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lib/node_modules/@stdlib/blas/base/dsyr2k/README.md

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# dsyr2k
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> Perform one of the symmetric rank `2K` operations `C = α*A*B**T + C = α*B*A**T + β*C` or `C = α*A**T*B + α*B**T*A + β*C` where `α` and `β` are scalars, `C` is an `N` by `N` symmetric matrix and `A` and `B` are `N` by `K` matrices in the first case and `K` by `N` matrices in the second case.
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> Perform one of the symmetric rank `2K` operations `C = α*A*B^T + C = α*B*A^T + β*C` or `C = α*A^T*B + α*B^T*A + β*C`.
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<section class="usage">
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var dsyr2k = require( '@stdlib/blas/base/dsyr2k' );
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```
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#### dsyr2k( ord, uplo, trans, N, K, α, A, lda, B, ldb, β, C, ldc )
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#### dsyr2k( order, uplo, trans, N, K, α, A, lda, B, ldb, β, C, ldc )
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Performs one of the symmetric rank `2K` operations `C = α*A*B**T + C = α*B*A**T + β*C` or `C = α*A**T*B + α*B**T*A + β*C` where `α` and `β` are scalars, `C` is an `N` by `N` symmetric matrix and `A` and `B` are `N` by `K` matrices in the first case and `K` by `N` matrices in the second case.
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Performs one of the symmetric rank `2K` operations `C = α*A*B^T + C = α*B*A^T + β*C` or `C = α*A^T*B + α*B^T*A + β*C` where `α` and `β` are scalars, `C` is an `N` by `N` symmetric matrix and `A` and `B` are `N` by `K` matrices in the first case and `K` by `N` matrices in the second case.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 4.0, 5.0, 0.0, 0.0, 6.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 4.0, 5.0, 3.0, 5.0, 6.0 ] );
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dsyr2k( 'row-major', 'upper', 'no-transpose', 3, 3, 1.0, A, 3, B, 3, 1.0, C, 3 );
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 0.0, 158.0, 249.0, 0.0, 0.0, 394.0 ]
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 2.0, 158.0, 249.0, 3.0, 5.0, 394.0 ]
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```
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The function has the following parameters:
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- **ord**: storage layout.
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- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `C` is supplied.
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- **order**: storage layout.
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- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `C` to be referenced.
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- **trans**: specifies whether `C` should be transposed, conjugate-transposed, or not transposed.
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- **N**: order of the matrix `C`.
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- **K**: number of columns or number of rows of the matrices `A` and `B`.
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 4.0, 5.0, 6.0, 0.0, 0.0, 0.0, 7.0, 8.0, 9.0 ] );
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var B = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 4.0, 5.0, 6.0, 0.0, 0.0, 0.0, 7.0, 8.0, 9.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 4.0, 5.0, 0.0, 0.0, 6.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 4.0, 5.0, 3.0, 5.0, 6.0 ] );
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dsyr2k( 'row-major', 'upper', 'no-transpose', 3, 3, 1.0, A, 6, B, 6, 1.0, C, 3 );
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 0.0, 158.0, 249.0, 0.0, 0.0, 394.0 ]
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 2.0, 158.0, 249.0, 3.0, 5.0, 394.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### dsyr2k.ndarray( uplo, trans, N, K, α, A, sa1, sa2, oa, B, sb1, sb2, ob, β, C, sc1, sc2, oc )
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Performs one of the symmetric rank `2K` operations `C = α*A*B**T + C = α*B*A**T + β*C` or `C = α*A**T*B + α*B**T*A + β*C`, using alternative indexing semantics and where `α` and `β` are scalars, `C` is an `N` by `N` symmetric matrix and `A` and `B` are `N` by `K` matrices in the first case and `K` by `N` matrices in the second case.
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Performs one of the symmetric rank `2K` operations `C = α*A*B^T + C = α*B*A^T + β*C` or `C = α*A^T*B + α*B^T*A + β*C`, using alternative indexing semantics and where `α` and `β` are scalars, `C` is an `N` by `N` symmetric matrix and `A` and `B` are `N` by `K` matrices in the first case and `K` by `N` matrices in the second case.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 4.0, 5.0, 0.0, 0.0, 6.0 ] );
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var C = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 4.0, 5.0, 3.0, 5.0, 6.0 ] );
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dsyr2k.ndarray( 'upper', 'no-transpose', 3, 3, 1.0, A, 3, 1, 0, B, 3, 1, 0, 1.0, C, 3, 1, 0 );
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 0.0, 158.0, 249.0, 0.0, 0.0, 394.0 ]
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// C => <Float64Array>[ 29.0, 66.0, 103.0, 2.0, 158.0, 249.0, 3.0, 5.0, 394.0 ]
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```
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The function has the following additional parameters:
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var B = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
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var C = new Float64Array( [ 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 0.0, 4.0, 5.0, 0.0, 0.0, 6.0 ] );
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var C = new Float64Array( [ 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 2.0, 4.0, 5.0, 3.0, 5.0, 6.0 ] );
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dsyr2k.ndarray( 'upper', 'no-transpose', 3, 3, 1.0, A, 3, 1, 1, B, 3, 1, 2, 1.0, C, 3, 1, 3 );
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// C => <Float64Array>[ 0.0, 0.0, 0.0, 29.0, 66.0, 103.0, 0.0, 158.0, 249.0, 0.0, 0.0, 394.0 ]
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// C => <Float64Array>[ 0.0, 0.0, 0.0, 29.0, 66.0, 103.0, 2.0, 158.0, 249.0, 3.0, 5.0, 394.0 ]
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```
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</section>

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