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|
//#define WANT_STREAM
#include "include.h"
#include "config.h"
#include "newmatap.h"
//#include "newmatio.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
static int my_max(int p, int q) { return (p > q) ? p : q; }
static int my_min(int p, int q) { return (p < q) ? p : q; }
void BandFunctions(int l1, int u1, int l2, int u2)
{
int i, j;
BandMatrix BM1(20, l1, u1); BM1 = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l1 && i - j >= -u1) BM1(i, j) = 100 * i + j;
BandMatrix BM2 = BM1; Matrix M = BM2 - BM1; Print(M);
BM2.ReSize(20, l2, u2); BM2 = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l2 && i - j >= -u2) BM2(i, j) = (100 * i + j) * 11;
BandMatrix BMA = BM1 + BM2, BMS = BM1 - BM2, BMSP = SP(BM1, BM2),
BMM = BM1 * BM2, BMN = -BM1;
Matrix M1(20,20); M1 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l1 && i - j >= -u1) M1(i, j) = 100 * i + j;
Matrix M2(20,20); M2 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l2 && i - j >= -u2) M2(i, j) = (100 * i + j) * 11;
Matrix MA = M1 + M2, MS = M1 - M2, MSP = SP(M1, M2), MM = M1 * M2, MN = -M1;
MA -= BMA; MS -= BMS; MSP -= BMSP; MM -= BMM; MN -= BMN;
Print(MA); Print(MS); Print(MSP); Print(MM); Print(MN);
Matrix Test(7, 2);
Test(1,1) = BM1.BandWidth().Lower() - l1;
Test(1,2) = BM1.BandWidth().Upper() - u1;
Test(2,1) = BM2.BandWidth().Lower() - l2;
Test(2,2) = BM2.BandWidth().Upper() - u2;
Test(3,1) = BMA.BandWidth().Lower() - my_max(l1,l2);
Test(3,2) = BMA.BandWidth().Upper() - my_max(u1,u2);
Test(4,1) = BMS.BandWidth().Lower() - my_max(l1,l2);
Test(4,2) = BMS.BandWidth().Upper() - my_max(u1,u2);
Test(5,1) = BMSP.BandWidth().Lower() - my_min(l1,l2);
Test(5,2) = BMSP.BandWidth().Upper() - my_min(u1,u2);
Test(6,1) = BMM.BandWidth().Lower() - (l1 + l2);
Test(6,2) = BMM.BandWidth().Upper() - (u1 + u2);
Test(7,1) = BMN.BandWidth().Lower() - l1;
Test(7,2) = BMN.BandWidth().Upper() - u1;
Print(Test);
// test element function
BandMatrix BM1E(20, l1, u1); BM1E = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l1 && i - j >= -u1) BM1E.element(i-1, j-1) = 100 * i + j;
BandMatrix BM2E = BM1E; BM2E.ReSize(BM2); BM2E = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l2 && i - j >= -u2)
BM2E.element(i-1, j-1) = (100 * i + j) * 11;
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test element function with constant
BM1E = 444444.04; BM2E = 555555.0;
const BandMatrix BM1C = BM1, BM2C = BM2;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l1 && i - j >= -u1)
BM1E.element(i-1, j-1) = BM1C.element(i-1, j-1);
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l2 && i - j >= -u2)
BM2E.element(i-1, j-1) = BM2C.element(i-1, j-1);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test subscript function with constant
BM1E = 444444.04; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l1 && i - j >= -u1) BM1E(i, j) = BM1C(i, j);
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
if (i - j <= l2 && i - j >= -u2) BM2E(i, j) = BM2C(i, j);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
}
void LowerBandFunctions(int l1, int l2)
{
int i, j;
LowerBandMatrix BM1(20, l1); BM1 = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1(i, j) = 100 * i + j;
LowerBandMatrix BM2 = BM1; Matrix M = BM2 - BM1; Print(M);
BM2.ReSize(20, l2); BM2 = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2(i, j) = (100 * i + j) * 11;
