
}
Expand Down Expand Up @@ -358,7 +358,7 @@ namespace nm {
*p_a -= u[k] * innerproduct;
}
}

// Postmultiply QA by Q
for (p_row = a, i = 0; i < nrows; p_row += nrows, i++) {
for (innerproduct = 0.0, k = col + 1; k < nrows; k++) {
Expand Down Expand Up @@ -386,23 +386,23 @@ namespace nm {
if (M == 2) {
DType det = A[0] * A[lda+1] - A[1] * A[lda];
if (det == 0) {
rb_raise(nm_eNotInvertibleError,
rb_raise(nm_eNotInvertibleError,
"matrix must have non-zero determinant to be invertible (not getting this error does not mean matrix is invertible if you're dealing with floating points)");
}
DType index= A[0];
B[0] = A[lda+1] / det;
B[1] = -A[1] / det;
B[ldb] = -A[lda] / det;
B[ldb+1] = -A[0] / det;
B[ldb+1] = index/ det;

} else if (M == 3) {
// Calculate the exact determinant.
DType det;
det_exact<DType>(M, A_elements, lda, reinterpret_cast<void*>(&det));
if (det == 0) {
rb_raise(nm_eNotInvertibleError,
rb_raise(nm_eNotInvertibleError,
"matrix must have non-zero determinant to be invertible (not getting this error does not mean matrix is invertible if you're dealing with floating points)");
}

B[0] = ( A[lda+1] * A[2*lda+2] - A[lda+2] * A[2*lda+1]) / det; // A = ei - fh
B[1] = (- A[1] * A[2*lda+2] + A[2] * A[2*lda+1]) / det; // D = -bi + ch
B[2] = ( A[1] * A[lda+2] - A[2] * A[lda+1]) / det; // G = bf - ce
Expand All @@ -411,7 +411,7 @@ namespace nm {
B[ldb+2] = (- A[0] * A[lda+2] + A[2] * A[lda]) / det; // H = -af + cd
B[2*ldb] = ( A[lda] * A[2*lda+1] - A[lda+1] * A[2*lda]) / det; // C = dh - eg
B[2*ldb+1]= ( -A[0] * A[2*lda+1] + A[1] * A[2*lda]) / det; // F = -ah + bg
B[2*ldb+2]= ( A[0] * A[lda+1] - A[1] * A[lda]) / det; // I = ae - bd
B[2*ldb+2]= ( A[0] * A[lda+1] - A[1] * A[lda]) / det; // I = ae -bd
} else if (M == 1) {
B[0] = 1 / A[0];
} else {
Expand Down Expand Up @@ -1087,7 +1087,7 @@ void nm_math_hessenberg(VALUE a) {
NULL, NULL, // does not support Complex
NULL // no support for Ruby Object
};

ttable[NM_DTYPE(a)](NM_SHAPE0(a), NM_STORAGE_DENSE(a)->elements);
}
/*
Expand Down
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