FEATool  v1.9Finite Element Analysis Toolbox

## Description

SF_QUAD_Q5 Biquintic conforming shape function for quadrilaterals (Q5).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_QUAD_Q5( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming biquintic Q5 shape functions on quadrilaterals with values defined in the nodes, edges, and cell center. XI is [-1..1]^2 reference coordinates.

```Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
>1             Evaluate values of derivatives
n_sdim      scalar:  2             Number of space dimensions
n_vert      scalar:  4             Number of vertices per cell
i_dof       scalar: 1-36           Local basis function to evaluate
xi          [n_sdim]               Local coordinates of evaluation point
aInvJac     [n,n_sdim*n_sdim]      Inverse of transformation Jacobian
vBase       [n]                    Preallocated output vector
.
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
vBase       [n]                    Evaluated function values
nLDof       [4]                    Number of local degrees of freedom on
vertices, edges, faces, and cell interiors
xLDof       [n_sdim,n_ldof]        Local coordinates of local dofs
sfun        string                 Function name of called shape function
```

# Code listing

``` nLDof = [4 16 0 16];
xLDof = [-1  1 1 -1  -3/5  1   3/5 -1    -1/5  1   1/5 -1     1/5  1   -1/5 -1     3/5  1   -3/5 -1    -3/5  3/5 3/5 -3/5  -1/5  3/5 1/5 -3/5   1/5 3/5 -1/5 -3/5  -1/5  1/5 1/5 -1/5;
-1 -1 1  1  -1   -3/5 1    3/5  -1   -1/5 1    1/5  -1    1/5  1   -1/5  -1    3/5  1   -3/5  -3/5 -3/5 3/5  3/5  -3/5 -1/5 3/5  1/5  -3/5 1/5  3/5 -1/5  -1/5 -1/5 1/5  1/5];

switch i_eval

case 1

switch i_dof
case 1
vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256);
case 2
vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256);
case 3
vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256);
case 4
vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256);
case 5
vBase = -((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256);
case 6
vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 7
vBase = -((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256);
case 8
vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 9
vBase = ((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128);
case 10
vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 11
vBase = ((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128);
case 12
vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
case 13
vBase = -((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128);
case 14
vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
case 15
vBase = -((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128);
case 16
vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 17
vBase = ((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256);
case 18
vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 19
vBase = ((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256);
case 20
vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 21
vBase = ((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 22
vBase = -((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 23
vBase = ((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 24
vBase = -((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 25
vBase = -((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 26
vBase = ((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 27
vBase = -((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 28
vBase = ((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
case 29
vBase = ((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
case 30
vBase = -((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
case 31
vBase = ((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
case 32
vBase = -((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 33
vBase = ((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 34
vBase = -((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
case 35
vBase = ((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
case 36
vBase = -((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
end

case {2,3}

switch i_dof
case 1
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
case 2
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
case 3
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
case 4
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
case 5
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
case 6
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
case 7
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
case 8
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
case 9
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/384;
case 10
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/384;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
case 11
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/384;
case 12
dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/384;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
case 13
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/384;
case 14
dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/384;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
case 15
dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/384;
case 16
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/384;
dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
case 17
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
case 18
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
case 19
dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
case 20
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
case 21
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
case 22
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
case 23
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
case 24
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
case 25
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/384;
case 26
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/384;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
case 27
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/384;
case 28
dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/384;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
case 29
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/384;
case 30
dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/384;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
case 31
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/384;
case 32
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/384;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
case 33
dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/384;
dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/384;
case 34
dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/384;
dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/384;
case 35
dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/384;
dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/384;
case 36
dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/384;
dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/384;
end

if( i_eval==2 )
vBase = aInvJac(:,1).*dNdxi1 + aInvJac(:,2).*dNdxi2;
else
vBase = aInvJac(:,3).*dNdxi1 + aInvJac(:,4).*dNdxi2;
end

case {22,23,32,33}   % Evaluation of second order derivatives.
error('sf_quad_Q5: second order derivative evaluation not supported.')

otherwise
vBase = 0;

end```