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# BLAS [![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] > Base (i.e., lower-level) basic linear algebra subprograms (BLAS).
## Installation ```bash npm install @stdlib/blas-base ```
## Usage ```javascript var blas = require( '@stdlib/blas-base' ); ``` #### blas Namespace for "base" (i.e., lower-level) basic linear algebra subprograms (BLAS). ```javascript var o = blas; // returns {...} ``` ### BLAS Level 1
- [`caxpy( N, alpha, x, strideX, y, strideY )`][@stdlib/blas/base/caxpy]: scale a single-precision complex floating-point vector by a single-precision complex floating-point constant and add the result to a single-precision complex floating-point vector. - [`ccopy( N, x, strideX, y, strideY )`][@stdlib/blas/base/ccopy]: copy values from one complex single-precision floating-point vector to another complex single-precision floating-point vector. - [`cscal( N, alpha, x, strideX )`][@stdlib/blas/base/cscal]: scales a single-precision complex floating-point vector by a single-precision complex floating-point constant. - [`csrot( N, x, strideX, y, strideY, c, s )`][@stdlib/blas/base/csrot]: apply a plane rotation. - [`csscal( N, alpha, x, strideX )`][@stdlib/blas/base/csscal]: scale a single-precision complex floating-point vector by a single-precision floating-point constant. - [`cswap( N, x, strideX, y, strideY )`][@stdlib/blas/base/cswap]: interchange two complex single-precision floating-point vectors. - [`dasum( N, x, stride )`][@stdlib/blas/base/dasum]: compute the sum of absolute values (_L1_ norm). - [`daxpy( N, alpha, x, strideX, y, strideY )`][@stdlib/blas/base/daxpy]: multiply a vector `x` by a constant `alpha` and add the result to `y`. - [`dcopy( N, x, strideX, y, strideY )`][@stdlib/blas/base/dcopy]: copy values from `x` into `y`. - [`ddot( N, x, strideX, y, strideY )`][@stdlib/blas/base/ddot]: calculate the dot product of two double-precision floating-point vectors. - [`dnrm2( N, x, stride )`][@stdlib/blas/base/dnrm2]: calculate the L2-norm of a double-precision floating-point vector. - [`drot( N, x, strideX, y, strideY, c, s )`][@stdlib/blas/base/drot]: apply a plane rotation. - [`drotg( a, b )`][@stdlib/blas/base/drotg]: construct a Givens plane rotation. - [`drotm( N, x, strideX, y, strideY, param )`][@stdlib/blas/base/drotm]: apply a modified Givens plane rotation. - [`dscal( N, alpha, x, stride )`][@stdlib/blas/base/dscal]: multiply a double-precision floating-point vector `x` by a constant `alpha`. - [`dsdot( N, x, strideX, y, strideY )`][@stdlib/blas/base/dsdot]: calculate the dot product with extended accumulation and result of two single-precision floating-point vectors. - [`dswap( N, x, strideX, y, strideY )`][@stdlib/blas/base/dswap]: interchange two double-precision floating-point vectors. - [`dznrm2( N, x, strideX )`][@stdlib/blas/base/dznrm2]: compute the L2-norm of a complex double-precision floating-point vector. - [`gasum( N, x, stride )`][@stdlib/blas/base/gasum]: compute the sum of absolute values (_L1_ norm). - [`gaxpy( N, alpha, x, strideX, y, strideY )`][@stdlib/blas/base/gaxpy]: multiply `x` by a constant `alpha` and add the result to `y`. - [`gcopy( N, x, strideX, y, strideY )`][@stdlib/blas/base/gcopy]: copy values from `x` into `y`. - [`gdot( N, x, strideX, y, strideY )`][@stdlib/blas/base/gdot]: calculate