LowerBandMatrix BMA = BM1 + BM2, BMS = BM1 - BM2, BMSP = SP(BM1, BM2),
BMM = BM1 * BM2, BMN = -BM1;
Matrix M1(20,20); M1 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) M1(i, j) = 100 * i + j;
Matrix M2(20,20); M2 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) M2(i, j) = (100 * i + j) * 11;
Matrix MA = M1 + M2, MS = M1 - M2, MSP = SP(M1, M2), MM = M1 * M2, MN = -M1;
MA -= BMA; MS -= BMS; MSP -= BMSP; MM -= BMM; MN -= BMN;
Print(MA); Print(MS); Print(MSP); Print(MM); Print(MN);
Matrix Test(7, 2);
Test(1,1) = BM1.BandWidth().Lower() - l1;
Test(1,2) = BM1.BandWidth().Upper();
Test(2,1) = BM2.BandWidth().Lower() - l2;
Test(2,2) = BM2.BandWidth().Upper();
Test(3,1) = BMA.BandWidth().Lower() - my_max(l1,l2);
Test(3,2) = BMA.BandWidth().Upper();
Test(4,1) = BMS.BandWidth().Lower() - my_max(l1,l2);
Test(4,2) = BMS.BandWidth().Upper();
Test(5,1) = BMSP.BandWidth().Lower() - my_min(l1,l2);
Test(5,2) = BMSP.BandWidth().Upper();
Test(6,1) = BMM.BandWidth().Lower() - (l1 + l2);
Test(6,2) = BMM.BandWidth().Upper();
Test(7,1) = BMN.BandWidth().Lower() - l1;
Test(7,2) = BMN.BandWidth().Upper();
Print(Test);
// test element function
LowerBandMatrix BM1E(20, l1); BM1E = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(i-1, j-1) = 100 * i + j;
LowerBandMatrix BM2E = BM1E; BM2E.ReSize(BM2); BM2E = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(i-1, j-1) = (100 * i + j) * 11;
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test element function with constant
BM1E = 444444.04; BM2E = 555555.0;
const LowerBandMatrix BM1C = BM1, BM2C = BM2;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(i-1, j-1) = BM1C.element(i-1, j-1);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(i-1, j-1) = BM2C.element(i-1, j-1);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test subscript function with constant
BM1E = 444444.04; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E(i, j) = BM1C(i, j);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E(i, j) = BM2C(i, j);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
}
void UpperBandFunctions(int u1, int u2)
{
int i, j;
UpperBandMatrix BM1(20, u1); BM1 = 999999.0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u1) BM1(i, j) = 100 * i + j;
UpperBandMatrix BM2 = BM1; Matrix M = BM2 - BM1; Print(M);
BM2.ReSize(20, u2); BM2 = 777777.0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u2) BM2(i, j) = (100 * i + j) * 11;
UpperBandMatrix BMA = BM1 + BM2, BMS = BM1 - BM2, BMSP = SP(BM1, BM2),
BMM = BM1 * BM2, BMN = -BM1;
Matrix M1(20,20); M1 = 0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u1) M1(i, j) = 100 * i + j;
Matrix M2(20,20); M2 = 0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u2) M2(i, j) = (100 * i + j) * 11;
Matrix MA = M1 + M2, MS = M1 - M2, MSP = SP(M1, M2), MM = M1 * M2, MN = -M1;
MA -= BMA; MS -= BMS; MSP -= BMSP; MM -= BMM; MN -= BMN;
Print(MA); Print(MS); Print(MSP); Print(MM); Print(MN);
Matrix Test(7, 2);
Test(1,1) = BM1.BandWidth().Lower();
Test(1,2) = BM1.BandWidth().Upper() - u1;
Test(2,1) = BM2.BandWidth().Lower();
Test(2,2) = BM2.BandWidth().Upper() - u2;
Test(3,1) = BMA.BandWidth().Lower();
Test(3,2) = BMA.BandWidth().Upper() - my_max(u1,u2);
Test(4,1) = BMS.BandWidth().Lower();
Test(4,2) = BMS.BandWidth().Upper() - my_max(u1,u2);
Test(5,1) = BMSP.BandWidth().Lower();
Test(5,2) = BMSP.BandWidth().Upper() - my_min(u1,u2);
