//sucin
int
sucin (p_TMatrix ptm1, p_TMatrix ptm2)
{
int code, i = 0, j = 0, k = 0;
if (ptm1->m != ptm2->n)
return RET_INP;
TMatrix tmp;
tmp.n = ptm1->n;
tmp.m = ptm2->m;
if ((code = allocMat (&tmp)) != RET_OK)
return code;
zeroMat (&tmp);
for (i = 0; i < tmp.n; i++)
for (j = 0; j < tmp.m; j++)
for (k = 0; k < ptm1->m; k++)
tmp.add[i][j] += (ptm1->add[i][k] * ptm2->add[k][j]);
vypisMat (&tmp);
freeMat (&tmp);
return RET_OK;
}
//krizova rotacia
int
crot (p_TMatrix ptm1)
{
int code, i = 0, j = 0;
int l;
TMatrix tmp1;
tmp1.n = ptm1->n;
tmp1.m = ptm1->m;
//pomocna matica 1
if ((code = allocMat (&tmp1)) != RET_OK)
return code;
zeroMat (&tmp1);
//spravnim indexovanim naplnime pomocnu maticu posunutymi riadkami
for (i = 0; i < tmp1.n; i++)
{
l = ptm1->add[i][0];
l = l % (ptm1->m);
for (j = 0; j < ptm1->m; j++)
tmp1.add[i][j] = ptm1->add[i][(j - l + ptm1->m) % (ptm1->m)];
}
//podobne posunieme stlpce
TMatrix tmp2;
tmp2.n = ptm1->n;
tmp2.m = ptm1->m;
if ((code = allocMat (&tmp2)) != RET_OK)
return code;
zeroMat (&tmp2);
for (i = 0; i < tmp1.m; i++)
{
l = tmp1.add[0][i];
l = l % (ptm1->n);
for (j = 0; j < ptm1->n; j++)
tmp2.add[j][i] = tmp1.add[(j - l + ptm1->n) % (ptm1->n)][i];
}
vypisMat (&tmp2);
freeMat (&tmp1);
freeMat (&tmp2);
return RET_OK;
}
//将矩阵拟上三角化
void hessenbergMat(double **a)
{
int r, i, j;
double c, d, h, t, u[10], p[10], q[10], w[10];
for (r = 0; r<8; r++) {
zeroMat(a);
c = 0; d = 0; h = 0;
for (i = r + 2; i<10; i++)
d += a[i][r] * a[i][r];
if (d == 0)
continue;
else {
d += a[r + 1][r] * a[r + 1][r];
d = pow(d, 0.5);
if (a[r + 1][r] != 0)
c = -fabs(a[r + 1][r]) / a[r + 1][r] * d;
else
c = d;
h = c*c - c*a[r + 1][r];
for (i = 0; i<r + 1; i++)
u[i] = 0;
u[r + 1] = a[r + 1][r] - c;
for (i = r + 2; i<10; i++)
u[i] = a[i][r];
for (i = 0; i<10; i++) {
p[i] = 0; q[i] = 0;
for (j = 0; j<10; j++) {
p[i] += a[j][i] * u[j] / h;
q[i] += a[i][j] * u[j] / h;
}
}
t = 0;
for (i = 0; i<10; i++)
t += p[i] * u[i] / h;
for (i = 0; i<10; i++)
w[i] = q[i] - t*u[i];
for (i = 0; i<10; i++) {
for (j = 0; j<10; j++)
a[i][j] -= (w[i] * u[j] + u[i] * p[j]);
}
}
}
printf("A(n-1)\n");
zeroMat(a);
printMat(a);
}
//QR分解中的迭代运算
void iterate(double **M, double **a, int m)
{
int r, i, j;
double c, d, h, t, u[10], v[10], p[10], q[10], w[10];
for (r = 0; r<m - 1; r++) {
zeroMat(M);
c = 0; d = 0; h = 0;
for (i = r + 1; i<m; i++)
d += M[i][r] * M[i][r];
if (fabs(d) == 0)
continue;
else {
d += M[r][r] * M[r][r];
d = pow(d, 0.5);
if (M[r][r] != 0)
c = -fabs(M[r][r]) / M[r][r] * d;
else
c = d;
h = c*c - c*M[r][r];
for (i = 0; i<r; i++)u[i] = 0;
u[r] = M[r][r] - c;
for (i = r + 1; i<m; i++)
u[i] = M[i][r];
for (i = 0; i<m; i++) {
v[i] = 0;
for (j = 0; j<m; j++)
v[i] += M[j][i] * u[j] / h;
}
for (i = 0; i<m; i++) {
