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docs: update eqn divs
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‎lib/node_modules/@stdlib/lapack/base/dgttrf/README.md

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@@ -38,37 +38,37 @@ A = L U
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where `L` is a product of permutation and unit lower bidiagonal matrices and `U` is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
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For a tridiagonal matrix `A`, its elements are stored in three arrays:
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For a 5 x 5 tridiagonal matrix `A`, its elements are stored in three arrays:
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<!-- <equation class="equation" label="eq:matrix_a" align="center" raw="A = \left[
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\begin{array}{rrrrr}
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d_1 & du_1 & 0 & \cdots & 0 \\
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dl_1 & d_2 & du_2 & \ddots & \vdots \\
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0 & dl_2 & d_3 & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & du_{n-1} \\
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0 & \cdots & 0 & dl_{n-1} & d_n
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d_1 & du_1 & 0 & 0 & 0 \\
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dl_1 & d_2 & du_2 & 0 & 0 \\
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0 & dl_2 & d_3 & du_3 & 0 \\
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0 & 0 & dl_3 & d_4 & du_4 \\
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0 & 0 & 0 & dl_4 & d_5
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\end{array}
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\right]" alt="Representation of matrix A."> -->
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```math
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A = \left[
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\begin{array}{rrrrr}
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d_1 & du_1 & 0 & \cdots & 0 \\
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dl_1 & d_2 & du_2 & \ddots & \vdots \\
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0 & dl_2 & d_3 & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & du_{n-1} \\
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0 & \cdots & 0 & dl_{n-1} & d_n
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d_1 & du_1 & 0 & 0 & 0 \\
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dl_1 & d_2 & du_2 & 0 & 0 \\
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0 & dl_2 & d_3 & du_3 & 0 \\
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0 & 0 & dl_3 & d_4 & du_4 \\
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0 & 0 & 0 & dl_4 & d_5
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\end{array}
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\right]
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```
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<!-- <div class="equation" align="center" data-raw-text="A = \left[
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\begin{array}{rrrrr}
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d_1 & du_1 & 0 & \cdots & 0 \\
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dl_1 & d_2 & du_2 & \ddots & \vdots \\
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0 & dl_2 & d_3 & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & du_{n-1} \\
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0 & \cdots & 0 & dl_{n-1} & d_n
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d_1 & du_1 & 0 & 0 & 0 \\
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dl_1 & d_2 & du_2 & 0 & 0 \\
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0 & dl_2 & d_3 & du_3 & 0 \\
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0 & 0 & dl_3 & d_4 & du_4 \\
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0 & 0 & 0 & dl_4 & d_5
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\end{array}
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\right]" data-equation="eq:matrix_a"></div> -->
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@@ -90,77 +90,74 @@ The resulting `L` and `U` matrices have the following structure:
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<!-- <equation class="equation" label="eq:matrix_l" align="center" raw="L = \left[
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\begin{array}{rrrrr}
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1 & 0 & \cdots & \cdots & 0 \\
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l_1 & 1 & \ddots & \ddots & \vdots \\
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0 & l_2 & 1 & \ddots & \vdots \\
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\vdots & \ddots & \ddots & \ddots & 0 \\
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0 & \cdots & 0 & l_{n-1} & 1
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1 & 0 & 0 & 0 & 0 \\
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l_1 & 1 & 0 & 0 & 0 \\
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0 & l_2 & 1 & 0 & 0 \\
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0 & 0 & l_3 & 1 & 0 \\
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0 & 0 & 0 & l_4 & 1
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\end{array}
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\right]" alt="Representation of matrix L as derived from DL."> -->
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```math
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L = \left[
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\begin{array}{rrrrr}
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1 & 0 & \cdots & \cdots & 0 \\
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l_1 & 1 & \ddots & \ddots & \vdots \\
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0 & l_2 & 1 & \ddots & \vdots \\
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\vdots & \ddots & \ddots & \ddots & 0 \\
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0 & \cdots & 0 & l_{n-1} & 1
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1 & 0 & 0 & 0 & 0 \\
