CuPy Reference

Review: 2026-10-01. Code below is illustrative unless explicitly described as CPU-tested. GPU execution, performance, GDS, and multi-GPU behavior require validation on target hardware.

CuPy is a NumPy/SciPy-compatible array library for GPU-accelerated computing. It wraps NVIDIA's optimized libraries (cuBLAS, cuFFT, cuSOLVER, cuSPARSE, cuRAND) so standard array operations are already highly tuned. Most NumPy code works by simply changing the import.

Full documentation: https://docs.cupy.dev/en/stable/

Table of Contents

1. Installation and Setup
2. The Drop-In Replacement Pattern
3. Core API: cupy.ndarray
4. Supported Operations
5. Custom Kernels
6. Kernel Fusion
7. Memory Management
8. Streams and Async Operations
9. Multi-GPU
10. Performance Optimization
11. Interoperability
12. Key Differences from NumPy
13. Common Pitfalls
14. Environment Variables

Installation and Setup

Use uv add in standalone examples; follow the user's existing project package manager when one is already configured.

uv add "cupy-cuda12x==14.2.*"    # For CUDA 12.x
uv add "cupy-cuda13x==14.2.*"    # For CUDA 13.x

CuPy 14.2 requires CUDA >= 12.0, Python >= 3.10, and NumPy >= 2.0 (it follows NumPy 2 type-promotion rules, NEP 50), and supports free-threaded Python. The [ctk] extra (e.g. cupy-cuda13x[ctk]) pulls the required CUDA runtime components from PyPI, so only the NVIDIA driver needs to be pre-installed.

Verify:

import cupy as cp
print(cp.cuda.runtime.getDeviceCount())  # >= 1 means GPU is available
print(cp.show_config())                  # Full environment info

The Drop-In Replacement Pattern

The fastest way to GPU-accelerate NumPy code: change the import.

# Before (CPU)
import numpy as np
a = np.random.rand(10_000_000)
b = np.fft.fft(a)
c = np.sort(b.real)

# After (GPU)
import cupy as cp
a = cp.random.rand(10_000_000)
b = cp.fft.fft(a)
c = cp.sort(b.real)

Data Transfer Between CPU and GPU

# NumPy → CuPy (CPU → GPU)
gpu_array = cp.asarray(numpy_array)     # Zero-copy if already on current device
gpu_array = cp.array(numpy_array)       # Always copies

# CuPy → NumPy (GPU → CPU)
cpu_array = cp.asnumpy(gpu_array)       # Copy to CPU
cpu_array = gpu_array.get()             # Same thing

Writing CPU/GPU Agnostic Code

def normalize(x):
    xp = cp.get_array_module(x)  # Returns cupy or numpy depending on input
    return x / xp.linalg.norm(x)

# Works with both NumPy and CuPy arrays
normalize(numpy_array)   # Runs on CPU
normalize(cupy_array)    # Runs on GPU

CuPy arrays implement __array_ufunc__ and __array_function__, so NumPy functions can dispatch to CuPy automatically when given CuPy arrays (NumPy >= 1.17).

Core API

cupy.ndarray mirrors numpy.ndarray — same attributes (shape, dtype, ndim, size, strides, T), plus device (which GPU the array lives on).

Important: cupy.ndarray and numpy.ndarray are NOT implicitly convertible. Every conversion incurs a host-device data transfer.

Array Creation

cp.empty((1000, 1000), dtype=cp.float32)
cp.zeros((1000,), dtype=cp.float64)
cp.ones((512, 512), dtype=cp.float32)
cp.full((100,), fill_value=3.14, dtype=cp.float32)
cp.arange(0, 100, 0.1)
cp.linspace(0, 1, 1000)
cp.eye(100)
cp.random.rand(1000, 1000)                    # Uniform [0, 1)
cp.random.randn(1000, 1000)                   # Standard normal
cp.random.default_rng(42).normal(0, 1, 1000)  # Generator API

Many CuPy random methods accept dtype; check each method. NumPy Generator.random also supports float32/float64. Choose precision from the numerical contract.

Supported Operations

CuPy implements most of NumPy and large parts of SciPy. All are GPU-accelerated.

