/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
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* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
* conditions of this Agreement. For the avoidance of doubt, you acquire
* only a limited right to use the SOFTWARE hereunder, and FLL or any
* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
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* purposes. You may use the SOFTWARE only for non-commercial and
* non-profit purposes only, such as academic, research and internal
* business use.
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* international copyright treaties. If you make copies of the SOFTWARE,
* with or without modification, as permitted hereunder, you shall affix
* to all such copies of the SOFTWARE the above copyright notice.
* (3) An explicit reference to this SOFTWARE and its copyright owner
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* results obtained by use of the SOFTWARE.
* (4) In the event that you modify the SOFTWARE, you shall notify FLL by
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* for such modification or the source code of the modified part of the
* SOFTWARE.
*
* THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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* $OpenXM: OpenXM_contrib2/asir2000/engine/mat.c,v 1.5 2002/03/01 06:27:23 saito Exp $
*/
#include "ca.h"
#include "../parse/parse.h"
extern int StrassenSize;
void addmat(vl,a,b,c)
VL vl;
MAT a,b,*c;
{
int row,col,i,j;
MAT t;
pointer *ab,*bb,*tb;
if ( !a )
*c = b;
else if ( !b )
*c = a;
else if ( (a->row != b->row) || (a->col != b->col) ) {
*c = 0; error("addmat : size mismatch add");
} else {
row = a->row; col = a->col;
MKMAT(t,row,col);
for ( i = 0; i < row; i++ )
for ( j = 0, ab = BDY(a)[i], bb = BDY(b)[i], tb = BDY(t)[i];
j < col; j++ )
addr(vl,(Obj)ab[j],(Obj)bb[j],(Obj *)&tb[j]);
*c = t;
}
}
void submat(vl,a,b,c)
VL vl;
MAT a,b,*c;
{
int row,col,i,j;
MAT t;
pointer *ab,*bb,*tb;
if ( !a )
chsgnmat(b,c);
else if ( !b )
*c = a;
else if ( (a->row != b->row) || (a->col != b->col) ) {
*c = 0; error("submat : size mismatch sub");
} else {
row = a->row; col = a->col;
MKMAT(t,row,col);
for ( i = 0; i < row; i++ )
for ( j = 0, ab = BDY(a)[i], bb = BDY(b)[i], tb = BDY(t)[i];
j < col; j++ )
subr(vl,(Obj)ab[j],(Obj)bb[j],(Obj *)&tb[j]);
*c = t;
}
}
void mulmat(vl,a,b,c)
VL vl;
Obj a,b,*c;
{
if ( !a || !b )
*c = 0;
else if ( OID(a) <= O_R )
mulrmat(vl,(Obj)a,(MAT)b,(MAT *)c);
else if ( OID(b) <= O_R )
mulrmat(vl,(Obj)b,(MAT)a,(MAT *)c);
else
switch ( OID(a) ) {
case O_VECT:
switch ( OID(b) ) {
case O_MAT:
