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# SparseMultiply(_:_:_:_:)

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

```
func SparseMultiply(_ 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, and then by a dense matrix. The following equation is an example of a scalar-matrix-matrix multiplication where the first matrix is sparse:

![A mathematical formula that describes the matrix multiplication, Y equals alpha times A X. 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-3703075@2x.png)

Call [`SparseMultiply(_:_:_:_:)`](/documentation/Accelerate/SparseMultiply(_:_:_:_:)-73ruq)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]

let alpha: Float = 2.0

/// The values for _Y_ in _Y = alpha * AX_.
let yValues = [Float](unsafeUninitializedCapacity: xValues.count) {
    resultBuffer, count 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: resultBuffer.baseAddress!)
        
        SparseMultiply(alpha, A, X, Y)
    }
    
    count = xValues.count
}

// On return, `yValues` contains:
//      `[ 280.0, 0.0, 0.0,  400.0,
//        2800.0, 0.0, 0.0, 4000.0]`
```

---

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