The function constructs a Splinets-object that is made of subsampled
elements of the input Splinets-object.
The input objects have to be of the same order and over the same knots.
Details
The output Splinet-object made of subsampled splines is always is of the regular type, i.e. SLOT type='sp'.
References
Liu, X., Nassar, H., Podg\(\mbox{\'o}\)rski, K. "Dyadic diagonalization of positive definite band matrices and efficient B-spline orthogonalization." Journal of Computational and Applied Mathematics (2022) <https://doi.org/10.1016/j.cam.2022.114444>.
Podg\(\mbox{\'o}\)rski, K. (2021)
"Splinets – splines through the Taylor expansion, their support sets and orthogonal bases." <arXiv:2102.00733>.
Nassar, H., Podg\(\mbox{\'o}\)rski, K. (2023) "Splinets 1.5.0 – Periodic Splinets." <arXiv:2302.07552>
See also
is.splinets for diagnostic of Splinets-objects;
construct for constructing such a Splinets-object;
gather for combining Splinets-objects;
refine for refinment of a spline to a larger number of knots;
plot,Splinets-method for plotting Splinets-objects;
Examples
#-----------------------------------------------------#
#---------------------Subsampling---------------------#
#-----------------------------------------------------#
#Example with different support ranges, the 3rd order
n=25; xi=sort(runif(n+2)); xi[1]=0; xi[n+2]=1; k=3
supp=list(t(c(2,12)),t(c(4,20)),t(c(6,25))) #defining support ranges for three splines
#Initial random matrices of the derivative for each spline
set.seed(5)
SS1=matrix(rnorm((supp[[1]][1,2]-supp[[1]][1,1]+1)*(k+1)),ncol=(k+1))
SS2=matrix(rnorm((supp[[2]][1,2]-supp[[2]][1,1]+1)*(k+1)),ncol=(k+1))
SS3=matrix(rnorm((supp[[3]][1,2]-supp[[3]][1,1]+1)*(k+1)),ncol=(k+1))
spl=construct(xi,k,SS1,supp[[1]]) #constructing the first correct spline
#>
#> Using method RRM to correct the derivative matrix entries.
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#> The boundary zero conditions are not satisfied for spline 1 in the input 'Splinets' object.
#> Correction of the first and last rows of the derivative matrices over the support component 1 of spline 1 in the output 'Splinets' object.
#>
#> Spline 1 support 1 's highest derivative at the central knot is not zero.
#> Now it is set to zero.
#>
#> The matrix of derivatives at the knots for spline 1 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 1.311759 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 1 support 1 has the derivative matrix corrected by the RRM method.
#> The matrix derivative is now corrected by method RRM .
nspl=construct(xi,k,SS2,supp[[2]],'CRFC')
#>
#> Using method CRFC to correct the derivative matrix entries.
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#> The boundary zero conditions are not satisfied for spline 1 in the input 'Splinets' object.
#> Correction of the first and last rows of the derivative matrices over the support component 1 of spline 1 in the output 'Splinets' object.
#>
#> Spline 1 support 1 's highest derivative at the central knot is not zero.
#> Now it is set to zero.
#>
#> The matrix of derivatives at the knots for spline 1 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 1.29385 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 1 support 1 has the derivative matrix corrected by the RRM method.The zero boundary conditions are not satisfied.
#> The correction of the first and last rows of the derivative matrix has been made.
#>
#>
#> The highest order derivative at the central knot is not equal to zero.
#> It has been made equal to zero now.
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The matrix derivative is now corrected by method CRFC .
#See 'gather' function for more details on what follows
spl=gather(spl,nspl) #the second and the first ones
nspl=construct(xi,k,SS3,supp[[3]],'CRLC')
#>
#> Using method CRLC to correct the derivative matrix entries.
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#> The boundary zero conditions are not satisfied for spline 1 in the input 'Splinets' object.
#> Correction of the first and last rows of the derivative matrices over the support component 1 of spline 1 in the output 'Splinets' object.
#>
#> Spline 1 , support 1 - highest derivative is not symmetric at the center (equal values at the two central knots).
#> The two values have been made equal by averaging.
#>
#> The matrix of derivatives at the knots for spline 1 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 1.646284 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> There are less than 5 knots, the first 2 entries of the 5 nd row counting from the end in the input will be changed in the output.
#>
#>
#> Correction of the RHS part of the matrix
#> There are less than 5 knots, the first 2 entries of the 5 nd row counting from the end in the input will be changed in the output.