the dot product of two vectors. - [`gnrm2( N, x, stride )`][@stdlib/blas/base/gnrm2]: calculate the L2-norm of a vector. - [`gscal( N, alpha, x, stride )`][@stdlib/blas/base/gscal]: multiply a vector by a scalar constant. - [`gswap( N, x, strideX, y, strideY )`][@stdlib/blas/base/gswap]: interchange two vectors. - [`idamax( N, x, strideX )`][@stdlib/blas/base/idamax]: find the index of the first element having the maximum absolute value. - [`igamax( N, x, strideX )`][@stdlib/blas/base/igamax]: find the index of the first element having the maximum absolute value. - [`isamax( N, x, strideX )`][@stdlib/blas/base/isamax]: find the index of the first element having the maximum absolute value. - [`sasum( N, x, stride )`][@stdlib/blas/base/sasum]: compute the sum of absolute values (_L1_ norm). - [`saxpy( N, alpha, x, strideX, y, strideY )`][@stdlib/blas/base/saxpy]: multiply a vector `x` by a constant `alpha` and add the result to `y`. - [`scasum( N, x, strideX )`][@stdlib/blas/base/scasum]: compute the sum of the absolute values of the real and imaginary components of a single-precision complex floating-point vector. - [`scnrm2( N, x, strideX )`][@stdlib/blas/base/scnrm2]: compute the L2-norm of a complex single-precision floating-point vector. - [`scopy( N, x, strideX, y, strideY )`][@stdlib/blas/base/scopy]: copy values from `x` into `y`. - [`sdot( N, x, strideX, y, strideY )`][@stdlib/blas/base/sdot]: calculate the dot product of two single-precision floating-point vectors. - [`sdsdot( N, scalar, x, strideX, y, strideY )`][@stdlib/blas/base/sdsdot]: calculate the dot product of two single-precision floating-point vectors with extended accumulation. - [`snrm2( N, x, stride )`][@stdlib/blas/base/snrm2]: calculate the L2-norm of a single-precision floating-point vector. - [`srot( N, x, strideX, y, strideY, c, s )`][@stdlib/blas/base/srot]: apply a plane rotation. - [`srotg( a, b )`][@stdlib/blas/base/srotg]: construct a Givens plane rotation. - [`srotm( N, x, strideX, y, strideY, param )`][@stdlib/blas/base/srotm]: apply a modified Givens plane rotation. - [`sscal( N, alpha, x, stride )`][@stdlib/blas/base/sscal]: multiply a single-precision floating-point vector `x` by a constant `alpha`. - [`sswap( N, x, strideX, y, strideY )`][@stdlib/blas/base/sswap]: interchange two single-precision floating-point vectors. - [`zaxpy( N, alpha, x, strideX, y, strideY )`][@stdlib/blas/base/zaxpy]: scale a double-precision complex floating-point vector by a double-precision complex floating-point constant and add the result to a double-precision complex floating-point vector. - [`zcopy( N, x, strideX, y, strideY )`][@stdlib/blas/base/zcopy]: copy values from one complex double-precision floating-point vector to another complex double-precision floating-point vector. - [`zdrot( N, x, strideX, y, strideY, c, s )`][@stdlib/blas/base/zdrot]: apply a plane rotation. - [`zdscal( N, alpha, x, strideX )`][@stdlib/blas/base/zdscal]: scale a double-precision complex floating-point vector by a double-precision floating-point constant. - [`zscal( N, alpha, x, strideX )`][@stdlib/blas/base/zscal]: scales a double-precision complex floating-point vector by a double-precision complex floating-point constant. - [`zswap( N, x, strideX, y, strideY )`][@stdlib/blas/base/zswap]: interchange two complex double-precision floating-point vectors.
