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

Performs the multiply operation *y += alpha * Ax* on a vector of single-precision, floating-point values.

```
func SparseMultiplyAdd(_ alpha: Float, _ A: SparseMatrix_Float, _ x: DenseVector_Float, _ y: DenseVector_Float)
```

## Parameters

`alpha`

The scalar value *alpha* in *y* *+= alpha * Ax*.

`A`

The sparse matrix *A* in *y* *+= Ax*.

`x`

The dense vector *x* in *y* *+= Ax*.

`y`

The dense vector *y* in *y* *+= Ax*.

## Discussion

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

![A mathematical formula that describes the matrix multiplication, y plus-equals alpha times A x. A four-element column matrix added to a scalar value multiplied by a four-by-four matrix multiplied by a four-element column matrix equals a four-element column matrix.](images/com.apple.accelerate/media-3703087@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+=Ax_.
let A = SparseConvertFromCoordinate(rowCount, columnCount,
                                    blockCount, blockSize,
                                    SparseAttributes_t(),
                                    rowIndices, columnIndices,
                                    data)
defer {
    SparseCleanup(A)
}

/// The values for _x_ in _y+=Ax_.
var xValues: [Float] = [10.0, -1.0, -1.0, 10.0]

var yValues: [Float] = [1.0, 1.0, 1.0, 1.0]

let alpha: Float = 2.0

/// The values for _y_ in _y+=Ax_.
yValues.withUnsafeMutableBufferPointer { yValuesPtr in
    
    xValues.withUnsafeMutableBufferPointer { xValuesPtr in
        /// The _x_ in _y+=Ax_.
        let x = DenseVector_Float(count: 4,
                                  data: xValuesPtr.baseAddress!)
        
        /// The _y_ in _y+=Ax_.
        let y = DenseVector_Float(count: 4,
                                  data: yValuesPtr.baseAddress!)
        
        SparseMultiplyAdd(alpha, A, x, y)
    }
}

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

---

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