Test(6,1) = BMM.BandWidth().Lower();
Test(6,2) = BMM.BandWidth().Upper() - (u1 + u2);
Test(7,1) = BMN.BandWidth().Lower();
Test(7,2) = BMN.BandWidth().Upper() - u1;
Print(Test);
// test element function
UpperBandMatrix BM1E(20, u1); BM1E = 999999.0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u1) BM1E.element(i-1, j-1) = 100 * i + j;
UpperBandMatrix BM2E = BM1E; BM2E.ReSize(BM2); BM2E = 777777.0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u2) BM2E.element(i-1, j-1) = (100 * i + j) * 11;
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test element function with constant
BM1E = 444444.04; BM2E = 555555.0;
const UpperBandMatrix BM1C = BM1, BM2C = BM2;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u1) BM1E.element(i-1, j-1) = BM1C.element(i-1, j-1);
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u2) BM2E.element(i-1, j-1) = BM2C.element(i-1, j-1);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test subscript function with constant
BM1E = 444444.04; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u1) BM1E(i, j) = BM1C(i, j);
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
if (i - j >= -u2) BM2E(i, j) = BM2C(i, j);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
}
void SymmetricBandFunctions(int l1, int l2)
{
int i, j;
SymmetricBandMatrix BM1(20, l1); BM1 = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1(i, j) = 100 * i + j;
SymmetricBandMatrix BM2 = BM1; Matrix M = BM2 - BM1; Print(M);
BM2.ReSize(20, l2); BM2 = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2(i, j) = (100 * i + j) * 11;
SymmetricBandMatrix BMA = BM1 + BM2, BMS = BM1 - BM2, BMSP = SP(BM1, BM2),
BMN = -BM1;
BandMatrix BMM = BM1 * BM2;
SymmetricMatrix M1(20); M1 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) M1(i, j) = 100 * i + j;
SymmetricMatrix M2(20); M2 = 0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) M2(i, j) = (100 * i + j) * 11;
SymmetricMatrix MA = M1 + M2, MS = M1 - M2, MSP = SP(M1, M2), MN = -M1;
Matrix MM = M1 * M2;
MA -= BMA; MS -= BMS; MSP -= BMSP; MM -= BMM; MN -= BMN;
Print(MA); Print(MS); Print(MSP); Print(MM); Print(MN);
Matrix Test(7, 2);
Test(1,1) = BM1.BandWidth().Lower() - l1;
Test(1,2) = BM1.BandWidth().Upper() - l1;
Test(2,1) = BM2.BandWidth().Lower() - l2;
Test(2,2) = BM2.BandWidth().Upper() - l2;
Test(3,1) = BMA.BandWidth().Lower() - my_max(l1,l2);
Test(3,2) = BMA.BandWidth().Upper() - my_max(l1,l2);
Test(4,1) = BMS.BandWidth().Lower() - my_max(l1,l2);
Test(4,2) = BMS.BandWidth().Upper() - my_max(l1,l2);
Test(5,1) = BMSP.BandWidth().Lower() - my_min(l1,l2);
Test(5,2) = BMSP.BandWidth().Upper() - my_min(l1,l2);
Test(6,1) = BMM.BandWidth().Lower() - (l1 + l2);
Test(6,2) = BMM.BandWidth().Upper() - (l1 + l2);
Test(7,1) = BMN.BandWidth().Lower() - l1;
Test(7,2) = BMN.BandWidth().Upper() - l1;
Print(Test);
// test element function
SymmetricBandMatrix BM1E(20, l1); BM1E = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(i-1, j-1) = 100 * i + j;
SymmetricBandMatrix BM2E = BM1E; BM2E.ReSize(BM2); BM2E = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(i-1, j-1) = (100 * i + j) * 11;
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// reverse subscripts
BM1E = 999999.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(j-1, i-1) = 100 * i + j;
BM2E = 777777.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(j-1, i-1) = (100 * i + j) * 11;
