docs: update docs

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---

lib/node_modules/@stdlib/lapack/base/dgebal/lib/base.js

@@ -47,7 +47,13 @@ var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
 * -   'scale': scale only
 * -   'both': both permute and scale
 *
-* The matrix `A` is overwritten by the balanced matrix. Scale factors are stored in the `scale` array.
+* The matrix `A` is overwritten by the balanced matrix. Scale factors are stored in the `scale` array. If `P[ j ]` is the index of the row and column interchanged with row and column j (zero-based) and `D[ j ]` is the scaling factor applied to row and column j, then:
+*
+* -   `scale[ j ]` = `P[ j ]`    for j = `0`,...,`out[ 0 ]-1`
+* -   `scale[ j ]` = `D[ j ]`    for j = `out[ 0 ]`,...,`out[ 1 ]`
+* -   `scale[ j ]` = `P[ j ]`    for j = `out[ 1 ]+1`,...,`N-1`.
+*
+* The order in which the interchanges are made is `N-1` to `out[ 1 ]+1`, then `0` to `out[ 0 ]-1`.
 *
 * @private
 * @param {string} job - indicates the operations to be performed

lib/node_modules/@stdlib/lapack/base/dgebal/lib/dgebal.js

@@ -39,7 +39,14 @@ var base = require( './base.js' );
 * -   'permute': permute only
 * -   'scale': scale only
 * -   'both': both permute and scale
-* -   The matrix `A` is overwritten by the balanced matrix.
+*
+* The matrix `A` is overwritten by the balanced matrix. Scale factors are stored in the `scale` array. If `P[ j ]` is the index of the row and column interchanged with row and column j (zero-based) and `D[ j ]` is the scaling factor applied to row and column j, then:
+*
+* -   `scale[ j ]` = `P[ j ]`    for j = `0`,...,`out[ 0 ]-1`
+* -   `scale[ j ]` = `D[ j ]`    for j = `out[ 0 ]`,...,`out[ 1 ]`
+* -   `scale[ j ]` = `P[ j ]`    for j = `out[ 1 ]+1`,...,`N-1`.
+*
+* The order in which the interchanges are made is `N-1` to `out[ 1 ]+1`, then `0` to `out[ 0 ]-1`.
 *
 * @private
 * @param {string} order - storage layout of `A`

lib/node_modules/@stdlib/lapack/base/dgebal/lib/ndarray.js

@@ -37,7 +37,14 @@ var base = require( './base.js' );
 * -   'permute': permute only
 * -   'scale': scale only
 * -   'both': both permute and scale
-* -   The matrix `A` is overwritten by the balanced matrix.
+*
+* The matrix `A` is overwritten by the balanced matrix. Scale factors are stored in the `scale` array. If `P[ j ]` is the index of the row and column interchanged with row and column j (zero-based) and `D[ j ]` is the scaling factor applied to row and column j, then:
+*
+* -   `scale[ j ]` = `P[ j ]`    for j = `0`,...,`out[ 0 ]-1`
+* -   `scale[ j ]` = `D[ j ]`    for j = `out[ 0 ]`,...,`out[ 1 ]`
+* -   `scale[ j ]` = `P[ j ]`    for j = `out[ 1 ]+1`,...,`N-1`.
+*
+* The order in which the interchanges are made is `N-1` to `out[ 1 ]+1`, then `0` to `out[ 0 ]-1`.
 *
 * @private
 * @param {string} job - indicates the operations to be performed