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‎lib/node_modules/@stdlib/blas/base/zgbmv/docs/repl.txt‎

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{{alias}}( order, trans, M, N, KL, KU, α, A, lda, x, sx, β, y, sy )
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Performs one of the matrix-vector operations `y = α*A*x + β*y` or
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`y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are scalars,
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`x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL`
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sub-diagonals and `KU` super-diagonals.
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Indexing is relative to the first index. To introduce an offset, use typed
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array views.
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If `M` or `N` is equal to `0`, the function returns `y` unchanged.
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If `α` equals `0 + 0i` and `β` equals `1 + 0i`, the function returns `y`
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unchanged.
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Parameters
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----------
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order: string
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Row-major (C-style) or column-major (Fortran-style) order.
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trans: string
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Specifies whether `A` should be transposed, conjugate-transposed, or not
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transposed.
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M: integer
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Number of rows in `A`.
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N: integer
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Number of columns in `A`.
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KL: integer
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Number of sub-diagonals of matrix `A`.
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KU: integer
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Number of super-diagonals of matrix `A`.
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α: Complex128
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Scalar constant.
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A: Complex128Array
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Input matrix.
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lda: integer
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Stride of the first dimension of `A` (a.k.a., leading dimension of the
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matrix `A`).
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x: Complex128Array
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First input vector.
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sx: integer
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Index increment for `x`.
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β: Complex128
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Scalar constant.
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y: Complex128Array
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Second input vector.
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sy: integer
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Index increment for `y`.
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Returns
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-------
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y: Complex128Array
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Second input vector.
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Examples
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--------
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// Standard usage:
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> var x = new {{alias:@stdlib/array/complex128}}([1.0,1.0,2.0,2.0,3.0,3.0]);
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> var y = new {{alias:@stdlib/array/complex128}}([3.0,3.0,2.0,2.0,1.0,1.0]);
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> var buf1 = [ 0.0,0.0,1.0,1.0,3.0,3.0 ];
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> var buf2 = [ 2.0,2.0,4.0,4.0,6.0,6.0 ];
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> var buf3 = [ 5.0,5.0,7.0,7.0,0.0,0.0 ];
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> var buf = buf1.concat( buf2, buf3 );
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> var A = new {{alias:@stdlib/array/complex128}}( buf );
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> var alpha = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, 0.5 );
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> var beta = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, -0.5 );
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> var ord = 'row-major';
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> var trans = 'no-transpose';
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> {{alias}}( ord, trans, 3, 3, 1, 1, alpha, A, 3, x, 1, beta, y, 1 )
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<Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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// Advanced indexing:
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> x = new {{alias:@stdlib/array/complex128}}([3.0,3.0,2.0,2.0,1.0,1.0]);
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> y = new {{alias:@stdlib/array/complex128}}([1.0,1.0,2.0,2.0,3.0,3.0]);
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> buf1 = [ 0.0,0.0,1.0,1.0,3.0,3.0 ];
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> buf2 = [ 2.0,2.0,4.0,4.0,6.0,6.0 ];
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> buf3 = [ 5.0,5.0,7.0,7.0,0.0,0.0 ];
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> buf = buf1.concat( buf2, buf3 );
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> A = new {{alias:@stdlib/array/complex128}}( buf );
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> alpha = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, 0.5 );
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> beta = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, -0.5 );
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> ord = 'row-major';
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> trans = 'no-transpose';
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> {{alias}}( ord, trans, 3, 3, 1, 1, alpha, A, 3, x, -1, beta, y, -1 )
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<Complex128Array>[ -30.0, 31.0, -26.0, 28.0, -4.0, 7.0 ]
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// Using typed array views:
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> var x0buf = [0.0,0.0,1.0,1.0,2.0,2.0,3.0,3.0];
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> var x0 = new {{alias:@stdlib/array/complex128}}( x0buf );
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> var y0buf = [0.0,0.0,3.0,3.0,2.0,2.0,1.0,1.0];
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> var y0 = new {{alias:@stdlib/array/complex128}}( y0buf );
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> var x0bytes = x0.BYTES_PER_ELEMENT*1;
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> var x1 = new {{alias:@stdlib/array/complex128}}( x0.buffer, x0bytes );
