cuBLAS

The API Reference guide for cuBLAS, the CUDA Basic Linear Algebra Subroutine library.

1. Introduction

The cuBLAS library is an implementation of BLAS (Basic Linear Algebra Subprograms) on top of the NVIDIA® CUDA® runtime. It allows the user to access the computational resources of NVIDIA Graphics Processing Unit (GPU).

The cuBLAS Library exposes three sets of API:
• The cuBLAS API, which is simply called cuBLAS API in this document (starting with CUDA 6.0),
• The cuBLASXt API (starting with CUDA 6.0), and
• The cuBLASLt API (starting with CUDA 10.1)

To use the cuBLAS API, the application must allocate the required matrices and vectors in the GPU memory space, fill them with data, call the sequence of desired cuBLAS functions, and then upload the results from the GPU memory space back to the host. The cuBLAS API also provides helper functions for writing and retrieving data from the GPU.

To use the cuBLASXt API, the application may have the data on the Host or any of the devices involved in the computation, and the Library will take care of dispatching the operation to, and transferring the data to, one or multiple GPUs present in the system, depending on the user request.

The cuBLASLt is a lightweight library dedicated to GEneral Matrix-to-matrix Multiply (GEMM) operations with a new flexible API. This library adds flexibility in matrix data layouts, input types, compute types, and also in choosing the algorithmic implementations and heuristics through parameter programmability. After a set of options for the intended GEMM operation are identified by the user, these options can be used repeatedly for different inputs. This is analogous to how cuFFT and FFTW first create a plan and reuse for same size and type FFTs with different input data.

1.1. Data Layout

For maximum compatibility with existing Fortran environments, the cuBLAS library uses column-major storage, and 1-based indexing. Since C and C++ use row-major storage, applications written in these languages can not use the native array semantics for two-dimensional arrays. Instead, macros or inline functions should be defined to implement matrices on top of one-dimensional arrays. For Fortran code ported to C in mechanical fashion, one may chose to retain 1-based indexing to avoid the need to transform loops. In this case, the array index of a matrix element in row “i” and column “j” can be computed via the following macro

#define IDX2F(i,j,ld) ((((j)-1)*(ld))+((i)-1))

Here, ld refers to the leading dimension of the matrix, which in the case of column-major storage is the number of rows of the allocated matrix (even if only a submatrix of it is being used). For natively written C and C++ code, one would most likely choose 0-based indexing, in which case the array index of a matrix element in row “i” and column “j” can be computed via the following macro

#define IDX2C(i,j,ld) (((j)*(ld))+(i))

1.2. New and Legacy cuBLAS API

Starting with version 4.0, the cuBLAS Library provides a new API, in addition to the existing legacy API. This section discusses why a new API is provided, the advantages of using it, and the differences with the existing legacy API.

Warning: The legacy cuBLAS API is deprecated and will be removed in a future release.

The new cuBLAS library API can be used by including the header file “cublas_v2.h”. It has the following features that the legacy cuBLAS API does not have:

• The handle to the cuBLAS library context is initialized using the function and is explicitly passed to every subsequent library function call. This allows the user to have more control over the library setup when using multiple host threads and multiple GPUs. This also allows the cuBLAS APIs to be reentrant.
• The scalars $\alpha$ and $\beta$ can be passed by reference on the host or the device, instead of only being allowed to be passed by value on the host. This change allows library functions to execute asynchronously using streams even when $\alpha$ and $\beta$ are generated by a previous kernel.
• When a library routine returns a scalar result, it can be returned by reference on the host or the device, instead of only being allowed to be returned by value only on the host. This change allows library routines to be called asynchronously when the scalar result is generated and returned by reference on the device resulting in maximum parallelism.
• The error status cublasStatus_t is returned by all cuBLAS library function calls. This change facilitates debugging and simplifies software development. Note that cublasStatus was renamed cublasStatus_t to be more consistent with other types in the cuBLAS library.
• The cublasAlloc() and cublasFree() functions have been deprecated. This change removes these unnecessary wrappers around cudaMalloc() and cudaFree(), respectively.
• The function cublasSetKernelStream() was renamed cublasSetStream() to be more consistent with the other CUDA libraries.

The legacy cuBLAS API, explained in more detail in the Appendix A, can be used by including the header file “cublas.h”. Since the legacy API is identical to the previously released cuBLAS library API, existing applications will work out of the box and automatically use this legacy API without any source code changes.

The current and the legacy cuBLAS APIs cannot be used simultaneously in a single translation unit: including both “cublas.h” and “cublas_v2.h” header files will lead to compilation errors due to incompatible symbol redeclarations.

In general, new applications should not use the legacy cuBLAS API, and existing applications should convert to using the new API if it requires sophisticated and optimal stream parallelism, or if it calls cuBLAS routines concurrently from multiple threads.

For the rest of the document, the new cuBLAS Library API will simply be referred to as the cuBLAS Library API.

As mentioned earlier the interfaces to the legacy and the cuBLAS library APIs are the header file “cublas.h” and “cublas_v2.h”, respectively. In addition, applications using the cuBLAS library need to link against:
• The DSO cublas.so for Linux,
• The DLL cublas.dll for Windows, or
• The dynamic library cublas.dylib for Mac OS X.
Note: The same dynamic library implements both the new and legacy cuBLAS APIs.

1.3. Example Code

The following code examples show an application written in C using the cuBLAS library API with two indexing styles. Example 1 shows 1-based indexing and Example 2 shows 0-based indexing.

//Example 1. Application Using C and cuBLAS: 1-based indexing
//-----------------------------------------------------------
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <cuda_runtime.h>
#include "cublas_v2.h"
#define M 6
#define N 5
#define IDX2F(i,j,ld) ((((j)-1)*(ld))+((i)-1))

static __inline__ void modify (cublasHandle_t handle, float *m, int ldm, int n, int p, int q, float alpha, float beta){
cublasSscal (handle, n-q+1, &alpha, &m[IDX2F(p,q,ldm)], ldm);
cublasSscal (handle, ldm-p+1, &beta, &m[IDX2F(p,q,ldm)], 1);
}

int main (void){
cudaError_t cudaStat;
cublasStatus_t stat;
cublasHandle_t handle;
int i, j;
float* devPtrA;
float* a = 0;
a = (float *)malloc (M * N * sizeof (*a));
if (!a) {
printf ("host memory allocation failed");
return EXIT_FAILURE;
}
for (j = 1; j <= N; j++) {
for (i = 1; i <= M; i++) {
a[IDX2F(i,j,M)] = (float)((i-1) * N + j);
}
}
cudaStat = cudaMalloc ((void**)&devPtrA, M*N*sizeof(*a));
if (cudaStat != cudaSuccess) {
printf ("device memory allocation failed");
return EXIT_FAILURE;
}
stat = cublasCreate(&handle);
if (stat != CUBLAS_STATUS_SUCCESS) {
printf ("CUBLAS initialization failed\n");
return EXIT_FAILURE;
}
stat = cublasSetMatrix (M, N, sizeof(*a), a, M, devPtrA, M);
if (stat != CUBLAS_STATUS_SUCCESS) {
cudaFree (devPtrA);
cublasDestroy(handle);
return EXIT_FAILURE;
}
modify (handle, devPtrA, M, N, 2, 3, 16.0f, 12.0f);
stat = cublasGetMatrix (M, N, sizeof(*a), devPtrA, M, a, M);
if (stat != CUBLAS_STATUS_SUCCESS) {
cudaFree (devPtrA);
cublasDestroy(handle);
return EXIT_FAILURE;
}
cudaFree (devPtrA);
cublasDestroy(handle);
for (j = 1; j <= N; j++) {
for (i = 1; i <= M; i++) {
printf ("%7.0f", a[IDX2F(i,j,M)]);
}
printf ("\n");
}
free(a);
return EXIT_SUCCESS;
}

----------------------------------------------

//Example 2. Application Using C and cuBLAS: 0-based indexing
//-----------------------------------------------------------
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <cuda_runtime.h>
#include "cublas_v2.h"
#define M 6
#define N 5
#define IDX2C(i,j,ld) (((j)*(ld))+(i))

static __inline__ void modify (cublasHandle_t handle, float *m, int ldm, int n, int p, int q, float alpha, float beta){
cublasSscal (handle, n-q, &alpha, &m[IDX2C(p,q,ldm)], ldm);
cublasSscal (handle, ldm-p, &beta, &m[IDX2C(p,q,ldm)], 1);
}

int main (void){
cudaError_t cudaStat;
cublasStatus_t stat;
cublasHandle_t handle;
int i, j;
float* devPtrA;
float* a = 0;
a = (float *)malloc (M * N * sizeof (*a));
if (!a) {
printf ("host memory allocation failed");
return EXIT_FAILURE;
}
for (j = 0; j < N; j++) {
for (i = 0; i < M; i++) {
a[IDX2C(i,j,M)] = (float)(i * N + j + 1);
}
}
cudaStat = cudaMalloc ((void**)&devPtrA, M*N*sizeof(*a));
if (cudaStat != cudaSuccess) {
printf ("device memory allocation failed");
return EXIT_FAILURE;
}
stat = cublasCreate(&handle);
if (stat != CUBLAS_STATUS_SUCCESS) {
printf ("CUBLAS initialization failed\n");
return EXIT_FAILURE;
}
stat = cublasSetMatrix (M, N, sizeof(*a), a, M, devPtrA, M);
if (stat != CUBLAS_STATUS_SUCCESS) {
cudaFree (devPtrA);
cublasDestroy(handle);
return EXIT_FAILURE;
}
modify (handle, devPtrA, M, N, 1, 2, 16.0f, 12.0f);
stat = cublasGetMatrix (M, N, sizeof(*a), devPtrA, M, a, M);
if (stat != CUBLAS_STATUS_SUCCESS) {
cudaFree (devPtrA);
cublasDestroy(handle);
return EXIT_FAILURE;
}
cudaFree (devPtrA);
cublasDestroy(handle);
for (j = 0; j < N; j++) {
for (i = 0; i < M; i++) {
printf ("%7.0f", a[IDX2C(i,j,M)]);
}
printf ("\n");
}
free(a);
return EXIT_SUCCESS;
}

2. Using the cuBLAS API

2.1. General Description

This section describes how to use the cuBLAS library API.

2.1.1. Error status

All cuBLAS library function calls return the error status cublasStatus_t.

2.1.2. cuBLAS context

The application must initialize the handle to the cuBLAS library context by calling the cublasCreate() function. Then, the handle is explicitly passed to every subsequent library function call. Once the application finishes using the library, it must call the function cublasDestroy() to release the resources associated with the cuBLAS library context.

