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Hilbert Slice. Test case 1 of size 3.
MATRIX FOLLOWS
0| 1.0000e+00 5.0000e-01 3.3333e-01
1| 5.0000e-01 3.3333e-01 2.5000e-01
2| 3.3333e-01 2.5000e-01 2.0000e-01
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00
RIGHT HAND SIDE
0| 6.6667e-01 2.5000e-01 1.3333e-01
TRANSPOSE RIGHT HAND SIDE
0| 6.6667e-01 2.5000e-01 1.3333e-01
One-Norm(A) ---------- 1.833333e+00.
FACTORED MATRIX FOLLOWS
0| 1.0000e+00 5.0000e-01 3.3333e-01
1| -5.0000e-01 8.3333e-02 8.3333e-02
2| -3.3333e-01 -1.0000e+00 5.5556e-03
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00
Solution
0| 1.0000e+00 1.7881e-07 -1.0000e+00
For Ax=b. Absolute error = 1.884864e-07. Relative error = 1.332800e-07.
Solution to transposed system
0| 1.0000e+00 1.5497e-06 -1.0000e+00
For A^Tx=b. Absolute error = 2.061321e-06. Relative error = 1.457574e-06.
**********************************************************************
Hilbert Slice. Test case 2 of size 6.
MATRIX FOLLOWS
0| 1.0000e+00 5.0000e-01 3.3333e-01 2.5000e-01 0.0000e+00 0.0000e+00
1| 5.0000e-01 3.3333e-01 2.5000e-01 2.0000e-01 1.6667e-01 0.0000e+00
2| 3.3333e-01 2.5000e-01 2.0000e-01 1.6667e-01 1.4286e-01 1.2500e-01
3| 0.0000e+00 2.0000e-01 1.6667e-01 1.4286e-01 1.2500e-01 1.1111e-01
4| 0.0000e+00 0.0000e+00 1.4286e-01 1.2500e-01 1.1111e-01 1.0000e-01
5| 0.0000e+00 0.0000e+00 0.0000e+00 1.1111e-01 1.0000e-01 9.0909e-02
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
RIGHT HAND SIDE
0| 6.6667e-01 4.1667e-01 2.7619e-01 -4.1667e-02 -3.1746e-02 1.0000e-01
TRANSPOSE RIGHT HAND SIDE
0| 6.6667e-01 2.5000e-01 2.7619e-01 2.0833e-01 -3.1746e-02 -2.5000e-02
One-Norm(A) ---------- 1.833333e+00.
FACTORED MATRIX FOLLOWS
0| 1.0000e+00 5.0000e-01 3.3333e-01 2.5000e-01 0.0000e+00 0.0000e+00
1| -5.0000e-01 2.0000e-01 1.6667e-01 1.4286e-01 1.2500e-01 1.1111e-01
2| -3.3333e-01 -4.1667e-01 1.4286e-01 1.2500e-01 1.1111e-01 1.0000e-01
3| 0.0000e+00 -4.1667e-01 -9.7222e-02 1.1111e-01 1.0000e-01 9.0909e-02
4| 0.0000e+00 0.0000e+00 -1.3611e-01 -6.1161e-02 1.0079e-01 -5.8738e-02
5| 0.0000e+00 0.0000e+00 0.0000e+00 -2.9911e-02 -6.8989e-01 1.0006e-01
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 -6.7055e-08 1.0000e+00 -1.4893e-07
For Ax=b. Absolute error = 2.889978e-07. Relative error = 1.668530e-07.
Solution to transposed system
0| 1.0000e+00 -5.9605e-08 -1.0000e+00 5.9605e-08 1.0000e+00 -1.5274e-07
For A^Tx=b. Absolute error = 1.843548e-07. Relative error = 1.064373e-07.
**********************************************************************
Hilbert Slice. Test case 3 of size 9.
One-Norm(A) ---------- 1.833333e+00.
For Ax=b. Absolute error = 1.155101e-05. Relative error = 5.165769e-06.
For A^Tx=b. Absolute error = 4.500883e-06. Relative error = 2.012856e-06.
