17 April 2015 11:20:41 PM
TEST_MAT_PRB
C++ version
Test the TEST_MAT library.
BVEC_NEXT_GRLEX_TEST
BVEC_NEXT_GRLEX computes binary vectors in GRLEX order.
0: 0000
1: 0001
2: 0010
3: 0100
4: 1000
5: 0011
6: 0101
7: 0110
8: 1001
9: 1010
10: 1100
11: 0111
12: 1011
13: 1101
14: 1110
15: 1111
16: 0000
LEGENDRE_ZEROS_TEST:
LEGENDRE_ZEROS computes the zeros of the N-th Legendre
polynomial.
Legendre zeros
0: 0
Legendre zeros
0: -0.57735
1: 0.57735
Legendre zeros
0: -0.774597
1: 0
2: 0.774597
Legendre zeros
0: -0.861136
1: -0.339981
2: 0.339981
3: 0.861136
Legendre zeros
0: -0.90618
1: -0.538469
2: 0
3: 0.538469
4: 0.90618
Legendre zeros
0: -0.93247
1: -0.661209
2: -0.238619
3: 0.238619
4: 0.661209
5: 0.93247
Legendre zeros
0: -0.949108
1: -0.741531
2: -0.405845
3: 0
4: 0.405845
5: 0.741531
6: 0.949108
MERTENS_TEST
MERTENS computes the Mertens function.
N Exact MERTENS(N)
1 1 1
2 0 0
3 -1 -1
4 -1 -1
5 -2 -2
6 -1 -1
7 -2 -2
8 -2 -2
9 -2 -2
10 -1 -1
11 -2 -2
12 -2 -2
100 1 1
1000 2 2
10000 -23 -23
MOEBIUS_TEST
MOEBIUS computes the Moebius function.
N Exact MOEBIUS(N)
1 1 1
2 -1 -1
3 -1 -1
4 0 0
5 -1 -1
6 1 1
7 -1 -1
8 0 0
9 0 0
10 1 1
11 -1 -1
12 0 0
13 -1 -1
14 1 1
15 1 1
16 0 0
17 -1 -1
18 0 0
19 -1 -1
20 0 0
R8MAT_IS_EIGEN_LEFT_TEST:
R8MAT_IS_EIGEN_LEFT tests the error in the left eigensystem
A' * X - X * LAMBDA = 0
Matrix A:
Col: 0 1 2 3
Row
0: 0.136719 0.605469 0.253906 0.00390625
1: 0.0585938 0.527344 0.394531 0.0195312
2: 0.0195312 0.394531 0.527344 0.0585938
3: 0.00390625 0.253906 0.605469 0.136719
Eigenmatrix X:
Col: 0 1 2 3
Row
0: 1 1 1 1
1: 11 3 -1 -3
2: 11 -3 -1 3
3: 1 -1 1 -1
Eigenvalues LAM:
0: 1
1: 0.25
2: 0.0625
3: 0.015625
Frobenius norm of A'*X-X*LAMBDA is 9.40908
R8MAT_IS_EIGEN_LEFT_TEST
Normal end of execution.
R8MAT_IS_LLT_TEST:
R8MAT_IS_LLT tests the error in a lower triangular
Cholesky factorization A = L * L' by looking at A-L*L'
Matrix A:
Col: 0 1 2 3
Row
0: 2 1 0 0
1: 1 2 1 0
2: 0 1 2 1
3: 0 0 1 2
Cholesky factor L:
Col: 0 1 2 3
Row
0: 1.41421 0 0 0
1: 0.707107 1.22474 0 0
2: 0 0.816497 1.1547 0
3: 0 0 0.866025 1.11803
Frobenius norm of A-L*L' is 2.18689e-15
R8MAT_IS_LLT_TEST
Normal end of execution.
R8MAT_IS_NULL_LEFT_TEST:
R8MAT_IS_NULL_LEFT tests whether the M vector X
is a left null vector of A, that is, x'*A=0.
Matrix A:
Col: 0 1 2
Row
0: 1 2 3
1: 4 5 6
2: 7 8 9
Vector X:
0: 1
1: -2
2: 1
Frobenius norm of X'*A is 0
R8MAT_IS_NULL_RIGHT_TEST:
R8MAT_IS_NULL_RIGHT tests whether the N vector X
is a right null vector of A, that is, A*x=0.
Matrix A:
Col: 0 1 2
Row
0: 1 2 3
1: 4 5 6
2: 7 8 9
Vector X:
0: 1
1: -2
2: 1
Frobenius norm of A*x is 0
R8MAT_IS_SOLUTION_TEST:
R8MAT_IS_SOLUTION tests whether X is the solution of
A*X=B by computing the Frobenius norm of the residual.