### BLAS Level 2
- [`dgemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )`][@stdlib/blas/base/dgemv]: perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`. - [`dger( ord, M, N, α, x, sx, y, sy, A, lda )`][@stdlib/blas/base/dger]: perform the rank 1 operation `A = α*x*y^T + A`. - [`dspmv( order, uplo, N, α, AP, x, sx, β, y, sy )`][@stdlib/blas/base/dspmv]: perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors and, `A` is an `N` by `N` symmetric matrix supplied in packed form. - [`dspr( order, uplo, N, α, x, sx, AP )`][@stdlib/blas/base/dspr]: perform the symmetric rank 1 operation `A = α*x*x^T + A`. - [`dsymv( order, uplo, N, α, A, LDA, x, sx, β, y, sy )`][@stdlib/blas/base/dsymv]: perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix. - [`dsyr( order, uplo, N, α, x, sx, A, LDA )`][@stdlib/blas/base/dsyr]: perform the symmetric rank 1 operation `A = α*x*x^T + A`. - [`dsyr2( order, uplo, N, α, x, sx, y, sy, A, LDA )`][@stdlib/blas/base/dsyr2]: perform the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A`. - [`dtrmv( order, uplo, trans, diag, N, A, LDA, x, sx )`][@stdlib/blas/base/dtrmv]: perform one of the matrix-vector operations `x = A*x` or `x = A^T*x`. - [`dtrsv( order, uplo, trans, diag, N, A, LDA, x, sx )`][@stdlib/blas/base/dtrsv]: solve one of the systems of equations `A*x = b` or `A^T*x = b`. - [`ggemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )`][@stdlib/blas/base/ggemv]: perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`. - [`gger( order, M, N, α, x, sx, y, sy, A, lda )`][@stdlib/blas/base/gger]: perform the rank 1 operation `A = α*x*y^T + A`. - [`gsyr( order, uplo, N, α, x, sx, A, LDA )`][@stdlib/blas/base/gsyr]: perform the symmetric rank 1 operation `A = α*x*x^T + A`. - [`sgemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )`][@stdlib/blas/base/sgemv]: perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`. - [`sger( order, M, N, α, x, sx, y, sy, A, lda )`][@stdlib/blas/base/sger]: perform the rank 1 operation `A = α*x*y^T + A`. - [`sspmv( order, uplo, N, α, AP, x, sx, β, y, sy )`][@stdlib/blas/base/sspmv]: perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors and, `A` is an `N` by `N` symmetric matrix supplied in packed form. - [`sspr( order, uplo, N, α, x, sx, AP )`][@stdlib/blas/base/sspr]: perform the symmetric rank 1 operation `A = α*x*x^T + A`. - [`ssymv( order, uplo, N, α, A, LDA, x, sx, β, y, sy )`][@stdlib/blas/base/ssymv]: perform the matrix-vector operation `y = α*A*x + β*y`. - [`ssyr( order, uplo, N, α, x, sx, A, LDA )`][@stdlib/blas/base/ssyr]: perform the symmetric rank 1 operation `A = α*x*x^T + A`. - [`ssyr2( order, uplo, N, α, x, sx, y, sy, A, LDA )`][@stdlib/blas/base/ssyr2]: perform the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A`. - [`strmv( order, uplo, trans, diag, N, A, LDA, x, sx )`][@stdlib/blas/base/strmv]: perform one of the matrix-vector operations `x = A*x` or `x = A^T*x`. - [`strsv( order, uplo, trans, diag, N, A, LDA, x, sx )`][@stdlib/blas/base/strsv]: solve one of the systems of equations `A*x = b` or `A^T*x = b`.
### BLAS Level 3
- [`dgemm( ord, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )`][@stdlib/blas/base/dgemm]: perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`. - [`ggemm( ord, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )`][@stdlib/blas/base/ggemm]: perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`. - [`sgemm( ord, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )`][@stdlib/blas/base/sgemm]: perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`.
### Scalar Operations
- [`dcabs1( z )`][@stdlib/blas/base/dcabs1]: compute the sum of the absolute values of the real part and imaginary components of a double-precision complex floating-point number. - [`scabs1( z )`][@stdlib/blas/base/scabs1]: compute the sum of the absolute values of the real and imaginary components of a single-precision complex floating-point number.