This approach allows the user to explicitly control the library setup when using multiple host threads and multiple GPUs. For example, the application can use cudaSetDevice() to associate different devices with different host threads and in each of those host threads it can initialize a unique handle to the cuBLAS library context, which will use the particular device associated with that host thread. Then, the cuBLAS library function calls made with different handle will automatically dispatch the computation to different devices.

The device associated with a particular cuBLAS context is assumed to remain unchanged between the corresponding cublasCreate() and cublasDestroy() calls. In order for the cuBLAS library to use a different device in the same host thread, the application must set the new device to be used by calling cudaSetDevice() and then create another cuBLAS context, which will be associated with the new device, by calling cublasCreate().

A cuBLAS library context is tightly coupled with the CUDA context that is current at the time of the cublasCreate() call. An application that uses multiple CUDA contexts is required to create a cuBLAS context per CUDA context and make sure the former never outlives the latter.

The library is thread safe and its functions can be called from multiple host threads, even with the same handle. When multiple threads share the same handle, extreme care needs to be taken when the handle configuration is changed because that change will affect potentially subsequent cuBLAS calls in all threads. It is even more true for the destruction of the handle. So it is not recommended that multiple thread share the same cuBLAS handle.

2.1.4. Results Reproducibility

By design, all cuBLAS API routines from a given toolkit version generate the same bit-wise results at every run when executed on GPUs with the same architecture and the same number of SMs. However, bit-wise reproducibility is not guaranteed across toolkit versions because the implementation might differ due to some implementation changes.

This guarantee holds when a single CUDA stream is active only. If multiple concurrent streams are active, the library may optimize total performance by picking different internal implementations.

Note: The non-deterministic behavior of multi-stream execution is due to library optimizations in selecting internal workspace for the routines running in parallel streams. To avoid this effect, users can either:

• provide a separate workspace for each used stream using the cublasSetWorkspace() function, or
• have one cuBLAS handle per stream, or
• use cublasLtMatmul() instead of the *gemm*() family of functions and provide user-owned workspace, or
• set the debug environment variable CUBLAS_WORKSPACE_CONFIG to ":16:8" (may limit overall performance) or ":4096:8" (will increase library footprint in GPU memory by approximately 24MiB).
Any of those settings will allow for deterministic behavior even with multiple concurrent streams sharing a single cuBLAS handle.

This behavior is expected to change in a future release.

For some routines such as cublas<t>symv and cublas<t>hemv, an alternate significantly faster routine can be chosen using the routine cublasSetAtomicsMode(). In that case, the results are not guaranteed to be bit-wise reproducible because atomics are used for the computation.

2.1.5. Scalar Parameters

There are two categories of the functions that use scalar parameters:

• Functions that take alpha and beta parameters by reference on the host or the device as scaling factors, such as gemm.
• Functions that return a scalar result on the host or the device such as amax(), amin, asum(), rotg(), rotmg(), dot(), and nrm2().

For the functions of the first category, when the pointer mode is set to CUBLAS_POINTER_MODE_HOST, the scalar parameters alpha and beta can be on the stack or allocated on the heap, and should not be placed in managed memory. Underneath, the CUDA kernels related to those functions will be launched with the value of alpha and beta. Therefore if they were allocated on the heap, they can be freed just after the return of the call even though the kernel launch is asynchronous. When the pointer mode is set to CUBLAS_POINTER_MODE_DEVICE, alpha and beta must be accessible on the device, and their values should not be modified until the kernel is done. Note that since cudaFree() does an implicit cudaDeviceSynchronize(), cudaFree() can still be called on alpha and beta just after the call but it would defeat the purpose of using this pointer mode in that case.

For the functions of the second category, when the pointer mode is set to CUBLAS_POINTER_MODE_HOST, these functions block the CPU, until the GPU has completed its computation and the results have been copied back to the host. When the pointer mode is set to CUBLAS_POINTER_MODE_DEVICE, these functions return immediately. In this case, similar to matrix and vector results, the scalar result is ready only when execution of the routine on the GPU has completed. This requires proper synchronization in order to read the result from the host.

In either case, the pointer mode CUBLAS_POINTER_MODE_DEVICE allows the library functions to execute completely asynchronously from the Host even when alpha and/or beta are generated by a previous kernel. For example, this situation can arise when iterative methods for solution of linear systems and eigenvalue problems are implemented using the cuBLAS library.

2.1.6. Parallelism with Streams

If the application uses the results computed by multiple independent tasks, CUDA streams can be used to overlap the computation performed in these tasks.

The application can conceptually associate each stream with each task. In order to achieve the overlap of computation between the tasks, the user should create CUDA streams using the function cudaStreamCreate() and set the stream to be used by each individual cuBLAS library routine by calling cublasSetStream() just before calling the actual cuBLAS routine. Note that cublasSetStream() resets the user-provided workspace to the default workspace pool; refer to cublasSetWorkspace(). Then, the computation performed in separate streams would be overlapped automatically when possible on the GPU. This approach is especially useful when the computation performed by a single task is relatively small and is not enough to fill the GPU with work.

We recommend using the new cuBLAS API with scalar parameters and results passed by reference in the device memory to achieve maximum overlap of the computation when using streams.

A particular application of streams, batching of multiple small kernels, is described in the following section.

2.1.7. Batching Kernels

In this section, we explain how to use streams to batch the execution of small kernels. For instance, suppose that we have an application where we need to make many small independent matrix-matrix multiplications with dense matrices.

It is clear that even with millions of small independent matrices we will not be able to achieve the same GFLOPS rate as with a one large matrix. For example, a single $n×n$ large matrix-matrix multiplication performs ${n}^{3}$ operations for ${n}^{2}$ input size, while 1024 $\frac{n}{32}×\frac{n}{32}$ small matrix-matrix multiplications perform $1024{\left(\frac{n}{32}\right)}^{3}=\frac{{n}^{3}}{32}$ operations for the same input size. However, it is also clear that we can achieve a significantly better performance with many small independent matrices compared with a single small matrix.

The architecture family of GPUs allows us to execute multiple kernels simultaneously. Hence, in order to batch the execution of independent kernels, we can run each of them in a separate stream. In particular, in the above example we could create 1024 CUDA™ streams using the function cudaStreamCreate(), then preface each call to cublas<t>gemm() with a call to cublasSetStream() with a different stream for each of the matrix-matrix multiplications (note that cublasSetStream() resets user-provided workspace to the default workspace pool, see cublasSetWorkspace()). This will ensure that when possible the different computations will be executed concurrently. Although the user can create many streams, in practice it is not possible to have more than 32 concurrent kernels executing at the same time.

2.1.8. Cache Configuration

On some devices, L1 cache and shared memory use the same hardware resources. The cache configuration can be set directly with the CUDA Runtime function cudaDeviceSetCacheConfig. The cache configuration can also be set specifically for some functions using the routine cudaFuncSetCacheConfig. Refer to the CUDA Runtime API documentation for details about the cache configuration settings.

Because switching from one configuration to another can affect kernel's concurrency, the cuBLAS Library does not set any cache configuration preference and relies on the current setting. However, some cuBLAS routines, especially Level-3 routines, rely heavily on shared memory. Thus the cache preference setting might affect adversely their performance.

2.1.9. Static Library Support

The cuBLAS Library is also delivered in a static form as libcublas_static.a on Linux. The static cuBLAS library and all other static math libraries depend on a common thread abstraction layer library called libculibos.a.

For example, on Linux, to compile a small application using cuBLAS, against the dynamic library, the following command can be used:

nvcc myCublasApp.c  -lcublas  -o myCublasApp


Whereas to compile against the static cuBLAS library, the following command must be used:

nvcc myCublasApp.c  -lcublas_static   -lculibos -o myCublasApp


It is also possible to use the native Host C++ compiler. Depending on the Host operating system, some additional libraries like pthread or dl might be needed on the linking line. The following command on Linux is suggested :

g++ myCublasApp.c  -lcublas_static   -lculibos -lcudart_static -lpthread -ldl -I <cuda-toolkit-path>/include -L <cuda-toolkit-path>/lib64 -o myCublasApp


Note that in the latter case, the library cuda is not needed. The CUDA Runtime will try to open explicitly the cuda library if needed. In the case of a system which does not have the CUDA driver installed, this allows the application to gracefully manage this issue and potentially run if a CPU-only path is available.

Starting with release 11.2, using the typed functions instead of the extension functions (cublas**Ex()) helps in reducing the binary size when linking to static cuBLAS Library.

2.1.10. GEMM Algorithms Numerical Behavior

Some GEMM algorithms split the computation along the dimension K to increase the GPU occupancy, especially when the dimension K is large compared to dimensions M and N. When this type of algorithm is chosen by the cuBLAS heuristics or explicitly by the user, the results of each split is summed deterministically into the resulting matrix to get the final result.

For the routines cublas<t>gemmEx and cublasGemmEx, when the compute type is greater than the output type, the sum of the split chunks can potentially lead to some intermediate overflows thus producing a final resulting matrix with some overflows. Those overflows might not have occurred if all the dot products had been accumulated in the compute type before being converted at the end in the output type. This computation side-effect can be easily exposed when the computeType is CUDA_R_32F and Atype, Btype and Ctype are in CUDA_R_16F. This behavior can be controlled using the compute precision mode CUBLAS_MATH_DISALLOW_REDUCED_PRECISION_REDUCTION with cublasSetMathMode()

2.1.11. Tensor Core Usage

Tensor cores were first introduced with Volta GPUs (compute capability>=sm_70) and significantly accelerate matrix multiplications. Starting with cuBLAS version 11.0.0, the library will automatically make use of Tensor Core capabilities wherever possible, unless they are explicitly disabled by selecting pedantic compute modes in cuBLAS (refer to cublasSetMathMode(), cublasMath_t).

It should be noted that the library will pick a Tensor Core enabled implementation wherever it determines that it would provide the best performance.

Starting with cuBLAS version 11.0.0 there are no longer any restrictions on matrix dimensions and memory alignments to use Tensor Cores. However, the best performance when using Tensor Cores can be achieved when the matrix dimensions and pointers meet certain memory alignment requirements. Specifically, all of the following conditions must be satisfied to get the most performance out of Tensor Cores:
• m % 8 == 0
• k % 8 == 0
• op_B == CUBLAS_OP_N || n%8 == 0
• intptr_t(A) % 16 == 0
• intptr_t(B) % 16 == 0
• intptr_t(C) % 16 == 0
• intptr_t(A+lda) % 16 == 0
• intptr_t(B+ldb) % 16 == 0
• intptr_t(C+ldc) % 16 == 0

2.1.12. CUDA Graphs Support

cuBLAS routines can be captured in CUDA Graph stream capture without restrictions in most situations.

