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‎lib/node_modules/@stdlib/lapack/base/dlanv2/README.md‎

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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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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.

‎lib/node_modules/@stdlib/lapack/base/dlanv2/docs/repl.txt‎

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{{alias}}( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
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Computes the real Schur factorization of a 2-by-2 real nonsymmetric
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matrix using an orthogonal similarity transformation.
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Given matrix:
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[ A B ]
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[ C D ]
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The routine computes an orthogonal rotation (cosine CS, sine SN) such
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that:
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Q^T * [ A B ] * Q = [ AA BB ]
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[ C D ] [ CC DD ]
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where Q is a 2x2 rotation matrix:
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Q = [ CS SN ]
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[ -SN CS ]
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and the result is either real upper triangular (real eigenvalues) or
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2x2 block diagonal (complex conjugate eigenvalues).
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Indexing is relative to the first index. To introduce an offset, use
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typed array views.
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Parameters
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----------
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A: Float64Array
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Input element A(1,1).
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B: Float64Array
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Input element A(1,2).
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C: Float64Array
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Input element A(2,1).
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D: Float64Array
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Input element A(2,2).
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RT1R: Float64Array
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Output: real part of the first eigenvalue.
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RT1I: Float64Array
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Output: imaginary part of the first eigenvalue.
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RT2R: Float64Array
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Output: real part of the second eigenvalue.
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RT2I: Float64Array
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Output: imaginary part of the second eigenvalue.
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CS: Float64Array
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Output: cosine of the rotation.
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SN: Float64Array
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Output: sine of the rotation.
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Returns
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-------
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undefined
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Examples
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--------
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> var Float64Array = require( '@stdlib/array/float64' );
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> var dlanv2 = require( '@stdlib/lapack/base/dlanv2' );
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> var A = new Float64Array( [ 4.0 ] );
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> var B = new Float64Array( [ -5.0 ] );
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> var C = new Float64Array( [ 2.0 ] );
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> var D = new Float64Array( [ -3.0 ] );
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> var RT1R = new Float64Array( 1 );
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> var RT1I = new Float64Array( 1 );
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> var RT2R = new Float64Array( 1 );
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> var RT2I = new Float64Array( 1 );
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> var CS = new Float64Array( 1 );
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> var SN = new Float64Array( 1 );
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> dlanv2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN );
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> A
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<Float64Array>[ 2.0 ]
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> B
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<Float64Array>[ -7.0 ]
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> C
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<Float64Array>[ 0.0 ]
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> D
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<Float64Array>[ -1.0 ]
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> RT1R
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<Float64Array>[ 2.0 ]
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> RT1I
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<Float64Array>[ 0.0 ]
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> RT2R
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<Float64Array>[ -1.0 ]
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> RT2I
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<Float64Array>[ 0.0 ]
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> CS
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<Float64Array>[ ~0.93 ]
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> SN
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<Float64Array>[ ~0.34 ]
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{{alias}}.ndarray( A,oa,B,ob,C,oc,D,od,R1,or1,I1,oi1,R2,or2,I2,oi2,CS,ocs,SN,osn )
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Computes the Schur factorization of a 2-by-2 real nonsymmetric matrix
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using alternative indexing semantics.
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Given matrix:
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[ A B ]
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[ C D ]
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The routine computes an orthogonal rotation (cosine CS, sine SN) such
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that:
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Q^T * [ A B ] * Q = [ AA BB ]
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[ C D ] [ CC DD ]
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where Q is a 2x2 rotation matrix:
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Q = [ CS SN ]
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[ -SN CS ]
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and the result is either real upper triangular (real eigenvalues) or
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2x2 block diagonal (complex conjugate eigenvalues).
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While typed array views mandate a view offset based on the underlying
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buffer, the offset parameters support indexing semantics based on starting
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indices.
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Parameters
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----------
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A: Float64Array
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Input element A(1,1).
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oa: integer
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Starting index for `A`.
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B: Float64Array
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Input element A(1,2).
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ob: integer
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Starting index for `B`.
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C: Float64Array
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Input element A(2,1).
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oc: integer
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Starting index for `C`.
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D: Float64Array
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Input element A(2,2).
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od: integer
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Starting index for `D`.
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R1: Float64Array
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Output: real part of the first eigenvalue.
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or1: integer
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Starting index for `R1`.
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I1: Float64Array
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Output: imaginary part of the first eigenvalue.
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oi1: integer
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Starting index for `I1`.
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R2: Float64Array
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Output: real part of the second eigenvalue.
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or2: integer
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Starting index for `R2`.
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I2: Float64Array
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Output: imaginary part of the second eigenvalue.
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oi2: integer
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Starting index for `I2`.
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CS: Float64Array
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Output: cosine of the rotation.
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ocs: integer
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Starting index for `CS`.
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SN: Float64Array
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Output: sine of the rotation.
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osn: integer
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Starting index for `SN`.
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Examples
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--------
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> var Float64Array = require( '@stdlib/array/float64' );
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> var A = new Float64Array( [ 0.0, 4.0 ] );
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> var B = new Float64Array( [ 0.0, -5.0 ] );
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> var C = new Float64Array( [ 0.0, 2.0 ] );
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> var D = new Float64Array( [ 0.0, -3.0 ] );
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> var RT1R = new Float64Array( 2 );
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> var RT1I = new Float64Array( 2 );
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> var RT2R = new Float64Array( 2 );
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> var RT2I = new Float64Array( 2 );
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> var CS = new Float64Array( 2 );
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> var SN = new Float64Array( 2 );
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> dlanv2.ndarray( A, 1, B, 1, C, 1, D, 1,
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RT1R, 1, RT1I, 1, RT2R, 1, RT2I, 1, CS, 1, SN, 1 );
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> A
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<Float64Array>[ 0.0, 2.0 ]
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> C
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<Float64Array>[ 0.0, 0.0 ]
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> RT1R
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<Float64Array>[ 0.0, 2.0 ]
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> RT2R
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<Float64Array>[ 0.0, -1.0 ]

‎lib/node_modules/@stdlib/lapack/base/dlanv2/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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* Copyright (c) 2025 The Stdlib Authors.
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*
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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.

‎lib/node_modules/@stdlib/lapack/base/dlanv2/docs/types/test.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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* Copyright (c) 2025 The Stdlib Authors.
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*
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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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