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test element function with constant
BM1E = 444444.04; BM2E = 555555.0;
const SymmetricBandMatrix BM1C = BM1, BM2C = BM2;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(i-1, j-1) = BM1C.element(i-1, j-1);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(i-1, j-1) = BM2C.element(i-1, j-1);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// reverse subscripts
BM1E = 444444.0; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E.element(j-1, i-1) = BM1C.element(j-1, i-1);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E.element(j-1, i-1) = BM2C.element(j-1, i-1);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// test subscript function with constant
BM1E = 444444.0; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E(i, j) = BM1C(i, j);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E(i, j) = BM2C(i, j);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// reverse subscripts
BM1E = 444444.0; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E(j, i) = BM1C(j, i);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E(j, i) = BM2C(j, i);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
// partly reverse subscripts
BM1E = 444444.0; BM2E = 555555.0;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l1) BM1E(j, i) = BM1C(i, j);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
if (i - j <= l2) BM2E(j, i) = BM2C(i, j);
M1 = BM1E - BM1; Print(M1);
M2 = BM2E - BM2; Print(M2);
}
void trymath()
{
// cout << "\nSeventeenth test of Matrix package\n";
// cout << "\n";
Tracer et("Seventeenth test of Matrix package");
Tracer::PrintTrace();
{
Tracer et1("Stage 1");
int i, j;
BandMatrix B(8,3,1);
for (i=1; i<=8; i++) for (j=-3; j<=1; j++)
{ int k = i+j; if (k>0 && k<=8) B(i,k) = i + k/64.0; }
IdentityMatrix I(8); BandMatrix B1; B1 = I;
UpperTriangularMatrix UT = I; Print(Matrix(B1-UT));
Print(Matrix(B * B - B * 2 + I - (B - I) * (B - I)));
Matrix A = B; BandMatrix C; C = B;
Print(Matrix(B * A - C * 2 + I - (A - I) * (B - I)));
C.ReSize(8,2,2); C = 0.0; C.Inject(B);
Matrix X = A.t();
B1.ReSize(8,2,2); B1.Inject(X); Print(Matrix(C.t()-B1));
Matrix BI = B.i(); A = A.i()-BI; Clean(A,0.000000001); Print(A);
BandLUMatrix BLU = B.t();
BI = BLU.i(); A = X.i()-BI; Clean(A,0.000000001); Print(A);
X.ReSize(1,1);
X(1,1) = BLU.LogDeterminant().Value()-B.LogDeterminant().Value();
Clean(X,0.000000001); Print(X);
UpperBandMatrix U; U << B; LowerBandMatrix L; L << B;
DiagonalMatrix D; D << B;
Print( Matrix(L + (U - D - B)) );
for (i=1; i<=8; i++) A.Column(i) << B.Column(i);
Print(Matrix(A-B));
}
{
Tracer et1("Stage 2");
BandMatrix A(7,2,2);
int i,j;
for (i=1; i<=7; i++) for (j=1; j<=7; j++)
{
int k=i-j; if (k<0) k = -k;
if (k==0) A(i,j)=6;
else if (k==1) A(i,j) = -4;
else if (k==2) A(i,j) = 1;
A(1,1) = A(7,7) = 5;
}
DiagonalMatrix D(7); D = 0.0; A = A - D;
BandLUMatrix B(A); Matrix M = A;
ColumnVector V(6);
V(1) = LogDeterminant(B).Value();
V(2) = LogDeterminant(A).Value();
V(3) = LogDeterminant(M).Value();
V(4) = Determinant(B);
V(5) = Determinant(A);
V(6) = Determinant(M);
V = V / 64 - 1; Clean(V,0.000000001); Print(V);
ColumnVector X(7);
#ifdef ATandT
Real a[7];
// the previous statement causes a core dump in tmti.cpp
// on the HP9000 - seems very strange. Possibly the exception
// mechanism is failing to track the stack correctly. If you get
// this problem replace by the following statement.