mulvectmat(vl,(VECT)a,(MAT)b,(VECT *)c); break;
case O_VECT: default:
notdef(vl,a,b,c); break;
}
break;
case O_MAT:
switch ( OID(b) ) {
case O_VECT:
mulmatvect(vl,(MAT)a,(VECT)b,(VECT *)c); break;
case O_MAT:
mulmatmat(vl,(MAT)a,(MAT)b,(MAT *)c); break;
default:
notdef(vl,a,b,c); break;
}
break;
default:
notdef(vl,a,b,c); break;
}
}
void divmat(vl,a,b,c)
VL vl;
Obj a,b,*c;
{
Obj t;
if ( !b )
error("divmat : division by 0");
else if ( !a )
*c = 0;
else if ( OID(b) > O_R )
notdef(vl,a,b,c);
else {
divr(vl,(Obj)ONE,b,&t); mulrmat(vl,t,(MAT)a,(MAT *)c);
}
}
void chsgnmat(a,b)
MAT a,*b;
{
MAT t;
int row,col,i,j;
pointer *ab,*tb;
if ( !a )
*b = 0;
else {
row = a->row; col = a->col;
MKMAT(t,row,col);
for ( i = 0; i < row; i++ )
for ( j = 0, ab = BDY(a)[i], tb = BDY(t)[i];
j < col; j++ )
chsgnr((Obj)ab[j],(Obj *)&tb[j]);
*b = t;
}
}
void pwrmat(vl,a,r,c)
VL vl;
MAT a;
Obj r;
MAT *c;
{
if ( !a )
*c = 0;
else if ( !r || !NUM(r) || !RATN(r) ||
!INT(r) || (SGN((Q)r)<0) || (PL(NM((Q)r))>1) ) {
*c = 0; error("pwrmat : invalid exponent");
} else if ( a->row != a->col ) {
*c = 0; error("pwrmat : non square matrix");
} else
pwrmatmain(vl,a,QTOS((Q)r),c);
}
void pwrmatmain(vl,a,e,c)
VL vl;
MAT a;
int e;
MAT *c;
{
MAT t,s;
if ( e == 1 ) {
*c = a;
return;
}
pwrmatmain(vl,a,e/2,&t);
mulmat(vl,(Obj)t,(Obj)t,(Obj *)&s);
if ( e % 2 )
mulmat(vl,(Obj)s,(Obj)a,(Obj *)c);
else
*c = s;
}
void mulrmat(vl,a,b,c)
VL vl;
Obj a;
MAT b,*c;
{
int row,col,i,j;
MAT t;
pointer *bb,*tb;
if ( !a || !b )
*c = 0;
else {
row = b->row; col = b->col;
MKMAT(t,row,col);
for ( i = 0; i < row; i++ )
for ( j = 0, bb = BDY(b)[i], tb = BDY(t)[i];
j < col; j++ )
mulr(vl,(Obj)a,(Obj)bb[j],(Obj *)&tb[j]);
*c = t;
}
}
void mulmatmat(vl,a,b,c)
VL vl;
MAT a,b,*c;
{
#if 0
int arow,bcol,i,j,k,m;
MAT t;
pointer s,u,v;
pointer *ab,*tb;
/* Mismach col and row */
if ( a->col != b->row ) {
*c = 0; error("mulmat : size mismatch");
} else {
arow = a->row; m = a->col; bcol = b->col;
MKMAt(t,arow,bcol);
for ( i = 0; i < arow; i++ )
for ( j = 0, ab = BDY(a)[i], tb = BDY(t)[i]; j < bcol; j++ ) {
for ( k = 0, s = 0; k < m; k++ ) {
mulr(vl,(Obj)ab[k],(Obj)BDY(b)[k][j],(Obj *)&u);
addr(vl,(Obj)s,(Obj)u,(Obj *)&v);
s = v;
}
tb[j] = s;
}
*c = t;
}
}
void Strassen(arg, c)
NODE arg;
Obj *c;
{
MAT a,b;
VL vl;
/* tomo */
a = (MAT)ARG0(arg);
b = (MAT)ARG1(arg);
vl = CO;
strassen(CO, a, b, c);
}
void strassen(vl,a,b,c)
VL vl;
MAT a,b,*c;
{
#endif
int arow,bcol,i,j,k,m, h, arowh, bcolh;
MAT t, a11, a12, a21, a22;
MAT p, b11, b12, b21, b22;
MAT ans1, ans2, ans3, c11, c12, c21, c22;
MAT s1, s2, t1, t2, u1, v1, w1, aa, bb;
pointer s,u,v;
pointer *ab,*tb;
