---
title: Accelerate
framework: accelerate
role: collection
role_heading: Framework
path: accelerate
---

# Accelerate

Make large-scale mathematical computations and image calculations, optimized for high performance and low energy consumption.

## Overview

Overview Accelerate provides high-performance, energy-efficient computation on the CPU by leveraging its vector-processing capability. The following Accelerate libraries abstract that capability so that code written for them executes appropriate instructions for the processor available at runtime: Although not part of the Accelerate framework, the following libraries are closely related:

## Topics

### Neural Networks

- [Training a neural network to recognize digits](accelerate/training-a-neural-network-to-recognize-digits.md)
- [BNNS](accelerate/bnns-library.md)

### Directories, Files, and Data Archives

- [Compressing single files](accelerate/compressing-single-files.md)
- [Decompressing single files](accelerate/decompressing-single-files.md)
- [Compressing file system directories](accelerate/compressing-file-system-directories.md)
- [Decompressing and extracting an archived directory](accelerate/decompressing-and-extracting-an-archived-directory.md)
- [Compressing and saving a string to the file system](accelerate/compressing-and-saving-a-string-to-the-file-system.md)
- [Decompressing and parsing an archived string](accelerate/decompressing-and-parsing-an-archived-string.md)

### Compression

- [Compressing and decompressing files with stream compression](accelerate/compressing-and-decompressing-files-with-stream-compression.md)
- [Compressing and decompressing data with buffer compression](accelerate/compressing-and-decompressing-data-with-buffer-compression.md)
- [Compressing and decompressing data with input and output filters](accelerate/compressing-and-decompressing-data-with-input-and-output-filters.md)

### Image Processing Essentials

- [Converting bitmap data between Core Graphics images and vImage buffers](accelerate/converting-bitmap-data-between-core-graphics-images-and-vimage-buffers.md)
- [Creating and Populating Buffers from Core Graphics Images](accelerate/creating-and-populating-buffers-from-core-graphics-images.md)
- [Creating a Core Graphics Image from a vImage Buffer](accelerate/creating-a-core-graphics-image-from-a-vimage-buffer.md)
- [Building a Basic Image-Processing Workflow](accelerate/building-a-basic-image-processing-workflow.md)
- [Applying geometric transforms to images](accelerate/applying-geometric-transforms-to-images.md)
- [Compositing images with alpha blending](accelerate/compositing-images-with-alpha-blending.md)
- [Compositing images with vImage blend modes](accelerate/compositing-images-with-vimage-blend-modes.md)
- [Applying vImage operations to regions of interest](accelerate/applying-vimage-operations-to-regions-of-interest.md)
- [Optimizing image-processing performance](accelerate/optimizing-image-processing-performance.md)
- [vImage](accelerate/vimage-library.md)

### Signal Processing Essentials

- [Controlling vDSP operations with stride](accelerate/controlling-vdsp-operations-with-stride.md)
- [Using linear interpolation to construct new data points](accelerate/using-linear-interpolation-to-construct-new-data-points.md)
- [Using vDSP for vector-based arithmetic](accelerate/using-vdsp-for-vector-based-arithmetic.md)
- [Resampling a signal with decimation](accelerate/resampling-a-signal-with-decimation.md)
- [vDSP](accelerate/vdsp-library.md)

### Fourier and Cosine Transforms

- [Understanding data packing for Fourier transforms](accelerate/understanding-data-packing-for-fourier-transforms.md)
- [Finding the component frequencies in a composite sine wave](accelerate/finding-the-component-frequencies-in-a-composite-sine-wave.md)
- [Performing Fourier transforms on interleaved-complex data](accelerate/performing-fourier-transforms-on-interleaved-complex-data.md)
- [Reducing spectral leakage with windowing](accelerate/reducing-spectral-leakage-with-windowing.md)
- [Signal extraction from noise](accelerate/signal-extraction-from-noise.md)
- [Performing Fourier Transforms on Multiple Signals](accelerate/performing-fourier-transforms-on-multiple-signals.md)
- [Halftone descreening with 2D fast Fourier transform](accelerate/halftone-descreening-with-2d-fast-fourier-transform.md)
- [Fast Fourier transforms](accelerate/fast-fourier-transforms.md)
- [Discrete Fourier transforms](accelerate/discrete-fourier-transforms.md)
- [Discrete Cosine transforms](accelerate/discrete-cosine-transforms.md)

### Core Video Interoperation

- [Using vImage pixel buffers to generate video effects](accelerate/using-vimage-pixel-buffers-to-generate-video-effects.md)
- [Integrating vImage pixel buffers into a Core Image workflow](accelerate/integrating-vimage-pixel-buffers-into-a-core-image-workflow.md)
- [Applying vImage operations to video sample buffers](accelerate/applying-vimage-operations-to-video-sample-buffers.md)
- [Improving the quality of quantized images with dithering](accelerate/improving-the-quality-of-quantized-images-with-dithering.md)
- [Core Video interoperability](accelerate/core-video-interoperability.md)

### Vectors, Matrices, and Quaternions

- [Working with Vectors](accelerate/working-with-vectors.md)
- [Working with Matrices](accelerate/working-with-matrices.md)
- [Working with Quaternions](accelerate/working-with-quaternions.md)
- [Rotating a cube by transforming its vertices](accelerate/rotating-a-cube-by-transforming-its-vertices.md)
- [simd](accelerate/simd-library.md)
- [vForce](accelerate/vforce-library.md)

