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docs: add index.d.ts
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‎lib/node_modules/@stdlib/lapack/base/dlanv2/docs/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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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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// TypeScript Version: 4.1
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/**
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* Interface describing `dlanv2`.
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*/
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interface Routine {
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/**
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* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form.
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*
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* Given a real 2×2 matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* A & B \\
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* C & D
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* \end{bmatrix}
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* ```
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*
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* this routine computes an orthogonal matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{CS} & \text{SN} \\
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* -\text{SN} & \text{CS}
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* \end{bmatrix}
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* ```
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*
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* such that the matrix is reduced to Schur (quasi-triangular) form:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{AA} & \text{BB} \\
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* 0 & \text{DD}
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* \end{bmatrix}
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* ```
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*
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* @param A - array containing the element A(1,1)
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* @param B - array containing the element A(1,2)
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* @param C - array containing the element A(2,1)
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* @param D - array containing the element A(2,2)
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* @param RT1R - output array for the real part of the first eigenvalue
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* @param RT1I - output array for the imaginary part of the first eigenvalue
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* @param RT2R - output array for the real part of the second eigenvalue
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* @param RT2I - output array for the imaginary part of the second eigenvalue
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* @param CS - output array for cosine of the rotation
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* @param SN - output array for sine of the rotation
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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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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*
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* dlanv2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN );
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* // A => <Float64Array>[ 2.0 ]
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* // B => <Float64Array>[ -7.0 ]
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* // C => <Float64Array>[ 0.0 ]
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* // D => <Float64Array>[ -1.0 ]
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* // RT1R => <Float64Array>[ 2.0 ]
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* // RT1I => <Float64Array>[ 0.0 ]
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* // RT2R => <Float64Array>[ -1.0 ]
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* // RT2I => <Float64Array>[ 0.0 ]
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* // CS => <Float64Array>[ ~0.93 ]
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* // SN => <Float64Array>[ ~0.34 ]`
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*/
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( A: Float64Array, B: Float64Array, C: Float64Array, D: Float64Array, RT1R: Float64Array, RT1I: Float64Array, RT2R: Float64Array, RT2I: Float64Array, CS: Float64Array, SN: Float64Array ): void;
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/**
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* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form using alternative indexing semantics.
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*
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* Given a real 2×2 matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* A & B \\
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* C & D
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* \end{bmatrix}
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* ```
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*
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* this routine computes an orthogonal matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{CS} & \text{SN} \\
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* -\text{SN} & \text{CS}
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* \end{bmatrix}
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* ```
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*
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* such that the matrix is reduced to Schur (quasi-triangular) form:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{AA} & \text{BB} \\
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* 0 & \text{DD}
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* \end{bmatrix}
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* ```
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*
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* @param A - array containing the element A(1,1)
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* @param offsetA - index in `A` of the element A(1,1)
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* @param B - array containing the element A(1,2)
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* @param offsetB - index in `B` of the element A(1,2)
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* @param C - array containing the element A(2,1)
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* @param offsetC - index in `C` of the element A(2,1)
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* @param D - array containing the element A(2,2)
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* @param offsetD - index in `D` of the element A(2,2)
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* @param RT1R - output array for the real part of the first eigenvalue
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* @param offsetRT1R - index in `RT1R` at which to store the value
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* @param RT1I - output array for the imaginary part of the first eigenvalue
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* @param offsetRT1I - index in `RT1I` at which to store the value
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* @param RT2R - output array for the real part of the second eigenvalue
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* @param offsetRT2R - index in `RT2R` at which to store the value
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* @param RT2I - output array for the imaginary part of the second eigenvalue
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* @param offsetRT2I - index in `RT2I` at which to store the value
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* @param CS - output array for cosine of the rotation