A is 3 by 10
X is 10 by 9
B is 3 by 9
Frobenius error in A*X-B is 2.36629e-14
R8MAT_NORM_FRO_TEST
R8MAT_NORM_FRO computes the Frobenius norm of a matrix.
Matrix A:
Col: 0 1 2 3
Row
0: 1 2 3 4
1: 5 6 7 8
2: 9 10 11 12
3: 13 14 15 16
4: 17 18 19 20
Expected Frobenius norm = 53.5724
Computed Frobenius norm = 53.5724
TEST_CONDITION
Compute the L1 condition number of an example of each
test matrix
Title N COND COND
AEGERTER 5 24 24
BAB 5 8.46751 8.46751
BAUER 6 8.52877e+06 8.52877e+06
BIS 5 42.9756 42.9756
BIW 5 59.9171 59.9171
BODEWIG 4 10.4366 10.4366
BOOTHROYD 5 1.002e+06 1.002e+06
COMBIN 5 11.9644 11.9644
COMPANION 5 14.5786 14.5786
CONEX1 4 68.0622 68.0622
CONEX2 3 17.7034 17.7034
CONEX3 5 80 80
CONEX4 4 4488 4488
DAUB2 4 2 2
DAUB4 8 2.79904 2.79904
DAUB6 12 3.44146 3.44146
DAU8 16 3.47989 3.47989
DAUB10 20 4.00375 4.00375
DAUB12 24 4.80309 4.80309
DIAGONAL 5 7.39629 7.39629
DIF2 5 18 18
DOWNSHIFT 5 1 1
EXCHANGE 5 1 1
FIBONACCI2 5 15 15
GFPP 5 12.2633 12.2633
GIVENS 5 50 50
HANKEL_N 5 5.8368 5.8368
HARMAN 8 77.069 77.069
HARTLEY 5 5 5
IDENTITY 5 1 1
ILL3 3 216775 216775
JORDAN 5 2.08956 2.08956
KERSHAW 4 49 49
LIETZKE 5 38 38
MAXIJ 5 100 100
MINIJ 5 60 60
ORTH_SYMM 5 4.39765 4.39765
OTO 5 18 18
PASCAL1 5 100 100
PASCAL3 5 14333.5 14333.5
PEI 5 4.90227 4.90227
RODMAN 5 5.859 5.859
RUTIS1 4 15 15
RUTIS2 4 11.44 11.44
RUTIS3 4 6 6
RUTIS5 4 62608 62608
SUMMATION 5 10 10
SWEET1 6 16.9669 16.9669
SWEET2 6 49.2227 49.2227
SWEET3 6 24.7785 24.7785
SWEET4 13 51.1709 51.1709
TRI_UPPER 5 2599.9 2599.9
UPSHIFT 5 1 1
WILK03 3 2.6e+10 2.6e+10
WILK04 4 2.45892e+16 2.85325e+16
WILK05 5 7.93703e+06 7.93703e+06
WILSON 4 4488 4488
TEST_DETERMINANT
Compute the determinants of an example of each
test matrix; compare with the determinant routine,
if available. Print the matrix Frobenius norm
for an estimate of magnitude.
Title N Determ Determ ||A||
A123 3 0 6.66134e-16 16.8819
AEGERTER 5 -25 -25 9.43398
ANTICIRCULANT 3 -235.484 -235.484 10.9008
ANTICIRCULANT 4 1407.78 1407.78 12.6475
ANTICIRCULANT 5 7148.67 7148.67 14.2666
ANTIHADAMARD 5 1 1 3.31662
ANTISYMM_RANDOM 5 0 2.87369
ANTISYMM_RANDOM 6 0.097353 3.33451
BAB 5 -1980.11 -1980.11 14.3605
BAUER 6 1 1 185.855
BERNSTEIN 5 96 96 25.2784
BIMARKOV_RANDOM 5 -8.62803e-05 1.38793
BIS 5 -177.02 -177.02 11.0876
BIW 5 0.0547223 0.0547223 2.36051
BODEWIG 4 568 568 12.7279
BOOTHROYD 5 1 1 886.71
BORDERBAND 5 -0.328125 -0.328125 2.76699
CARRY 5 1.65382e-08 1.65382e-08 1.41391
CAUCHY 5 38.7671 38.7671 682.273
CAUCHY 5 -2.13163e-14 13.4722
CHEBY_DIFF1 5 -2.13163e-14 13.4722
CHEBY_T 5 64 64 12.6886
CHEBY_U 5 1024 1024 22.4277
CHEBY_U 5 18 4.30116
CHEBY_VAN2 2 -2 -2 2
CHEBY_VAN2 3 -1.41421 -1.41421 2
CHEBY_VAN2 4 1 1 2.08167
CHEBY_VAN2 5 0.707107 0.707107 2.17945