// Real* a = new Real [7]; if (!a) exit(1);
a[0]=1; a[1]=2; a[2]=3; a[3]=4; a[4]=5; a[5]=6; a[6]=7;
#else
Real a[] = {1,2,3,4,5,6,7};
#endif
X << a;
// include these if you are using the previous dynamic definition of a
//#ifdef ATandT
// delete [] a;
//#endif
M = (M.i()*X).t() - (B.i()*X).t() * 2.0 + (A.i()*X).t();
Clean(M,0.000000001); Print(M);
BandMatrix P(80,2,5); ColumnVector CX(80);
for (i=1; i<=80; i++) for (j=1; j<=80; j++)
{ int d = i-j; if (d<=2 && d>=-5) P(i,j) = i + j/100.0; }
for (i=1; i<=80; i++) CX(i) = i*100.0;
Matrix MP = P;
ColumnVector V1 = P.i() * CX; ColumnVector V2 = MP.i() * CX;
V = V1 - V2; Clean(V,0.000000001); Print(V);
V1 = P * V1; V2 = MP * V2; V = V1 - V2; Clean(V,0.000000001); Print(V);
RowVector XX(1);
XX = LogDeterminant(P).Value() / LogDeterminant(MP).Value() - 1.0;
Clean(XX,0.000000001); Print(XX);
LowerBandMatrix LP(80,5);
for (i=1; i<=80; i++) for (j=1; j<=80; j++)
{ int d = i-j; if (d<=5 && d>=0) LP(i,j) = i + j/100.0; }
MP = LP;
XX.ReSize(4);
XX(1) = LogDeterminant(LP).Value();
XX(2) = LogDeterminant(MP).Value();
V1 = LP.i() * CX; V2 = MP.i() * CX;
V = V1 - V2; Clean(V,0.000000001); Print(V);
UpperBandMatrix UP(80,4);
for (i=1; i<=80; i++) for (j=1; j<=80; j++)
{ int d = i-j; if (d<=0 && d>=-4) UP(i,j) = i + j/100.0; }
MP = UP;
XX(3) = LogDeterminant(UP).Value();
XX(4) = LogDeterminant(MP).Value();
V1 = UP.i() * CX; V2 = MP.i() * CX;
V = V1 - V2; Clean(V,0.000000001); Print(V);
XX = XX / SumAbsoluteValue(XX) - .25; Clean(XX,0.000000001); Print(XX);
}
{
Tracer et1("Stage 3");
SymmetricBandMatrix SA(8,5);
int i,j;
for (i=1; i<=8; i++) for (j=1; j<=8; j++)
if (i-j<=5 && 0<=i-j) SA(i,j) =i + j/128.0;
DiagonalMatrix D(8); D = 10; SA = SA + D;
Matrix MA1(8,8); Matrix MA2(8,8);
for (i=1; i<=8; i++)
{ MA1.Column(i) << SA.Column(i); MA2.Row(i) << SA.Row(i); }
Print(Matrix(MA1-MA2));
D = 10; SA = SA.t() + D; MA1 = MA1 + D;
Print(Matrix(MA1-SA));
UpperBandMatrix UB(8,3); LowerBandMatrix LB(8,4);
D << SA; UB << SA; LB << SA;
SA = SA * 5.0; D = D * 5.0; LB = LB * 5.0; UB = UB * 5.0;
BandMatrix B = LB - D + UB - SA; Print(Matrix(B));
SymmetricBandMatrix A(7,2); A = 100.0;
for (i=1; i<=7; i++) for (j=1; j<=7; j++)
{
int k=i-j;
if (k==0) A(i,j)=6;
else if (k==1) A(i,j) = -4;
else if (k==2) A(i,j) = 1;
A(1,1) = A(7,7) = 5;
}
BandLUMatrix C(A); Matrix M = A;
ColumnVector X(8);
X(1) = LogDeterminant(C).Value() - 64;
X(2) = LogDeterminant(A).Value() - 64;