The exception are routines that output results into host buffers (e.g. cublas<t>dot while pointer mode CUBLAS_POINTER_MODE_HOST is configured), as it enforces synchronization.

For input coefficients (such as alpha, beta) behavior depends on the pointer mode setting:
• In the case of CUBLAS(LT)_POINTER_MODE_HOST, coefficient values are captured in the graph.
• In the case of pointer modes with device pointers, coefficient value is accessed using the device pointer at the time of graph execution.
Note: Every time cuBLAS routines are captured in a new CUDA Graph, cuBLAS will allocate workspace memory on the device. This memory is only freed when the cuBLAS handle used during capture is deleted. To avoid this, use cublasSetWorkspace() function to provide user-owned workspace memory.

2.2.1. cublasHandle_t

The cublasHandle_t type is a pointer type to an opaque structure holding the cuBLAS library context. The cuBLAS library context must be initialized using cublasCreate() and the returned handle must be passed to all subsequent library function calls. The context should be destroyed at the end using cublasDestroy().

2.2.2. cublasStatus_t

The type is used for function status returns. All cuBLAS library functions return their status, which can have the following values.

Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The cuBLAS library was not initialized. This is usually caused by the lack of a prior cublasCreate() call, an error in the CUDA Runtime API called by the cuBLAS routine, or an error in the hardware setup.

To correct: call cublasCreate() before the function call; and check that the hardware, an appropriate version of the driver, and the cuBLAS library are correctly installed.

CUBLAS_STATUS_ALLOC_FAILED

Resource allocation failed inside the cuBLAS library. This is usually caused by a cudaMalloc() failure.

To correct: prior to the function call, deallocate previously allocated memory as much as possible.

CUBLAS_STATUS_INVALID_VALUE

An unsupported value or parameter was passed to the function (a negative vector size, for example).

To correct: ensure that all the parameters being passed have valid values.

CUBLAS_STATUS_ARCH_MISMATCH

The function requires a feature absent from the device architecture; usually caused by compute capability lower than 5.0.

To correct: compile and run the application on a device with appropriate compute capability.

CUBLAS_STATUS_MAPPING_ERROR

An access to GPU memory space failed, which is usually caused by a failure to bind a texture.

To correct: before the function call, unbind any previously bound textures.

CUBLAS_STATUS_EXECUTION_FAILED

The GPU program failed to execute. This is often caused by a launch failure of the kernel on the GPU, which can be caused by multiple reasons.

To correct: check that the hardware, an appropriate version of the driver, and the cuBLAS library are correctly installed.

CUBLAS_STATUS_INTERNAL_ERROR

An internal cuBLAS operation failed. This error is usually caused by a cudaMemcpyAsync() failure.

To correct: check that the hardware, an appropriate version of the driver, and the cuBLAS library are correctly installed. Also, check that the memory passed as a parameter to the routine is not being deallocated before the routine’s completion.

CUBLAS_STATUS_NOT_SUPPORTED

The functionality requested is not supported.

The functionality requested requires some license and an error was detected when trying to check the current licensing. This error can happen if the license is not present or is expired or if the environment variable NVIDIA_LICENSE_FILE is not set properly.

2.2.3. cublasOperation_t

The cublasOperation_t type indicates which operation needs to be performed with the dense matrix. Its values correspond to Fortran characters ‘N’ or ‘n’ (non-transpose), ‘T’ or ‘t’ (transpose) and ‘C’ or ‘c’ (conjugate transpose) that are often used as parameters to legacy BLAS implementations.

Value Meaning

CUBLAS_OP_N

The non-transpose operation is selected.

CUBLAS_OP_T

The transpose operation is selected.

CUBLAS_OP_C

The conjugate transpose operation is selected.

2.2.4. cublasFillMode_t

The type indicates which part (lower or upper) of the dense matrix was filled and consequently should be used by the function. Its values correspond to Fortran characters ‘L’ or ‘l’ (lower) and ‘U’ or ‘u’ (upper) that are often used as parameters to legacy BLAS implementations.

Value Meaning

CUBLAS_FILL_MODE_LOWER

The lower part of the matrix is filled.

CUBLAS_FILL_MODE_UPPER

The upper part of the matrix is filled.

CUBLAS_FILL_MODE_FULL

The full matrix is filled.

2.2.5. cublasDiagType_t

The type indicates whether the main diagonal of the dense matrix is unity and consequently should not be touched or modified by the function. Its values correspond to Fortran characters ‘N’ or ‘n’ (non-unit) and ‘U’ or ‘u’ (unit) that are often used as parameters to legacy BLAS implementations.

Value Meaning

CUBLAS_DIAG_NON_UNIT

The matrix diagonal has non-unit elements.

CUBLAS_DIAG_UNIT

The matrix diagonal has unit elements.

2.2.6. cublasSideMode_t

The type indicates whether the dense matrix is on the left or right side in the matrix equation solved by a particular function. Its values correspond to Fortran characters ‘L’ or ‘l’ (left) and ‘R’ or ‘r’ (right) that are often used as parameters to legacy BLAS implementations.

Value Meaning

CUBLAS_SIDE_LEFT

The matrix is on the left side in the equation.

CUBLAS_SIDE_RIGHT

The matrix is on the right side in the equation.

2.2.7. cublasPointerMode_t

The cublasPointerMode_t type indicates whether the scalar values are passed by reference on the host or device. It is important to point out that if several scalar values are present in the function call, all of them must conform to the same single pointer mode. The pointer mode can be set and retrieved using cublasSetPointerMode() and cublasGetPointerMode() routines, respectively.

Value Meaning

CUBLAS_POINTER_MODE_HOST

The scalars are passed by reference on the host.

CUBLAS_POINTER_MODE_DEVICE

The scalars are passed by reference on the device.

2.2.8. cublasAtomicsMode_t

The type indicates whether cuBLAS routines which have an alternate implementation using atomics can be used. The atomics mode can be set and queried using cublasSetAtomicsMode() and cublasGetAtomicsMode() and routines, respectively.

Value Meaning

CUBLAS_ATOMICS_NOT_ALLOWED

The usage of atomics is not allowed.

CUBLAS_ATOMICS_ALLOWED

The usage of atomics is allowed.

2.2.9. cublasGemmAlgo_t

cublasGemmAlgo_t type is an enumerant to specify the algorithm for matrix-matrix multiplication on GPU architectures up to sm_75. On sm_80 and newer GPU architectures, this enumarant has no effect. cuBLAS has the following algorithm options:

Value Meaning

CUBLAS_GEMM_DEFAULT

Apply Heuristics to select the GEMM algorithm.

CUBLAS_GEMM_ALGO0 to CUBLAS_GEMM_ALGO23

Explicitly choose an Algorithm [0,23]. Note: Has no effect on NVIDIA Ampere Architecture GPUs and newer.

CUBLAS_GEMM_DEFAULT_TENSOR_OP[DEPRECATED]

This mode is deprecated and will be removed in a future release. Apply Heuristics to select the GEMM algorithm, while allowing use of reduced precision CUBLAS_COMPUTE_32F_FAST_16F kernels (for backward compatibility).

CUBLAS_GEMM_ALGO0_TENSOR_OP to CUBLAS_GEMM_ALGO15_TENSOR_OP[DEPRECATED]

Those values are deprecated and will be removed in a future release. Explicitly choose a Tensor core GEMM Algorithm [0,15]. Allows use of reduced precision CUBLAS_COMPUTE_32F_FAST_16F kernels (for backward compatibility). Note: Has no effect on NVIDIA Ampere Architecture GPUs and newer.

2.2.10. cublasMath_t

cublasMath_t enumerate type is used in cublasSetMathMode() to choose compute precision modes as defined in the following table. Since this setting does not directly control the use of Tensor Cores, the mode CUBLAS_TENSOR_OP_MATH is being deprecated, and will be removed in a future release.

Value Meaning

CUBLAS_DEFAULT_MATH

This is the default and highest-performance mode that uses compute and intermediate storage precisions with at least the same number of mantissa and exponent bits as requested. Tensor Cores will be used whenever possible.

CUBLAS_PEDANTIC_MATH

This mode uses the prescribed precision and standardized arithmetic for all phases of calculations and is primarily intended for numerical robustness studies, testing, and debugging. This mode might not be as performant as the other modes.

CUBLAS_TF32_TENSOR_OP_MATH

Enable acceleration of single-precision routines using TF32 tensor cores.

CUBLAS_MATH_DISALLOW_REDUCED_PRECISION_REDUCTION

Forces any reductions during matrix multiplications to use the accumulator type (that is, compute type) and not the output type in case of mixed precision routines where output type precision is less than the compute type precision. This is a flag that can be set (using a bitwise or operation) alongside any of the other values.

CUBLAS_TENSOR_OP_MATH [DEPRECATED]

This mode is deprecated and will be removed in a future release. Allows the library to use Tensor Core operations whenever possible. For single-precision GEMM routines cuBLAS will use the CUBLAS_COMPUTE_32F_FAST_16F compute type.

2.2.11. cublasComputeType_t

cublasComputeType_t enumerate type is used in cublasGemmEx and cublasLtMatmul (including all batched and strided batched variants) to choose compute precision modes as defined below.

Value Meaning

CUBLAS_COMPUTE_16F

This is the default and highest-performance mode for 16-bit half precision floating point and all compute and intermediate storage precisions with at least 16-bit half precision. Tensor Cores will be used whenever possible.

CUBLAS_COMPUTE_16F_PEDANTIC

This mode uses 16-bit half precision floating point standardized arithmetic for all phases of calculations and is primarily intended for numerical robustness studies, testing, and debugging. This mode might not be as performant as the other modes since it disables use of tensor cores.

CUBLAS_COMPUTE_32F

This is the default 32-bit single precision floating point and uses compute and intermediate storage precisions of at least 32-bits.

CUBLAS_COMPUTE_32F_PEDANTIC

Uses 32-bit single-precision floating point arithmetic for all phases of calculations and also disables algorithmic optimizations such as Gaussian complexity reduction (3M).

CUBLAS_COMPUTE_32F_FAST_16F

Allows the library to use Tensor Cores with automatic down-conversion and 16-bit half-precision compute for 32-bit input and output matrices.

CUBLAS_COMPUTE_32F_FAST_16BF

Allows the library to use Tensor Cores with automatic down-conversion and bfloat16 compute for 32-bit input and output matrices. See Alternate Floating Point section for more details on bfloat16.

CUBLAS_COMPUTE_32F_FAST_TF32

Allows the library to use Tensor cores with TF32 compute for 32-bit input and output matrices. See Alternate Floating Point section for more details on TF32 compute.

