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/* generated code, do not edit. */
#include "ode/matrix.h"
/* solve L*X=B, with B containing 1 right hand sides.
* L is an n*n lower triangular matrix with ones on the diagonal.
* L is stored by rows and its leading dimension is lskip.
* B is an n*1 matrix that contains the right hand sides.
* B is stored by columns and its leading dimension is also lskip.
* B is overwritten with X.
* this processes blocks of 2*2.
* if this is in the factorizer source file, n must be a multiple of 2.
*/
static void dSolveL1_1 (const dReal *L, dReal *B, int n, int lskip1)
{
/* declare variables - Z matrix, p and q vectors, etc */
dReal Z11,m11,Z21,m21,p1,q1,p2,*ex;
const dReal *ell;
int i,j;
/* compute all 2 x 1 blocks of X */
for (i=0; i < n; i+=2) {
/* compute all 2 x 1 block of X, from rows i..i+2-1 */
/* set the Z matrix to 0 */
Z11=0;
Z21=0;
ell = L + i*lskip1;
ex = B;
/* the inner loop that computes outer products and adds them to Z */
for (j=i-2; j >= 0; j -= 2) {
/* compute outer product and add it to the Z matrix */
p1=ell[0];
q1=ex[0];
m11 = p1 * q1;
p2=ell[lskip1];
m21 = p2 * q1;
Z11 += m11;
Z21 += m21;
/* compute outer product and add it to the Z matrix */
p1=ell[1];
q1=ex[1];
m11 = p1 * q1;
p2=ell[1+lskip1];
m21 = p2 * q1;
/* advance pointers */
ell += 2;
ex += 2;
Z11 += m11;
Z21 += m21;
/* end of inner loop */
}
/* compute left-over iterations */
j += 2;
for (; j > 0; j--) {
/* compute outer product and add it to the Z matrix */
p1=ell[0];
q1=ex[0];
m11 = p1 * q1;
p2=ell[lskip1];
m21 = p2 * q1;
/* advance pointers */
ell += 1;
ex += 1;
Z11 += m11;
Z21 += m21;
}
/* finish computing the X(i) block */
Z11 = ex[0] - Z11;
ex[0] = Z11;
p1 = ell[lskip1];
Z21 = ex[1] - Z21 - p1*Z11;
ex[1] = Z21;
/* end of outer loop */
}
}
/* solve L*X=B, with B containing 2 right hand sides.
* L is an n*n lower triangular matrix with ones on the diagonal.
* L is stored by rows and its leading dimension is lskip.
* B is an n*2 matrix that contains the right hand sides.
* B is stored by columns and its leading dimension is also lskip.
* B is overwritten with X.
* this processes blocks of 2*2.
* if this is in the factorizer source file, n must be a multiple of 2.
*/
static void dSolveL1_2 (const dReal *L, dReal *B, int n, int lskip1)
{
/* declare variables - Z matrix, p and q vectors, etc */
dReal Z11,m11,Z12,m12,Z21,m21,Z22,m22,p1,q1,p2,q2,*ex;
const dReal *ell;
int i,j;
/* compute all 2 x 2 blocks of X */
for (i=0; i < n; i+=2) {
/* compute all 2 x 2 block of X, from rows i..i+2-1 */
/* set the Z matrix to 0 */
Z11=0;
Z12=0;
Z21=0;
Z22=0;
ell = L + i*lskip1;
ex = B;
/* the inner loop that computes outer products and adds them to Z */
for (j=i-2; j >= 0; j -= 2) {
/* compute outer product and add it to the Z matrix */
p1=ell[0];
q1=ex[0];
m11 = p1 * q1;
q2=ex[lskip1];
m12 = p1 * q2;
p2=ell[lskip1];
m21 = p2 * q1;
m22 = p2 * q2;
Z11 += m11;
Z12 += m12;
Z21 += m21;
Z22 += m22;
/* compute outer product and add it to the Z matrix */
p1=ell[1];
q1=ex[1];
m11 = p1 * q1;
q2=ex[1+lskip1];
m12 = p1 * q2;
p2=ell[1+lskip1];
m21 = p2 * q1;
m22 = p2 * q2;
/* advance pointers */
ell += 2;
ex += 2;
Z11 += m11;
Z12 += m12;
Z21 += m21;
Z22 += m22;
/* end of inner loop */
}
/* compute left-over iterations */
j += 2;