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> var y0bytes = y0.BYTES_PER_ELEMENT*1;
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> var y1 = new {{alias:@stdlib/array/complex128}}( y0.buffer, y0bytes );
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> buf1 = [ 0.0,0.0,1.0,1.0,3.0,3.0 ];
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> buf2 = [ 2.0,2.0,4.0,4.0,6.0,6.0 ];
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> buf3 = [ 5.0,5.0,7.0,7.0,0.0,0.0 ];
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> buf = buf1.concat( buf2, buf3 );
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> A = new {{alias:@stdlib/array/complex128}}( buf );
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> alpha = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, 0.5 );
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> beta = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, -0.5 );
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> ord = 'row-major';
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> trans = 'no-transpose';
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> {{alias}}( ord, trans, 3, 3, 1, 1, alpha, A, 3, x1, 1, beta, y1, 1 )
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<Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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{{alias}}.ndarray(trans,M,N,KL,KU,α,A,sa1,sa2,oa,x,sx,ox,β,y,sy,oy)
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Performs one of the matrix-vector operations `y = α*A*x + β*y` or
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`y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are scalars,
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`x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL`
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sub-diagonals and `KU` super-diagonals.
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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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trans: string
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Specifies whether `A` should be transposed, conjugate-transposed, or not
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transposed.
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M: integer
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Number of rows in `A`.
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N: integer
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Number of columns in `A`.
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KL: integer
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Number of sub-diagonals of matrix `A`.
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KU: integer
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Number of super-diagonals of matrix `A`.
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α: Complex128
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Scalar constant.
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A: Complex128Array
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Input matrix.
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sa1: integer
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Stride of the first dimension of `A`.
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sa2: integer
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Stride of the second dimension of `A`.
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oa: integer
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Starting index (offset) for `A`.
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x: Complex128Array
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First input vector.
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sx: integer
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Index increment for `x`.
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ox: integer
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Starting index (offset) for `x`.
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β: Complex128
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Scalar constant.
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y: Complex128Array
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Second input vector.
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sy: integer
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Index increment for `y`.
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oy: integer
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Starting index (offset) for `y`.
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Returns
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-------
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y: Complex128Array
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Second input vector.
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Examples
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--------
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> x = new {{alias:@stdlib/array/complex128}}([1.0,1.0,2.0,2.0,3.0,3.0]);
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> y = new {{alias:@stdlib/array/complex128}}([3.0,3.0,2.0,2.0,1.0,1.0]);
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> buf1 = [ 0.0,0.0,1.0,1.0,3.0,3.0 ];
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> buf2 = [ 2.0,2.0,4.0,4.0,6.0,6.0 ];
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> buf3 = [ 5.0,5.0,7.0,7.0,0.0,0.0 ];
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> buf = buf1.concat( buf2, buf3 );
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> A = new {{alias:@stdlib/array/complex128}}( buf );
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> alpha = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, 0.5 );
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> beta = new {{alias:@stdlib/complex/float64/ctor}}( 0.5, -0.5 );
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> ord = 'row-major';
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> trans = 'no-transpose';
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> {{alias}}.ndarray(trans,3,3,1,1,alpha,A,3,1,0,x,1,0,beta,y,1,0)
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<Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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See Also
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--------

‎lib/node_modules/@stdlib/blas/base/zgbmv/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) 2026 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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/// <reference types="@stdlib/types"/>
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import { Complex128Array } from '@stdlib/types/array';
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import { Layout, TransposeOperation } from '@stdlib/types/blas';
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import { Complex128 } from '@stdlib/types/complex';
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/**
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* Interface describing `zgbmv`.
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*/
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interface Routine {
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/**
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* Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL` sub-diagonals and `KU` super-diagonals.