CHEBY_VAN2 6 -0.5 -0.5 2.28035
CHEBY_VAN2 7 -0.353553 -0.353553 2.38048
CHEBY_VAN2 8 0.25 0.25 2.47848
CHEBY_VAN2 9 0.176777 0.176777 2.57391
CHEBY_VAN2 10 -0.125 -0.125 2.66667
CHEBY_VAN3 5 13.9754 13.9754 3.87298
CHOW 5 -70.5488 -70.5488 202.501
CIRCULANT 5 7148.67 7148.67 14.2666
CIRCULANT2 3 18 18 6.48074
CIRCULANT2 4 -160 -160 10.9545
CIRCULANT2 5 1875 1875 16.5831
CLEMENT1 5 0 0 6.32456
CLEMENT1 6 -225 -225 8.3666
CLEMENT2 5 0 0 8.979
CLEMENT2 6 -178.154 -178.154 10.16
COMBIN 5 1257.33 1257.33 20.7778
COMPANION 5 -2.81582 -2.81582 6.68633
COMPLEX_I 2 1 1 1.41421
CONEX1 4 -2.81582 -2.81582 8.12995
CONEX2 3 -0.355137 -0.355137 2.64876
CONEX3 5 -1 -1 3.87298
CONEX4 4 -1 -1 30.545
CONFERENCE 6 -125 -125 5.47723
CREATION 5 0 0 5.47723
DAUB2 4 1 1 2
DAUB4 8 -1 -1 2.82843
DAUB6 12 1 1 3.4641
DAUB8 16 -1 -1 4
DAUB10 20 1 1 4.47214
DAUB12 24 -1 -1 4.89898
DIAGONAL 5 22.1228 22.1228 6.3802
DIF1 5 0 0 2.82843
DIF1 6 1 1 3.16228
DIF1CYCLIC 5 0 0 3.16228
DIF2 5 6 6 5.2915
DIF2CYCLIC 5 0 0 5.47723
DORR 5 -6.33817e+10 -6.33817e+10 533.003
DOWNSHIFT 5 1 1 2.23607
EBERLEIN 5 0 -1.02318e-12 18.1002
EULERIAN 5 1 1 77.2981
EXCHANGE 5 1 1 2.23607
FIBONACCI1 5 0 -0 95.3527
FIBONACCI2 5 -1 -1 3
FIBONACCI3 5 8 8 3.60555
FIEDLER 7 1332.21 1332.21 30.135
FORSYTHE 5 1975.68 1975.68 10.7723
FORSYTHE 5 1975.68 1975.68 10.7723
FOURIER_COSINE 5 1 1 2.23607
FOURIER_SINE 5 1 1 2.23607
FRANK 5 1 1 11.619
GRCAR 4 -2.44929e-16 -0 2.82843
GRCAR 5 2 2 3.16228
GRCAR 6 -4 -4 3.4641
GRCAR 7 2 2 3.74166
GRCAR 8 4.89859e-16 0 4
GFPP 5 212.007 212.007 9.39618
GIVENS 5 16 16 20.6155
GK316 5 -25 -25 9.43398
GK323 5 32 32 10
GK324 5 11.953 11.953 11.4577
GRCAR 5 8 3.60555
HADAMARD 5 0 4
HANKEL 5 -2823.88 15.2126
HANKEL_N 5 3125 3125 15
HANOWA 6 1803.1 1803.1 8.69327
HARMAN 8 0.000954779 0.000954779 5.05359
HARTLEY 5 55.9017 55.9017 5
HARTLEY 6 -216 -216 6
HARTLEY 7 -907.493 -907.493 7
HARTLEY 8 -4096 -4096 8
HELMERT 5 1 1 2.23607
HELMERT2 5 1 2.23607
HERMITE 5 1024 1024 54.1941
HERNDON 5 -0.04 -0.04 1.77133
HILBERT 5 3.7493e-12 3.7493e-12 1.58091
HOUSEHOLDER 5 -1 -1 2.23607
IDEM_RANDOM 5 0 0 1
IDENTITY 5 1 1 2.23607
IJFACT1 5 7.16636e+09 7.16636e+09 3.66559e+06
IJFACT2 5 1.4948e-21 1.4948e-21 0.55772
ILL3 3 6 6 817.763
INTEGRATION 5 1 1 4.03579
INVOL 5 -1 -1 1942.46
INVOL_RANDOM 5 -1 2.23607
JACOBI 5 0 0 1.49071
JACOBI 6 -0.021645 -0.021645 1.65145
JORDAN 5 -177.02 -177.02 6.60637
KAHAN 5 -3.78564e-08 -3.78564e-08 0.715639
KERSHAW 4 1 1 8.24621
KERSHAW_TRI 5 553.995 553.995 8.73845
KMS 5 2304.83 2304.83 101.704
LAGUERRE 5 0.00347222 0.00347222 6.85376
LEGENDRE 5 16.4062 16.4062 6.80762
LEHMER 5 0.065625 0.065625 3.28041
LESLIE 4 0.605244 0.605244 1.78414
LESP 5 -42300 -42300 22.3487
LIETZKE 5 48 48 18.0278