**********************************************************************
Monoelemental. Test case 4 of size 1.
MATRIX FOLLOWS
0| 3.0000e+00
SOLUTION
0| 1.0000e+00
RIGHT HAND SIDE
0| 3.0000e+00
TRANSPOSE RIGHT HAND SIDE
0| 3.0000e+00
One-Norm(A) ---------- 3.000000e+00.
FACTORED MATRIX FOLLOWS
0| 3.0000e+00
True Solution
0| 1.0000e+00
Solution
0| 1.0000e+00
For Ax=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
Solution to transposed system
0| 1.0000e+00
For A^Tx=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
**********************************************************************
Monoelemental. Test case 5 of size 1.
MATRIX FOLLOWS
0| 0.0000e+00
SOLUTION
0| 1.0000e+00
RIGHT HAND SIDE
0| 0.0000e+00
TRANSPOSE RIGHT HAND SIDE
0| 0.0000e+00
One-Norm(A) ---------- 0.000000e+00.
Zero Column 1 found
**********************************************************************
Tridiagional. Test case 6 of size 15.
One-Norm(A) ---------- 6.000000e+00.
For Ax=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
For A^Tx=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
**********************************************************************
Tridiagional. Test case 7 of size 15.
One-Norm(A) ---------- 1.050000e+02.
For Ax=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
For A^Tx=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
**********************************************************************
Tridiagional. Test case 8 of size 15.
One-Norm(A) ---------- 1.050000e+02.
For Ax=b. Absolute error = 2.625374e+07. Relative error = 9.282099e+06.
For A^Tx=b. Absolute error = 1.000835e+00. Relative error = 3.538487e-01.
**********************************************************************
Rank One. Test case 9 of size 5.
MATRIX FOLLOWS
0| 1.0000e+00 1.0000e-01 1.0000e-02 1.0000e-03 1.0000e-04
1| 1.0000e+01 1.0000e+00 1.0000e-01 1.0000e-02 1.0000e-03
2| 1.0000e+02 1.0000e+01 1.0000e+00 1.0000e-01 1.0000e-02
3| 1.0000e+03 1.0000e+02 1.0000e+01 1.0000e+00 1.0000e-01
4| 1.0000e+04 1.0000e+03 1.0000e+02 1.0000e+01 1.0000e+00
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00
RIGHT HAND SIDE
0| 9.9010e-01 9.9010e+00 9.9010e+01 9.9010e+02 9.9010e+03
TRANSPOSE RIGHT HAND SIDE
0| 9.9010e+03 9.9010e+02 9.9010e+01 9.9010e+00 9.9010e-01
One-Norm(A) ---------- 1.111100e+04.
FACTORED MATRIX FOLLOWS
0| 1.0000e+04 1.0000e+03 1.0000e+02 1.0000e+01 1.0000e+00
1| -1.0000e-03 7.6294e-06 9.5367e-07 5.9605e-08 7.4506e-09
2| -1.0000e-02 0.0000e+00 -9.3132e-10 5.8208e-11 -7.2760e-12
3| -1.0000e-01 -7.8125e-03 0.0000e+00 7.4506e-09 0.0000e+00
4| -1.0000e-04 -9.7656e-04 0.0000e+00 6.2500e-02 5.8208e-11
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00
Solution
0| -2.3230e-01 -8.0000e+00 -6.4000e+01 1.0240e+03 1.6384e+04
For Ax=b. Absolute error = 1.641509e+04. Relative error = 9.477259e+03.
Solution to transposed system
0| -8.1920e+03 0.0000e+00 1.2800e+02 0.0000e+00 5.2930e-01
For A^Tx=b. Absolute error = 8.194016e+03. Relative error = 4.730817e+03.
**********************************************************************
Zero Column. Test case 10 of size 4.
