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matfunc.c
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/*
* matfunc - extended precision rational arithmetic matrix functions
*
* Copyright (C) 1999-2007 David I. Bell
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1990/02/15 01:48:18
* File existed as early as: before 1990
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Extended precision rational arithmetic matrix functions.
* Matrices can contain arbitrary types of elements.
*/
#include "value.h"
#include "zrand.h"
#include "calcerr.h"
#include "have_unused.h"
E_FUNC long irand(long s);
S_FUNC void matswaprow(MATRIX *m, long r1, long r2);
S_FUNC void matsubrow(MATRIX *m, long oprow, long baserow, VALUE *mulval);
S_FUNC void matmulrow(MATRIX *m, long row, VALUE *mulval);
S_FUNC MATRIX *matident(MATRIX *m);
/*
* Add two compatible matrices.
*/
MATRIX *
matadd(MATRIX *m1, MATRIX *m2)
{
int dim;
long min1, min2, max1, max2, index;
VALUE *v1, *v2, *vres;
MATRIX *res;
MATRIX tmp;
if (m1->m_dim != m2->m_dim) {
math_error("Incompatible matrix dimensions for add");
/*NOTREACHED*/
}
tmp.m_dim = m1->m_dim;
tmp.m_size = m1->m_size;
for (dim = 0; dim < m1->m_dim; dim++) {
min1 = m1->m_min[dim];
max1 = m1->m_max[dim];
min2 = m2->m_min[dim];
max2 = m2->m_max[dim];
if ((min1 && min2 && (min1 != min2)) ||
((max1-min1) != (max2-min2))) {
math_error("Incompatible matrix bounds for add");
/*NOTREACHED*/
}
tmp.m_min[dim] = (min1 ? min1 : min2);
tmp.m_max[dim] = tmp.m_min[dim] + (max1 - min1);
}
res = matalloc(m1->m_size);
*res = tmp;
v1 = m1->m_table;
v2 = m2->m_table;
vres = res->m_table;
for (index = m1->m_size; index > 0; index--)
addvalue(v1++, v2++, vres++);
return res;
}
/*
* Subtract two compatible matrices.
*/
MATRIX *
matsub(MATRIX *m1, MATRIX *m2)
{
int dim;
long min1, min2, max1, max2, index;
VALUE *v1, *v2, *vres;
MATRIX *res;
MATRIX tmp;
if (m1->m_dim != m2->m_dim) {
math_error("Incompatible matrix dimensions for sub");
/*NOTREACHED*/
}
tmp.m_dim = m1->m_dim;
tmp.m_size = m1->m_size;
for (dim = 0; dim < m1->m_dim; dim++) {
min1 = m1->m_min[dim];
max1 = m1->m_max[dim];
min2 = m2->m_min[dim];
max2 = m2->m_max[dim];
if ((min1 && min2 && (min1 != min2)) ||
((max1-min1) != (max2-min2))) {
math_error("Incompatible matrix bounds for sub");
/*NOTREACHED*/
}
tmp.m_min[dim] = (min1 ? min1 : min2);
tmp.m_max[dim] = tmp.m_min[dim] + (max1 - min1);
}
res = matalloc(m1->m_size);
*res = tmp;
v1 = m1->m_table;
v2 = m2->m_table;
vres = res->m_table;
for (index = m1->m_size; index > 0; index--)
subvalue(v1++, v2++, vres++);
return res;
}
/*
* Produce the negative of a matrix.
*/
MATRIX *
matneg(MATRIX *m)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
negvalue(val++, vres++);
return res;
}
/*
* Multiply two compatible matrices.