LIGHTS_OUT -----Not ready----
LINE_ADJ 5 0 0 2.82843
LINE_ADJ 6 -1 -1 3.16228
LINE_LOOP_ADJ 5 0 -0 3.60555
LOEWNER 5 -29.0825 20.5227
LOTKIN 5 1.87465e-11 1.87465e-11 2.45676
MARKOV_RANDOM 5 0.00488558 1.33584
MAXIJ 5 5 5 19.8746
MILNES 5 11.953 11.953 11.4577
MINIJ 5 1 1 12.4499
MOLER1 5 1 1 61.885
MOLER2 5 0 1.02538e-07 101035
MOLER3 5 1 1 8.66025
MOLER4 4 1 1 2.82843
NEUMANN 25 0 0.00124631 23.2379
ONE 5 0 0 5
ORTEGA 5 -16.5253 -16.5253 244.268
ORTH_RANDOM 5 1 2.23607
ORTH_SYMM 5 1 1 2.23607
OTO 5 6 6 5.2915
PARTER 5 131.917 131.917 6.34077
PASCAL1 5 1 1 9.94987
PASCAL2 5 1 1 92.4608
PASCAL3 5 1 1 124.742
PDS_RANDOM 5 0.0404187 0.0404187 1.4623
PEI 5 137.311 137.311 6.04036
PERMUTATION_RANDOM 5 1 1 2.23607
PLU 5 -1.93261e+07 -1.93261e+07 139.254
POISSON 25 3.25655e+13 3.25655e+13 21.9089
PROLATE 5 -5651.77 12.5984
RECTANGLE_ADJ -----Not ready-----
REDHEFFER 5 -2 -2 3.74166
REF_RANDOM 5 0 0 2.6356
REF_RANDOM 5 1 1 2.81894
RIEMANN 5 -66 6.9282
RING_ADJ 1 1 1 1
RING_ADJ 2 -1 -1 1.41421
RING_ADJ 3 2 2 2.44949
RING_ADJ 4 0 -0 2.82843
RING_ADJ 5 2 2 3.16228
RING_ADJ 6 -4 -4 3.4641
RING_ADJ 7 2 2 3.74166
RING_ADJ 8 0 -0 4
RIS 5 4.12239 4.12239 3.17039
RODMAN 5 -2175.88 -2175.88 12.7897
ROSSER1 8 0 -9480.58 2482.26
ROUTH 5 7.85813 7.85813 5.15491
RUTIS1 4 -375 -375 16.6132
RUTIS2 4 100 100 11.4018
RUTIS3 4 624 624 14.1421
RUTIS4 4 125 125 50.7149
RUTIS5 4 1 1 23.7697
SCHUR_BLOCK 5 589.771 589.771 8.39978
SKEW_CIRCULANT 5 -10310.4 -10310.4 14.2666
SPLINE 5 -2566.72 -2566.72 20.8244
STIRLING 5 1 1 67.9191
STRIPE 5 2112 14.8324
SUMMATION 5 1 1 3.87298
SWEET1 6 -2.04682e+07 -2.04682e+07 70.1997
SWEET2 6 9562.52 9562.52 30.1433
SWEET3 6 -5.40561e+07 -5.40561e+07 73.4234
SWEET4 13 -6.46348e+16 -6.46348e+16 119.704
SYLVESTER 5 -222.565 12.4995
SYLVESTER_KAC 5 0 0 7.74597
SYLVESTER_KAC 6 -225 -225 10.4881
SYMM_RANDOM 5 22.1228 22.1228 6.3802
TOEPLITZ 5 -2823.88 15.2126
TOEPLITZ_5DIAG 5 -747.438 12.8468
TOEPLITZ_5S 25 -1.51735e+17 40.3981
TOEPLITZ_PDS 5 0.0849362 3.41573
TOURNAMENT_RANDOM 5 0 0 4.47214
TRANSITION_RANDOM 5 0.00486764 1.32331
TRENCH 5 -37.7411 7.03032
TRI_UPPER 5 1 1 9.18086
TRIS 5 6683.42 6683.42 13.3888
TRIV 5 -700.369 -700.369 11.1204
TRIW 5 1 1 9.39629
UPSHIFT 5 1 1 2.23607
VAND1 5 133985 133985 466.164
VAND2 5 133985 133985 466.164
WATHEN -----Not ready-----
WILK03 3 9e-21 9e-21 1.39284
WILK04 4 4.42923e-17 4.42923e-17 1.89545
WILK05 5 3.7995e-15 3.79947e-15 1.51485
WILK12 12 1 1 53.591
WILK20 20 1.4763e+25 100.389
WILK21 21 -4.15825e+12 -4.15825e+12 28.4605
WILSON 4 1 1 30.545
ZERO 5 0 0 0
ZIELKE 5 469.417 13.6953
TEST_EIGEN_LEFT
Compute the Frobenius norm of the eigenvalue error:
X * A - LAMBDA * X
given K left eigenvectors X and eigenvalues LAMBDA.
