<!--
{
  "availability" : [
    "iOS: 11.0.0 -",
    "iPadOS: 11.0.0 -",
    "macCatalyst: 13.1.0 -",
    "macOS: 10.13.0 -",
    "tvOS: 11.0.0 -",
    "visionOS: 1.0.0 -",
    "watchOS: 4.0.0 -"
  ],
  "documentType" : "symbol",
  "framework" : "Accelerate",
  "identifier" : "/documentation/Accelerate/SparseMultiplyAdd(_:_:_:_:)-n61k",
  "metadataVersion" : "0.1.0",
  "role" : "Function",
  "symbol" : {
    "kind" : "Function",
    "modules" : [
      "Accelerate"
    ],
    "preciseIdentifier" : "c:@F@SparseMultiplyAdd#f#$@SA@SparseMatrix_Float#$@SA@DenseMatrix_Float#S1_#"
  },
  "title" : "SparseMultiplyAdd(_:_:_:_:)"
}
-->

# SparseMultiplyAdd(_:_:_:_:)

Performs the multiply operation *Y += alpha * AX* on a sparse matrix of single-precision, floating-point values.

```
func SparseMultiplyAdd(_ alpha: Float, _ A: SparseMatrix_Float, _ X: DenseMatrix_Float, _ Y: DenseMatrix_Float)
```

## Parameters

`alpha`

The scalar value *alpha* in *Y += alpha * AX*.

`A`

The sparse matrix *A* in *Y* *+= AX*.

`X`

The dense matrix *X* in *Y* *+= AX*.

`Y`

The dense matrix *Y* in *Y* *+= AX*.

## Discussion

Use this function to multiply a scalar value by a sparse matrix, then by a dense matrix, and accumulate the result. The following equation is an example of a matrix-matrix multiplication where the first matrix is sparse:

![A mathematical formula that describes the matrix multiplication, Y plus-equals alpha times A X. A four-by-two matrix added to a scalar value multiplied by a four-by-four matrix multiplied by a four-by-two matrix equals a four-by-two matrix.](images/com.apple.accelerate/media-3703072@2x.png)

Call [`SparseMultiplyAdd(_:_:_:_:)`](/documentation/Accelerate/SparseMultiplyAdd(_:_:_:_:)-3oa6n) to calculate the result.

```swift
let rowCount = Int32(4)
let columnCount = Int32(4)
let blockCount = 4
let blockSize = UInt8(1)
let rowIndices: [Int32] = [0, 3, 0, 3]
let columnIndices: [Int32] = [0, 0, 3, 3]
let data: [Float] = [1.0, 4.0, 13.0, 16.0]

/// The _A_ in _Y += alpha * AX_.
let A = SparseConvertFromCoordinate(rowCount, columnCount,
                                    blockCount, blockSize,
                                    SparseAttributes_t(),
                                    rowIndices, columnIndices,
                                    data)
defer {
    SparseCleanup(A)
}

/// The values for _X_ in _Y += alpha * AX_.
var xValues: [Float] = [10.0, -1.0, -1.0, 10.0,
                        100.0, -1.0, -1.0, 100.0]

/// The values for _Y_ in _Y += alpha * AX_.
var yValues = [Float](repeating: 1,
                      count: xValues.count)

let alpha: Float = 2.0

yValues.withUnsafeMutableBufferPointer { yValuesPtr in
    xValues.withUnsafeMutableBufferPointer { denseMatrixPtr in
        /// The _X_ in _Y += alpha * AX_.
        let X = DenseMatrix_Float(rowCount: 4,
                                  columnCount: 2,
                                  columnStride: 4,
                                  attributes: SparseAttributes_t(),
                                  data: denseMatrixPtr.baseAddress!)
        
        /// The _Y_ in _Y += alpha * AX_.
        let Y = DenseMatrix_Float(rowCount: 4,
                                  columnCount: 2,
                                  columnStride: 4,
                                  attributes: SparseAttributes_t(),
                                  data: yValuesPtr.baseAddress!)
        
        SparseMultiplyAdd(alpha, A, X, Y)
    }
}

// On return, `yValues` contains:
//      `[ 281.0, 1.0, 1.0,  401.0,
//        2801.0, 1.0, 1.0, 4001.0]`
```

---

Copyright &copy; 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)