*/
MATRIX *
matmul(MATRIX *m1, MATRIX *m2)
{
register MATRIX *res;
long i1, i2, max1, max2, index, maxindex;
VALUE *v1, *v2, *vres;
VALUE sum, tmp1, tmp2;
if (m1->m_dim == 0) {
i2 = m2->m_size;
v2 = m2->m_table;
res = matalloc(i2);
*res = *m2;
vres = res->m_table;
while (i2-- > 0)
mulvalue(m1->m_table, v2++, vres++);
return res;
}
if (m2->m_dim == 0) {
i1 = m1->m_size;
v1 = m1->m_table;
res = matalloc(i1);
*res = *m1;
vres = res->m_table;
while (i1-- > 0)
mulvalue(v1++, m2->m_table, vres++);
return res;
}
if (m1->m_dim == 1 && m2->m_dim == 1) {
if (m1->m_max[0]-m1->m_min[0] != m2->m_max[0]-m2->m_min[0]) {
math_error("Incompatible bounds for 1D * 1D matmul");
/*NOTREACHED*/
}
res = matalloc(m1->m_size);
*res = *m1;
v1 = m1->m_table;
v2 = m2->m_table;
vres = res->m_table;
for (index = m1->m_size; index > 0; index--)
mulvalue(v1++, v2++, vres++);
return res;
}
if (m1->m_dim == 1 && m2->m_dim == 2) {
if (m1->m_max[0]-m1->m_min[0] != m2->m_max[0]-m2->m_min[0]) {
math_error("Incompatible bounds for 1D * 2D matmul");
/*NOTREACHED*/
}
res = matalloc(m2->m_size);
*res = *m2;
i1 = m1->m_max[0] - m1->m_min[0] + 1;
max2 = m2->m_max[1] - m2->m_min[1] + 1;
v1 = m1->m_table;
v2 = m2->m_table;
vres = res->m_table;
while (i1-- > 0) {
i2 = max2;
while (i2-- > 0)
mulvalue(v1, v2++, vres++);
v1++;
}
return res;
}
if (m1->m_dim == 2 && m2->m_dim == 1) {
if (m1->m_max[1]-m1->m_min[1] != m2->m_max[0]-m2->m_min[0]) {
math_error("Incompatible bounds for 2D * 1D matmul");
/*NOTREACHED*/
}
res = matalloc(m1->m_size);
*res = *m1;
i1 = m1->m_max[0] - m1->m_min[0] + 1;
max1 = m1->m_max[1] - m1->m_min[1] + 1;
v1 = m1->m_table;
vres = res->m_table;
while (i1-- > 0) {
v2 = m2->m_table;
i2 = max1;
while (i2-- > 0)
mulvalue(v1++, v2++, vres++);
}
return res;
}
if ((m1->m_dim != 2) || (m2->m_dim != 2)) {
math_error("Matrix dimensions not compatible for mul");
/*NOTREACHED*/
}
if ((m1->m_max[1]-m1->m_min[1]) != (m2->m_max[0]-m2->m_min[0])) {
math_error("Incompatible bounds for 2D * 2D matrix mul");
/*NOTREACHED*/
}
max1 = (m1->m_max[0] - m1->m_min[0] + 1);
max2 = (m2->m_max[1] - m2->m_min[1] + 1);
maxindex = (m1->m_max[1] - m1->m_min[1] + 1);
res = matalloc(max1 * max2);
res->m_dim = 2;
res->m_min[0] = m1->m_min[0];
res->m_max[0] = m1->m_max[0];
res->m_min[1] = m2->m_min[1];
res->m_max[1] = m2->m_max[1];
for (i1 = 0; i1 < max1; i1++) {
for (i2 = 0; i2 < max2; i2++) {
sum.v_type = V_NULL;
sum.v_subtype = V_NOSUBTYPE;
v1 = &m1->m_table[i1 * maxindex];
v2 = &m2->m_table[i2];
for (index = 0; index < maxindex; index++) {
mulvalue(v1, v2, &tmp1);
addvalue(&sum, &tmp1, &tmp2);
freevalue(&tmp1);
freevalue(&sum);
sum = tmp2;
v1++;
if (index+1 < maxindex)
v2 += max2;
}
index = (i1 * max2) + i2;
res->m_table[index] = sum;
}
}
return res;
}
/*
* Square a matrix.