Array Math and Element-wise Operations

sin, cos, tan, exp, log, log2, log10, sqrt, square, abs, power, add, subtract, multiply, divide, mod, clip, sign, ceil, floor, round, maximum, minimum

Reductions

sum, prod, mean, std, var, min, max, argmin, argmax, cumsum, cumprod, any, all, nansum, nanmean, nanstd, nanvar

Linear Algebra (cupy.linalg — powered by cuBLAS/cuSOLVER)

dot, matmul, @ operator, tensordot, einsum, inner, outer, cholesky, qr, svd, eig, eigh, eigvalsh, norm, solve, inv, pinv, lstsq, det, slogdet, matrix_rank, matrix_power

FFT (cupy.fft — powered by cuFFT)

fft, ifft, fft2, ifft2, fftn, ifftn, rfft, irfft, rfft2, irfft2, rfftn, irfftn, fftfreq, rfftfreq, fftshift, ifftshift

Sorting and Searching

sort, argsort, partition, argpartition, argmin, argmax, where, nonzero, unique, searchsorted

Array Manipulation

reshape, ravel, flatten, transpose, swapaxes, concatenate, stack, vstack, hstack, dstack, split, hsplit, vsplit, tile, repeat, pad, flip, fliplr, flipud, roll, rot90, broadcast_to, expand_dims, squeeze

Sparse Matrices (cupyx.scipy.sparse)

CSR, CSC, COO formats. Matrix-vector multiply, matrix-matrix multiply, conversions between formats. Powered by cuSPARSE. CuPy v14 adds support for large sparse matrices with 64-bit dimensions and nonzero counts.

Signal Processing (cupyx.scipy.signal)

Convolution, correlation, filtering, window functions.

Special Functions (cupyx.scipy.special)

Bessel functions, error functions, gamma functions, and more.

Statistics

mean, median, std, var, percentile, quantile, corrcoef, cov, histogram, bincount, digitize

Custom Kernels

When built-in operations aren't enough, CuPy offers several ways to write custom GPU code, ordered from simplest to most powerful.

ElementwiseKernel — Custom Element-wise Operations

CuPy handles indexing and broadcasting automatically. You just write the per-element logic in C++.

squared_diff = cp.ElementwiseKernel(
    'float32 x, float32 y',   # Input params
    'float32 z',               # Output params
    'z = (x - y) * (x - y)',  # Per-element operation (C++ code)
    'squared_diff'             # Kernel name
)

result = squared_diff(a, b)  # Broadcasting works automatically

Type-generic kernels: Use single-letter type placeholders. Same letter = same type, resolved from arguments at call time.

generic_squared_diff = cp.ElementwiseKernel(
    'T x, T y', 'T z',
    'z = (x - y) * (x - y)',
    'generic_squared_diff'
)
# Works with float32, float64, etc. — type inferred from inputs

Raw indexing: Prefix with raw to disable automatic indexing. Use i for loop index.

# Access neighbors — raw disables auto-indexing so you can index manually
stencil = cp.ElementwiseKernel(
    'raw T x', 'T y',
    'y = (x[i > 0 ? i-1 : 0] + x[i] + x[i < _ind.size()-1 ? i+1 : _ind.size()-1]) / 3',
    'stencil_1d'
)

ReductionKernel — Custom Reductions

Four-part reduction: map each element, reduce pairs, post-process the result.

l2norm = cp.ReductionKernel(
    'T x',           # Input
    'T y',           # Output
    'x * x',         # Map: square each element
    'a + b',         # Reduce: sum pairs (a, b are the binary operands)
    'y = sqrt(a)',   # Post-map: sqrt of final sum
    '0',             # Identity element
    'l2norm'         # Kernel name
)

norm = l2norm(array)        # Full reduction → scalar
norms = l2norm(matrix, axis=1)  # Reduce along axis → vector

RawKernel — Full CUDA C/C++

For complete control over grid, blocks, shared memory — write raw CUDA.

import numpy as np

kernel_code = r'''
extern "C" __global__
void vector_add(const float* a, const float* b, float* c, int n) {
    int tid = blockDim.x * blockIdx.x + threadIdx.x;
    if (tid < n) {
        c[tid] = a[tid] + b[tid];
    }
}
'''
vector_add = cp.RawKernel(kernel_code, 'vector_add')

n = 1_000_000
a = cp.random.rand(n, dtype=cp.float32)
b = cp.random.rand(n, dtype=cp.float32)
c = cp.zeros(n, dtype=cp.float32)

threads = 256
blocks = (n + threads - 1) // threads
vector_add((blocks,), (threads,), (a, b, c, np.int32(n)))  # CUDA int is int32

Important RawKernel caveats:

• Ignores array views/strides — matrix.T is treated as matrix. Handle strides yourself.
• Use extern "C" to prevent C++ name mangling.
• For complex numbers, include <cupy/complex.cuh>.
• Compiled binaries cached in ~/.cupy/kernel_cache.

