//------------------------------------------------------------------------------
// Invert
//------------------------------------------------------------------------------
bool Matrix::invert()
{
bool ok = mda != nullptr && rows > 0 && cols > 0 && isSquare();
if (ok) {
Matrix m(rows, cols);
m.makeIdent();
unsigned int origCols = cols; // 'cols' is changed after augment()
augment(m);
for (unsigned int k = 0; k < origCols; k++) {
pivotRow(k,k);
mulRow(k, 1.0/getElem(k,k));
for (unsigned int i=0; i<rows; i++) {
if (i != k) {
addRow(i, k, -getElem(i,k));
}
}
}
remCols(0, origCols-1);
}
return ok;
}
/*
* 行最简式，Error
*/
Matrix* calc_rref(Matrix* p)
{
Matrix *oldAns = ans;
int i, j, k;
int l = 0;
if (p == NULL)
{
//Error
return NULL;
}
ans = NULL;
if (!stor_createAns(p->m, p->n))
{
//Error
return NULL;
}
if (!stor_assign(ans, p))
{
//Error
return NULL;
}
if (!ans)
{
//Error
return NULL;
}
for (i = 0; i < ans->m; i++)
{
k = isZeroLine(ans, i);
if (k == -1)
{
continue;
}
if (util_isZero(*stor_entry(ans, i, k)))
{
//Error
return NULL;
}
mulRow(ans, i, (double)1.0 / *stor_entry(ans, i, k));
if (!ans)
{
//Error
return NULL;
}
for (j = 0; j < ans->m; j++)
{
if (i != j && !util_isZero(*stor_entry(ans, j, k)))
{
addRow(ans, j, i, -*stor_entry(ans, j, k));
}
}
}
l = 0;
for (i = 0; i < p->n; i++)
{
for (j = i; j < p->m; j++)
{
if (!util_isZero(*stor_entry(ans, j, i))) break;
}
if (j < p->m)
{
if (i != j)
swapRow(ans, l, j);
l++;
}
}
stor_freeMatrix(oldAns);
return ans;
}
/*
* return value(ans only 1*1) should be treated as int, Error
*/
Matrix* calc_rank(Matrix *p)
{
Matrix *oldAns = ans;
int i, j, k;
int count = 0;
if (p == NULL)
{
//Error
return NULL;
}
ans = NULL;
if (p->m > p->n)
{
if (!calc_trans(p))
{
//Error
return NULL;
}
}
else
{
if (!stor_createAns(p->m, p->n))
{
//Error
return NULL;
}
if (!stor_assign(ans, p))
{
//Error
return NULL;
}
}
if (ans == NULL)
{
//Error
return NULL;
}
for (i = 0; i < ans->m; i++)
{
k = count;
while (k < ans->n && util_isZero(*stor_entry(ans, i, k))) k++;
if (k >= ans->n)
{
continue;
}
if (k != count)
{
swapColum(ans, count, k);
}
if (util_isZero(*stor_entry(ans, i, count)))
{
//Error
return NULL;
}
mulRow(ans, i, (double)1.0 / *stor_entry(ans, i, count));
if (!ans)
{
//Error
return NULL;
}
for (j = i + 1; j < ans->m; j++)
{
addRow(ans, j, i, -*stor_entry(ans, j, count));
}
count++;
}
if (!stor_createAns(1, 1))
{
//Error
return NULL;
}
*stor_entry(ans, 0, 0) = count;
stor_freeMatrix(oldAns);
return ans;
}
/*
* return value(ans only 1*1) should be treated as double, Error
*/
Matrix* calc_det(Matrix* p)
{
Matrix *oldAns = ans;
Matrix *temp = NULL;
int i, j, k, n;
if (p == NULL)
{
//Error
return NULL;
}
if (p->m != p->n)
{
//Error
return NULL;
}
n = p->m;
if (!stor_createMatrix(&temp, n, n))
{
//Error
return NULL;
}
if (!stor_assign(temp, p))
{
//Error
return NULL;
}
ans = NULL;
if (!stor_createAns(1, 1))
{
//Error
return NULL;
}
*stor_entry(ans, 0, 0) = 1;
for (i = 0; i < n; i++)
{
k = i;
while (k < n && util_isZero(*stor_entry(temp, i, k))) k++;
if (k >= n)
{
*stor_entry(ans, 0, 0) = 0;
return ans;
}
if (i != k)
{
swapColum(temp, i, k);
}
*stor_entry(ans, 0, 0) *= *stor_entry(temp, i, i);
if (util_isZero(*stor_entry(temp, i, i)))
{
//Error
return NULL;
}
mulRow(temp, i, (double)1.0/ *stor_entry(temp, i, i));
for (j = i + 1; j < n; j++)
{
if (!util_isZero(*stor_entry(temp, j, i)))
{
addRow(temp, j, i, -*stor_entry(temp, j, i));
}
}
}
stor_freeMatrix(temp);
stor_freeMatrix(oldAns);
return ans;
}
/*
*the inverse of matrix, Error
*/
Matrix* calc_inverse(Matrix* p)
{
Matrix *oldAns = ans;
int i, j, k;
int n;
double temp, temp2;
Matrix *t = NULL;
if (p == NULL){
//Error
return NULL;
}
else if (p->m != p->n){
//Error
return NULL;
}
n = p->m;
if (!stor_createMatrix(&t, n, n))
{
//Error
return NULL;
}
if (!stor_assign(t, p))
{
//Error
return NULL;
}
ans = NULL;
if (!calc_eye(n))
{
//Error
return NULL;
}
for (i = 0; i < n; i++)
{
k = i; //the first line that the i colum is not zero
while (k < n && util_isZero(*stor_entry(t, i, k))) k++;//一定要是列增
if (k >= n)
{
//Error,非满秩矩阵
return NULL;
}
if (k != i)
{
swapColum(t, i, k);
swapColum(ans, i, k);
}
//k is no use since
temp = *stor_entry(t, i, i);
if (util_isZero(temp))
{
//Error
return NULL;
}
mulRow(t, i, (double)1.0 / temp);
mulRow(ans, i, (double)1.0 / temp);
//the [i][i] is 1 now
for (j = i + 1; j < n; j++)
{
if (!util_isZero(*stor_entry(t, j, i)))
{
temp2 = *stor_entry(t, j, i);
addRow(t, j, i, -temp2);
addRow(ans, j, i, -temp2);
}
}
}
//现在是阶梯型,阶梯头是1
for (i = n - 1; i >= 0; i--)
{
for (j = i - 1; j >= 0; j--)
{
if (!util_isZero(*stor_entry(t, j, i)))
{
temp2 = *stor_entry(t, j, i);
addRow(t, j, i, -temp2);
addRow(ans, j, i, -temp2);
}
}
}
stor_freeMatrix(t);
stor_freeMatrix(oldAns);
return ans;
}