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 1 support 1 has the derivative matrix corrected by the RRM method.The zero boundary conditions are not satisfied.
#> The correction of the first and last rows of the derivative matrix has been made.
#>
#>
#> The highest order derivative is not symmetrically defined at the center.
#> The values at the two central knots should be equal.
#> The highest order derivative values at the two central knots
#> have been made equal by averaging the two central values.
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The matrix derivative is now corrected by method CRLC .
spl=gather(spl,nspl) #the third is added
#Replicating by subsampling with replacement
sz=length(spl@der)
ss=sample(1:sz,size=10,rep=TRUE)
spl=subsample(spl,ss)
is.splinets(spl)[[1]]
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#>
#> The matrix of derivatives at the knots for spline 3 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 3 support 1 has the derivative matrix corrected by the RRM method.
#> The matrix of derivatives at the knots for spline 5 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 5 support 1 has the derivative matrix corrected by the RRM method.
#> The matrix of derivatives at the knots for spline 6 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 6 support 1 has the derivative matrix corrected by the RRM method.
#> The matrix of derivatives at the knots for spline 7 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 7 support 1 has the derivative matrix corrected by the RRM method.
#> [1] FALSE
spl@supp
#> [[1]]
#> [,1] [,2]
#> [1,] 2 12
#>
#> [[2]]
#> [,1] [,2]
#> [1,] 6 25
#>
#> [[3]]
#> [,1] [,2]
#> [1,] 4 20
#>
#> [[4]]
#> [,1] [,2]
#> [1,] 2 12
#>
#> [[5]]
#> [,1] [,2]
#> [1,] 4 20
#>
#> [[6]]
#> [,1] [,2]
#> [1,] 4 20
#>
#> [[7]]
#> [,1] [,2]
#> [1,] 4 20
#>
#> [[8]]
#> [,1] [,2]
#> [1,] 6 25
#>
#> [[9]]
#> [,1] [,2]
#> [1,] 2 12
#>
#> [[10]]
#> [,1] [,2]
#> [1,] 6 25
#>
spl@der
#> [[1]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.00000000 0.0000000 0.000000 -1.701607e+04
#> [2,] -0.18861400 -13.9660365 -689.415684 8.006952e+04
#> [3,] -0.52285124 -9.5045431 1090.758120 -6.718437e+04
#> [4,] -0.58130959 -0.6501706 1.545744 -1.009533e+00
#> [5,] -0.59556091 -0.6156176 1.523010 -2.000473e+00
#> [6,] -0.60290798 -0.5973131 1.498774 0.000000e+00
#> [7,] -0.62170714 -0.5481955 1.494093 -1.426081e-01
#> [8,] -0.63737252 -0.5029851 1.540283 1.550060e+00
#> [9,] -0.63323135 5.4788975 4307.928400 1.551204e+06
#> [10,] -0.02086494 10.9898246 -3858.985284 -3.326554e+05
#> [11,] 0.00000000 0.0000000 0.000000 6.775253e+05
#>
#> [[2]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000000 0.0000000 0.000000 -6.115597e+04
#> [2,] -0.018124452 -4.4880780 -740.908607 3.970527e+04
#> [3,] -0.330537636 -7.4186308 562.342214 -1.883325e+04
#> [4,] -0.384988728 0.9768266 1.134166 3.320349e-01
#> [5,] -0.382272531 0.9799765 1.135087 1.572288e+00
#> [6,] -0.357867495 1.0083175 1.173688 -1.069471e+00
#> [7,] -0.352105409 1.0149851 1.167597 9.162865e-01
#> [8,] -0.346805381 1.0210763 1.172367 -5.949929e-01
#> [9,] -0.309577061 1.0625867 1.151107 2.181647e+00