int a1row,a2row, a3row,a4row, a1col, a2col, a3col, a4col;
int b1row,b2row, b3row,b4row, b1col, b2col, b3col, b4col;
int pflag1, pflag2;
/* mismach col and row */
if ( a->col != b->row ) {
*c = 0; error("mulmat : size mismatch");
}
else {
pflag1 = 0; pflag2 = 0;
arow = a->row; m = a->col; bcol = b->col;
arowh = arow/2; bcolh = bcol/2;
MKMAT(t,arow,bcol);
/* StrassenSize == 0 or matrix size less then StrassenSize,
then calc cannonical algorithm. */
if((StrassenSize == 0)||(a->row<=StrassenSize || a->col <= StrassenSize) || (b->row<=StrassenSize || b->col <= StrassenSize)) {
for ( i = 0; i < arow; i++ )
for ( j = 0, ab = BDY(a)[i], tb = BDY(t)[i]; j < bcol; j++ ) {
for ( k = 0, s = 0; k < m; k++ ) {
mulr(vl,(Obj)ab[k],(Obj)BDY(b)[k][j],(Obj *)&u);
addr(vl,(Obj)s,(Obj)u,(Obj *)&v);
s = v;
}
tb[j] = s;
}
*c = t;
return;
}
/* padding odd col and row to even number for zero */
i = arow/2;
j = arow - i;
if (i != j) {
arow++;
pflag1 = 1;
}
i = m/2;
j = m - i;
if (i != j) {
m++;
pflag2 = 1;
}
MKMAT(aa, arow, m);
for (i = 0; i < a->row; i++) {
for (j = 0; j < a->col; j++) {
aa->body[i][j] = a->body[i][j];
}
}
i = bcol/2;
j = bcol - i;
if (i != j) {
bcol++;
}
MKMAT(bb, m, bcol);
for (i = 0; i < b->row; i++) {
for ( j = 0; j < b->col; j++) {
bb->body[i][j] = b->body[i][j];
}
}
/* split matrix A and B */
a1row = aa->row/2; a1col = aa->col/2;
MKMAT(a11,a1row,a1col);
MKMAT(a21,a1row,a1col);
MKMAT(a12,a1row,a1col);
MKMAT(a22,a1row,a1col);
b1row = bb->row/2; b1col = bb->col/2;
MKMAT(b11,b1row,b1col);
MKMAT(b21,b1row,b1col);
MKMAT(b12,b1row,b1col);
MKMAT(b22,b1row,b1col);
/* make a11 matrix */
for (i = 0; i < a1row; i++) {
for (j = 0; j < a1col; j++) {
a11->body[i][j] = aa->body[i][j];
}
}
/* make a21 matrix */
for (i = a1row; i < aa->row; i++) {
for (j = 0; j < a1col; j++) {
a21->body[i-a1row][j] = aa->body[i][j];
}
}
/* create a12 matrix */
for (i = 0; i < a1row; i++) {
for (j = a1col; j < aa->col; j++) {
a12->body[i][j-a1col] = aa->body[i][j];
}
}
/* create a22 matrix */
for (i = a1row; i < aa->row; i++) {
for (j = a1col; j < aa->col; j++) {
a22->body[i-a1row][j-a1col] = aa->body[i][j];
}
}
/* create b11 submatrix */
for (i = 0; i < b1row; i++) {
for (j = 0; j < b1col; j++) {
b11->body[i][j] = bb->body[i][j];
}
}
/* create b21 submatrix */
for (i = b1row; i < bb->row; i++) {
for (j = 0; j < b1col; j++) {
b21->body[i-b1row][j] = bb->body[i][j];
}
}
/* create b12 submatrix */
for (i = 0; i < b1row; i++) {
for (j = b1col; j < bb->col; j++) {
b12->body[i][j-b1col] = bb->body[i][j];
}
}
/* create b22 submatrix */
for (i = b1row; i < bb->row; i++) {
for (j = b1col; j < bb->col; j++) {
b22->body[i-b1row][j-b1col] = bb->body[i][j];
