# QLinearMatMul¶

## QLinearMatMul - 21¶

### Version¶

• domain: main

• since_version: 21

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 21.

### Summary¶

Matrix product that behaves like numpy.matmul. It consumes two quantized input tensors, their scales and zero points, scale and zero point of output, and computes the quantized output. The quantization formula is y = saturate((x / y_scale) + y_zero_point). For (x / y_scale), it is rounding to nearest ties to even. Refer to https://en.wikipedia.org/wiki/Rounding for details. Scale and zero point must have same shape. They must be either scalar (per tensor) or N-D tensor (per row for ‘a’ and per column for ‘b’). Scalar refers to per tensor quantization whereas N-D refers to per row or per column quantization. If the input is 2D of shape [M, K] then zero point and scale tensor may be an M element vector [v_1, v_2, …, v_M] for per row quantization and K element vector of shape [v_1, v_2, …, v_K] for per column quantization. If the input is N-D tensor with shape [D1, D2, M, K] then zero point and scale tensor may have shape [D1, D2, M, 1] for per row quantization and shape [D1, D2, 1, K] for per column quantization. Production must never overflow, and accumulation may overflow if and only if in 32 bits.

### Inputs¶

• a (heterogeneous) - T1:

N-dimensional quantized matrix a

• a_scale (heterogeneous) - TS:

scale of quantized input a

• a_zero_point (heterogeneous) - T1:

zero point of quantized input a

• b (heterogeneous) - T2:

N-dimensional quantized matrix b

• b_scale (heterogeneous) - TS:

scale of quantized input b

• b_zero_point (heterogeneous) - T2:

zero point of quantized input b

• y_scale (heterogeneous) - TS:

scale of quantized output y

• y_zero_point (heterogeneous) - T3:

zero point of quantized output y

### Outputs¶

• y (heterogeneous) - T3:

Quantized matrix multiply results from a * b

### Type Constraints¶

• TS in ( tensor(bfloat16), tensor(float), tensor(float16) ):

Constrain scales.

• T1 in ( tensor(float8e4m3fn), tensor(float8e4m3fnuz), tensor(float8e5m2), tensor(float8e5m2fnuz), tensor(int8), tensor(uint8) ):

The type of input a and its zeropoint.

• T2 in ( tensor(float8e4m3fn), tensor(float8e4m3fnuz), tensor(float8e5m2), tensor(float8e5m2fnuz), tensor(int8), tensor(uint8) ):

The type of input b and its zeropoint.

• T3 in ( tensor(float8e4m3fn), tensor(float8e4m3fnuz), tensor(float8e5m2), tensor(float8e5m2fnuz), tensor(int8), tensor(uint8) ):

The type of the output and its zeropoint.

## QLinearMatMul - 10¶

### Version¶

• domain: main

• since_version: 10

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 10.

### Summary¶

Matrix product that behaves like numpy.matmul. It consumes two quantized input tensors, their scales and zero points, scale and zero point of output, and computes the quantized output. The quantization formula is y = saturate((x / y_scale) + y_zero_point). For (x / y_scale), it is rounding to nearest ties to even. Refer to https://en.wikipedia.org/wiki/Rounding for details. Scale and zero point must have same shape. They must be either scalar (per tensor) or N-D tensor (per row for ‘a’ and per column for ‘b’). Scalar refers to per tensor quantization whereas N-D refers to per row or per column quantization. If the input is 2D of shape [M, K] then zero point and scale tensor may be an M element vector [v_1, v_2, …, v_M] for per row quantization and K element vector of shape [v_1, v_2, …, v_K] for per column quantization. If the input is N-D tensor with shape [D1, D2, M, K] then zero point and scale tensor may have shape [D1, D2, M, 1] for per row quantization and shape [D1, D2, 1, K] for per column quantization. Production must never overflow, and accumulation may overflow if and only if in 32 bits.

### Inputs¶

• a (heterogeneous) - T1:

N-dimensional quantized matrix a

• a_scale (heterogeneous) - tensor(float):

scale of quantized input a

• a_zero_point (heterogeneous) - T1:

zero point of quantized input a

• b (heterogeneous) - T2:

N-dimensional quantized matrix b

• b_scale (heterogeneous) - tensor(float):

scale of quantized input b

• b_zero_point (heterogeneous) - T2:

zero point of quantized input b

• y_scale (heterogeneous) - tensor(float):

scale of quantized output y

• y_zero_point (heterogeneous) - T3:

zero point of quantized output y

### Outputs¶

• y (heterogeneous) - T3:

Quantized matrix multiply results from a * b

### Type Constraints¶

• T1 in ( tensor(int8), tensor(uint8) ):

Constrain input a and its zero point data type to 8-bit integer tensor.

• T2 in ( tensor(int8), tensor(uint8) ):

Constrain input b and its zero point data type to 8-bit integer tensor.

• T3 in ( tensor(int8), tensor(uint8) ):

Constrain output y and its zero point data type to 8-bit integer tensor.