X(3) = LogDeterminant(M).Value() - 64;
X(4) = SumSquare(M) - SumSquare(A);
X(5) = SumAbsoluteValue(M) - SumAbsoluteValue(A);
X(6) = MaximumAbsoluteValue(M) - MaximumAbsoluteValue(A);
X(7) = Trace(M) - Trace(A);
X(8) = Sum(M) - Sum(A);
Clean(X,0.000000001); Print(X);
#ifdef ATandT
Real a[7]; a[0]=1; a[1]=2; a[2]=3; a[3]=4; a[4]=5; a[5]=6; a[6]=7;
#else
Real a[] = {1,2,3,4,5,6,7};
#endif
X.ReSize(7);
X << a;
X = M.i()*X - C.i()*X * 2 + A.i()*X;
Clean(X,0.000000001); Print(X);
LB << A; UB << A; D << A;
BandMatrix XA = LB + (UB - D);
Print(Matrix(XA - A));
for (i=1; i<=7; i++) for (j=1; j<=7; j++)
{
int k=i-j;
if (k==0) A(i,j)=6;
else if (k==1) A(i,j) = -4;
else if (k==2) A(i,j) = 1;
A(1,1) = A(7,7) = 5;
}
D = 1;
M = LB.i() * LB - D; Clean(M,0.000000001); Print(M);
M = UB.i() * UB - D; Clean(M,0.000000001); Print(M);
M = XA.i() * XA - D; Clean(M,0.000000001); Print(M);
Matrix MUB = UB; Matrix MLB = LB;
M = LB.i() * UB - LB.i() * MUB; Clean(M,0.000000001); Print(M);
M = UB.i() * LB - UB.i() * MLB; Clean(M,0.000000001); Print(M);
M = LB.i() * UB - LB.i() * Matrix(UB); Clean(M,0.000000001); Print(M);
M = UB.i() * LB - UB.i() * Matrix(LB); Clean(M,0.000000001); Print(M);
}
{
// some tests about adding and subtracting band matrices of different
// sizes - check bandwidth of results
Tracer et1("Stage 4");
BandFunctions(9, 3, 9, 3); // equal
BandFunctions(4, 7, 4, 7); // equal
BandFunctions(9, 3, 5, 8); // neither < or >
BandFunctions(5, 8, 9, 3); // neither < or >
BandFunctions(9, 8, 5, 3); // >
BandFunctions(3, 5, 8, 9); // <
LowerBandFunctions(9, 9); // equal
LowerBandFunctions(4, 4); // equal
LowerBandFunctions(9, 5); // >
LowerBandFunctions(3, 8); // <
UpperBandFunctions(3, 3); // equal
UpperBandFunctions(7, 7); // equal
UpperBandFunctions(8, 3); // >
UpperBandFunctions(5, 9); // <
SymmetricBandFunctions(9, 9); // equal
SymmetricBandFunctions(4, 4); // equal
SymmetricBandFunctions(9, 5); // >
SymmetricBandFunctions(3, 8); // <
DiagonalMatrix D(6); D << 2 << 3 << 4.5 << 1.25 << 9.5 << -5;
BandMatrix BD = D;
UpperBandMatrix UBD; UBD = D;
LowerBandMatrix LBD; LBD = D;
SymmetricBandMatrix SBD = D;
Matrix X = BD - D; Print(X); X = UBD - D; Print(X);
X = LBD - D; Print(X); X = SBD - D; Print(X);
Matrix Test(9,2);
Test(1,1) = BD.BandWidth().Lower(); Test(1,2) = BD.BandWidth().Upper();
Test(2,1) = UBD.BandWidth().Lower(); Test(2,2) = UBD.BandWidth().Upper();