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* @param offsetCS - index in `CS` at which to store the value
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* @param SN - output array for sine of the rotation
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* @param offsetSN - index in `SN` at which to store the value
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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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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*
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* dlanv2( A, 0, B, 0, C, 0, D, 0, RT1R, 0, RT1I, 0, RT2R, 0, RT2I, 0, CS, 0, SN, 0 );
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* // A => <Float64Array>[ 2.0 ]
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* // B => <Float64Array>[ -7.0 ]
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* // C => <Float64Array>[ 0.0 ]
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* // D => <Float64Array>[ -1.0 ]
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* // RT1R => <Float64Array>[ 2.0 ]
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* // RT1I => <Float64Array>[ 0.0 ]
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* // RT2R => <Float64Array>[ -1.0 ]
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* // RT2I => <Float64Array>[ 0.0 ]
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* // CS => <Float64Array>[ ~0.93 ]
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* // SN => <Float64Array>[ ~0.34 ]
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*/
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ndarray( A: Float64Array, offsetA: number, B: Float64Array, offsetB: number, C: Float64Array, offsetC: number, D: Float64Array, offsetD: number, RT1R: Float64Array, offsetRT1R: number, RT1I: Float64Array, offsetRT1I: number, RT2R: Float64Array, offsetRT2R: number, RT2I: Float64Array, offsetRT2I: number, CS: Float64Array, offsetCS: number, SN: Float64Array, offsetSN: number ): void;
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}
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/**
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* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form using alternative indexing semantics.
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*
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* Given a real 2×2 matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* A & B \\
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* C & D
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* \end{bmatrix}
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* ```
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*
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* this routine computes an orthogonal matrix:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{CS} & \text{SN} \\
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* -\text{SN} & \text{CS}
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* \end{bmatrix}
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* ```
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*
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* such that the matrix is reduced to Schur (quasi-triangular) form:
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*
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* ```tex
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* \begin{bmatrix}
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* \text{AA} & \text{BB} \\
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* 0 & \text{DD}
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* \end{bmatrix}
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* ```
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*
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* @param A - array containing the element A(1,1)
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* @param B - array containing the element A(1,2)
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* @param C - array containing the element A(2,1)
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* @param D - array containing the element A(2,2)
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* @param RT1R - output array for the real part of the first eigenvalue
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* @param RT1I - output array for the imaginary part of the first eigenvalue
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* @param RT2R - output array for the real part of the second eigenvalue
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* @param RT2I - output array for the imaginary part of the second eigenvalue
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* @param CS - output array for cosine of the rotation
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* @param SN - output array for sine of the rotation
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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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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*
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* dlanv2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN );
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* // A => <Float64Array>[ 2.0 ]
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* // B => <Float64Array>[ -7.0 ]
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* // C => <Float64Array>[ 0.0 ]
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* // D => <Float64Array>[ -1.0 ]
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* // RT1R => <Float64Array>[ 2.0 ]
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* // RT1I => <Float64Array>[ 0.0 ]
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* // RT2R => <Float64Array>[ -1.0 ]
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* // RT2I => <Float64Array>[ 0.0 ]
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* // CS => <Float64Array>[ ~0.93 ]
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* // SN => <Float64Array>[ ~0.34 ]
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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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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*
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* dlanv2( A, 0, B, 0, C, 0, D, 0, RT1R, 0, RT1I, 0, RT2R, 0, RT2I, 0, CS, 0, SN, 0 );
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* // A => <Float64Array>[ 2.0 ]
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* // B => <Float64Array>[ -7.0 ]
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* // C => <Float64Array>[ 0.0 ]
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* // D => <Float64Array>[ -1.0 ]
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* // RT1R => <Float64Array>[ 2.0 ]
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* // RT1I => <Float64Array>[ 0.0 ]
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* // RT2R => <Float64Array>[ -1.0 ]
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* // RT2I => <Float64Array>[ 0.0 ]
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* // CS => <Float64Array>[ ~0.93 ]
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* // SN => <Float64Array>[ ~0.34 ]
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*/
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declare var dlanv2: Routine;
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// EXPORTS //
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export = dlanv2;

‎lib/node_modules/@stdlib/lapack/base/dlanv2/lib/ndarray.js‎

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// MAIN //
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/**
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* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form.
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* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form using alternative indexing semantics.
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*
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* Given a real 2×2 matrix:
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*

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