#> [10,] -0.301041386 1.0718631 1.168556 3.314296e-02
#> [11,] -0.214273504 1.1627137 1.171130 3.314296e-02
#> [12,] -0.182175832 1.1949644 1.197662 9.743826e-01
#> [13,] -0.175861339 1.2012589 1.190998 -1.264473e+00
#> [14,] -0.073105262 1.2982348 1.168191 -2.774214e-01
#> [15,] -0.017615961 1.3470762 1.160245 -1.893987e-01
#> [16,] -0.011188490 1.3525965 1.158416 -3.840249e-01
#> [17,] 0.025061016 1.3835517 1.178040 7.405880e-01
#> [18,] 0.067815404 0.2229417 -55.743323 -1.338059e+03
#> [19,] 0.007379618 -0.6149995 34.168383 1.157503e+03
#> [20,] 0.000000000 0.0000000 0.000000 -9.491701e+02
#>
#> [[3]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000e+00 0.000000e+00 0.000000e+00 -2535361836
#> [2,] -1.800618e+03 -3.331951e+05 -4.110402e+07 6338705399
#> [3,] -7.661648e+03 3.484016e+05 1.016387e+08 -13560055910
#> [4,] -4.602446e-01 5.846235e+05 -6.264228e+07 2469520918
#> [5,] -7.243285e-01 -1.412136e+05 1.841509e+07 -899614499
#> [6,] -6.921116e-02 8.119456e+03 -8.392332e+06 3177689711
#> [7,] 1.463249e+00 -2.933671e+03 4.294365e+05 -23789154
#> [8,] 1.877261e-01 4.400007e+02 -1.546032e+05 27144223
#> [9,] 1.022023e+00 -2.796661e-01 2.387233e+00 0
#> [10,] -5.918348e-01 -9.294155e+02 -3.569389e+05 -68561227
#> [11,] -1.122007e-01 8.276058e+03 8.721990e+05 34399415
#> [12,] -9.249531e-01 -2.034494e+04 -8.029150e+06 -1112933354
#> [13,] 7.533048e-01 3.525286e+05 1.763181e+07 330424825
#> [14,] -1.126091e-01 -9.452061e+05 -1.129498e+08 -4795574597
#> [15,] -5.802955e+03 -1.115047e+06 4.849832e+07 30633231265
#> [16,] -4.150852e+03 2.968282e+05 -1.415082e+07 -762050940
#> [17,] 0.000000e+00 0.000000e+00 0.000000e+00 337309290
#>
#> [[4]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.00000000 0.0000000 0.000000 -1.701607e+04
#> [2,] -0.18861400 -13.9660365 -689.415684 8.006952e+04
#> [3,] -0.52285124 -9.5045431 1090.758120 -6.718437e+04
#> [4,] -0.58130959 -0.6501706 1.545744 -1.009533e+00
#> [5,] -0.59556091 -0.6156176 1.523010 -2.000473e+00
#> [6,] -0.60290798 -0.5973131 1.498774 0.000000e+00
#> [7,] -0.62170714 -0.5481955 1.494093 -1.426081e-01
#> [8,] -0.63737252 -0.5029851 1.540283 1.550060e+00
#> [9,] -0.63323135 5.4788975 4307.928400 1.551204e+06
#> [10,] -0.02086494 10.9898246 -3858.985284 -3.326554e+05
#> [11,] 0.00000000 0.0000000 0.000000 6.775253e+05
#>
#> [[5]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000e+00 0.000000e+00 0.000000e+00 -2535361836
#> [2,] -1.800618e+03 -3.331951e+05 -4.110402e+07 6338705399
#> [3,] -7.661648e+03 3.484016e+05 1.016387e+08 -13560055910
#> [4,] -4.602446e-01 5.846235e+05 -6.264228e+07 2469520918
#> [5,] -7.243285e-01 -1.412136e+05 1.841509e+07 -899614499
#> [6,] -6.921116e-02 8.119456e+03 -8.392332e+06 3177689711
#> [7,] 1.463249e+00 -2.933671e+03 4.294365e+05 -23789154
#> [8,] 1.877261e-01 4.400007e+02 -1.546032e+05 27144223
#> [9,] 1.022023e+00 -2.796661e-01 2.387233e+00 0
#> [10,] -5.918348e-01 -9.294155e+02 -3.569389e+05 -68561227
#> [11,] -1.122007e-01 8.276058e+03 8.721990e+05 34399415
#> [12,] -9.249531e-01 -2.034494e+04 -8.029150e+06 -1112933354
#> [13,] 7.533048e-01 3.525286e+05 1.763181e+07 330424825
#> [14,] -1.126091e-01 -9.452061e+05 -1.129498e+08 -4795574597