p[i] = 0; q[i] = 0;
for (j = 0; j<m; j++) {
M[i][j] -= u[i] * v[j];
p[i] += a[j][i] * u[j] / h;
q[i] += a[i][j] * u[j] / h;
}
}
t = 0;
for (i = 0; i<m; i++)
t += p[i] * u[i] / h;
for (i = 0; i<m; i++)
w[i] = q[i] - t*u[i];
for (i = 0; i<m; i++) {
for (j = 0; j<m; j++) {
a[i][j] -= (w[i] * u[j] + u[i] * p[j]);
}
}
}
}
}
int
plough (p_TMatrix ptm1)
{
int code = 0, i = 0, j = 0, k = 0, l = 0;
TMatrix tmp;
tmp.n = ptm1->n;
tmp.m = ptm1->m;
//Alokacia pomocnej matice
if ((code = allocMat (&tmp)) != RET_OK)
return code;
zeroMat (&tmp);
code = start;
/* v zdrojovej matici sa pohybujeme premennymi k,l
v kazdej iteracii zistujeme ci nedoslo k zmene podmienky daneho stavu
ak ano prepneme na novy smer */
for (i = 0; i < ptm1->n; i++)
for (j = 0; j < ptm1->m; j++)
if (!((k == ptm1->n - 1) && (l == ptm1->m - 1)))
{
switch (code)
{
case start:
tmp.add[i][j] = ptm1->add[k][l];
code = right;
break;
case right:
l++;
tmp.add[i][j] = ptm1->add[k][l];
if (k == 0)
code = down_left;
if (k == ptm1->n - 1)
code = up_right;
break;
case down_left:
k++;
l--;
tmp.add[i][j] = ptm1->add[k][l];
if ((k == ptm1->n - 1))
code = right;
else if ((l == 0) && (k != ptm1->n - 1))
code = down;
else
code = down_left;
break;
case down:
k++;
tmp.add[i][j] = ptm1->add[k][l];
if (l == 0)
code = up_right;
if (l == ptm1->m - 1)
code = down_left;
break;
case up_right:
k--;
l++;
tmp.add[i][j] = ptm1->add[k][l];
if ((l == ptm1->m - 1))
code = down;
else if ((k == 0) && (k != ptm1->m - 1))
code = right;
else
code = up_right;
break;
}
}
vypisMat (&tmp);
freeMat (&tmp);
return RET_OK;
}
/**
* 11.
* @brief Create an zero matrix of the requested size.
* @param[in] n The dimension of the zero matrix.
* @return Zero matrix of the required size.
*/
static matrix_type zeros(int m, int n) {
matrix_type zeroMat(m,n);
elem::Zero(zeroMat);
return zeroMat;
}
//带双布位移的QR分解方法
void QRmethod(double **a)
{
int k, m, i, j, r;
double s, t, det;
double **M;
ComplexNumber L[10];
M = (double**)malloc(10 * sizeof(double *));
for (k = 0; k<10; k++)
M[k] = (double*)malloc(10 * sizeof(double));
m = 9; r = 0;
for (k = 0; k<Max; k++)
{
if (m == 0) {
L[r].Re = a[m][m];
L[r].Im = 0; break;
}
else if (m < 0) {
break;
}
if (fabs(a[m][m - 1])<e) {
L[r].Re = a[m][m];
L[r].Im = 0;
m--; r++;
}
else {
if (m == 1) {
det = (a[m][m] + a[m - 1][m - 1])*(a[m][m] + a[m - 1][m - 1]) - 4 * (a[m][m] * a[m - 1][m - 1] - a[m - 1][m] * a[m][m - 1]);
if (det > 0) {
L[r].Re = (a[m][m] + a[m - 1][m - 1]) / 2 + sqrt(det) / 2;
L[r].Im = 0;
L[r + 1].Re = (a[m][m] + a[m - 1][m - 1]) / 2 - sqrt(det) / 2;
L[r + 1].Im = 0;
}
else {
L[r].Re = (a[m][m] + a[m - 1][m - 1]) / 2;
L[r].Im = sqrt(-det) / 2;
L[r + 1].Re = (a[m][m] + a[m - 1][m - 1]) / 2;
L[r + 1].Im = -sqrt(-det) / 2;
}
m -= 2;