CuPy dtype to CUDA type mapping:

RawModule — Large CUDA Codebases

For multi-kernel CUDA files or precompiled binaries:

module = cp.RawModule(code=cuda_source)       # From source string
from pathlib import Path
module = cp.RawModule(code=Path('kernels.cu').read_text())  # CUDA source file
module = cp.RawModule(path='kernels.cubin')   # From precompiled

kernel = module.get_function('my_kernel')
kernel((blocks,), (threads,), args)  # args is the kernel argument tuple

JIT Kernel (cupyx.jit.rawkernel) — CUDA Kernels in Python Syntax

Write CUDA-style kernels using Python syntax instead of C++.

@cupyx.jit.rawkernel()
def my_kernel(x, y, size):
    tid = cupyx.jit.grid(1)
    if tid < size:
        y[tid] = x[tid] * 2.0

my_kernel[blocks, threads](x, y, n)

Available JIT primitives:

• cupyx.jit.threadIdx, blockIdx, blockDim, gridDim
• cupyx.jit.grid(ndim), gridsize(ndim)
• cupyx.jit.syncthreads(), syncwarp()
• cupyx.jit.shared_memory(dtype, size)
• cupyx.jit.atomic_add/min/max/and/or/xor(array, index, value)
• Warp shuffles: shfl_sync, shfl_up_sync, shfl_down_sync, shfl_xor_sync

Limitation: Does not work in Python REPL (needs source code access). Use from .py files.

Kernel Fusion

Combine multiple element-wise operations into a single kernel launch — eliminates intermediate arrays and reduces kernel launch overhead.

@cp.fuse()
def fused_op(x, y):
    return cp.sqrt((x - y) ** 2 + 1.0)

# This compiles into ONE kernel instead of multiple
result = fused_op(a, b)

Limitation: Only fuses elementwise and simple reduction operations. Does not support matmul, reshape, indexing, etc.

Memory Management

Memory Pools (Default Behavior)

CuPy uses memory pools by default — this is critical for performance. The pool caches freed GPU memory for reuse, avoiding expensive cudaMalloc/cudaFree calls and implicit synchronization.

Key insight: Memory is NOT freed to the OS when arrays go out of scope — it's returned to the pool. This is expected behavior (shows up in nvidia-smi as still-allocated).

mempool = cp.get_default_memory_pool()
mempool.used_bytes()        # Currently allocated by CuPy arrays
mempool.total_bytes()       # Total held by pool (including free blocks)
mempool.free_all_blocks()   # Release all unused memory back to OS

pinned_mempool = cp.get_default_pinned_memory_pool()
pinned_mempool.free_all_blocks()

Limiting GPU Memory

mempool = cp.get_default_memory_pool()
with cp.cuda.Device(0):
    mempool.set_limit(size=4 * 1024**3)  # 4 GiB limit for GPU 0

Or via environment variable (set before import cupy):

export CUPY_GPU_MEMORY_LIMIT="50%"     # Percentage of total GPU memory
export CUPY_GPU_MEMORY_LIMIT="4294967296"  # Bytes

Managed (Unified) Memory

Data auto-migrates between CPU and GPU. Useful when data doesn't fit in GPU memory.

cp.cuda.set_allocator(cp.cuda.MemoryPool(cp.cuda.malloc_managed).malloc)

Pinned Memory for Fast Transfers

# High-level API
pinned_array = cupyx.empty_pinned((1000,), dtype=np.float32)
pinned_array = cupyx.zeros_pinned((1000,), dtype=np.float32)

# These are NumPy arrays backed by page-locked memory — transfers to GPU are faster

Disabling Pools

cp.cuda.set_allocator(None)                    # Disable device pool
cp.cuda.set_pinned_memory_allocator(None)      # Disable pinned pool

Must be done before any CuPy operations.

