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‎lib/node_modules/@stdlib/lapack/base/dgtts2/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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<!-- lint disable max-len -->
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# dgtts2
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> Solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf].
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<section class="usage">
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## Usage
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```javascript
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var dgtts2 = require( '@stdlib/lapack/base/dgtts2' );
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```
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#### dgtts2( order, itrans, N, nrhs, DL, D, DU, DU2, IPIV, B, LDB )
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Solves a system of linear equations with a tri diagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf].
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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 DL = new Float64Array( [ 0.25, 0.26666667 ] );
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var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
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var DU = new Float64Array( [ 1.0, 0.73333333 ] );
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var DU2 = new Float64Array( [ 0.0 ] );
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var IPIV = new Int32Array( [ 0, 1, 2 ] );
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var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
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var out = dgtts2( 'column-major', 1, 3, 1, DL, D, DU, DU2, IPIV, B, 3 );
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// out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **itrans**: specifies the form of the system of equations.
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- **N**: order of the matrix `A`.
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- **nrhs**: number of right-hand sides, i.e., the number of columns of the matrix `B`.
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- **DL**: multipliers that define the matrix `L`.
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- **D**: diagonal elements of the upper triangular matrix `U`.
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- **DU**: elements of the first super-diagonal of `U`.
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- **DU2**: elements of the second super-diagonal of `U`.
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- **IPIV**: vector of pivot indices.
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- **B**: right-hand side matrix B, overwritten by the solution matrix `X`.
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- **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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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 DL0 = new Float64Array( [ 0.0, 0.25, 0.26666667 ] );
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var D0 = new Float64Array( [ 0.0, 4.0, 3.75, 3.73333333 ] );
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var DU0 = new Float64Array( [ 0.0, 1.0, 0.73333333 ] );
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var DU20 = new Float64Array( [ 0.0, 0.0 ] );
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var IPIV0 = new Int32Array( [ 0, 0, 1, 2 ] );
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var B0 = new Float64Array( [ 0.0, 7.0, 8.0, 7.0 ] );
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// Create offset views...
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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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var B = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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dgtts2( 'column-major', 1, 3, 1, DL, D, DU, DU2, IPIV, B, 3 );
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// B0 => <Float64Array>[ 0.0, ~1.44, ~1.25, ~1.55 ]
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```
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#### dgtts2.ndarray( itrans, N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob )
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Solves a system of linear equations with a tri diagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf] and alternative indexing semantics.
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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 DL = new Float64Array( [ 0.25, 0.26666667 ] );
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var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
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var DU = new Float64Array( [ 1.0, 0.73333333 ] );
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var DU2 = new Float64Array( [ 0.0 ] );
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var IPIV = new Int32Array( [ 0, 1, 2 ] );
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var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
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var out = dgtts2.ndarray( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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// out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
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```
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The function has the following parameters:
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- **itrans**: specifies the form of the system of equations.
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- **N**: order of the matrix `A`.
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- **nrhs**: number of right-hand sides, i.e., the number of columns of the matrix `B`.
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- **DL**: multipliers that define the matrix `L`.
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- **sdl**: stride length for `DL`.
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- **odl**: starting index for `DL`.
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- **D**: diagonal elements of the upper triangular matrix `U`.
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- **sd**: stride length for `D`.
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- **od**: starting index for `D`.
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- **DU**: elements of the first super-diagonal of `U`.
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- **sdu**: stride length for `DU`.
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- **odu**: starting index for `DU`.
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- **DU2**: elements of the second super-diagonal of `U`.
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- **sdu2**: stride length for `DU2`.
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- **odu2**: starting index for `DU2`.
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- **IPIV**: vector of pivot indices.
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- **si**: stride length for `IPIV`.
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- **oi**: starting index for `IPIV`.
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- **B**: right-hand side matrix B, overwritten by the solution matrix `X`.
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- **sb1**: stride length for first dimension of `B`.
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- **sb2**: stride length for second dimension of `B`.
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- **ob**: starting index for `B`.
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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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```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 DL = new Float64Array( [ 0.0, 0.25, 0.26666667 ] );
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var D = new Float64Array( [ 0.0, 4.0, 3.75, 3.73333333 ] );
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var DU = new Float64Array( [ 0.0, 1.0, 0.73333333 ] );
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var DU2 = new Float64Array( [ 0.0, 0.0 ] );
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var IPIV = new Int32Array( [ 0, 0, 1, 2 ] );
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var B = new Float64Array( [ 0.0, 7.0, 8.0, 7.0 ] );
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var out = dgtts2.ndarray( 1, 3, 1, DL, 1, 1, D, 1, 1, DU, 1, 1, DU2, 1, 1, IPIV, 1, 1, B, 1, 1, 1 );
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// out => <Float64Array>[ 0.0, ~1.44, ~1.25, ~1.55 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `dgtts2()` corresponds to the [LAPACK][lapack] routine [`dgtts2`][lapack-dgtts2].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
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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 dgtts2 = require( '@stdlib/lapack/base/dgtts2' );
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var shape = [ 3, 3 ];
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var order = 'row-major';
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var strides = shape2strides( shape, order );
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var B = new Float64Array( [ 7.0, 8.0, 7.0, 2.0, 3.0, 4.0, 1.0, 1.5, 2.0 ] );
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console.log( ndarray2array( B, shape, strides, 0, order ) );
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var DL = new Float64Array( [ 0.25, 0.26666667 ] );
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var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
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var DU = new Float64Array( [ 1.0, 0.73333333 ] );
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var DU2 = new Float64Array( [ 0.0 ] );
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var IPIV = new Int32Array( [ 0, 1, 2 ] );
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var X = dgtts2( 'row-major', 1, 3, 3, DL, D, DU, DU2, IPIV, B, 3 );
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console.log( ndarray2array( X, shape, strides, 0, order ) );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-dgtts2]: https://www.netlib.org/lapack/explore-html/d2/dea/group__gtts2_gae123fb2b13f2398457e4c47f5c7f7fcd.html#gae123fb2b13f2398457e4c47f5c7f7fcd
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[lapack-dgttrf]: https://www.netlib.org/lapack/explore-html/d6/d46/group__gttrf_ga8d1e46216e6c861c89bd4328b8be52a1.html#ga8d1e46216e6c861c89bd4328b8be52a1
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->
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‎lib/node_modules/@stdlib/lapack/base/dgtts2/lib/base.js‎