Title N K ||A|| ||X*A-Lambda*X||
A123 3 3 16.8819 1.23246e-14
CARRY 5 5 1.41391 3.57943e-15
CHOW 5 5 202.501 1.17497e-12
DIAGONAL 5 5 6.3802 0
ROSSER1 8 8 2482.26 2.61994e-11
SYMM_RANDOM 5 5 6.3802 2.28663e-15
TEST_EIGEN_RIGHT
Compute the Frobenius norm of the eigenvalue error:
A * X - X * LAMBDA
given K right eigenvectors X and eigenvalues LAMBDA.
Title N K ||A|| ||A*X-X*Lambda||
A123 3 3 16.8819 1.33427e-14
BAB 5 5 14.3605 5.61986e-15
BODEWIG 4 4 12.7279 9.17346e-15
CARRY 5 5 1.41391 1.17642e-15
CHOW 5 5 202.501 9.72047e-13
COMBIN 5 5 20.7778 7.10543e-15
DIF2 5 5 5.2915 1.19584e-15
EXCHANGE 5 5 2.23607 0
IDEM_RANDOM 5 5 1.73205 1.09055e-15
IDENTITY 5 5 2.23607 0
ILL3 3 3 817.763 1.62356e-11
KERSHAW 4 4 8.24621 4.80549e-15
KMS 5 5 2.32288 3.2055e-08
LINE_ADJ 5 5 2.82843 1.13399e-15
LINE_LOOP_ADJ 5 5 3.60555 1.19901e-15
ONE 5 5 5 0
ORTEGA 5 5 244.268 5.85061e-13
OTO 5 5 5.2915 1.19584e-15
PDS_RANDOM 5 5 1.4623 5.48387e-16
PEI 5 5 6.04036 0
RODMAN 5 5 12.7897 0
ROSSER1 8 8 2482.26 2.61994e-11
RUTIS1 4 4 16.6132 0
RUTIS2 4 4 11.4018 0
RUTIS5 4 4 23.7697 1.46286e-14
SYLVESTER_KAC 5 5 7.74597 0
SYMM_RANDOM 5 5 6.3802 2.48618e-15
WILK12 12 12 53.591 3.87684e-13
WILSON 4 4 30.545 2.48731e-14
ZERO 5 5 0 0
TEST_INVERSE
A = a test matrix of order N;
B = inverse as computed by a routine.
C = inverse as computed by R8MAT_INVERSE.
||A|| = Frobenius norm of A.
||C|| = Frobenius norm of C.
||I-AC|| = Frobenius norm of I-A*C.
||I-AB|| = Frobenius norm of I-A*B.