### Audio Processing

- [Visualizing sound as an audio spectrogram](accelerate/visualizing-sound-as-an-audio-spectrogram.md)
- [Applying biquadratic filters to a music loop](accelerate/applying-biquadratic-filters-to-a-music-loop.md)
- [Equalizing audio with discrete cosine transforms (DCTs)](accelerate/equalizing-audio-with-discrete-cosine-transforms-dcts.md)
- [Biquadratic IIR filters](accelerate/biquadratic-iir-filters.md)
- [Discrete Cosine transforms](accelerate/discrete-cosine-transforms.md)

### Conversion Between Image Formats

- [Building a basic image conversion workflow](accelerate/building-a-basic-image-conversion-workflow.md)
- [Converting color images to grayscale](accelerate/converting-color-images-to-grayscale.md)
- [Applying color transforms to images with a multidimensional lookup table](accelerate/applying-color-transforms-to-images-with-a-multidimensional-lookup-table.md)
- [Building a basic image conversion workflow](accelerate/building-a-basic-image-conversion-workflow.md)
- [Converting luminance and chrominance planes to an ARGB image](accelerate/converting-luminance-and-chrominance-planes-to-an-argb-image.md)
- [Conversion](accelerate/conversion.md)

### Image Resampling

- [Resampling in vImage](accelerate/resampling-in-vimage.md)
- [Reducing artifacts with custom resampling filters](accelerate/reducing-artifacts-with-custom-resampling-filters.md)
- [Image shearing](accelerate/image-shearing.md)

### Convolution and Morphology

- [Blurring an image](accelerate/blurring-an-image.md)
- [Adding a bokeh effect to images](accelerate/adding-a-bokeh-effect-to-images.md)
- [Convolution](accelerate/convolution.md)
- [Morphology](accelerate/morphology.md)

### Color and Tone Adjustment

- [Adjusting the brightness and contrast of an image](accelerate/adjusting-the-brightness-and-contrast-of-an-image.md)
- [Adjusting saturation and applying tone mapping](accelerate/adjusting-saturation-and-applying-tone-mapping.md)
- [Applying tone curve adjustments to images](accelerate/applying-tone-curve-adjustments-to-images.md)
- [Adjusting the hue of an image](accelerate/adjusting-the-hue-of-an-image.md)
- [Specifying histograms with vImage](accelerate/specifying-histograms-with-vimage.md)
- [Enhancing image contrast with histogram manipulation](accelerate/enhancing-image-contrast-with-histogram-manipulation.md)
- [Histogram](accelerate/histogram.md)

### vImage / vDSP Interoperability

- [Finding the sharpest image in a sequence of captured images](accelerate/finding-the-sharpest-image-in-a-sequence-of-captured-images.md)
- [Visualizing sound as an audio spectrogram](accelerate/visualizing-sound-as-an-audio-spectrogram.md)

### Sparse Matrices

- [Creating sparse matrices](accelerate/creating-sparse-matrices.md)
- [Solving systems using direct methods](accelerate/solving-systems-using-direct-methods.md)
- [Solving systems using iterative methods](accelerate/solving-systems-using-iterative-methods.md)
- [Creating a sparse matrix from coordinate format arrays](accelerate/creating-a-sparse-matrix-from-coordinate-format-arrays.md)
- [Sparse Solvers](accelerate/sparse-solvers-library.md)

### Arithmetic and Transcendental Functions

- [vecLib](accelerate/veclib.md)

### Linear Algebra

- [Solving systems of linear equations with LAPACK](accelerate/solving-systems-of-linear-equations-with-lapack.md)
- [Finding an interpolating polynomial using the Vandermonde method](accelerate/finding-an-interpolating-polynomial-using-the-vandermonde-method.md)
- [Compressing an image using linear algebra](accelerate/compressing-an-image-using-linear-algebra.md)
- [BLAS](accelerate/blas-library.md)

### Definite Integration

- [Quadrature](accelerate/quadrature-collection.md)

### Macros

- [Macros](accelerate/macros.md)

### Functions

- [clarf1f_(_:_:_:_:_:_:_:_:_:)](accelerate/clarf1f_(_:_:_:_:_:_:_:_:_:).md)
- [clarf1l_(_:_:_:_:_:_:_:_:_:)](accelerate/clarf1l_(_:_:_:_:_:_:_:_:_:).md)
- [dlarf1f_(_:_:_:_:_:_:_:_:_:)](accelerate/dlarf1f_(_:_:_:_:_:_:_:_:_:).md)
- [dlarf1l_(_:_:_:_:_:_:_:_:_:)](accelerate/dlarf1l_(_:_:_:_:_:_:_:_:_:).md)
- [slarf1f_(_:_:_:_:_:_:_:_:_:)](accelerate/slarf1f_(_:_:_:_:_:_:_:_:_:).md)
- [slarf1l_(_:_:_:_:_:_:_:_:_:)](accelerate/slarf1l_(_:_:_:_:_:_:_:_:_:).md)
- [zlarf1f_(_:_:_:_:_:_:_:_:_:)](accelerate/zlarf1f_(_:_:_:_:_:_:_:_:_:).md)
- [zlarf1l_(_:_:_:_:_:_:_:_:_:)](accelerate/zlarf1l_(_:_:_:_:_:_:_:_:_:).md)