*/
MATRIX *
matsquare(MATRIX *m)
{
register MATRIX *res;
long i1, i2, max, index;
VALUE *v1, *v2;
VALUE sum, tmp1, tmp2;
if (m->m_dim < 2) {
res = matalloc(m->m_size);
*res = *m;
v1 = m->m_table;
v2 = res->m_table;
for (index = m->m_size; index > 0; index--)
squarevalue(v1++, v2++);
return res;
}
if (m->m_dim != 2) {
math_error("Matrix dimension exceeds two for square");
/*NOTREACHED*/
}
if ((m->m_max[0] - m->m_min[0]) != (m->m_max[1] - m->m_min[1])) {
math_error("Squaring non-square matrix");
/*NOTREACHED*/
}
max = (m->m_max[0] - m->m_min[0] + 1);
res = matalloc(max * max);
res->m_dim = 2;
res->m_min[0] = m->m_min[0];
res->m_max[0] = m->m_max[0];
res->m_min[1] = m->m_min[1];
res->m_max[1] = m->m_max[1];
for (i1 = 0; i1 < max; i1++) {
for (i2 = 0; i2 < max; i2++) {
sum.v_type = V_NULL;
sum.v_subtype = V_NOSUBTYPE;
v1 = &m->m_table[i1 * max];
v2 = &m->m_table[i2];
for (index = 0; index < max; index++) {
mulvalue(v1, v2, &tmp1);
addvalue(&sum, &tmp1, &tmp2);
freevalue(&tmp1);
freevalue(&sum);
sum = tmp2;
v1++;
v2 += max;
}
index = (i1 * max) + i2;
res->m_table[index] = sum;
}
}
return res;
}
/*
* Compute the result of raising a matrix to an integer power if
* dimension <= 2 and for dimension == 2, the matrix is square.
* Negative powers mean the positive power of the inverse.
* Note: This calculation could someday be improved for large powers
* by using the characteristic polynomial of the matrix.
*
* given:
* m matrix to be raised
* q power to raise it to
*/
MATRIX *
matpowi(MATRIX *m, NUMBER *q)
{
MATRIX *res, *tmp;
long power; /* power to raise to */
FULL bit; /* current bit value */
if (m->m_dim > 2) {
math_error("Matrix dimension greater than 2 for power");
/*NOTREACHED*/
}
if (m->m_dim == 2 && (m->m_max[0] - m->m_min[0] !=
m->m_max[1] - m->m_min[1])) {
math_error("Raising non-square 2D matrix to a power");
/*NOTREACHED*/
}
if (qisfrac(q)) {
math_error("Raising matrix to non-integral power");
/*NOTREACHED*/
}
if (zge31b(q->num)) {
math_error("Raising matrix to very large power");
/*NOTREACHED*/
}
power = ztolong(q->num);
if (qisneg(q))
power = -power;
/*
* Handle some low powers specially
*/
if ((power <= 4) && (power >= -2)) {
switch ((int) power) {
case 0:
return matident(m);
case 1:
return matcopy(m);
case -1:
return matinv(m);
case 2:
return matsquare(m);
case -2:
tmp = matinv(m);
res = matsquare(tmp);
matfree(tmp);
return res;
case 3:
tmp = matsquare(m);
res = matmul(m, tmp);
matfree(tmp);
return res;
case 4:
tmp = matsquare(m);
res = matsquare(tmp);
matfree(tmp);
return res;
}
}
if (power < 0) {
m = matinv(m);
power = -power;
}
/*
* Compute the power by squaring and multiplying.
* This uses the left to right method of power raising.
*/
bit = TOPFULL;
while ((bit & power) == 0)
bit >>= 1L;
bit >>= 1L;
res = matsquare(m);
if (bit & power) {
tmp = matmul(res, m);
matfree(res);
res = tmp;
}
bit >>= 1L;
while (bit) {
tmp = matsquare(res);
matfree(res);
res = tmp;
if (bit & power) {
tmp = matmul(res, m);
matfree(res);
res = tmp;
}
bit >>= 1L;
}
if (qisneg(q))
matfree(m);
return res;
}
/*
* Calculate the cross product of two one dimensional matrices each
* with three components.