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l_1 & 1 & 0 & 0 & 0 \\
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0 & l_2 & 1 & 0 & 0 \\
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0 & 0 & l_3 & 1 & 0 \\
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0 & 0 & 0 & l_4 & 1
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\end{array}
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\right]
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```
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<!-- <div class="equation" align="center" data-raw-text="L = \left[
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\begin{array}{rrrrr}
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1 & 0 & \cdots & \cdots & 0 \\
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l_1 & 1 & \ddots & \ddots & \vdots \\
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0 & l_2 & 1 & \ddots & \vdots \\
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\vdots & \ddots & \ddots & \ddots & 0 \\
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0 & \cdots & 0 & l_{n-1} & 1
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1 & 0 & 0 & 0 & 0 \\
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l_1 & 1 & 0 & 0 & 0 \\
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0 & l_2 & 1 & 0 & 0 \\
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0 & 0 & l_3 & 1 & 0 \\
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0 & 0 & 0 & l_4 & 1
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\end{array}
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\right]" data-equation="eq:matrix_l"></div> -->
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<!-- </equation> -->
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<!-- <equation class="equation" label="eq:matrix_u" align="center" raw="U = \left[
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\begin{array}{rrrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & \cdots & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & \ddots & \vdots \\
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\vdots & \ddots & u_{3,3} & u_{3,4} & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-2,n} \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-1,n} \\
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0 & \cdots & \cdots & \cdots & 0 & u_{n,n}
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\begin{array}{rrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & 0 \\
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0 & 0 & u_{3,3} & u_{3,4} & u_{3,5} \\
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0 & 0 & 0 & u_{4,4} & u_{4,5} \\
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0 & 0 & 0 & 0 & u_{5,5}
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\end{array}
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\right]" alt="Representation of matrix U as derived from D, DU, DU2."> -->
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```math
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U = \left[
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\begin{array}{rrrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & \cdots & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & \ddots & \vdots \\
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\vdots & \ddots & u_{3,3} & u_{3,4} & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-2,n} \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-1,n} \\
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0 & \cdots & \cdots & \cdots & 0 & u_{n,n}
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\begin{array}{rrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & 0 \\
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0 & 0 & u_{3,3} & u_{3,4} & u_{3,5} \\
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0 & 0 & 0 & u_{4,4} & u_{4,5} \\
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0 & 0 & 0 & 0 & u_{5,5}
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\end{array}
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\right]
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```
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<!-- <div class="equation" align="center" data-raw-text="U = \left[
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\begin{array}{rrrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & \cdots & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & \ddots & \vdots \\
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\vdots & \ddots & u_{3,3} & u_{3,4} & \ddots & 0 \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-2,n} \\
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\vdots & \ddots & \ddots & \ddots & \ddots & u_{n-1,n} \\
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0 & \cdots & \cdots & \cdots & 0 & u_{n,n}
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\begin{array}{rrrrr}
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u_{1,1} & u_{1,2} & u_{1,3} & 0 & 0 \\
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0 & u_{2,2} & u_{2,3} & u_{2,4} & 0 \\
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0 & 0 & u_{3,3} & u_{3,4} & u_{3,5} \\
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0 & 0 & 0 & u_{4,4} & u_{4,5} \\
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0 & 0 & 0 & 0 & u_{5,5}
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\end{array}
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\right]" data-equation="eq:matrix_u"></div> -->
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<!-- </equation> -->
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where the `l_i` values are stored in `DL`, the diagonal elements `u_{i,i}` are stored in `D`, and the superdiagonal elements `u_{i,i+1}` and `u_{i,i+2}` are stored in `DU` and `DU2` respectively.
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where the `l(i)` values are stored in `DL`, the diagonal elements `u(i,i)` are stored in `D`, and the superdiagonal elements `u(i,i+1)` and `u(i,i+2)` are stored in `DU` and `DU2` respectively.
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</section>
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