Title N ||A|| ||C|| ||I-AC|| ||I-AB||
AEGERTER 5 9.43398 1.77133 5.72869e-16 7.1089e-16
BAB 5 14.3605 0.720652 1.06903e-15 9.51853e-16
BAUER 6 185.855 21078.4 1.06558e-10 0
BERNSTEIN 5 25.2784 3.19613 0 0
BIS 5 11.0876 3.89011 8.88178e-16 8.88178e-16
BIW 5 2.36051 26.4794 3.76822e-15 2.03507e-15
BODEWIG 4 12.7279 0.683062 7.1575e-16 7.08784e-16
BOOTHROYD 5 886.71 886.71 1.92659e-11 0
BORDERBAND 5 2.76699 6.80053 0 0
CARRY 5 1.41391 3126.49 3.06614e-13 1.06315e-13
CAUCHY 5 682.273 60.9954 1.0411e-12 3.27596e-14
CHEBY_T 5 12.6886 1.87916 0 0
CHEBY_U 5 22.4277 1.22793 0 0
CHEBY_VAN2 5 2.17945 2.5 4.62778e-16 5.91396e-16
CHEBY_VAN3 5 3.87298 1.34164 1.11446e-15 8.74631e-16
CHOW 5 202.501 269.085 4.66001e-13 1.59593e-13
CIRCULANT 5 14.2666 0.405717 1.01758e-15 7.78549e-16
CIRCULANT2 5 16.5831 0.635959 9.22566e-16 1.83613e-15
CLEMENT1 6 8.3666 1.51731 6.47646e-16 0
CLEMENT2 6 10.16 2.66667 4.46571e-16 8.88178e-16
COMBIN 5 20.7778 0.712031 1.00228e-15 1.10466e-15
COMPANION 5 6.68633 2.87405 4.96507e-16 1.11022e-16
COMPLEX_I 2 1.41421 1.41421 0 0
CONEX1 4 8.12995 6.40059 0 0
CONEX2 3 2.64876 4.27223 2.22045e-16 2.22045e-16
CONEX3 5 3.87298 10.8167 0 0
CONFERENCE 6 5.47723 1.09545 7.75668e-16 0
DAUB2 4 2 2 0 8.88178e-16
DAUB4 8 2.82843 2.82843 2.69133e-16 2.26448e-15
DAUB6 12 3.4641 3.4641 1.01953e-15 1.57726e-15
DAUB8 16 4 4 1.70404e-15 4.70844e-15
DAUB10 20 4.47214 4.47214 1.68801e-15 8.75081e-15
DAUB12 24 4.89898 4.89898 2.19403e-15 1.95459e-14
DIAGONAL 5 6.3802 2.07065 0 0
DIF1 6 3.16228 3.4641 0 0
DIF2 5 5.2915 3.91933 1.04148e-15 6.86635e-16
DORR 5 533.003 0.0382712 1.64016e-15 1.60599e-15
DOWNSHIFT 5 2.23607 2.23607 0 0
EULERIAN 5 77.2981 784.774 2.54716e-13 0
EXCHANGE 5 2.23607 2.23607 0 0
FIBONACCI2 5 3 3.4641 0 0
FIBONACCI3 5 3.60555 1.58114 1.57009e-16 0
FIEDLER 7 30.135 3.26387 6.99264e-15 4.44956e-15
FORSYTHE 5 10.7723 0.520231 2.3017e-16 6.07649e-17
FOURIER_COSINE 5 2.23607 2.23607 1.05407e-15 1.18165e-15
FOURIER_SINE 5 2.23607 2.23607 8.44609e-16 1.98448e-15
FRANK 5 11.619 59.439 5.19793e-14 0
GFPP 5 9.39618 1.02503 1.58393e-16 1.53657e-14
GIVENS 5 20.6155 2.73861 0 0
GK316 5 9.43398 1.77133 5.72869e-16 7.1089e-16
GK323 5 10 2.30489 0 0
GK324 5 11.4577 5.59148 1.80048e-15 1.79018e-15
HANKEL_N 5 15 0.550372 6.9069e-16 0
HANOWA 6 8.69327 0.714 5.66105e-16 6.47366e-16
HARMAN 8 5.05359 14.6831 4.64392e-15 1.01653e-14
HARTLEY 5 5 1 7.48404e-16 2.69465e-15
HELMERT 5 2.23607 2.23607 4.85723e-16 7.58596e-16
HELMERT2 5 2.23607 2.23607 6.4278e-16 5.36183e-16
HERMITE 5 54.1941 1.80818 0 0
HERNDON 5 1.77133 9.43398 1.113e-15 7.1089e-16
HILBERT 5 1.58091 304160 8.65244e-12 7.27596e-12
HOUSEHOLDER 5 2.23607 2.23607 1.11383e-15 1.00796e-15
IDENTITY 5 2.23607 2.23607 0 0
ILL3 3 817.763 337.323 1.58731e-11 0