* m3 = matcross(m1, m2);
*/
MATRIX *
matcross(MATRIX *m1, MATRIX *m2)
{
MATRIX *res;
VALUE *v1, *v2, *vr;
VALUE tmp1, tmp2;
res = matalloc(3L);
res->m_dim = 1;
res->m_min[0] = 0;
res->m_max[0] = 2;
v1 = m1->m_table;
v2 = m2->m_table;
vr = res->m_table;
mulvalue(v1 + 1, v2 + 2, &tmp1);
mulvalue(v1 + 2, v2 + 1, &tmp2);
subvalue(&tmp1, &tmp2, vr + 0);
freevalue(&tmp1);
freevalue(&tmp2);
mulvalue(v1 + 2, v2 + 0, &tmp1);
mulvalue(v1 + 0, v2 + 2, &tmp2);
subvalue(&tmp1, &tmp2, vr + 1);
freevalue(&tmp1);
freevalue(&tmp2);
mulvalue(v1 + 0, v2 + 1, &tmp1);
mulvalue(v1 + 1, v2 + 0, &tmp2);
subvalue(&tmp1, &tmp2, vr + 2);
freevalue(&tmp1);
freevalue(&tmp2);
return res;
}
/*
* Return the dot product of two matrices.
* result = matdot(m1, m2);
*/
VALUE
matdot(MATRIX *m1, MATRIX *m2)
{
VALUE *v1, *v2;
VALUE result, tmp1, tmp2;
long len;
v1 = m1->m_table;
v2 = m2->m_table;
mulvalue(v1, v2, &result);
len = m1->m_size;
while (--len > 0) {
mulvalue(++v1, ++v2, &tmp1);
addvalue(&result, &tmp1, &tmp2);
freevalue(&tmp1);
freevalue(&result);
result = tmp2;
}
return result;
}
/*
* Scale the elements of a matrix by a specified power of two.
*
* given:
* m matrix to be scaled
* n scale factor
*/
MATRIX *
matscale(MATRIX *m, long n)
{
register VALUE *val, *vres;
VALUE temp;
long index;
MATRIX *res; /* resulting matrix */
if (n == 0)
return matcopy(m);
temp.v_type = V_NUM;
temp.v_subtype = V_NOSUBTYPE;
temp.v_num = itoq(n);
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
scalevalue(val++, &temp, vres++);
qfree(temp.v_num);
return res;
}
/*
* Shift the elements of a matrix by the specified number of bits.
* Positive shift means leftwards, negative shift rightwards.
*
* given:
* m matrix to be shifted
* n shift count
*/
MATRIX *
matshift(MATRIX *m, long n)
{
register VALUE *val, *vres;
VALUE temp;
long index;
MATRIX *res; /* resulting matrix */
if (n == 0)
return matcopy(m);
temp.v_type = V_NUM;
temp.v_subtype = V_NOSUBTYPE;
temp.v_num = itoq(n);
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
shiftvalue(val++, &temp, FALSE, vres++);
qfree(temp.v_num);
return res;
}
/*
* Multiply the elements of a matrix by a specified value.
*
* given:
* m matrix to be multiplied
* vp value to multiply by
*/
MATRIX *
matmulval(MATRIX *m, VALUE *vp)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
mulvalue(val++, vp, vres++);
return res;
}
/*
* Divide the elements of a matrix by a specified value, keeping
* only the integer quotient.
*
* given:
* m matrix to be divided
* vp value to divide by
* v3 rounding type parameter
*/
MATRIX *
matquoval(MATRIX *m, VALUE *vp, VALUE *v3)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
if ((vp->v_type == V_NUM) && qiszero(vp->v_num)) {
math_error("Division by zero");
/*NOTREACHED*/
}
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
quovalue(val++, vp, v3, vres++);
return res;
}
/*
* Divide the elements of a matrix by a specified value, keeping
* only the remainder of the division.