for (; j > 0; j--) {
/* compute outer product and add it to the Z matrix */
p1=ell[0];
q1=ex[0];
m11 = p1 * q1;
q2=ex[lskip1];
m12 = p1 * q2;
p2=ell[lskip1];
m21 = p2 * q1;
m22 = p2 * q2;
/* advance pointers */
ell += 1;
ex += 1;
Z11 += m11;
Z12 += m12;
Z21 += m21;
Z22 += m22;
}
/* finish computing the X(i) block */
Z11 = ex[0] - Z11;
ex[0] = Z11;
Z12 = ex[lskip1] - Z12;
ex[lskip1] = Z12;
p1 = ell[lskip1];
Z21 = ex[1] - Z21 - p1*Z11;
ex[1] = Z21;
Z22 = ex[1+lskip1] - Z22 - p1*Z12;
ex[1+lskip1] = Z22;
/* end of outer loop */
}
}
void dFactorLDLT (dReal *A, dReal *d, int n, int nskip1)
{
int i,j;
dReal sum,*ell,*dee,dd,p1,p2,q1,q2,Z11,m11,Z21,m21,Z22,m22;
if (n < 1) return;
for (i=0; i<=n-2; i += 2) {
/* solve L*(D*l)=a, l is scaled elements in 2 x i block at A(i,0) */
dSolveL1_2 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 2 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
Z21 = 0;
Z22 = 0;
ell = A+i*nskip1;
dee = d;
for (j=i-6; j >= 0; j -= 6) {
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[1];
p2 = ell[1+nskip1];
dd = dee[1];
q1 = p1*dd;
q2 = p2*dd;
ell[1] = q1;
ell[1+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[2];
p2 = ell[2+nskip1];
dd = dee[2];
q1 = p1*dd;
q2 = p2*dd;
ell[2] = q1;
ell[2+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[3];
p2 = ell[3+nskip1];
dd = dee[3];
q1 = p1*dd;
q2 = p2*dd;
ell[3] = q1;
ell[3+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[4];
p2 = ell[4+nskip1];
dd = dee[4];
q1 = p1*dd;
q2 = p2*dd;
ell[4] = q1;
ell[4+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[5];
p2 = ell[5+nskip1];
dd = dee[5];
q1 = p1*dd;
q2 = p2*dd;
ell[5] = q1;
ell[5+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
ell += 6;
dee += 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
ell++;
dee++;
}
/* solve for diagonal 2 x 2 block at A(i,i) */
Z11 = ell[0] - Z11;
Z21 = ell[nskip1] - Z21;
Z22 = ell[1+nskip1] - Z22;
dee = d + i;
/* factorize 2 x 2 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* factorize row 2 */
sum = 0;
q1 = Z21;
q2 = q1 * dee[0];
Z21 = q2;
sum += q1*q2;
dee[1] = dRecip(Z22 - sum);
/* done factorizing 2 x 2 block */
ell[nskip1] = Z21;
}
/* compute the (less than 2) rows at the bottom */
switch (n-i) {
case 0:
break;
case 1:
dSolveL1_1 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 1 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
ell = A+i*nskip1;
dee = d;
for (j=i-6; j >= 0; j -= 6) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[1];
dd = dee[1];
q1 = p1*dd;
ell[1] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[2];
dd = dee[2];
q1 = p1*dd;
ell[2] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[3];
dd = dee[3];
q1 = p1*dd;
ell[3] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[4];
dd = dee[4];
q1 = p1*dd;
ell[4] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[5];
dd = dee[5];
q1 = p1*dd;
ell[5] = q1;
m11 = p1*q1;
Z11 += m11;
ell += 6;
dee += 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
ell++;
dee++;
}
/* solve for diagonal 1 x 1 block at A(i,i) */
Z11 = ell[0] - Z11;
dee = d + i;
/* factorize 1 x 1 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* done factorizing 1 x 1 block */
break;
default: *((char*)0)=0; /* this should never happen! */
}
}
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