INTEGRATION 5 4.03579 7.46725 0 1.01754e-15
INVOL 5 1942.46 1942.46 5.2446e-11 7.27596e-12
JACOBI 6 1.65145 6.48074 7.36439e-16 0
JORDAN 5 6.60637 0.837134 2.22045e-16 2.22045e-16
KAHAN 5 0.715639 433.301 3.85094e-16 4.35468e-16
KERSHAW 4 8.24621 8.24621 3.55271e-15 0
KERSHAWTRI 5 8.73845 0.689986 3.61558e-16 4.82153e-16
KMS 5 101.704 2.51888 4.78765e-15 1.94337e-14
LAGUERRE 5 6.85376 202.65 2.98979e-14 0
LEGENDRE 5 6.80762 1.86931 0 3.14018e-16
LEHMER 5 3.28041 7.7202 1.72652e-15 1.41744e-15
LESP 5 22.3487 0.320749 4.24778e-16 7.47998e-16
LIETZKE 5 18.0278 2.3863 3.3605e-15 6.95553e-16
LINE_ADJ 6 3.16228 3.4641 0 0
LOTKIN 5 2.45676 242794 1.70489e-11 0
MAXIJ 5 19.8746 4.65188 2.7555e-15 0
MILNES 5 11.4577 5.59148 1.80048e-15 1.79018e-15
MINIJ 5 12.4499 5 0 0
MOLER1 5 61.885 28220.2 3.95437e-11 4.14105e-11
MOLER3 5 8.66025 115.659 0 0
ORTEGA 5 244.268 91.1607 2.12779e-12 2.32466e-12
ORTH_SYMM 5 2.23607 2.23607 8.76061e-16 1.96898e-15
OTO 5 5.2915 3.91933 1.04148e-15 6.86635e-16
PARTER 5 6.34077 0.943311 7.34737e-16 5.55112e-17
PASCAL1 5 9.94987 9.94987 0 0
PASCAL2 5 92.4608 92.4608 0 0
PASCAL3 5 124.742 124.742 2.73039e-13 5.72858e-14
PDS_RANDOM 5 1.4623 5.69873 8.66919e-16 4.80916e-15
PEI 5 6.04036 0.845046 1.32995e-15 2.00148e-16
PERMUTATION_RANDOM 5 2.23607 2.23607 0 0
PLU 5 139.254 0.121172 1.42651e-15 1.39746e-15
RIS 5 3.17039 1.88662 7.08478e-16 8.37173e-17
RODMAN 5 12.7897 0.533114 5.48831e-16 8.00593e-16
RUTIS1 4 16.6132 1.04137 1.74485e-15 1.05471e-15
RUTIS2 4 11.4018 1.14018 5.81544e-16 6.83824e-16
RUTIS3 4 14.1421 0.577813 7.5758e-16 5.92697e-16
RUTIS4 5 59.127 51.9905 2.48423e-13 3.36548e-13
RUTIS5 4 23.7697 1871.74 4.03548e-12 0
SCHUR_BLOCK 5 8.39978 0.652412 7.85046e-17 6.32925e-16
SPLINE 5 20.8244 0.966266 5.9712e-16 1.39536e-15
STIRLING 5 67.9191 32.45 2.85044e-14 0
SUMMATION 5 3.87298 3 0 0
SWEET1 6 70.1997 0.263219 1.4354e-15 1.08864e-13
SWEET2 6 30.1433 1.39919 3.85043e-15 3.48958e-14
SWEET3 6 73.4234 0.337964 1.30118e-15 1.43485e-13
SWEET4 13 119.704 0.384221 4.39293e-15 2.5206e-13
SYLVESTER_KAC 6 10.4881 2.54209 0 0
SYMM_RANDOM 5 6.3802 2.07065 1.54262e-15 3.5603e-15
TRI_UPPER 5 9.18086 167.99 0 6.02916e-14
TRIS 5 13.3888 0.395936 4.83138e-16 7.74425e-16
TRIV 5 11.1204 1.08925 1.54874e-15 8.6593e-16
TRIW 5 9.39629 455.452 0 0
UPSHIFT 5 2.23607 2.23607 0 0
VAND1 5 466.164 1.3093 5.83344e-15 4.16362e-15
VAND2 5 466.164 1.3093 8.2848e-14 6.60021e-15
WILK03 3 1.39284 1.78816e+10 0 0
WILK04 4 1.89545 1.15398e+16 9.64303e-05 10.0957
WILK05 5 1.51485 3.0639e+06 2.98752e-10 1.02452e-09
WILK21 21 28.4605 4.30755 1.49579e-15 3.82082e-15
WILSON 4 30.545 98.5292 1.70382e-13 0
TEST_LLT
A = a test matrix of order M by M
L is an M by N lower triangular Cholesky factor.
||A|| = Frobenius norm of A.
||A-LLT|| = Frobenius norm of A-L*L'.