*
* given:
* m matrix to be divided
* vp value to divide by
* v3 rounding type parameter
*/
MATRIX *
matmodval(MATRIX *m, VALUE *vp, VALUE *v3)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
if ((vp->v_type == V_NUM) && qiszero(vp->v_num)) {
math_error("Division by zero");
/*NOTREACHED*/
}
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
modvalue(val++, vp, v3, vres++);
return res;
}
VALUE
mattrace(MATRIX *m)
{
VALUE *vp;
VALUE sum;
VALUE tmp;
long i, j;
if (m->m_dim < 2) {
matsum(m, &sum);
return sum;
}
if (m->m_dim != 2)
return error_value(E_MATTRACE2);
i = (m->m_max[0] - m->m_min[0] + 1);
j = (m->m_max[1] - m->m_min[1] + 1);
if (i != j)
return error_value(E_MATTRACE3);
vp = m->m_table;
copyvalue(vp, &sum);
j++;
while (--i > 0) {
vp += j;
addvalue(&sum, vp, &tmp);
freevalue(&sum);
sum = tmp;
}
return sum;
}
/*
* Transpose a 2-dimensional matrix
*/
MATRIX *
mattrans(MATRIX *m)
{
register VALUE *v1, *v2; /* current values */
long rows, cols; /* rows and columns in new matrix */
long row, col; /* current row and column */
MATRIX *res;
if (m->m_dim < 2)
return matcopy(m);
res = matalloc(m->m_size);
res->m_dim = 2;
res->m_min[0] = m->m_min[1];
res->m_max[0] = m->m_max[1];
res->m_min[1] = m->m_min[0];
res->m_max[1] = m->m_max[0];
rows = (m->m_max[1] - m->m_min[1] + 1);
cols = (m->m_max[0] - m->m_min[0] + 1);
v1 = res->m_table;
for (row = 0; row < rows; row++) {
v2 = &m->m_table[row];
for (col = 0; col < cols; col++) {
copyvalue(v2, v1);
v1++;
v2 += rows;
}
}
return res;
}
/*
* Produce a matrix with values all of which are conjugated.
*/
MATRIX *
matconj(MATRIX *m)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
conjvalue(val++, vres++);
return res;
}
/*
* Round elements of a matrix to specified number of decimal digits
*/
MATRIX *
matround(MATRIX *m, VALUE *v2, VALUE *v3)
{
VALUE *p, *q;
long s;
MATRIX *res;
s = m->m_size;
res = matalloc(s);
*res = *m;
p = m->m_table;
q = res->m_table;
while (s-- > 0)
roundvalue(p++, v2, v3, q++);
return res;
}
/*
* Round elements of a matrix to specified number of binary digits
*/
MATRIX *
matbround(MATRIX *m, VALUE *v2, VALUE *v3)
{
VALUE *p, *q;
long s;
MATRIX *res;
s = m->m_size;
res = matalloc(s);
*res = *m;
p = m->m_table;
q = res->m_table;
while (s-- > 0)
broundvalue(p++, v2, v3, q++);
return res;
}
/*
* Approximate a matrix by approximating elemenbs to be multiples of
* v2, rounding type determined by v3.
*/
MATRIX *
matappr(MATRIX *m, VALUE *v2, VALUE *v3)
{
VALUE *p, *q;
long s;
MATRIX *res;
s = m->m_size;
res = matalloc(s);
*res = *m;
p = m->m_table;
q = res->m_table;
while (s-- > 0)
apprvalue(p++, v2, v3, q++);
return res;
}
/*
* Produce a matrix with values all of which have been truncated to integers.
*/
MATRIX *
matint(MATRIX *m)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
intvalue(val++, vres++);
return res;
}
/*
* Produce a matrix with values all of which have only the fraction part left.
*/
MATRIX *
matfrac(MATRIX *m)
{
register VALUE *val, *vres;
long index;
MATRIX *res;
res = matalloc(m->m_size);
*res = *m;
val = m->m_table;
vres = res->m_table;
for (index = m->m_size; index > 0; index--)
fracvalue(val++, vres++);
return res;
}
/*
* Index a matrix normally by the specified set of index values.