Using RMM (RAPIDS Memory Manager)

When using CuPy alongside cuDF/RAPIDS, align on a single allocator:

import rmm
from rmm.allocators.cupy import rmm_cupy_allocator

rmm.reinitialize(pool_allocator=True)  # Configure before allocating any live device arrays
cp.cuda.set_allocator(rmm_cupy_allocator)

Streams and Async Operations

Streams enable overlapping computation with data transfer and running multiple operations concurrently.

stream = cp.cuda.Stream()

# Context manager style
with stream:
    d_data = cp.asarray(host_data)     # H→D transfer on this stream
    result = cp.sum(d_data)            # Kernel on this stream
# Operations enqueued but may not be complete here

stream.synchronize()  # Wait for all operations on this stream

Multiple Streams for Overlap

s1 = cp.cuda.Stream()
s2 = cp.cuda.Stream()

with s1:
    d_a = cp.asarray(data_a)
    result_a = cp.fft.fft(d_a)

with s2:
    d_b = cp.asarray(data_b)  # Overlaps with s1's FFT
    result_b = cp.fft.fft(d_b)

cp.cuda.Device().synchronize()  # Wait for all streams

Events for Timing

start = cp.cuda.Event()
end = cp.cuda.Event()

start.record()
# ... GPU operations ...
end.record()
end.synchronize()

elapsed_ms = cp.cuda.get_elapsed_time(start, end)

Per-Thread Default Stream

export CUPY_CUDA_PER_THREAD_DEFAULT_STREAM=1

Enables per-thread default streams for better concurrency in multi-threaded applications.

Multi-GPU

# Set current device
cp.cuda.Device(0).use()

# Context manager
with cp.cuda.Device(1):
    x = cp.array([1, 2, 3])  # Allocated on GPU 1

# Check which device an array is on
print(x.device)  # Device 1

Cross-device operations may work via P2P (peer-to-peer) memory access if the GPU topology supports it. Use cp.asarray() to explicitly transfer arrays between devices.

Per-Device Memory Limits

mempool = cp.get_default_memory_pool()
with cp.cuda.Device(0):
    mempool.set_limit(size=4 * 1024**3)
with cp.cuda.Device(1):
    mempool.set_limit(size=4 * 1024**3)

Performance Optimization

Benchmarking (Critical First Step)

An unsynchronized time.perf_counter() or %timeit measures enqueue latency. For end-to-end wall time, synchronize the relevant device/streams before starting and before stopping the timer. For GPU region timing use CUDA events or the benchmark helper below.

from cupyx.profiler import benchmark

result = benchmark(my_function, (arg1, arg2), n_repeat=100, n_warmup=10)
print(result)  # Shows CPU and GPU elapsed times with statistics

In IPython/Jupyter:

%load_ext cupyx.profiler
%gpu_timeit my_function(args)

One-Time Overheads

• Context initialization: First CuPy call may take 1-5 seconds (CUDA context creation). This is one-time.
• Kernel JIT compilation: First call to any operation triggers on-the-fly kernel compilation. Cached in ~/.cupy/kernel_cache. Persist this directory across CI/CD runs.

CUB and cuTENSOR Acceleration

# CuPy v11+ uses CUB by default
export CUPY_ACCELERATORS=cub          # CUB only (default)
export CUPY_ACCELERATORS=cub,cutensor # Both (requires cuTENSOR installed)

CUB accelerates reductions (sum, prod, amin, amax, argmin, argmax), inclusive scans (cumsum), histograms, sparse matrix-vector multiply, and ReductionKernel. The benefit depends on dtype, shape, axis, and hardware; benchmark the target operation.

cuTENSOR accelerates: binary elementwise ufuncs, reduction, tensor contraction.

Key Optimization Strategies

1. Prefer float32 over float64 when the numerical contract allows it. Throughput differences

depend on GPU architecture; validate accuracy and benchmark the target device.

1. Minimize CPU-GPU transfers. Every cp.asnumpy() / .get() triggers synchronization and PCI-e transfer. Keep data on GPU as long as possible.

1. Use kernel fusion. @cp.fuse() combines multiple elementwise operations into one kernel, eliminating intermediate arrays.

1. Batch operations. Fewer large operations usually beat many small ones. Measure launch

overhead on the target system rather than relying on a fixed latency.

1. Pre-allocate output arrays. Use out= parameter in ufuncs to avoid repeated allocation: ``python cp.add(a, b, out=result) # Writes into existing array

1. Use in-place operations. a += b avoids allocating a new array.

1. Use streams to overlap computation and data transfer.

1. Profile with NVTX markers for Nsight Systems analysis: ``python with cupyx.profiler.time_range('my_operation', color_id=0): result = heavy_computation()

Decision Tree: Which Kernel Approach?