#> [15,] -5.802955e+03 -1.115047e+06 4.849832e+07 30633231265
#> [16,] -4.150852e+03 2.968282e+05 -1.415082e+07 -762050940
#> [17,] 0.000000e+00 0.000000e+00 0.000000e+00 337309290
#>
#> [[6]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000e+00 0.000000e+00 0.000000e+00 -2535361836
#> [2,] -1.800618e+03 -3.331951e+05 -4.110402e+07 6338705399
#> [3,] -7.661648e+03 3.484016e+05 1.016387e+08 -13560055910
#> [4,] -4.602446e-01 5.846235e+05 -6.264228e+07 2469520918
#> [5,] -7.243285e-01 -1.412136e+05 1.841509e+07 -899614499
#> [6,] -6.921116e-02 8.119456e+03 -8.392332e+06 3177689711
#> [7,] 1.463249e+00 -2.933671e+03 4.294365e+05 -23789154
#> [8,] 1.877261e-01 4.400007e+02 -1.546032e+05 27144223
#> [9,] 1.022023e+00 -2.796661e-01 2.387233e+00 0
#> [10,] -5.918348e-01 -9.294155e+02 -3.569389e+05 -68561227
#> [11,] -1.122007e-01 8.276058e+03 8.721990e+05 34399415
#> [12,] -9.249531e-01 -2.034494e+04 -8.029150e+06 -1112933354
#> [13,] 7.533048e-01 3.525286e+05 1.763181e+07 330424825
#> [14,] -1.126091e-01 -9.452061e+05 -1.129498e+08 -4795574597
#> [15,] -5.802955e+03 -1.115047e+06 4.849832e+07 30633231265
#> [16,] -4.150852e+03 2.968282e+05 -1.415082e+07 -762050940
#> [17,] 0.000000e+00 0.000000e+00 0.000000e+00 337309290
#>
#> [[7]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000e+00 0.000000e+00 0.000000e+00 -2535361836
#> [2,] -1.800618e+03 -3.331951e+05 -4.110402e+07 6338705399
#> [3,] -7.661648e+03 3.484016e+05 1.016387e+08 -13560055910
#> [4,] -4.602446e-01 5.846235e+05 -6.264228e+07 2469520918
#> [5,] -7.243285e-01 -1.412136e+05 1.841509e+07 -899614499
#> [6,] -6.921116e-02 8.119456e+03 -8.392332e+06 3177689711
#> [7,] 1.463249e+00 -2.933671e+03 4.294365e+05 -23789154
#> [8,] 1.877261e-01 4.400007e+02 -1.546032e+05 27144223
#> [9,] 1.022023e+00 -2.796661e-01 2.387233e+00 0
#> [10,] -5.918348e-01 -9.294155e+02 -3.569389e+05 -68561227
#> [11,] -1.122007e-01 8.276058e+03 8.721990e+05 34399415
#> [12,] -9.249531e-01 -2.034494e+04 -8.029150e+06 -1112933354
#> [13,] 7.533048e-01 3.525286e+05 1.763181e+07 330424825
#> [14,] -1.126091e-01 -9.452061e+05 -1.129498e+08 -4795574597
#> [15,] -5.802955e+03 -1.115047e+06 4.849832e+07 30633231265
#> [16,] -4.150852e+03 2.968282e+05 -1.415082e+07 -762050940
#> [17,] 0.000000e+00 0.000000e+00 0.000000e+00 337309290
#>
#> [[8]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000000 0.0000000 0.000000 -6.115597e+04
#> [2,] -0.018124452 -4.4880780 -740.908607 3.970527e+04
#> [3,] -0.330537636 -7.4186308 562.342214 -1.883325e+04
#> [4,] -0.384988728 0.9768266 1.134166 3.320349e-01
#> [5,] -0.382272531 0.9799765 1.135087 1.572288e+00
#> [6,] -0.357867495 1.0083175 1.173688 -1.069471e+00
#> [7,] -0.352105409 1.0149851 1.167597 9.162865e-01
#> [8,] -0.346805381 1.0210763 1.172367 -5.949929e-01
#> [9,] -0.309577061 1.0625867 1.151107 2.181647e+00
#> [10,] -0.301041386 1.0718631 1.168556 3.314296e-02
#> [11,] -0.214273504 1.1627137 1.171130 3.314296e-02
#> [12,] -0.182175832 1.1949644 1.197662 9.743826e-01
#> [13,] -0.175861339 1.2012589 1.190998 -1.264473e+00
#> [14,] -0.073105262 1.2982348 1.168191 -2.774214e-01