### Auxiliary BLAS ### Utilities
- [`assert`][@stdlib/blas/base/assert]: base BLAS assertion utilities. - [`diagonalTypeEnum2Str( value )`][@stdlib/blas/base/diagonal-type-enum2str]: return the BLAS diagonal type string associated with a BLAS diagonal type enumeration constant. - [`diagonalTypeResolveEnum( value )`][@stdlib/blas/base/diagonal-type-resolve-enum]: return the enumeration constant associated with a supported BLAS diagonal type value. - [`diagonalTypeResolveStr( value )`][@stdlib/blas/base/diagonal-type-resolve-str]: return the diagonal type string associated with a supported BLAS diagonal type value. - [`diagonalTypeStr2Enum( diagonal )`][@stdlib/blas/base/diagonal-type-str2enum]: return the enumeration constant associated with a BLAS diagonal type. - [`diagonalTypes()`][@stdlib/blas/base/diagonal-types]: BLAS diagonal element types. - [`layoutEnum2Str( layout )`][@stdlib/blas/base/layout-enum2str]: return the BLAS memory layout string associated with a BLAS memory layout enumeration constant. - [`layoutResolveEnum( layout )`][@stdlib/blas/base/layout-resolve-enum]: return the enumeration constant associated with a supported BLAS memory layout value. - [`layoutResolveStr( layout )`][@stdlib/blas/base/layout-resolve-str]: return the layout string associated with a supported BLAS memory layout value. - [`layoutStr2Enum( layout )`][@stdlib/blas/base/layout-str2enum]: return the enumeration constant associated with a BLAS memory layout string. - [`layouts()`][@stdlib/blas/base/layouts]: BLAS memory layouts. - [`matrixOrientationEnum2Str( value )`][@stdlib/blas/base/matrix-orientation-enum2str]: return the matrix orientation string associated with a matrix orientation enumeration constant. - [`matrixOrientationResolveEnum( value )`][@stdlib/blas/base/matrix-orientation-resolve-enum]: return the enumeration constant associated with a supported matrix orientation value. - [`matrixOrientationResolveStr( value )`][@stdlib/blas/base/matrix-orientation-resolve-str]: return the matrix orientation string associated with a supported matrix orientation value. - [`matrixOrientationStr2Enum( value )`][@stdlib/blas/base/matrix-orientation-str2enum]: return the enumeration constant associated with a matrix orientation. - [`matrixOrientations()`][@stdlib/blas/base/matrix-orientations]: BLAS matrix orientations. - [`matrixTriangleEnum2Str( value )`][@stdlib/blas/base/matrix-triangle-enum2str]: return the BLAS matrix triangle string associated with a BLAS matrix triangle enumeration constant. - [`matrixTriangleResolveEnum( value )`][@stdlib/blas/base/matrix-triangle-resolve-enum]: return the enumeration constant associated with a supported BLAS matrix triangle value. - [`matrixTriangleResolveStr( value )`][@stdlib/blas/base/matrix-triangle-resolve-str]: return the matrix triangle string associated with a supported BLAS matrix triangle value. - [`matrixTriangleStr2Enum( operation )`][@stdlib/blas/base/matrix-triangle-str2enum]: return the enumeration constant associated with a BLAS matrix triangle. - [`matrixTriangles()`][@stdlib/blas/base/matrix-triangles]: BLAS matrix triangles. - [`operationSideEnum2Str( operation )`][@stdlib/blas/base/operation-side-enum2str]: return the BLAS operation side string associated with a BLAS operation side enumeration constant. - [`operationSideResolveEnum( operation )`][@stdlib/blas/base/operation-side-resolve-enum]: return the enumeration constant associated with a supported BLAS operation side value. - [`operationSideResolveStr( operation )`][@stdlib/blas/base/operation-side-resolve-str]: return the operation side string associated with a supported BLAS operation side value. - [`operationSideStr2Enum( operation )`][@stdlib/blas/base/operation-side-str2enum]: return the enumeration constant associated with a BLAS operation side. - [`operationSides()`][@stdlib/blas/base/operation-sides]: BLAS operation sides. - [`transposeOperationEnum2Str( operation )`][@stdlib/blas/base/transpose-operation-enum2str]: return the BLAS transpose operation string associated with a BLAS transpose operation enumeration constant. - [`transposeOperationResolveEnum( operation )`][@stdlib/blas/base/transpose-operation-resolve-enum]: return the enumeration constant associated with a supported BLAS transpose operation value. - [`transposeOperationResolveStr( operation )`][@stdlib/blas/base/transpose-operation-resolve-str]: return the transpose operation string associated with a supported BLAS transpose operation value. - [`transposeOperationStr2Enum( operation )`][@stdlib/blas/base/transpose-operation-str2enum]: return the enumeration constant associated with a BLAS transpose operation. - [`transposeOperations()`][@stdlib/blas/base/transpose-operations]: BLAS transpose operations.
## Examples ```javascript var objectKeys = require( '@stdlib/utils-keys' ); var blas = require( '@stdlib/blas-base' ); console.log( objectKeys( blas ) ); ```
* * * ## Notice This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more. For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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