r += 2;
continue;
}
else if (fabs(a[m - 1][m - 2])<e) {
det = (a[m][m] + a[m - 1][m - 1])*(a[m][m] + a[m - 1][m - 1]) - 4 * (a[m][m] * a[m - 1][m - 1] - a[m - 1][m] * a[m][m - 1]);
if (det>0) {
L[r].Re = (a[m][m] + a[m - 1][m - 1]) / 2 + sqrt(det) / 2;
L[r].Im = 0;
L[r + 1].Re = (a[m][m] + a[m - 1][m - 1]) / 2 - sqrt(det) / 2;
L[r + 1].Im = 0;
}
else {
L[r].Re = (a[m][m] + a[m - 1][m - 1]) / 2;
L[r].Im = sqrt(-det) / 2;
L[r + 1].Re = (a[m][m] + a[m - 1][m - 1]) / 2;
L[r + 1].Im = -sqrt(-det) / 2;
}
m -= 2;
r += 2;
continue;
}
else {
s = a[m - 1][m - 1] + a[m][m];
t = a[m - 1][m - 1] * a[m][m] - a[m][m - 1] * a[m - 1][m];
muiltiplyMat(a, a, M, m + 1);
for (i = 0; i<10; i++)
{
for (j = 0; j<10; j++)
M[i][j] -= s*a[i][j];
M[i][i] += t;
}
iterate(M, a, m + 1);
zeroMat(a);
}
}
}
zeroMat(a);
printf("after QR method\n");
printMat(a);
for (int r = 0; r<10; r++) {
printf("\n");
if (L[r].Im == 0) {
printf("lambda[%d] = (%.12e + i*%.12e)\n", r + 1, L[r].Re, L[r].Im);
gauss(L[r].Re);
}
else {
printf("lambda[%d] = (%.12e + i*%.12e)\n", r + 1, L[r].Re, L[r].Im);
}
}
for (int i = 0; i < 10; i++) {
free(M[i]);
}
free(M);
}
//求Q、R和RQ
void QR_and_RQ(double **a)
{
int i, j, r;
double c, d, h, w[10], p[10], u[10];
double **Q, **R, **RQ;
Q = (double **)malloc(10 * sizeof(double *));
for (i = 0; i < 10; i++)
Q[i] = (double *)malloc(11 * sizeof(double));
R = (double **)malloc(10 * sizeof(double *));
for (i = 0; i < 10; i++)
R[i] = (double *)malloc(11 * sizeof(double));
RQ = (double **)malloc(10 * sizeof(double *));
for (i = 0; i<10; i++)
RQ[i] = (double *)malloc(11 * sizeof(double));
for(i = 0; i < 10; i++) {
for(j = 0; j < 10; j++){
if(i == j)
Q[i][i] = 1;
else
Q[i][j] = 0;
}
}
for(i = 0; i < 10; i++) {
for(j = 0; j < 10; j++)
R[i][j] = a[i][j];
}
zeroMat(R);
for(r = 0; r < 9; r++){
d = 0;
for(i = r + 1; i < 10; i++)
d += R[i][r] * R[i][r];
if(fabs(d) == 0)
continue;
else {
d += R[r][r] * R[r][r];
d = sqrt(d);
if (R[r][r] == 0)
c = d;
else
c = -sgn(R[r][r]) * d;
h = c * c - c * R[r][r];
for(i = 0; i < r; i++)
u[i] = 0;
u[r] = R[r][r] - c;
for(i = r + 1; i < 10; i++)
u[i] = R[i][r];
for(i = 0; i < 10; i++) {
w[i] = 0;
for(j = 0; j < 10; j++)
w[i] += Q[i][j] * u[j];
}
for(i = 0; i < 10; i++) {
for(j = 0; j < 10; j++)
Q[i][j] -= w[i] * u[j] / h;
}
for(i = 0; i < 10; i++){
p[i] = 0;
for(j = 0; j < 10; j ++ )
p[i] += R[j][i] * u[j] / h;
}
for(i = 0; i < 10; i++){
for(j = 0; j < 10; j++)
R[i][j] -= u[i] * p[j];
}
}
}
zeroMat(R);
zeroMat(Q);
zeroMat(RQ);
printf("Q:\n");
printMat(Q);
printf("R:\n");
printMat(R);
muiltiplyMat(R, Q, RQ, 10);
printf("RQ:\n");
printMat(RQ);
for (i = 0; i < 10; i++)
free(Q[i]);
free(Q);
for (i = 0; i < 10; i++)
free(R[i]);
free(R);
for (i = 0; i<10; i++)
free(RQ[i]);
free(RQ);
}