* Returns the address of the matrix element if it is valid, or generates
* an error if the index values are out of range. The create flag is TRUE
* if the element is to be written, but this is ignored here.
*
* given:
* mp matrix to operate on
* create TRUE => create if element does not exist
* dim dimension of the indexing
* indices table of values being indexed by
*/
/*ARGSUSED*/
VALUE *
matindex(MATRIX *mp, BOOL UNUSED create, long dim, VALUE *indices)
{
NUMBER *q; /* index value */
VALUE *vp;
long index; /* index value as an integer */
long offset; /* current offset into array */
int i; /* loop counter */
if (dim < 0) {
math_error("Negative dimension %ld for matrix", dim);
/*NOTREACHED*/
}
for (;;) {
if (dim < mp->m_dim) {
math_error(
"Indexing a %ldd matrix as a %ldd matrix",
mp->m_dim, dim);
/*NOTREACHED*/
}
offset = 0;
for (i = 0; i < mp->m_dim; i++) {
if (indices->v_type != V_NUM) {
math_error("Non-numeric index for matrix");
/*NOTREACHED*/
}
q = indices->v_num;
if (qisfrac(q)) {
math_error("Non-integral index for matrix");
/*NOTREACHED*/
}
index = qtoi(q);
if (zge31b(q->num) || (index < mp->m_min[i]) ||
(index > mp->m_max[i])) {
math_error("Index out of bounds for matrix");
/*NOTREACHED*/
}
offset *= (mp->m_max[i] - mp->m_min[i] + 1);
offset += (index - mp->m_min[i]);
indices++;
}
vp = mp->m_table + offset;
dim -= mp->m_dim;
if (dim == 0)
break;
if (vp->v_type != V_MAT) {
math_error("Non-matrix argument for matindex");
/*NOTREACHED*/
}
mp = vp->v_mat;
}
return vp;
}
/*
* Returns the list of indices for a matrix element with specified
* double-bracket index.
*/
LIST *
matindices(MATRIX *mp, long index)
{
LIST *lp;
int j;
long d;
VALUE val;
if (index < 0 || index >= mp->m_size)
return NULL;
lp = listalloc();
val.v_type = V_NUM;
j = mp->m_dim;
while (--j >= 0) {
d = mp->m_max[j] - mp->m_min[j] + 1;
val.v_num = itoq(index % d + mp->m_min[j]);
insertlistfirst(lp, &val);
qfree(val.v_num);
index /= d;
}
return lp;
}
/*
* Search a matrix for the specified value, starting with the specified index.
* Returns 0 and stores index if value found; otherwise returns 1.
*/
int
matsearch(MATRIX *m, VALUE *vp, long i, long j, ZVALUE *index)
{
register VALUE *val;
val = &m->m_table[i];
if (i < 0 || j > m->m_size) {
math_error("This should not happen in call to matsearch");
/*NOTREACHED*/
}
while (i < j) {
if (acceptvalue(val++, vp)) {
utoz(i, index);
return 0;
}
i++;
}
return 1;
}
/*
* Search a matrix backwards for the specified value, starting with the
* specified index. Returns 0 and stores index if value found; otherwise
* returns 1.
*/
int
matrsearch(MATRIX *m, VALUE *vp, long i, long j, ZVALUE *index)
{
register VALUE *val;
if (i < 0 || j > m->m_size) {
math_error("This should not happen in call to matrsearch");
/*NOTREACHED*/
}
val = &m->m_table[--j];
while (j >= i) {
if (acceptvalue(val--, vp)) {
utoz(j, index);
return 0;
}
j--;
}
return 1;
}
/*
* Fill all of the elements of a matrix with one of two specified values.
* All entries are filled with the first specified value, except that if
* the matrix is w-dimensional and the second value pointer is non-NULL, then
* all diagonal entries are filled with the second value. This routine
* affects the supplied matrix directly, and doesn't return a copy.
*
* given:
* m matrix to be filled
* v1 value to fill most of matrix with
* v2 value for diagonal entries or null
*/
void