MATRIX FOLLOWS
0| -2.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00
1| -1.0000e+00 -5.0000e-01 0.0000e+00 5.0000e-01
2| -6.6667e-01 -3.3333e-01 0.0000e+00 3.3333e-01
3| -5.0000e-01 -2.5000e-01 0.0000e+00 2.5000e-01
SOLUTION
0| 1.0000e+00 1.0000e+01 -1.0000e+00 -1.0000e+01
RIGHT HAND SIDE
0| -2.2000e+01 -1.1000e+01 -7.3333e+00 -5.5000e+00
TRANSPOSE RIGHT HAND SIDE
0| -6.3333e+00 -3.1667e+00 0.0000e+00 3.1667e+00
One-Norm(A) ---------- 4.166667e+00.
Zero Column 4 found
**********************************************************************
Upper Triangular. Test case 11 of size 6.
MATRIX FOLLOWS
0| 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00 -3.0000e+00 -4.0000e+00
1| 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00 -3.0000e+00
2| 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00
3| 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00
4| 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
5| 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
RIGHT HAND SIDE
0| -1.0000e+00 -2.0000e+00 -2.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
TRANSPOSE RIGHT HAND SIDE
0| 1.0000e+00 0.0000e+00 -2.0000e+00 -2.0000e+00 -1.0000e+00 -2.0000e+00
One-Norm(A) ---------- 1.100000e+01.
FACTORED MATRIX FOLLOWS
0| 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00 -3.0000e+00 -4.0000e+00
1| 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00 -3.0000e+00
2| 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00 -2.0000e+00
3| 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 -1.0000e+00
4| 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
5| 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
For Ax=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
Solution to transposed system
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
For A^Tx=b. Absolute error = 0.000000e+00. Relative error = 0.000000e+00.
**********************************************************************
Lower Triangular. Test case 12 of size 6.
MATRIX FOLLOWS
0| 1.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
1| 2.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
2| 3.0000e+00 2.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
3| 4.0000e+00 3.0000e+00 2.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00
4| 5.0000e+00 4.0000e+00 3.0000e+00 2.0000e+00 1.0000e+00 0.0000e+00
5| 6.0000e+00 5.0000e+00 4.0000e+00 3.0000e+00 2.0000e+00 1.0000e+00
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
RIGHT HAND SIDE
0| 1.0000e+00 2.0000e+00 2.0000e+00 2.0000e+00 3.0000e+00 4.0000e+00
TRANSPOSE RIGHT HAND SIDE
0| 3.0000e+00 2.0000e+00 2.0000e+00 2.0000e+00 1.0000e+00 0.0000e+00
One-Norm(A) ---------- 2.100000e+01.
FACTORED MATRIX FOLLOWS
0| 6.0000e+00 5.0000e+00 4.0000e+00 3.0000e+00 2.0000e+00 1.0000e+00
1| -3.3333e-01 -8.3333e-01 -6.6667e-01 -5.0000e-01 -3.3333e-01 -1.6667e-01
2| -5.0000e-01 -6.0000e-01 -8.0000e-01 -6.0000e-01 -4.0000e-01 -2.0000e-01
3| -6.6667e-01 -4.0000e-01 -5.0000e-01 -7.5000e-01 -5.0000e-01 -2.5000e-01
4| -8.3333e-01 -2.0000e-01 -2.5000e-01 -3.3333e-01 -6.6667e-01 -3.3333e-01
5| -1.6667e-01 -8.0000e-01 -7.5000e-01 -6.6667e-01 -5.0000e-01 -5.0000e-01
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00
Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 -3.9736e-08 1.0000e+00 3.5763e-07
For Ax=b. Absolute error = 3.647319e-07. Relative error = 2.105781e-07.
Solution to transposed system
0| 1.0000e+00 5.9605e-08 -1.0000e+00 -2.9802e-07 1.0000e+00 5.9605e-08
For A^Tx=b. Absolute error = 7.609812e-07. Relative error = 4.393527e-07.