CUBLAS_COMPUTE_64F

This is the default 64-bit double precision floating point and uses compute and intermediate storage precisions of at least 64-bits.

CUBLAS_COMPUTE_64F_PEDANTIC

Uses 64-bit double precision floating point arithmetic for all phases of calculations and also disables algorithmic optimizations such as Gaussian complexity reduction (3M).

CUBLAS_COMPUTE_32I

This is the default 32-bit integer mode and uses compute and intermediate storage precisions of at least 32-bits.

CUBLAS_COMPUTE_32I_PEDANTIC

Uses 32-bit integer arithmetic for all phases of calculations.

Note: Setting the environment variable NVIDIA_TF32_OVERRIDE = 0 will override any defaults or programmatic configuration of NVIDIA libraries, and consequently, cuBLAS will not accelerate FP32 computations with TF32 tensor cores.

2.3. CUDA Datatypes Reference

This section describes types shared by multiple CUDA Libraries and defined in the header file library_types.h.

The cudaDataType_t type is an enumerant to specify the data precision. It is used when the data reference does not carry the type itself (such as void *).

For example, it is used in the routine cublasSgemmEx.

Value Meaning

CUDA_R_16F

The data type is a 16-bit real half precision floating-point.

CUDA_C_16F

The data type is a 32-bit structure comprised of two half precision floating-points representing a complex number.

CUDA_R_16BF

The data type is a 16-bit real bfloat16 floating-point.

CUDA_C_16BF

The data type is a 32-bit structure comprised of two bfloat16 floating-points representing a complex number.

CUDA_R_32F

The data type is a 32-bit real single precision floating-point.

CUDA_C_32F

The data type is a 64-bit structure comprised of two single precision floating-points representing a complex number.

CUDA_R_64F

The data type is a 64-bit real double precision floating-point.

CUDA_C_64F

The data type is a 128-bit structure comprised of two double precision floating-points representing a complex number.

CUDA_R_8I

The data type is an 8-bit real signed integer.

CUDA_C_8I

The data type is a 16-bit structure comprised of two 8-bit signed integers representing a complex number.

CUDA_R_8U

The data type is an 8-bit real unsigned integer.

CUDA_C_8U

The data type is a 16-bit structure comprised of two 8-bit unsigned integers representing a complex number.

CUDA_R_32I

The data type is a 32-bit real signed integer.

CUDA_C_32I

The data type is a 64-bit structure comprised of two 32-bit signed integers representing a complex number.

CUDA_R_8F_E4M3

The data type is an 8-bit real floating point in E4M3 format.

CUDA_R_8F_E5M2

The data type is an 8-bit real floating point in E5M2 format.

2.3.2. libraryPropertyType_t

The libraryPropertyType_t is used as a parameter to specify which property is requested when using the routine cublasGetProperty.

Value Meaning

MAJOR_VERSION

Enumerant to query the major version.

MINOR_VERSION

Enumerant to query the minor version.

PATCH_LEVEL

Number to identify the patch level.

2.4.1. cublasCreate()

cublasStatus_t
cublasCreate(cublasHandle_t *handle)

This function initializes the cuBLAS library and creates a handle to an opaque structure holding the cuBLAS library context. It allocates hardware resources on the host and device and must be called prior to making any other cuBLAS library calls. The cuBLAS library context is tied to the current CUDA device. To use the library on multiple devices, one cuBLAS handle needs to be created for each device. Furthermore, for a given device, multiple cuBLAS handles with different configurations can be created. Because cublasCreate() allocates some internal resources and the release of those resources by calling cublasDestroy() will implicitly call cublasDeviceSynchronize(), it is recommended to minimize the number of cublasCreate()/cublasDestroy() occurrences. For multi-threaded applications that use the same device from different threads, the recommended programming model is to create one cuBLAS handle per thread and use that cuBLAS handle for the entire life of the thread.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The initialization succeeded.

CUBLAS_STATUS_NOT_INITIALIZED

The CUDA™ Runtime initialization failed.

CUBLAS_STATUS_ALLOC_FAILED

The resources could not be allocated.

CUBLAS_STATUS_INVALID_VALUE

handle == NULL

2.4.2. cublasDestroy()

cublasStatus_t
cublasDestroy(cublasHandle_t handle)

This function releases hardware resources used by the cuBLAS library. This function is usually the last call with a particular handle to the cuBLAS library. Because cublasCreate() allocates some internal resources and the release of those resources by calling cublasDestroy() will implicitly call cublasDeviceSynchronize(), it is recommended to minimize the number of cublasCreate()/cublasDestroy() occurrences.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The shut down succeeded.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.3. cublasGetVersion()

cublasStatus_t
cublasGetVersion(cublasHandle_t handle, int *version)

This function returns the version number of the cuBLAS library.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The provided storage for library version number is not initialized (NULL).

2.4.4. cublasGetProperty()

cublasStatus_t
cublasGetProperty(libraryPropertyType type, int *value)

This function returns the value of the requested property in memory pointed to by value. Refer to libraryPropertyType for supported types.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

Invalid type value:

• If invalid type value or

• value == NULL

2.4.5. cublasGetStatusName()

const char* cublasGetStatusName(cublasStatus_t status)

This function returns the string representation of a given status.

Return Value Meaning

NULL-terminated string

The string representation of the status.

2.4.6. cublasGetStatusString()

const char* cublasGetStatusString(cublasStatus_t status)

This function returns the description string for a given status.

Return Value Meaning

NULL-terminated string

The description of the status.

2.4.7. cublasSetStream()

cublasStatus_t
cublasSetStream(cublasHandle_t handle, cudaStream_t streamId)

This function sets the cuBLAS library stream, which will be used to execute all subsequent calls to the cuBLAS library functions. If the cuBLAS library stream is not set, all kernels use the defaultNULL stream. In particular, this routine can be used to change the stream between kernel launches and then to reset the cuBLAS library stream back to NULL. Additionally this function unconditionally resets the cuBLAS library workspace back to the default workspace pool (see cublasSetWorkspace()).

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The stream was set successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.8. cublasSetWorkspace()

cublasStatus_t
cublasSetWorkspace(cublasHandle_t handle, void *workspace, size_t workspaceSizeInBytes)

This function sets the cuBLAS library workspace to a user-owned device buffer, which will be used to execute all subsequent calls to the cuBLAS library functions (on the currently set stream). If the cuBLAS library workspace is not set, all kernels will use the default workspace pool allocated during the cuBLAS context creation. In particular, this routine can be used to change the workspace between kernel launches. The workspace pointer has to be aligned to at least 256 bytes, otherwise CUBLAS_STATUS_INVALID_VALUE error is returned. The cublasSetStream() function unconditionally resets the cuBLAS library workspace back to the default workspace pool. Too small workspaceSizeInBytes may cause some routines to fail with CUBLAS_STATUS_ALLOC_FAILED error returned or cause large regressions in performance. Workspace size equal to or larger than 16KiB is enough to prevent CUBLAS_STATUS_ALLOC_FAILED error, while a larger workspace can provide performance benefits for some routines. Recommended size of user-provided workspace is at least 4MiB (to match cuBLAS’ default workspace pool).

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The stream was set successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

The workspace pointer wasn't aligned to at least 256 bytes.

2.4.9. cublasGetStream()

cublasStatus_t
cublasGetStream(cublasHandle_t handle, cudaStream_t *streamId)

This function gets the cuBLAS library stream, which is being used to execute all calls to the cuBLAS library functions. If the cuBLAS library stream is not set, all kernels use the defaultNULL stream.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The stream was returned successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

streamId == NULL

2.4.10. cublasGetPointerMode()

cublasStatus_t
cublasGetPointerMode(cublasHandle_t handle, cublasPointerMode_t *mode)

This function obtains the pointer mode used by the cuBLAS library. Please see the section on the cublasPointerMode_t type for more details.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The pointer mode was obtained successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

mode == NULL

2.4.11. cublasSetPointerMode()

cublasStatus_t
cublasSetPointerMode(cublasHandle_t handle, cublasPointerMode_t mode)

This function sets the pointer mode used by the cuBLAS library. The default is for the values to be passed by reference on the host. Please see the section on the cublasPointerMode_t type for more details.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The pointer mode was set successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

mode is not CUBLAS_POINTER_MODE_HOST or CUBLAS_POINTER_MODE_DEVICE

2.4.12. cublasSetVector()

cublasStatus_t
cublasSetVector(int n, int elemSize,
const void *x, int incx, void *y, int incy)

This function copies n elements from a vector x in host memory space to a vector y in GPU memory space. Elements in both vectors are assumed to have a size of elemSize bytes. The storage spacing between consecutive elements is given by incx for the source vector x and by incy for the destination vector y.

Since column-major format for two-dimensional matrices is assumed, if a vector is part of a matrix, a vector increment equal to 1 accesses a (partial) column of that matrix. Similarly, using an increment equal to the leading dimension of the matrix results in accesses to a (partial) row of that matrix.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters incx, incy, elemSize<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.13. cublasGetVector()

cublasStatus_t
cublasGetVector(int n, int elemSize,
const void *x, int incx, void *y, int incy)

This function copies n elements from a vector x in GPU memory space to a vector y in host memory space. Elements in both vectors are assumed to have a size of elemSize bytes. The storage spacing between consecutive elements is given by incx for the source vector and incy for the destination vector y.

