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docs: complete writing readme
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‎lib/node_modules/@stdlib/lapack/base/dgttrf/README.md

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@@ -67,21 +67,33 @@ Note that indexing is relative to the first index. To introduce an offset, use [
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var Int32Array = require( '@stdlib/array/int32' );
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// Initial arrays...
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var D0 = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
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var E0 = new Float64Array( [ 0.0, 1.0, 2.0 ] );
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var DL0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
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var D0 = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
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var DU0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
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var DU20 = new Float64Array( 2 );
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var IPIV0 = new Int32Array( 4 );
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// Create offset views...
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var D1 = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var E1 = new Float64Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var DL = new Float64Array( DL0.buffer, DL0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var D = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var DU = new Float64Array( DU0.buffer, DU0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var DU2 = new Float64Array( DU20.buffer, DU20.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var IPIV = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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dgttrf( 3, D1, E1 );
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// D0 => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
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// E0 => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
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dgttrf( 3, DL, D, DU, DU2, IPIV );
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// DL0 => <Float64Array>[ 0, 0.5, 0.4 ]
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// D0 => <Float64Array>[ 0, 2, 2.5, 0.6 ]
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// DU0 => <Float64Array>[ 0, 1, 1 ]
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// DU20 => <Float64Array>[ 0, 0 ]
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// IPIV0 => <Int32Array>[ 0, 0, 1, 2 ]
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```
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#### dgttrf.ndarray( N, D, strideD, offsetD, E, strideE, offsetE )
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<!-- lint disable maximum-heading-length -->
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#### dgttrf.ndarray( N, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi )
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Computes an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges and alternative indexing semantics.
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The function has the following additional parameters:
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- **strideD**: stride length for `D`.
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- **offsetD**: starting index for `D`.
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- **strideE**: stride length for `E`.
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- **offsetE**: starting index for `E`.
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- **sdl**: stride length for `DL`.
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- **odl**: starting index for `DL`.
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- **sd**: stride length for `D`.
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- **od**: starting index for `D`.
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- **sdu**: stride length for `DU`.
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- **odu**: starting index for `DU`.
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- **sdu2**: stride length for `DU2`.
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- **odu2**: starting index for `DU2`.
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- **si**: stride length for `IPIV`.
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- **oi**: starting index for `IPIV`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var Int32Array = require( '@stdlib/array/int32' );
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var D = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
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var E = new Float64Array( [ 0.0, 1.0, 2.0 ] );
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dgttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
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// D => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
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// E => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
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var DL = new Float64Array( [ 0.0, 1.0, 1.0 ] );
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var D = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
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var DU = new Float64Array( [ 0.0, 1.0, 1.0 ] );
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var DU2 = new Float64Array( 2 );
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var IPIV = new Int32Array( 4 );
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dgttrf.ndarray( 3, DL, 1, 1, D, 1, 1, DU, 1, 1, DU2, 1, 1, IPIV, 1, 1 );
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// DL => <Float64Array>[ 0, 0.5, 0.4 ]
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// D => <Float64Array>[ 0, 2, 2.5, 0.6 ]
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// DU => <Float64Array>[ 0, 1, 1 ]
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// DU2 => <Float64Array>[ 0, 0 ]
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// IPIV => <Int32Array>[ 0, 0, 1, 2 ]
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```
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</section>
@@ -140,8 +165,7 @@ dgttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
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- `0`: factorization was successful.
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- `<0`: the k-th argument had an illegal value, where `-k` equals the status code value.
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- `>0`: `U( k, k )` is exactly zero the factorization has been completed, but the factor `U` is exactly singular, and division
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by zero will occur if it is used to solve a system of equations, where `k` equals the status code value.
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- `>0`: `U( k, k )` is exactly zero the factorization has been completed, but the factor `U` is exactly singular, and division by zero will occur if it is used to solve a system of equations, where `k` equals the status code value.
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- `dgttrf()` corresponds to the [LAPACK][LAPACK] routine [`dgttrf`][lapack-dgttrf].
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‎lib/node_modules/@stdlib/lapack/base/dgttrf/docs/repl.txt

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> DU = new Float64Array( DU0.buffer, DU0.BYTES_PER_ELEMENT*1 );
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> {{alias}}( 3, DL, D, DU, DU2, IPIV )
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0
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> DL
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<Float64Array>[ 0.5, 0.4 ]
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> D
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<Float64Array>[ 2, 2.5, 0.6 ]
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> DU
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<Float64Array>[ 1, 1 ]
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> DL0
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<Float64Array>[ 0, 0.5, 0.4 ]
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> D0
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<Float64Array>[ 0, 2, 2.5, 0.6 ]
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> DU0
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<Float64Array>[ 0, 1, 1 ]
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> DU2
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<Float64Array>[ 0 ]
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> IPIV

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