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*
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* @param order - storage layout
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* @param trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
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* @param M - number of rows in the matrix `A`
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* @param N - number of columns in the matrix `A`
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* @param KL - number of sub-diagonals of matrix `A`
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* @param KU - number of super-diagonals of matrix `A`
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* @param alpha - scalar constant
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* @param A - input matrix (compact band storage)
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* @param LDA - stride of the first dimension of `A`
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* @param x - first input vector
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* @param strideX - `x` stride length
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* @param beta - scalar constant
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* @param y - second input vector
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* @param strideY - `y` stride length
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* @returns `y`
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*
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* @example
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* var Complex128Array = require( '@stdlib/array/complex128' );
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* var Complex128 = require( '@stdlib/complex/float64/ctor' );
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*
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* var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
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* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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* var alpha = new Complex128( 0.5, 0.5 );
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* var beta = new Complex128( 0.5, -0.5 );
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*
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* zgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, alpha, A, 3, x, 1, beta, y, 1 );
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* // y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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*/
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( order: Layout, trans: TransposeOperation, M: number, N: number, KL: number, KU: number, alpha: Complex128, A: Complex128Array, LDA: number, x: Complex128Array, strideX: number, beta: Complex128, y: Complex128Array, strideY: number ): Complex128Array;
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/**
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* Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL` sub-diagonals and `KU` super-diagonals.
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*
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* @param trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
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* @param M - number of rows in the matrix `A`
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* @param N - number of columns in the matrix `A`
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* @param KL - number of sub-diagonals of matrix `A`
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* @param KU - number of super-diagonals of matrix `A`
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* @param alpha - scalar constant
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* @param A - input band matrix (compact band storage)
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* @param strideA1 - stride of the first dimension of `A`
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* @param strideA2 - stride of the second dimension of `A`
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* @param offsetA - starting index for `A`
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* @param x - first input vector
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* @param strideX - `x` stride length
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* @param offsetX - starting index for `x`
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* @param beta - scalar constant
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* @param y - second input vector
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* @param strideY - `y` stride length
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* @param offsetY - starting index for `y`
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* @returns `y`
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*
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* @example
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* var Complex128Array = require( '@stdlib/array/complex128' );
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* var Complex128 = require( '@stdlib/complex/float64/ctor' );
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*
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* var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
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* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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* var alpha = new Complex128( 0.5, 0.5 );
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* var beta = new Complex128( 0.5, -0.5 );
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*
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* zgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 );
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* // y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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*/
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ndarray( trans: TransposeOperation, M: number, N: number, KL: number, KU: number, alpha: Complex128, A: Complex128Array, strideA1: number, strideA2: number, offsetA: number, x: Complex128Array, strideX: number, offsetX: number, beta: Complex128, y: Complex128Array, strideY: number, offsetY: number ): Complex128Array;
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}
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/**
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* Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL` sub-diagonals and `KU` super-diagonals.
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*
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* @param order - storage layout
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* @param trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
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* @param M - number of rows in the matrix `A`
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* @param N - number of columns in the matrix `A`
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* @param KL - number of sub-diagonals of matrix `A`
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* @param KU - number of super-diagonals of matrix `A`
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* @param alpha - complex scalar constant
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* @param A - input complex matrix (compact band storage)
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* @param LDA - stride of the first dimension of `A`
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* @param x - first input complex vector
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* @param strideX - `x` stride length
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* @param beta - complex scalar constant
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* @param y - second input complex vector
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* @param strideY - `y` stride length
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* @returns `y`
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*
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* @example
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* var Complex128Array = require( '@stdlib/array/complex128' );
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* var Complex128 = require( '@stdlib/complex/float64/ctor' );
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*
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* var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
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* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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* var alpha = new Complex128( 0.5, 0.5 );
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* var beta = new Complex128( 0.5, -0.5 );
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*
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* zgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, alpha, A, 3, x, 1, beta, y, 1 );
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* // y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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*
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* @example
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* var Complex128Array = require( '@stdlib/array/complex128' );
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* var Complex128 = require( '@stdlib/complex/float64/ctor' );
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*
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* var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
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* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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* var alpha = new Complex128( 0.5, 0.5 );
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* var beta = new Complex128( 0.5, -0.5 );
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*
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* zgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 );
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* // y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
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*/
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declare var zgbmv: Routine;
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// EXPORTS //
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export = zgbmv;

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