Since column-major format for two-dimensional matrices is assumed, if a vector is part of a matrix, a vector increment equal to 1 accesses a (partial) column of that matrix. Similarly, using an increment equal to the leading dimension of the matrix results in accesses to a (partial) row of that matrix.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters incx, incy, elemSize<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.14. cublasSetMatrix()

cublasStatus_t
cublasSetMatrix(int rows, int cols, int elemSize,
const void *A, int lda, void *B, int ldb)

This function copies a tile of rows x cols elements from a matrix A in host memory space to a matrix B in GPU memory space. It is assumed that each element requires storage of elemSize bytes and that both matrices are stored in column-major format, with the leading dimension of the source matrix A and destination matrix B given in lda and ldb, respectively. The leading dimension indicates the number of rows of the allocated matrix, even if only a submatrix of it is being used.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters rows, cols<0 or elemSize, lda, ldb<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.15. cublasGetMatrix()

cublasStatus_t
cublasGetMatrix(int rows, int cols, int elemSize,
const void *A, int lda, void *B, int ldb)

This function copies a tile of rows x cols elements from a matrix A in GPU memory space to a matrix B in host memory space. It is assumed that each element requires storage of elemSize bytes and that both matrices are stored in column-major format, with the leading dimension of the source matrix A and destination matrix B given in lda and ldb, respectively. The leading dimension indicates the number of rows of the allocated matrix, even if only a submatrix of it is being used.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters rows, cols<0 or elemSize, lda, ldb<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.16. cublasSetVectorAsync()

cublasStatus_t
cublasSetVectorAsync(int n, int elemSize, const void *hostPtr, int incx,
void *devicePtr, int incy, cudaStream_t stream)

This function has the same functionality as cublasSetVector(), with the exception that the data transfer is done asynchronously (with respect to the host) using the given CUDA stream parameter.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters incx, incy, elemSize<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.17. cublasGetVectorAsync()

cublasStatus_t
cublasGetVectorAsync(int n, int elemSize, const void *devicePtr, int incx,
void *hostPtr, int incy, cudaStream_t stream)

This function has the same functionality as cublasGetVector(), with the exception that the data transfer is done asynchronously (with respect to the host) using the given CUDA stream parameter.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters incx, incy, elemSize<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.18. cublasSetMatrixAsync()

cublasStatus_t
cublasSetMatrixAsync(int rows, int cols, int elemSize, const void *A,
int lda, void *B, int ldb, cudaStream_t stream)

This function has the same functionality as cublasSetMatrix(), with the exception that the data transfer is done asynchronously (with respect to the host) using the given CUDA stream parameter.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters rows, cols<0 or elemSize, lda, ldb<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.19. cublasGetMatrixAsync()

cublasStatus_t
cublasGetMatrixAsync(int rows, int cols, int elemSize, const void *A,
int lda, void *B, int ldb, cudaStream_t stream)

This function has the same functionality as cublasGetMatrix(), with the exception that the data transfer is done asynchronously (with respect to the host) using the given CUDA stream parameter.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

The parameters rows, cols<0 or elemSize, lda, ldb<=0.

CUBLAS_STATUS_MAPPING_ERROR

There was an error accessing GPU memory.

2.4.20. cublasSetAtomicsMode()

cublasStatus_t cublasSetAtomicsMode(cublasHandlet handle, cublasAtomicsMode_t mode)

Some routines like cublas<t>symv and cublas<t>hemv have an alternate implementation that uses atomics to cumulate results. This implementation is generally significantly faster but can generate results that are not strictly identical from one run to the others. Mathematically, those different results are not significant but when debugging those differences can be prejudicial.

This function allows or disallows the usage of atomics in the cuBLAS library for all routines which have an alternate implementation. When not explicitly specified in the documentation of any cuBLAS routine, it means that this routine does not have an alternate implementation that use atomics. When atomics mode is disabled, each cuBLAS routine should produce the same results from one run to the other when called with identical parameters on the same hardware.

The default atomics mode of default initialized cublasHandle_t object is CUBLAS_ATOMICS_NOT_ALLOWED. Please see the section on the type for more details.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The atomics mode was set successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.21. cublasGetAtomicsMode()

cublasStatus_t cublasGetAtomicsMode(cublasHandle_t handle, cublasAtomicsMode_t *mode)

This function queries the atomic mode of a specific cuBLAS context.

The default atomics mode of default initialized cublasHandle_t object is CUBLAS_ATOMICS_NOT_ALLOWED. Please see the section on the type for more details.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The atomics mode was queried successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE The argument mode is a NULL pointer.

2.4.22. cublasSetMathMode()

cublasStatus_t cublasSetMathMode(cublasHandle_t handle, cublasMath_t mode)

The cublasSetMathMode function enables you to choose the compute precision modes as defined by cublasMath_t (refer to cublasMath_t). Users are allowed to set the compute precision mode as a logical combination of them (except the deprecated CUBLAS_TENSOR_OP_MATH). For example, cublasSetMathMode(handle, CUBLAS_DEFAULT_MATH | CUBLAS_MATH_DISALLOW_REDUCED_PRECISION_REDUCTION). Note that the default math mode is CUBLAS_DEFAULT_MATH.

For matrix and compute precisions allowed for cublasGemmEx() and cublasLtMatmul() APIs and their strided variants please refer to: cublasGemmEx() , cublasGemmBatchedEx(), cublasGemmStridedBatchedEx()and cublasLtMatmul().

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The math mode was set successfully.

CUBLAS_STATUS_INVALID_VALUE

An invalid value for mode was specified.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.23. cublasGetMathMode()

cublasStatus_t cublasGetMathMode(cublasHandle_t handle, cublasMath_t *mode)

This function returns the math mode used by the library routines.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

The math type was returned successfully.

CUBLAS_STATUS_INVALID_VALUE

If mode is NULL.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.24. cublasSetSmCountTarget()

cublasStatus_t cublasSetSmCountTarget(cublasHandle_t handle, int smCountTarget)

The cublasSetSmCountTarget function allows overriding the number of multiprocessors available to the library during kernels execution.

This option can be used to improve the library performance when cuBLAS routines are known to run concurrently with other work on different CUDA streams. E.g. a NVIDIA A100 GPU has 108 SM and there is a concurrent kenrel running with grid size of 8, one can use cublasSetSmCountTarget with value 100 to override the library heuristics to optimize for running on 100 multiprocessors.

When set to 0 the library returns to its default behavior. The input value should not exceed the device's multiprocessor count, which can be obtained using cudaDeviceGetAttribute. Negative values are not accepted.

The user must ensure thread safety when modifying the library handle with this routine similar to when using cublasSetStream, and so on.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

SM count target was set successfully.

CUBLAS_STATUS_INVALID_VALUE

The value of smCountTarget outside of the allowed range.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.25. cublasGetSmCountTarget()

cublasStatus_t cublasGetSmCountTarget(cublasHandle_t handle, int *smCountTarget)

This function obtains the value previously programmed to the library handle.

Return Value Meaning

CUBLAS_STATUS_SUCCESS

SM count target was set successfully.

CUBLAS_STATUS_INVALID_VALUE

smCountTarget is NULL.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

2.4.26. cublasLoggerConfigure()

cublasStatus_t cublasLoggerConfigure(
int             logIsOn,
int             logToStdOut,
int             logToStdErr,
const char*     logFileName)

This function configures logging during runtime. Besides this type of configuration, it is possible to configure logging with special environment variables which will be checked by libcublas:

• CUBLAS_LOGINFO_DBG - Setup env. variable to "1" means turn on logging (by default, logging is off).
• CUBLAS_LOGDEST_DBG - Setup env. variable encodes how to log. "stdout", "stderr" means to output log messages to stdout or stderr, respectively. In the other case, its specifies "filename" of file.

Parameters

logIsOn

Input. Turn on/off logging completely. By default is off, but is turned on by calling cublasSetLoggerCallback to user defined callback function.

logToStdOut

Input. Turn on/off logging to standard error I/O stream. By default is off.

logToStdErr

Input. Turn on/off logging to standard error I/O stream. By default is off.

logFileName

Input. Turn on/off logging to file in filesystem specified by its name. cublasLoggerConfigure copies content of logFileName. You should provide a null pointer if you're not interested in this type of logging.

Returns

CUBLAS_STATUS_SUCCESS

Success.

2.4.27. cublasGetLoggerCallback()

cublasStatus_t cublasGetLoggerCallback(
cublasLogCallback* userCallback)

This function retrieves function pointer to previously installed custom user defined callback function via cublasSetLoggerCallback() or zero otherwise.

Parameters

userCallback

Output. Pointer to user defined callback function.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_INVALID_VALUE

userCallback is NULL.

2.4.28. cublasSetLoggerCallback()

cublasStatus_t cublasSetLoggerCallback(
cublasLogCallback   userCallback)

This function installs a custom user-defined callback function via cuBLAS C public API.

Parameters

userCallback

Input. Pointer to user defined callback function.

Returns

CUBLAS_STATUS_SUCCESS

Success.

2.5. cuBLAS Level-1 Function Reference

This section describes the Level-1 Basic Linear Algebra Subprograms (BLAS1) functions that perform scalar and vector-based operations. We will use abbreviations <type> for type and <t> for the corresponding short type to make a more concise and clear presentation of the implemented functions. Unless otherwise specified <type> and <t> have the following meanings:

<type> <t> Meaning

float

‘s’ or ‘S’

Real single-precision.

double

‘d’ or ‘D’

Real double-precision.

cuComplex

‘c’ or ‘C’

Complex single-precision.

cuDoubleComplex

‘z’ or ‘Z’

Complex double-precision.

When the parameters and returned values of the function differ, which sometimes happens for complex input, the <t> can also have the following meanings ‘Sc’, ‘Cs’, ‘Dz’ and ‘Zd’.

The abbreviation Re(.) and Im(.) will stand for the real and imaginary part of a number, respectively. Since the imaginary part of a real number does not exist, we will consider it to be zero, and can usually discard it from the equation where it is being used. Also, the $\stackrel{̄}{\alpha }$ will denote the complex conjugate of $\alpha$ .

In general throughout the documentation, the lowercase Greek symbols $\alpha$ and $\beta$ denote scalars, lowercase English letters in bold type $x$ and $y$ denote vectors and capital English letters $A$ , $B$ and $C$ denote matrices.

2.5.1. cublasI<t>amax()

cublasStatus_t cublasIsamax(cublasHandle_t handle, int n,
const float *x, int incx, int *result)
cublasStatus_t cublasIdamax(cublasHandle_t handle, int n,
const double *x, int incx, int *result)
cublasStatus_t cublasIcamax(cublasHandle_t handle, int n,
const cuComplex *x, int incx, int *result)
cublasStatus_t cublasIzamax(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx, int *result)

This function finds the (smallest) index of the element of the maximum magnitude. Hence, the result is the first $i$ such that $|Im\left(x\left[j\right]\right)|+|Re\left(x\left[j\right]\right)|$ is maximum for $i=1,\dots ,n$ and . Notice that the last equation reflects 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x.

x

device

input

<type> vector with elements.

incx

input

Stride between consecutive elements of x.

result

host or device

output

The resulting index, which is 0 if n,incx<=0.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_ALLOC_FAILED

The reduction buffer could not be allocated.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

CUBLAS_STATUS_INVALID_VALUE

result is NULL.