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* var IPIV = new Int32Array( [ 0, 1, 2 ] );
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* var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
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*
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* transpose( 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // B => <Float64Array>[ 1.4365079379889456, 1.2539682480442178, 1.5476190504889455 ]
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* var out = transpose( 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
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*/
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function transpose( N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob ) {
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var idu2;
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* var IPIV = new Int32Array( [ 0, 1, 2 ] );
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* var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
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*
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* noTranspose( 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // B => <Float64Array>[ 1.4031746026466836, 1.3873015894132654, 1.4285714242665817 ]
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* var out = noTranspose( 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // out => <Float64Array>[ ~1.40, ~1.39, ~1.43 ]
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*/
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function noTranspose( N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob ) {
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var temp;
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* var IPIV = new Int32Array( [ 0, 1, 2 ] );
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* var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
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*
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* base( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // B => <Float64Array>[ 1.4365079379889456, 1.2539682480442178, 1.5476190504889455 ]
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* var out = base( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
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*/
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function base( itrans, N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob ) {
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if ( N === 0 || nrhs === 0 ) {

‎lib/node_modules/@stdlib/lapack/base/dgtts2/lib/dgtts2.js‎

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* @param {NonNegativeInteger} N - order of the matrix A
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* @param {NonNegativeInteger} nrhs - number of right-hand sides, i.e., the number of columns of the matrix B
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* @param {Float64Array} DL - multipliers that define the matrix L
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* @param {Float64Array} D - N diagonal elements of the upper triangular matrix U
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* @param {Float64Array} D - diagonal elements of the upper triangular matrix U
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* @param {Float64Array} DU - elements of the first super-diagonal of U
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* @param {Float64Array} DU2 - elements of the second super-diagonal of U
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* @param {Int32Array} IPIV - vector of pivot indices

‎lib/node_modules/@stdlib/lapack/base/dgtts2/lib/ndarray.js‎

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* @param {integer} si - stride length for IPIV
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* @param {NonNegativeInteger} oi - starting index for IPIV
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* @param {Float64Array} B - right-hand side matrix B, overwritten by the solution matrix X
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* @param {integer} sb1 - stride of the first dimension of B
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* @param {integer} sb2 - stride of the second dimension of B
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* @param {integer} sb1 - stride length for the first dimension of B
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* @param {integer} sb2 - stride for the second dimension of B
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* @param {NonNegativeInteger} ob - starting index of B
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* @returns {Float64Array} the solution matrix X
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*
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* var IPIV = new Int32Array( [ 0, 1, 2 ] );
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*
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* dgtts2( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // B => <Float64Array>[ 1.4365079379889456, 1.2539682480442178, 1.5476190504889455 ]
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* var out = dgtts2( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
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* // out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
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*/
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function dgtts2( itrans, N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob ) { // eslint-disable-line max-len, max-params
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return base( itrans, N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob ); // eslint-disable-line max-len

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