1. Can be expressed as NumPy ops? → Use built-in CuPy functions (fastest development, often best performance)
2. Multiple chained elementwise ops? → Use @cp.fuse()
3. Custom elementwise with broadcasting? → Use ElementwiseKernel
4. Custom reduction? → Use ReductionKernel
5. Need full grid/block/shared memory control? → Use RawKernel or cupyx.jit.rawkernel
6. Large CUDA codebase? → Use RawModule

Interoperability

CuPy interoperates with other GPU libraries via the CUDA Array Interface and DLPack protocol — both enable zero-copy data sharing.

NumPy

# NumPy functions auto-dispatch to CuPy (NumPy >= 1.17)
import numpy as np
result = np.sum(cupy_array)  # Dispatches to CuPy, returns CuPy array

Numba

from numba import cuda

@cuda.jit
def numba_kernel(x, y):
    i = cuda.grid(1)
    if i < x.shape[0]:
        y[i] = x[i] * 2

# CuPy arrays pass directly to Numba kernels — zero copy
a = cp.arange(1000, dtype=cp.float32)
b = cp.zeros_like(a)
numba_kernel[4, 256](a, b)

PyTorch

import torch

# CuPy → PyTorch (zero copy via CUDA Array Interface)
cupy_array = cp.array([1.0, 2.0, 3.0], dtype=cp.float32)
torch_tensor = torch.as_tensor(cupy_array, device='cuda')

# PyTorch → CuPy (zero copy)
cupy_array = cp.asarray(torch_tensor)

# Via DLPack (also zero copy)
cupy_array = cp.from_dlpack(torch_tensor)
torch_tensor = torch.from_dlpack(cupy_array)

cuDF

import cudf

# cuDF → CuPy
arr = df.to_cupy()
arr = cp.asarray(df['column'])

# CuPy → cuDF
df = cudf.DataFrame(cupy_array)
s = cudf.Series(cupy_array)

Raw Pointer Interop

# Export pointer
ptr = cupy_array.data.ptr  # Raw device pointer as int

# Import foreign pointer
mem = cp.cuda.UnownedMemory(ptr, size_bytes, owner=owner_obj)
memptr = cp.cuda.MemoryPointer(mem, offset=0)
arr = cp.ndarray(shape, dtype, memptr=memptr)

Key Differences from NumPy

These are the behavioral differences that can cause bugs if you're not aware of them.

1. Reductions return 0-d arrays, not scalars. cp.sum(a) returns a 0-d cupy.ndarray, not a Python float. This avoids implicit GPU-CPU synchronization. Use .item() if you need a scalar.

1. Out-of-bounds integer-array indexing can wrap silently. Validate indices rather than relying on NumPy error behavior.

1. Duplicate indices in assignment are undefined. a[[0, 0]] = [1, 2] — NumPy stores the last value; CuPy stores an undefined value (GPU race condition).

1. Float-to-integer casts differ at edges. Casting negative float to unsigned int or infinity to int gives different results than NumPy.

1. No string/object dtypes. CuPy only supports numeric types. No structured arrays with string fields.

1. CuPy ufuncs require CuPy arrays. Unlike NumPy ufuncs, CuPy ufuncs don't accept lists or NumPy arrays — convert first.

1. Random streams differ. The same seed does not produce the same sequence across NumPy and CuPy or guarantee identical streams across versions. Use shared input fixtures for numerical comparisons.

Common Pitfalls

1. Unsynchronized timing. Use CUDA events/cupyx.profiler.benchmark() for device regions, or explicitly synchronize before and after wall-clock timing.

1. Unnecessary round-trips. Every cp.asnumpy() / .get() syncs the GPU and copies data across PCI-e. Restructure code to keep data on GPU.

1. "Memory leak" from pools. The memory pool caches freed blocks. nvidia-smi shows them as allocated. Use mempool.free_all_blocks() to release.

1. First-call latency. CUDA context init + kernel JIT compilation. Warm up before benchmarking.

1. Mixing devices. Using an array from GPU 0 on GPU 1 without explicit transfer can fail or be slow.

1. RawKernel ignoring views. Transposed or sliced arrays passed to RawKernel are treated as the original contiguous layout. You must handle strides manually.

1. **Forgetting synchronize() before reading results.** If you pass data back to CPU or use it in non-CuPy code, ensure the GPU is done first.

Environment Variables