Test(3,1) = LBD.BandWidth().Lower(); Test(3,2) = LBD.BandWidth().Upper();
Test(4,1) = SBD.BandWidth().Lower(); Test(4,2) = SBD.BandWidth().Upper();
IdentityMatrix I(10); I *= 5;
BD = I; UBD = I; LBD = I; SBD = I;
X = BD - I; Print(X); X = UBD - I; Print(X);
X = LBD - I; Print(X); X = SBD - I; Print(X);
Test(5,1) = BD.BandWidth().Lower(); Test(5,2) = BD.BandWidth().Upper();
Test(6,1) = UBD.BandWidth().Lower(); Test(6,2) = UBD.BandWidth().Upper();
Test(7,1) = LBD.BandWidth().Lower(); Test(7,2) = LBD.BandWidth().Upper();
Test(8,1) = SBD.BandWidth().Lower(); Test(8,2) = SBD.BandWidth().Upper();
RowVector RV = D.AsRow(); I.ReSize(6); BandMatrix BI = I; I = 1;
BD = RV.AsDiagonal() + BI; X = BD - D - I; Print(X);
Test(9,1) = BD.BandWidth().Lower(); Test(9,2) = BD.BandWidth().Upper();
Print(Test);
}
{
// various element functions
Tracer et1("Stage 5");
int i, j;
Matrix Count(1, 1); Count = 0; // for counting errors
Matrix M(20,30);
for (i = 1; i <= 20; ++i) for (j = 1; j <= 30; ++j)
M(i, j) = 100 * i + j;
const Matrix CM = M;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 30; ++j)
{
if (M(i, j) != CM(i, j)) ++Count(1,1);
if (M(i, j) != CM.element(i-1, j-1)) ++Count(1,1);
if (M(i, j) != M.element(i-1, j-1)) ++Count(1,1);
}
UpperTriangularMatrix U(20);
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
U(i, j) = 100 * i + j;
const UpperTriangularMatrix CU = U;
for (i = 1; i <= 20; ++i) for (j = i; j <= 20; ++j)
{
if (U(i, j) != CU(i, j)) ++Count(1,1);
if (U(i, j) != CU.element(i-1, j-1)) ++Count(1,1);
if (U(i, j) != U.element(i-1, j-1)) ++Count(1,1);
}
LowerTriangularMatrix L(20);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
L(i, j) = 100 * i + j;
const LowerTriangularMatrix CL = L;
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
{
if (L(i, j) != CL(i, j)) ++Count(1,1);
if (L(i, j) != CL.element(i-1, j-1)) ++Count(1,1);
if (L(i, j) != L.element(i-1, j-1)) ++Count(1,1);
}
SymmetricMatrix S(20);
for (i = 1; i <= 20; ++i) for (j = 1; j <= i; ++j)
S(i, j) = 100 * i + j;
const SymmetricMatrix CS = S;
for (i = 1; i <= 20; ++i) for (j = 1; j <= 20; ++j)
{
if (S(i, j) != CS(i, j)) ++Count(1,1);
if (S(i, j) != CS.element(i-1, j-1)) ++Count(1,1);
if (S(i, j) != S.element(i-1, j-1)) ++Count(1,1);
if (S(i, j) != S(j, i)) ++Count(1,1);
if (S(i, j) != CS(i, j)) ++Count(1,1);
if (S(i, j) != CS.element(i-1, j-1)) ++Count(1,1);
if (S(i, j) != S.element(i-1, j-1)) ++Count(1,1);