For references. refer to:

2.5.2. cublasI<t>amin()

cublasStatus_t cublasIsamin(cublasHandle_t handle, int n,
const float *x, int incx, int *result)
cublasStatus_t cublasIdamin(cublasHandle_t handle, int n,
const double *x, int incx, int *result)
cublasStatus_t cublasIcamin(cublasHandle_t handle, int n,
const cuComplex *x, int incx, int *result)
cublasStatus_t cublasIzamin(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx, int *result)

This function finds the (smallest) index of the element of the minimum magnitude. Hence, the result is the first $i$ such that $|Im\left(x\left[j\right]\right)|+|Re\left(x\left[j\right]\right)|$ is minimum for $i=1,\dots ,n$ and Notice that the last equation reflects 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x.

x

device

input

<type> vector with elements.

incx

input

Stride between consecutive elements of x.

result

host or device

output

The resulting index, which is 0 if n,incx<=0.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_ALLOC_FAILED

The reduction buffer could not be allocated.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

CUBLAS_STATUS_INVALID_VALUE

result is NULL.

isamin

2.5.3. cublas<t>asum()

cublasStatus_t  cublasSasum(cublasHandle_t handle, int n,
const float           *x, int incx, float  *result)
cublasStatus_t  cublasDasum(cublasHandle_t handle, int n,
const double          *x, int incx, double *result)
cublasStatus_t cublasScasum(cublasHandle_t handle, int n,
const cuComplex       *x, int incx, float  *result)
cublasStatus_t cublasDzasum(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx, double *result)

This function computes the sum of the absolute values of the elements of vector x. Hence, the result is ${\sum }_{i=1}^{n}|Im\left(x\left[j\right]\right)|+|Re\left(x\left[j\right]\right)|$ where . Notice that the last equation reflects 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x.

x

device

input

<type> vector with elements.

incx

input

Stride between consecutive elements of x.

result

host or device

output

The resulting index, which is 0.0 if n,incx<=0.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_ALLOC_FAILED

The reduction buffer could not be allocated.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

CUBLAS_STATUS_INVALID_VALUE

result is NULL.

2.5.4. cublas<t>axpy()

cublasStatus_t cublasSaxpy(cublasHandle_t handle, int n,
const float           *alpha,
const float           *x, int incx,
float                 *y, int incy)
cublasStatus_t cublasDaxpy(cublasHandle_t handle, int n,
const double          *alpha,
const double          *x, int incx,
double                *y, int incy)
cublasStatus_t cublasCaxpy(cublasHandle_t handle, int n,
const cuComplex       *alpha,
const cuComplex       *x, int incx,
cuComplex             *y, int incy)
cublasStatus_t cublasZaxpy(cublasHandle_t handle, int n,
const cuDoubleComplex *alpha,
const cuDoubleComplex *x, int incx,
cuDoubleComplex       *y, int incy)

This function multiplies the vector x by the scalar $\alpha$ and adds it to the vector y overwriting the latest vector with the result. Hence, the performed operation is $y\left[j\right]=\alpha ×x\left[k\right]+y\left[j\right]$ for $i=1,\dots ,n$ , and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

alpha

host or device

input

<type> scalar used for multiplication.

n

input

Number of elements in the vector x and y.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.5. cublas<t>copy()

cublasStatus_t cublasScopy(cublasHandle_t handle, int n,
const float           *x, int incx,
float                 *y, int incy)
cublasStatus_t cublasDcopy(cublasHandle_t handle, int n,
const double          *x, int incx,
double                *y, int incy)
cublasStatus_t cublasCcopy(cublasHandle_t handle, int n,
const cuComplex       *x, int incx,
cuComplex             *y, int incy)
cublasStatus_t cublasZcopy(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx,
cuDoubleComplex       *y, int incy)

This function copies the vector x into the vector y. Hence, the performed operation is $y\left[j\right]=x\left[k\right]$ for $i=1,\dots ,n$ , and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x and y.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

output

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.6. cublas<t>dot()

cublasStatus_t cublasSdot (cublasHandle_t handle, int n,
const float           *x, int incx,
const float           *y, int incy,
float           *result)
cublasStatus_t cublasDdot (cublasHandle_t handle, int n,
const double          *x, int incx,
const double          *y, int incy,
double          *result)
cublasStatus_t cublasCdotu(cublasHandle_t handle, int n,
const cuComplex       *x, int incx,
const cuComplex       *y, int incy,
cuComplex       *result)
cublasStatus_t cublasCdotc(cublasHandle_t handle, int n,
const cuComplex       *x, int incx,
const cuComplex       *y, int incy,
cuComplex       *result)
cublasStatus_t cublasZdotu(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *y, int incy,
cuDoubleComplex *result)
cublasStatus_t cublasZdotc(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *y, int incy,
cuDoubleComplex       *result)

This function computes the dot product of vectors x and y. Hence, the result is ${\sum }_{i=1}^{n}\left(x\left[k\right]×y\left[j\right]\right)$ where and . Notice that in the first equation the conjugate of the element of vector x should be used if the function name ends in character ‘c’ and that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vectors x and y.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

input

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

result

host or device

output

The resulting dot product, which is 0.0 if n<=0.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_ALLOC_FAILED

The reduction buffer could not be allocated.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.7. cublas<t>nrm2()

cublasStatus_t  cublasSnrm2(cublasHandle_t handle, int n,
const float           *x, int incx, float  *result)
cublasStatus_t  cublasDnrm2(cublasHandle_t handle, int n,
const double          *x, int incx, double *result)
cublasStatus_t cublasScnrm2(cublasHandle_t handle, int n,
const cuComplex       *x, int incx, float  *result)
cublasStatus_t cublasDznrm2(cublasHandle_t handle, int n,
const cuDoubleComplex *x, int incx, double *result)

This function computes the Euclidean norm of the vector x. The code uses a multiphase model of accumulation to avoid intermediate underflow and overflow, with the result being equivalent to $\sqrt{{\sum }_{i=1}^{n}\left(x\left[j\right]×x\left[j\right]\right)}$ where in exact arithmetic. Notice that the last equation reflects 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

result

host or device

output

The resulting norm, which is 0.0 if n,incx<=0.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_ALLOC_FAILED

The reduction buffer could not be allocated.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

CUBLAS_STATUS_INVALID_VALUE

result is NULL.

snrm2, snrm2, dnrm2, dnrm2, scnrm2, scnrm2, dznrm2

2.5.8. cublas<t>rot()

cublasStatus_t  cublasSrot(cublasHandle_t handle, int n,
float           *x, int incx,
float           *y, int incy,
const float  *c, const float           *s)
cublasStatus_t  cublasDrot(cublasHandle_t handle, int n,
double          *x, int incx,
double          *y, int incy,
const double *c, const double          *s)
cublasStatus_t  cublasCrot(cublasHandle_t handle, int n,
cuComplex       *x, int incx,
cuComplex       *y, int incy,
const float  *c, const cuComplex       *s)
cublasStatus_t cublasCsrot(cublasHandle_t handle, int n,
cuComplex       *x, int incx,
cuComplex       *y, int incy,
const float  *c, const float           *s)
cublasStatus_t  cublasZrot(cublasHandle_t handle, int n,
cuDoubleComplex *x, int incx,
cuDoubleComplex *y, int incy,
const double *c, const cuDoubleComplex *s)
cublasStatus_t cublasZdrot(cublasHandle_t handle, int n,
cuDoubleComplex *x, int incx,
cuDoubleComplex *y, int incy,
const double *c, const double          *s)

This function applies Givens rotation matrix (that is, rotation in the x,y plane counter-clockwise by angle defined by cos(alpha)=c, sin(alpha)=s):

$G=\left(\begin{array}{cc}\hfill c\hfill & \hfill s\hfill \\ \hfill -s\hfill & \hfill c\hfill \end{array}\right)$

to vectors x and y.

Hence, the result is $x\left[k\right]=c×x\left[k\right]+s×y\left[j\right]$ and $y\left[j\right]=-s×x\left[k\right]+c×y\left[j\right]$ where and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vectors x and y.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

c

host or device

input

Cosine element of the rotation matrix.

s

host or device

input

Sine element of the rotation matrix.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.9. cublas<t>rotg()

cublasStatus_t cublasSrotg(cublasHandle_t handle,
float           *a, float           *b,
float  *c, float           *s)
cublasStatus_t cublasDrotg(cublasHandle_t handle,
double          *a, double          *b,
double *c, double          *s)
cublasStatus_t cublasCrotg(cublasHandle_t handle,
cuComplex       *a, cuComplex       *b,
float  *c, cuComplex       *s)
cublasStatus_t cublasZrotg(cublasHandle_t handle,
cuDoubleComplex *a, cuDoubleComplex *b,
double *c, cuDoubleComplex *s)

This function constructs the Givens rotation matrix

$G=\left(\begin{array}{cc}\hfill c\hfill & \hfill s\hfill \\ \hfill -s\hfill & \hfill c\hfill \end{array}\right)$

that zeros out the second entry of a $2×1$ vector ${\left(a,b\right)}^{T}$ .

Then, for real numbers we can write

$\left(\begin{array}{cc}\hfill c\hfill & \hfill s\hfill \\ \hfill -s\hfill & \hfill c\hfill \end{array}\right)\left(\begin{array}{c}\hfill a\hfill \\ \hfill b\hfill \end{array}\right)=\left(\begin{array}{c}\hfill r\hfill \\ \hfill 0\hfill \end{array}\right)$

where ${c}^{2}+{s}^{2}=1$ and $r={a}^{2}+{b}^{2}$ . The parameters $a$ and $b$ are overwritten with $r$ and $z$ , respectively. The value of $z$ is such that $c$ and $s$ may be recovered using the following rules:

For complex numbers we can write

$\left(\begin{array}{cc}\hfill c\hfill & \hfill s\hfill \\ \hfill -\stackrel{̄}{s}\hfill & \hfill c\hfill \end{array}\right)\left(\begin{array}{c}\hfill a\hfill \\ \hfill b\hfill \end{array}\right)=\left(\begin{array}{c}\hfill r\hfill \\ \hfill 0\hfill \end{array}\right)$

where ${c}^{2}+\left(\stackrel{̄}{s}×s\right)=1$ and $r=\frac{a}{|a|}×\parallel {\left(a,b\right)}^{T}{\parallel }_{2}$ with $\parallel {\left(a,b\right)}^{T}{\parallel }_{2}=\sqrt{|a{|}^{2}+|b{|}^{2}}$ for $a\ne 0$ and $r=b$ for $a=0$ . Finally, the parameter $a$ is overwritten with $r$ on exit.

Param. Memory In/out Meaning

handle

input

Hhandle to the cuBLAS library context.

a

host or device

in/out

<type> scalar that is overwritten with $r$ .

b

host or device

in/out

<type> scalar that is overwritten with $z$ .

c

host or device

output

Cosine element of the rotation matrix.

s

host or device

output

Sine element of the rotation matrix.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.10. cublas<t>rotm()

cublasStatus_t cublasSrotm(cublasHandle_t handle, int n, float  *x, int incx,
float  *y, int incy, const float*  param)
cublasStatus_t cublasDrotm(cublasHandle_t handle, int n, double *x, int incx,
double *y, int incy, const double* param)

This function applies the modified Givens transformation

$H=\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

to vectors x and y.