**********************************************************************
Near Overflow. Test case 13 of size 5. BIG = 1.000000e+38
MATRIX FOLLOWS
0| 4.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36
1| 2.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36
2| 1.3333e+36 2.6667e+36 4.0000e+36 4.0000e+36 4.0000e+36
3| 1.0000e+36 2.0000e+36 3.0000e+36 4.0000e+36 4.0000e+36
4| 8.0000e+35 1.6000e+36 2.4000e+36 3.2000e+36 4.0000e+36
SOLUTION
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00
RIGHT HAND SIDE
0| 4.0000e+36 2.0000e+36 1.3333e+36 2.0000e+36 2.4000e+36
TRANSPOSE RIGHT HAND SIDE
0| 3.4667e+36 2.9333e+36 2.4000e+36 3.2000e+36 4.0000e+36
One-Norm(A) ---------- 2.000000e+37.
FACTORED MATRIX FOLLOWS
0| 4.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36 4.0000e+36
1| -5.0000e-01 2.0000e+36 2.0000e+36 2.0000e+36 2.0000e+36
2| -3.3333e-01 -6.6667e-01 1.3333e+36 1.3333e+36 1.3333e+36
3| -2.5000e-01 -5.0000e-01 -7.5000e-01 1.0000e+36 1.0000e+36
4| -2.0000e-01 -4.0000e-01 -6.0000e-01 -8.0000e-01 8.0000e+35
True Solution
0| 1.0000e+00 0.0000e+00 -1.0000e+00 0.0000e+00 1.0000e+00
Solution
0| 1.0000e+00 7.9228e-08 -1.0000e+00 5.5460e-07 1.0000e+00
For Ax=b. Absolute error = 7.571020e-07. Relative error = 4.371130e-07.
Solution to transposed system
0| 1.0000e+00 -1.4901e-07 -1.0000e+00 0.0000e+00 1.0000e+00
For A^Tx=b. Absolute error = 2.250026e-07. Relative error = 1.299053e-07.
**********************************************************************
Near Underflow. Test case 14 of size 5. SMALL = 1.000000e-38
MATRIX FOLLOWS
0| 2.5000e-37 2.5000e-37 2.5000e-37 2.5000e-37 2.5000e-37
1| 5.0000e-37 2.5000e-37 2.5000e-37 2.5000e-37 2.5000e-37
2| 7.5000e-37 3.7500e-37 2.5000e-37 2.5000e-37 2.5000e-37
3| 1.0000e-36 5.0000e-37 3.3333e-37 2.5000e-37 2.5000e-37
4| 1.2500e-36 6.2500e-37 4.1667e-37 3.1250e-37 2.5000e-37
SOLUTION
0| 1.0000e+00 1.4901e-07 -1.0000e+00 -1.4901e-07 1.0000e+00
RIGHT HAND SIDE
0| 2.5000e-37 5.0000e-37 7.5000e-37 9.1667e-37 1.0833e-36
TRANSPOSE RIGHT HAND SIDE
0| 7.5000e-37 5.0000e-37 4.1667e-37 3.1250e-37 2.5000e-37
One-Norm(A) ---------- 3.750000e-36.
FACTORED MATRIX FOLLOWS
0| 1.2500e-36 6.2500e-37 4.1667e-37 3.1250e-37 2.5000e-37
1| -4.0000e-01 1.2500e-37 1.6667e-37 1.8750e-37 2.0000e-37
2| -6.0000e-01 -1.7937e-07 8.3333e-38 1.2500e-37 1.5000e-37
3| -8.0000e-01 0.0000e+00 -2.6905e-07 6.2500e-38 1.0000e-37
4| -2.0000e-01 0.0000e+00 8.4078e-08 5.3810e-07 5.0000e-38
True Solution
0| 1.0000e+00 1.4901e-07 -1.0000e+00 -1.4901e-07 1.0000e+00
Solution
0| 1.0000e+00 1.7937e-07 -1.0000e+00 -3.0492e-06 1.0000e+00
For Ax=b. Absolute error = 4.261550e-06. Relative error = 2.460407e-06.
Solution to transposed system
0| 1.0000e+00 4.5402e-07 -1.0000e+00 4.4842e-07 1.0000e+00
For A^Tx=b. Absolute error = 1.016167e-06. Relative error = 5.866841e-07.
**********************************************************************
MATGEN: All tests complete.