}
DiagonalMatrix D(20);
for (i = 1; i <= 20; ++i) D(i) = 100 * i + i * i;
const DiagonalMatrix CD = D;
for (i = 1; i <= 20; ++i)
{
if (D(i, i) != CD(i, i)) ++Count(1,1);
if (D(i, i) != CD.element(i-1, i-1)) ++Count(1,1);
if (D(i, i) != D.element(i-1, i-1)) ++Count(1,1);
if (D(i, i) != D(i)) ++Count(1,1);
if (D(i) != CD(i)) ++Count(1,1);
if (D(i) != CD.element(i-1)) ++Count(1,1);
if (D(i) != D.element(i-1)) ++Count(1,1);
}
RowVector R(20);
for (i = 1; i <= 20; ++i) R(i) = 100 * i + i * i;
const RowVector CR = R;
for (i = 1; i <= 20; ++i)
{
if (R(i) != CR(i)) ++Count(1,1);
if (R(i) != CR.element(i-1)) ++Count(1,1);
if (R(i) != R.element(i-1)) ++Count(1,1);
}
ColumnVector C(20);
for (i = 1; i <= 20; ++i) C(i) = 100 * i + i * i;
const ColumnVector CC = C;
for (i = 1; i <= 20; ++i)
{
if (C(i) != CC(i)) ++Count(1,1);
if (C(i) != CC.element(i-1)) ++Count(1,1);
if (C(i) != C.element(i-1)) ++Count(1,1);
}
Print(Count);
}
{
// resize to another matrix size
Tracer et1("Stage 6");
Matrix A(20, 30); A = 3;
Matrix B(3, 4);
B.ReSize(A); B = 6; B -= 2 * A; Print(B);
A.ReSize(25,25); A = 12;
UpperTriangularMatrix U(5);
U.ReSize(A); U = 12; U << (U - A); Print(U);
LowerTriangularMatrix L(5);
L.ReSize(U); L = 12; L << (L - A); Print(L);
DiagonalMatrix D(5);
D.ReSize(U); D = 12; D << (D - A); Print(D);
SymmetricMatrix S(5);
S.ReSize(U); S = 12; S << (S - A); Print(S);
IdentityMatrix I(5);
I.ReSize(U); I = 12; D << (I - A); Print(D);
A.ReSize(10, 1); A = 17;
ColumnVector C(5); C.ReSize(A); C = 17; C -= A; Print(C);
A.ReSize(1, 10); A = 15;
RowVector R(5); R.ReSize(A); R = 15; R -= A; Print(R);
}
{
// generic matrix and identity matrix
Tracer et1("Stage 7");
IdentityMatrix I(5);
I *= 4;
GenericMatrix GM = I;
GM /= 2;
DiagonalMatrix D = GM;
Matrix A = GM + 10;
A -= 10;
A -= D;
Print(A);
}
{
// SP and upper and lower triangular matrices
Tracer et1("Stage 8");
UpperTriangularMatrix UT(4);
UT << 3 << 7 << 3 << 9
<< 5 << 2 << 6
<< 8 << 0
<< 4;
LowerTriangularMatrix LT; LT.ReSize(UT);
LT << 2
<< 7 << 9
<< 2 << 8 << 6
<< 1 << 0 << 3 << 5;
DiagonalMatrix D = SP(UT, LT);
DiagonalMatrix D1(4);
D1 << 6 << 45 << 48 << 20;
D -= D1; Print(D);
BandMatrix BM = SP(UT, LT);
Matrix X = BM - D1; Print(X);
RowVector RV(2);
RV(1) = BM.BandWidth().Lower();
RV(2) = BM.BandWidth().Upper();
Print(RV);
}
// cout << "\nEnd of Seventeenth test\n";
}
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