Title M N ||A|| ||A-LLT||
DIF2 5 5 5.2915 8.88178e-16
GIVENS 5 5 20.6155 4.23634e-15
KERSHAW 4 4 8.24621 2.57035e-15
LEHMER 5 5 3.28041 2.07704e-16
MINIJ 5 5 12.4499 0
MOLER1 5 5 61.885 6.15348e-15
MOLER3 5 5 8.66025 0
OTO 5 5 5.2915 7.36439e-16
PASCAL2 5 5 92.4608 0
WILSON 4 4 30.545 5.25453e-15
TEST_NULL_LEFT
A = a test matrix of order M by N
x = an M vector, candidate for a left null vector.
||A|| = Frobenius norm of A.
||x|| = L2 norm of x.
||A'*x||/||x|| = L2 norm of A'*x over L2 norm of x.
Title M N ||A|| ||x|| ||A'*x||/||x||
A123 3 3 16.8819 2.44949 0
CHEBY_DIFF1 5 5 13.4722 3.74166 4.45079e-16
CREATION 5 5 5.47723 1 0
DIF1 5 5 2.82843 1.73205 0
DIF1CYCLIC 5 5 3.16228 2.23607 0
DIF2CYCLIC 5 5 5.47723 2.23607 0
EBERLEIN 5 5 18.1002 2.23607 5.61733e-16
FIBONACCI1 5 5 95.3527 1.73205 0
LAUCHLI 6 5 6.68163 3.59567 0
LINE_ADJ 7 7 3.4641 2 0
MOLER2 5 5 101035 263.82 0
ONE 5 5 5 1.41421 0
RING_ADJ 12 12 4.89898 3.4641 0
ROSSER1 8 8 2482.26 22.3607 0
ZERO 5 5 0 2.23607 0
TEST_NULL_RIGHT
A = a test matrix of order M by N
x = an N vector, candidate for a right null vector.
||A|| = Frobenius norm of A.
||x|| = L2 norm of x.
||A*x||/||x|| = L2 norm of A*x over L2 norm of x.
Title M N ||A|| ||x|| ||A*x||/||x||
A123 3 3 16.8819 2.44949 0
ARCHIMEDES 7 8 93.397 1.87697e+07 0
CHEBY_DIFF1 5 5 13.4722 2.23607 6.49741e-16
CREATION 5 5 5.47723 1 0
DIF1 5 5 2.82843 1.73205 0
DIF1CYCLIC 5 5 3.16228 2.23607 0
DIF2CYCLIC 5 5 5.47723 2.23607 0
FIBONACCI1 5 5 95.3527 1.73205 0
HAMMING 5 31 8.94427 2.44949 0
LINE_ADJ 7 7 3.4641 2 0
MOLER2 5 5 101035 1016.3 0
NEUMANN 25 25 23.2379 5 0
ONE 5 5 5 1.41421 0
RING_ADJ 12 12 4.89898 3.4641 0
ROSSER1 8 8 2482.26 22.3607 0
ZERO 5 5 0 2.23607 0
TEST_PLU
A = a test matrix of order M by N
P, L, U are the PLU factors.
||A|| = Frobenius norm of A.
||A-PLU|| = Frobenius norm of A-P*L*U.
Title M N ||A|| ||A-PLU||
A123 3 3 16.8819 6.8798e-15
BODEWIG 4 4 12.7279 4.1243e-15
BORDERBAND 5 5 2.76699 0
DIF2 5 5 5.2915 0
GFPP 5 5 9.39618 2.92964e-14
GIVENS 5 5 20.6155 0
KMS 5 5 101.704 2.60787e-13
LEHMER 5 5 3.28041 1.11022e-16
MAXIJ 5 5 19.8746 0
MINIJ 5 5 12.4499 0
MOLER1 5 5 61.885 6.15348e-15
MOLER3 5 5 8.66025 0
OTO 5 5 5.2915 0
PASCAL2 5 5 92.4608 0
PLU 5 5 139.254 0
VAND2 4 4 107.076 1.64856e-14
WILSON 4 4 30.545 7.32411e-15
TEST_SOLUTION
Compute the Frobenius norm of the solution error:
A * X - B
given MxN matrix A, NxK solution X, MxK right hand side B.
Title M N K ||A|| ||A*X-B||
A123 3 3 1 16.8819 0
BODEWIG 4 4 1 12.7279 0
DIF2 10 10 2 7.61577 0
FRANK 10 10 2 38.6652 0
POISSON 20 20 1 19.5448 0
WILK03 3 3 1 1.39284 6.7435e-07
WILK04 4 4 1 1.89545 1.29463e+16
WILSON 4 4 1 30.545 0
TEST_TYPE
Demonstrate functions which test the type of a matrix.
Title M N ||A|| ||Transition Error||
BODEWIG 4 4 12.7279 1e+30
SNAKES 101 101 5.92077 9.80522e-16
TRANSITION_RANDOM 5 5 1.32331 0
TEST_MAT_PRB
Normal end of execution.
17 April 2015 11:20:41 PM