Hence, the result is $x\left[k\right]={h}_{11}×x\left[k\right]+{h}_{12}×y\left[j\right]$ and $y\left[j\right]={h}_{21}×x\left[k\right]+{h}_{22}×y\left[j\right]$ where and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

The elements , , and of matrix $H$ are stored in param[1], param[2], param[3] and param[4], respectively. The flag=param[0] defines the following predefined values for the matrix $H$ entries

flag=-1.0 flag= 0.0 flag= 1.0 flag=-2.0

$\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill 1.0\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill 1.0\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill 1.0\hfill \\ \hfill -1.0\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill 1.0\hfill & \hfill 0.0\hfill \\ \hfill 0.0\hfill & \hfill 1.0\hfill \end{array}\right)$

Notice that the values -1.0, 0.0 and 1.0 implied by the flag are not stored in param.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vectors x and y.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

param

host or device

input

<type> vector of 5 elements, where param[0] and param[1-4] contain the flag and matrix $H$ .

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.11. cublas<t>rotmg()

cublasStatus_t cublasSrotmg(cublasHandle_t handle, float  *d1, float  *d2,
float  *x1, const float  *y1, float  *param)
cublasStatus_t cublasDrotmg(cublasHandle_t handle, double *d1, double *d2,
double *x1, const double *y1, double *param)

This function constructs the modified Givens transformation

$H=\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

that zeros out the second entry of a $2×1$ vector ${\left(\sqrt{d1}*x1,\sqrt{d2}*y1\right)}^{T}$ .

The flag=param[0] defines the following predefined values for the matrix $H$ entries

flag=-1.0 flag= 0.0 flag= 1.0 flag=-2.0

$\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill 1.0\hfill & \hfill {h}_{12}\hfill \\ \hfill {h}_{21}\hfill & \hfill 1.0\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill {h}_{11}\hfill & \hfill 1.0\hfill \\ \hfill -1.0\hfill & \hfill {h}_{22}\hfill \end{array}\right)$

$\left(\begin{array}{cc}\hfill 1.0\hfill & \hfill 0.0\hfill \\ \hfill 0.0\hfill & \hfill 1.0\hfill \end{array}\right)$

Note that the values -1.0, 0.0 and 1.0 implied by the flag are not stored in param.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

d1

host or device

in/out

<type> scalar that is overwritten on exit.

d2

host or device

in/out

<type> scalar that is overwritten on exit.

x1

host or device

in/out

<type> scalar that is overwritten on exit.

y1

host or device

input

<type> scalar.

param

host or device

output

<type> vector of 5 elements, where param[0] and param[1-4] contain the flag and matrix $H$ .

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.12. cublas<t>scal()

cublasStatus_t  cublasSscal(cublasHandle_t handle, int n,
const float           *alpha,
float           *x, int incx)
cublasStatus_t  cublasDscal(cublasHandle_t handle, int n,
const double          *alpha,
double          *x, int incx)
cublasStatus_t  cublasCscal(cublasHandle_t handle, int n,
const cuComplex       *alpha,
cuComplex       *x, int incx)
cublasStatus_t cublasCsscal(cublasHandle_t handle, int n,
const float           *alpha,
cuComplex       *x, int incx)
cublasStatus_t  cublasZscal(cublasHandle_t handle, int n,
const cuDoubleComplex *alpha,
cuDoubleComplex *x, int incx)
cublasStatus_t cublasZdscal(cublasHandle_t handle, int n,
const double          *alpha,
cuDoubleComplex *x, int incx)

This function scales the vector x by the scalar $\alpha$ and overwrites it with the result. Hence, the performed operation is $x\left[j\right]=\alpha ×x\left[j\right]$ for $i=1,\dots ,n$ and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

alpha

host or device

input

<type> scalar used for multiplication.

n

input

Number of elements in the vector x.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.5.13. cublas<t>swap()

cublasStatus_t cublasSswap(cublasHandle_t handle, int n, float           *x,
int incx, float           *y, int incy)
cublasStatus_t cublasDswap(cublasHandle_t handle, int n, double          *x,
int incx, double          *y, int incy)
cublasStatus_t cublasCswap(cublasHandle_t handle, int n, cuComplex       *x,
int incx, cuComplex       *y, int incy)
cublasStatus_t cublasZswap(cublasHandle_t handle, int n, cuDoubleComplex *x,
int incx, cuDoubleComplex *y, int incy)

This function interchanges the elements of vector x and y. Hence, the performed operation is $y\left[j\right]⇔x\left[k\right]$ for $i=1,\dots ,n$ , and . Notice that the last two equations reflect 1-based indexing used for compatibility with Fortran.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

n

input

Number of elements in the vector x and y.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6. cuBLAS Level-2 Function Reference

This section describes the Level-2 Basic Linear Algebra Subprograms (BLAS2) functions that perform matrix-vector operations.

2.6.1. cublas<t>gbmv()

cublasStatus_t cublasSgbmv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n, int kl, int ku,
const float           *alpha,
const float           *A, int lda,
const float           *x, int incx,
const float           *beta,
float           *y, int incy)
cublasStatus_t cublasDgbmv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n, int kl, int ku,
const double          *alpha,
const double          *A, int lda,
const double          *x, int incx,
const double          *beta,
double          *y, int incy)
cublasStatus_t cublasCgbmv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n, int kl, int ku,
const cuComplex       *alpha,
const cuComplex       *A, int lda,
const cuComplex       *x, int incx,
const cuComplex       *beta,
cuComplex       *y, int incy)
cublasStatus_t cublasZgbmv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n, int kl, int ku,
const cuDoubleComplex *alpha,
const cuDoubleComplex *A, int lda,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *beta,
cuDoubleComplex *y, int incy)

This function performs the banded matrix-vector multiplication

where $A$ is a banded matrix with $kl$ subdiagonals and $ku$ superdiagonals, $x$ and $y$ are vectors, and $\alpha$ and $\beta$ are scalars. Also, for matrix $A$

The banded matrix $A$ is stored column by column, with the main diagonal stored in row $ku+1$ (starting in first position), the first superdiagonal stored in row $ku$ (starting in second position), the first subdiagonal stored in row $ku+2$ (starting in first position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(ku+1+i-j,j) for $j=1,\dots ,n$ and $i\in \left[max\left(1,j-ku\right),min\left(m,j+kl\right)\right]$ . Also, the elements in the array $A$ that do not conceptually correspond to the elements in the banded matrix (the top left $ku×ku$ and bottom right $kl×kl$ triangles) are not referenced.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

trans

input

Operation op(A) that is non- or (conj.) transpose.

m

input

Number of rows of matrix A.

n

input

Number of columns of matrix A.

kl

input

Number of subdiagonals of matrix A.

ku

input

Number of superdiagonals of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

A

device

input

<type> array of dimension lda x n with lda>=kl+ku+1.

lda

input

Leading dimension of two-dimensional array used to store matrix A.

x

device

input

<type> vector with n elements if transa == CUBLAS_OP_N and m elements otherwise.

incx

input

Stride between consecutive elements of x.

beta

host or device

input

<type> scalar used for multiplication, if beta == 0 then y does not have to be a valid input.

y

device

in/out

<type> vector with m elements if transa == CUBLAS_OP_N and n elements otherwise.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If m, n, kl, ku < 0 or

• if lda < (kl+ku+1) or

• if incx, incy == 0 or

• if trans != CUBLAS_OP_N, CUBLAS_OP_T, CUBLAS_OP_C or

• alpha, beta == NULL

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.2. cublas<t>gemv()

cublasStatus_t cublasSgemv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n,
const float           *alpha,
const float           *A, int lda,
const float           *x, int incx,
const float           *beta,
float           *y, int incy)
cublasStatus_t cublasDgemv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n,
const double          *alpha,
const double          *A, int lda,
const double          *x, int incx,
const double          *beta,
double          *y, int incy)
cublasStatus_t cublasCgemv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n,
const cuComplex       *alpha,
const cuComplex       *A, int lda,
const cuComplex       *x, int incx,
const cuComplex       *beta,
cuComplex       *y, int incy)
cublasStatus_t cublasZgemv(cublasHandle_t handle, cublasOperation_t trans,
int m, int n,
const cuDoubleComplex *alpha,
const cuDoubleComplex *A, int lda,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *beta,
cuDoubleComplex *y, int incy)

This function performs the matrix-vector multiplication

$\mathbf{\text{y}}=\alpha \text{op}\left(A\right)\mathbf{\text{x}}+\beta \mathbf{\text{y}}$

where $A$ is a $m×n$ matrix stored in column-major format, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ and $\beta$ are scalars. Also, for matrix $A$

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

trans

input

Operation op(A) that is non- or (conj.) transpose.

m

input

Number of rows of matrix A.

n

input

Number of columns of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

A

device

input

<type> array of dimension lda x n with lda >= max(1,m). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

lda

input

Leading dimension of two-dimensional array used to store matrix A. lda must be at least max(1,m).

x

device

input

<type> vector at least (1+(n-1)*abs(incx)) elements if transa==CUBLAS_OP_N and at least (1+(m-1)*abs(incx)) elements otherwise.

incx

input

Stride between consecutive elements of x.

beta

host or device

input

<type> scalar used for multiplication, if beta==0 then y does not have to be a valid input.

y

device

in/out

<type> vector at least (1+(m-1)*abs(incy)) elements if transa==CUBLAS_OP_N and at least (1+(n-1)*abs(incy)) elements otherwise.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

The parameters m,n<0 or incx,incy=0.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.3. cublas<t>ger()

cublasStatus_t  cublasSger(cublasHandle_t handle, int m, int n,
const float           *alpha,
const float           *x, int incx,
const float           *y, int incy,
float           *A, int lda)
cublasStatus_t  cublasDger(cublasHandle_t handle, int m, int n,
const double          *alpha,
const double          *x, int incx,
const double          *y, int incy,
double          *A, int lda)
cublasStatus_t cublasCgeru(cublasHandle_t handle, int m, int n,
const cuComplex       *alpha,
const cuComplex       *x, int incx,
const cuComplex       *y, int incy,
cuComplex       *A, int lda)
cublasStatus_t cublasCgerc(cublasHandle_t handle, int m, int n,
const cuComplex       *alpha,
const cuComplex       *x, int incx,
const cuComplex       *y, int incy,
cuComplex       *A, int lda)
cublasStatus_t cublasZgeru(cublasHandle_t handle, int m, int n,
const cuDoubleComplex *alpha,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *y, int incy,
cuDoubleComplex *A, int lda)
cublasStatus_t cublasZgerc(cublasHandle_t handle, int m, int n,
const cuDoubleComplex *alpha,
const cuDoubleComplex *x, int incx,
const cuDoubleComplex *y, int incy,
cuDoubleComplex *A, int lda)

This function performs the rank-1 update

where $A$ is a $m×n$ matrix stored in column-major format, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ is a scalar.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

m

input

Number of rows of matrix A.

n

input

Number of columns of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

x

device

input

<type> vector with m elements.

incx

input

Stride between consecutive elements of x.

y

device

input

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

A

device

in/out

<type> array of dimension lda x n with lda >= max(1,m).

lda

input

Leading dimension of two-dimensional array used to store matrix A.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If m < 0 or n < 0

• if incx = 0 or incy = 0 or

• if alpha == NULL or

• lda < max(1, m)

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.4. cublas<t>sbmv()

cublasStatus_t cublasSsbmv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, int k, const float  *alpha,
const float  *A, int lda,
const float  *x, int incx,
const float  *beta, float *y, int incy)
cublasStatus_t cublasDsbmv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, int k, const double *alpha,
const double *A, int lda,
const double *x, int incx,
const double *beta, double *y, int incy)

This function performs the symmetric banded matrix-vector multiplication

$\mathbf{\text{y}}=\alpha A\mathbf{\text{x}}+\beta \mathbf{\text{y}}$

where $A$ is a $n×n$ symmetric banded matrix with $k$ subdiagonals and superdiagonals, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ and $\beta$ are scalars.