#> [15,] -0.017615961 1.3470762 1.160245 -1.893987e-01
#> [16,] -0.011188490 1.3525965 1.158416 -3.840249e-01
#> [17,] 0.025061016 1.3835517 1.178040 7.405880e-01
#> [18,] 0.067815404 0.2229417 -55.743323 -1.338059e+03
#> [19,] 0.007379618 -0.6149995 34.168383 1.157503e+03
#> [20,] 0.000000000 0.0000000 0.000000 -9.491701e+02
#>
#> [[9]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.00000000 0.0000000 0.000000 -1.701607e+04
#> [2,] -0.18861400 -13.9660365 -689.415684 8.006952e+04
#> [3,] -0.52285124 -9.5045431 1090.758120 -6.718437e+04
#> [4,] -0.58130959 -0.6501706 1.545744 -1.009533e+00
#> [5,] -0.59556091 -0.6156176 1.523010 -2.000473e+00
#> [6,] -0.60290798 -0.5973131 1.498774 0.000000e+00
#> [7,] -0.62170714 -0.5481955 1.494093 -1.426081e-01
#> [8,] -0.63737252 -0.5029851 1.540283 1.550060e+00
#> [9,] -0.63323135 5.4788975 4307.928400 1.551204e+06
#> [10,] -0.02086494 10.9898246 -3858.985284 -3.326554e+05
#> [11,] 0.00000000 0.0000000 0.000000 6.775253e+05
#>
#> [[10]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000000 0.0000000 0.000000 -6.115597e+04
#> [2,] -0.018124452 -4.4880780 -740.908607 3.970527e+04
#> [3,] -0.330537636 -7.4186308 562.342214 -1.883325e+04
#> [4,] -0.384988728 0.9768266 1.134166 3.320349e-01
#> [5,] -0.382272531 0.9799765 1.135087 1.572288e+00
#> [6,] -0.357867495 1.0083175 1.173688 -1.069471e+00
#> [7,] -0.352105409 1.0149851 1.167597 9.162865e-01
#> [8,] -0.346805381 1.0210763 1.172367 -5.949929e-01
#> [9,] -0.309577061 1.0625867 1.151107 2.181647e+00
#> [10,] -0.301041386 1.0718631 1.168556 3.314296e-02
#> [11,] -0.214273504 1.1627137 1.171130 3.314296e-02
#> [12,] -0.182175832 1.1949644 1.197662 9.743826e-01
#> [13,] -0.175861339 1.2012589 1.190998 -1.264473e+00
#> [14,] -0.073105262 1.2982348 1.168191 -2.774214e-01
#> [15,] -0.017615961 1.3470762 1.160245 -1.893987e-01
#> [16,] -0.011188490 1.3525965 1.158416 -3.840249e-01
#> [17,] 0.025061016 1.3835517 1.178040 7.405880e-01
#> [18,] 0.067815404 0.2229417 -55.743323 -1.338059e+03
#> [19,] 0.007379618 -0.6149995 34.168383 1.157503e+03
#> [20,] 0.000000000 0.0000000 0.000000 -9.491701e+02
#>
#Subsampling without replacements
ss=c(3,8,1)
sspl=subsample(spl,ss)
sspl@supp
#> [[1]]
#> [,1] [,2]
#> [1,] 4 20
#>
#> [[2]]
#> [,1] [,2]
#> [1,] 6 25
#>
#> [[3]]
#> [,1] [,2]
#> [1,] 2 12
#>
sspl@der
#> [[1]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000e+00 0.000000e+00 0.000000e+00 -2535361836
#> [2,] -1.800618e+03 -3.331951e+05 -4.110402e+07 6338705399
#> [3,] -7.661648e+03 3.484016e+05 1.016387e+08 -13560055910
#> [4,] -4.602446e-01 5.846235e+05 -6.264228e+07 2469520918
#> [5,] -7.243285e-01 -1.412136e+05 1.841509e+07 -899614499
#> [6,] -6.921116e-02 8.119456e+03 -8.392332e+06 3177689711
#> [7,] 1.463249e+00 -2.933671e+03 4.294365e+05 -23789154
#> [8,] 1.877261e-01 4.400007e+02 -1.546032e+05 27144223
#> [9,] 1.022023e+00 -2.796661e-01 2.387233e+00 0
#> [10,] -5.918348e-01 -9.294155e+02 -3.569389e+05 -68561227
#> [11,] -1.122007e-01 8.276058e+03 8.721990e+05 34399415
#> [12,] -9.249531e-01 -2.034494e+04 -8.029150e+06 -1112933354
#> [13,] 7.533048e-01 3.525286e+05 1.763181e+07 330424825
#> [14,] -1.126091e-01 -9.452061e+05 -1.129498e+08 -4795574597