}
}
/* expand matrix by Strassen-Winograd algorithm */
/* s1=A21+A22 */
addmat(vl,a21,a22,&s1);
/* s2=s1-A11 */
submat(vl,s1,a11,&s2);
/* t1=B12-B11 */
submat(vl, b12, b11, &t1);
/* t2=B22-t1 */
submat(vl, b22, t1, &t2);
/* u=(A11-A21)*(B22-B12) */
submat(vl, a11, a21, &ans1);
submat(vl, b22, b12, &ans2);
mulmatmat(vl, ans1, ans2, &u1);
/* v=s1*t1 */
mulmatmat(vl, s1, t1, &v1);
/* w=A11*B11+s2*t2 */
mulmatmat(vl, a11, b11, &ans1);
mulmatmat(vl, s2, t2, &ans2);
addmat(vl, ans1, ans2, &w1);
/* C11 = A11*B11+A12*B21 */
mulmatmat(vl, a12, b21, &ans2);
addmat(vl, ans1, ans2, &c11);
/* C12 = w1+v1+(A12-s2)*B22 */
submat(vl, a12, s2, &ans1);
mulmatmat(vl, ans1, b22, &ans2);
addmat(vl, w1, v1, &ans1);
addmat(vl, ans1, ans2, &c12);
/* C21 = w1+u1+A22*(B21-t2) */
submat(vl, b21, t2, &ans1);
mulmatmat(vl, a22, ans1, &ans2);
for ( j=0; j < k; j++) {
t->body[i][j+c11->col] = c12->body[i][j];
}
}
if (pflag1 == 0) {
k = c22->row;
} else {
k = c22->row -1;
}
if (pflag2 == 0) {
h = c22->col;
} else {
h = c22->col - 1;
}
for(i =0; i<k; i++) {
for ( j=0; j < h; j++) {
t->body[i+c11->row][j+c11->col] = c22->body[i][j];
}
}
*c = t;
}
void mulmatvect(vl,a,b,c)
VL vl;
MAT a;
VECT b;
VECT *c;
{
int arow,i,j,m;
VECT t;
pointer s,u,v;
pointer *ab;
if ( !a || !b )
*c = 0;
else if ( a->col != b->len ) {
*c = 0; error("mulmatvect : size mismatch");
} else {
arow = a->row; m = a->col;
MKVECT(t,arow);
for ( i = 0; i < arow; i++ ) {
for ( j = 0, s = 0, ab = BDY(a)[i]; j < m; j++ ) {
mulr(vl,(Obj)ab[j],(Obj)BDY(b)[j],(Obj *)&u); addr(vl,(Obj)s,(Obj)u,(Obj *)&v); s = v;
}
BDY(t)[i] = s;
}
*c = t;
}
}
void mulvectmat(vl,a,b,c)
VL vl;
VECT a;
MAT b;
VECT *c;
{
int bcol,i,j,m;
VECT t;
pointer s,u,v;
if ( !a || !b )
*c = 0;
else if ( a->len != b->row ) {
*c = 0; error("mulvectmat : size mismatch");
} else {
bcol = b->col; m = a->len;
MKVECT(t,bcol);
for ( j = 0; j < bcol; j++ ) {
for ( i = 0, s = 0; i < m; i++ ) {
mulr(vl,(Obj)BDY(a)[i],(Obj)BDY(b)[i][j],(Obj *)&u); addr(vl,(Obj)s,(Obj)u,(Obj *)&v); s = v;
}
BDY(t)[j] = s;
}
*c = t;
}
}
int compmat(vl,a,b)
VL vl;
MAT a,b;
{
int i,j,t,row,col;
if ( !a )
return b?-1:0;
else if ( !b )
return 1;
else if ( a->row != b->row )
return a->row>b->row ? 1 : -1;
else if (a->col != b->col )
return a->col > b->col ? 1 : -1;
else {
row = a->row; col = a->col;
for ( i = 0; i < row; i++ )
for ( j = 0; j < col; j++ )
if ( t = compr(vl,(Obj)BDY(a)[i][j],(Obj)BDY(b)[i][j]) )
return t;
return 0;
}
}
pointer **almat_pointer(n,m)
int n,m;
{
pointer **mat;
int i;
mat = (pointer **)MALLOC(n*sizeof(pointer *));
for ( i = 0; i < n; i++ )
mat[i] = (pointer *)CALLOC(m,sizeof(pointer));
return mat;
}