#> [15,] -5.802955e+03 -1.115047e+06 4.849832e+07 30633231265
#> [16,] -4.150852e+03 2.968282e+05 -1.415082e+07 -762050940
#> [17,] 0.000000e+00 0.000000e+00 0.000000e+00 337309290
#>
#> [[2]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000000 0.0000000 0.000000 -6.115597e+04
#> [2,] -0.018124452 -4.4880780 -740.908607 3.970527e+04
#> [3,] -0.330537636 -7.4186308 562.342214 -1.883325e+04
#> [4,] -0.384988728 0.9768266 1.134166 3.320349e-01
#> [5,] -0.382272531 0.9799765 1.135087 1.572288e+00
#> [6,] -0.357867495 1.0083175 1.173688 -1.069471e+00
#> [7,] -0.352105409 1.0149851 1.167597 9.162865e-01
#> [8,] -0.346805381 1.0210763 1.172367 -5.949929e-01
#> [9,] -0.309577061 1.0625867 1.151107 2.181647e+00
#> [10,] -0.301041386 1.0718631 1.168556 3.314296e-02
#> [11,] -0.214273504 1.1627137 1.171130 3.314296e-02
#> [12,] -0.182175832 1.1949644 1.197662 9.743826e-01
#> [13,] -0.175861339 1.2012589 1.190998 -1.264473e+00
#> [14,] -0.073105262 1.2982348 1.168191 -2.774214e-01
#> [15,] -0.017615961 1.3470762 1.160245 -1.893987e-01
#> [16,] -0.011188490 1.3525965 1.158416 -3.840249e-01
#> [17,] 0.025061016 1.3835517 1.178040 7.405880e-01
#> [18,] 0.067815404 0.2229417 -55.743323 -1.338059e+03
#> [19,] 0.007379618 -0.6149995 34.168383 1.157503e+03
#> [20,] 0.000000000 0.0000000 0.000000 -9.491701e+02
#>
#> [[3]]
#> [,1] [,2] [,3] [,4]
#> [1,] 0.00000000 0.0000000 0.000000 -1.701607e+04
#> [2,] -0.18861400 -13.9660365 -689.415684 8.006952e+04
#> [3,] -0.52285124 -9.5045431 1090.758120 -6.718437e+04
#> [4,] -0.58130959 -0.6501706 1.545744 -1.009533e+00
#> [5,] -0.59556091 -0.6156176 1.523010 -2.000473e+00
#> [6,] -0.60290798 -0.5973131 1.498774 0.000000e+00
#> [7,] -0.62170714 -0.5481955 1.494093 -1.426081e-01
#> [8,] -0.63737252 -0.5029851 1.540283 1.550060e+00
#> [9,] -0.63323135 5.4788975 4307.928400 1.551204e+06
#> [10,] -0.02086494 10.9898246 -3858.985284 -3.326554e+05
#> [11,] 0.00000000 0.0000000 0.000000 6.775253e+05
#>
is.splinets(sspl)[[1]]
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#>
#> The matrix of derivatives at the knots for spline 1 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 1 support 1 has the derivative matrix corrected by the RRM method.
#> [1] FALSE
#A single spline sampled from a 'Splinets' object
is.splinets(subsample(sspl,1))
#>
#>
#> DIAGNOSTIC CHECK of a SPLINETS object
#>
#> THE KNOTS:
#>
#>
#> THE SUPPORT SETS:
#>
#>
#>
#> THE DERIVATIVES AT THE KNOTS:
#>
#>
#> The matrix of derivatives at the knots for spline 1 , support 1 does not satisfy the splie conditions (up to the accuracy set in SLOT 'epsilon').
#> The computed standard error per matrix entry is 3.272174e-07 .
#>
#>
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> Correction of the LHS part of the matrix
#> Correction of the RHS part of the matrix
#> The output object Spline 1 support 1 has the derivative matrix corrected by the RRM method.
#> $is
#> [1] FALSE
#>
#> $robject
#> splines
#> Knots: 27 non-equaly distributed knots between 0 and 1
#> Size: 1 spline functions
#> Order: 3
#> Support: Not the full range support, a single support interval for each spline.
#> $Er
#> [1] 4.818204e-12
#>