If uplo == CUBLAS_FILL_MODE_LOWER then the symmetric banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row 1, the first subdiagonal in row 2 (starting at first position), the second subdiagonal in row 3 (starting at first position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+i-j,j) for $j=1,\dots ,n$ and $i\in \left[j,min\left(m,j+k\right)\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the bottom right $k×k$ triangle) are not referenced.

If uplo == CUBLAS_FILL_MODE_UPPER then the symmetric banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row k+1, the first superdiagonal in row k (starting at second position), the second superdiagonal in row k-1 (starting at third position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+k+i-j,j) for $j=1,\dots ,n$ and $i\in \left[max\left(1,j-k\right),j\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the top left $k×k$ triangle) are not referenced.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix A lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix A.

k

input

Number of sub- and super-diagonals of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

A

device

input

<type> array of dimension lda x n with \lda >= k+1.

lda

input

Leading dimension of two-dimensional array used to store matrix A.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

beta

host or device

input

<type> scalar used for multiplication, if beta==0 then y does not have to be a valid input.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or k < 0 or

• if incx = 0 or incy = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• if alpha == NULL or beta == NULL or

• lda < (1 + k)

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.5. cublas<t>spmv()

cublasStatus_t cublasSspmv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const float  *alpha, const float  *AP,
const float  *x, int incx, const float  *beta,
float  *y, int incy)
cublasStatus_t cublasDspmv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const double *alpha, const double *AP,
const double *x, int incx, const double *beta,
double *y, int incy)

This function performs the symmetric packed matrix-vector multiplication

$\mathbf{\text{y}}=\alpha A\mathbf{\text{x}}+\beta \mathbf{\text{y}}$

where $A$ is a $n×n$ symmetric matrix stored in packed format, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ and $\beta$ are scalars.

If uplo == CUBLAS_FILL_MODE_LOWER then the elements in the lower triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+((2*n-j+1)*j)/2] for $j=1,\dots ,n$ and $i\ge j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

If uplo == CUBLAS_FILL_MODE_UPPER then the elements in the upper triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+(j*(j+1))/2] for $j=1,\dots ,n$ and $i\le j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix $A$ lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix $A$ .

alpha

host or device

input

<type> scalar used for multiplication.

AP

device

input

<type> array with $A$ stored in packed format.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

beta

host or device

input

<type> scalar used for multiplication, if beta==0 then y does not have to be a valid input.

y

device

input

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or incy = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• alpha == NULL or beta == NULL

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.6. cublas<t>spr()

cublasStatus_t cublasSspr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const float  *alpha,
const float  *x, int incx, float  *AP)
cublasStatus_t cublasDspr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const double *alpha,
const double *x, int incx, double *AP)

This function performs the packed symmetric rank-1 update

$A=\alpha \mathbf{\text{x}}{\mathbf{\text{x}}}^{T}+A$

where $A$ is a $n×n$ symmetric matrix stored in packed format, $\mathbf{x}$ is a vector, and $\alpha$ is a scalar.

If uplo == CUBLAS_FILL_MODE_LOWER then the elements in the lower triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+((2*n-j+1)*j)/2] for $j=1,\dots ,n$ and $i\ge j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

If uplo == CUBLAS_FILL_MODE_UPPER then the elements in the upper triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+(j*(j+1))/2] for $j=1,\dots ,n$ and $i\le j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix $A$ lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix $A$ .

alpha

host or device

input

<type> scalar used for multiplication.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

AP

device

in/out

<type> array with $A$ stored in packed format.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• alpha == NULL

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.7. cublas<t>spr2()

cublasStatus_t cublasSspr2(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const float  *alpha,
const float  *x, int incx,
const float  *y, int incy, float  *AP)
cublasStatus_t cublasDspr2(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const double *alpha,
const double *x, int incx,
const double *y, int incy, double *AP)

This function performs the packed symmetric rank-2 update

$A=\alpha \left(\mathbf{\text{x}}{\mathbf{\text{y}}}^{T}+\mathbf{\text{y}}{\mathbf{\text{x}}}^{T}\right)+A$

where $A$ is a $n×n$ symmetric matrix stored in packed format, $\mathbf{x}$ is a vector, and $\alpha$ is a scalar.

If uplo == CUBLAS_FILL_MODE_LOWER then the elements in the lower triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+((2*n-j+1)*j)/2] for $j=1,\dots ,n$ and $i\ge j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

If uplo == CUBLAS_FILL_MODE_UPPER then the elements in the upper triangular part of the symmetric matrix $A$ are packed together column by column without gaps, so that the element $A\left(i,j\right)$ is stored in the memory location AP[i+(j*(j+1))/2] for $j=1,\dots ,n$ and $i\le j$ . Consequently, the packed format requires only $\frac{n\left(n+1\right)}{2}$ elements for storage.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix $A$ lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix $A$ .

alpha

host or device

input

<type> scalar used for multiplication.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

input

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

AP

device

in/out

<type> array with $A$ stored in packed format.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or incy = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• alpha == NULL

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.8. cublas<t>symv()

cublasStatus_t cublasSsymv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const float           *alpha,
const float           *A, int lda,
const float           *x, int incx, const float           *beta,
float           *y, int incy)
cublasStatus_t cublasDsymv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const double          *alpha,
const double          *A, int lda,
const double          *x, int incx, const double          *beta,
double          *y, int incy)
cublasStatus_t cublasCsymv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const cuComplex       *alpha, /* host or device pointer */
const cuComplex       *A, int lda,
const cuComplex       *x, int incx, const cuComplex       *beta,
cuComplex       *y, int incy)
cublasStatus_t cublasZsymv(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const cuDoubleComplex *alpha,
const cuDoubleComplex *A, int lda,
const cuDoubleComplex *x, int incx, const cuDoubleComplex *beta,
cuDoubleComplex *y, int incy)

This function performs the symmetric matrix-vector multiplication.

$\mathbf{\text{y}}=\alpha A\mathbf{\text{x}}+\beta \mathbf{\text{y}}$

where $A$ is a $n×n$ symmetric matrix stored in lower or upper mode, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ and $\beta$ are scalars.

This function has an alternate faster implementation using atomics that can be enabled with cublasSetAtomicsMode().

Please see the section on the function cublasSetAtomicsMode() for more details about the usage of atomics.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

A

device

input

<type> array of dimension lda x n with lda>=max(1,n).

lda

input

Leading dimension of two-dimensional array used to store matrix A.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

beta

host or device

input

<type> scalar used for multiplication, if beta==0 then y does not have to be a valid input.

y

device

in/out

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or incy = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• lda < n

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.9. cublas<t>syr()

cublasStatus_t cublasSsyr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const float           *alpha,
const float           *x, int incx, float           *A, int lda)
cublasStatus_t cublasDsyr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const double          *alpha,
const double          *x, int incx, double          *A, int lda)
cublasStatus_t cublasCsyr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const cuComplex       *alpha,
const cuComplex       *x, int incx, cuComplex       *A, int lda)
cublasStatus_t cublasZsyr(cublasHandle_t handle, cublasFillMode_t uplo,
int n, const cuDoubleComplex *alpha,
const cuDoubleComplex *x, int incx, cuDoubleComplex *A, int lda)

This function performs the symmetric rank-1 update

$A=\alpha \mathbf{\text{x}}{\mathbf{\text{x}}}^{T}+A$

where $A$ is a $n×n$ symmetric matrix stored in column-major format, $\mathbf{x}$ is a vector, and $\alpha$ is a scalar.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix A lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

A

device

in/out

<type> array of dimensions lda x n, with lda>=max(1,n).

lda

input

Leading dimension of two-dimensional array used to store matrix A.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• if lda < max(1, n) or

• alpha == NULL

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.10. cublas<t>syr2()

cublasStatus_t cublasSsyr2(cublasHandle_t handle, cublasFillMode_t uplo, int n,
const float           *alpha, const float           *x, int incx,
const float           *y, int incy, float           *A, int lda
cublasStatus_t cublasDsyr2(cublasHandle_t handle, cublasFillMode_t uplo, int n,
const double          *alpha, const double          *x, int incx,
const double          *y, int incy, double          *A, int lda
cublasStatus_t cublasCsyr2(cublasHandle_t handle, cublasFillMode_t uplo, int n,
const cuComplex       *alpha, const cuComplex       *x, int incx,
const cuComplex       *y, int incy, cuComplex       *A, int lda
cublasStatus_t cublasZsyr2(cublasHandle_t handle, cublasFillMode_t uplo, int n,
const cuDoubleComplex *alpha, const cuDoubleComplex *x, int incx,
const cuDoubleComplex *y, int incy, cuDoubleComplex *A, int lda

This function performs the symmetric rank-2 update

$A=\alpha \left(\mathbf{\text{x}}{\mathbf{\text{y}}}^{T}+\mathbf{\text{y}}{\mathbf{\text{x}}}^{T}\right)+A$

where $A$ is a $n×n$ symmetric matrix stored in column-major format, $\mathbf{x}$ and $\mathbf{y}$ are vectors, and $\alpha$ is a scalar.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix A lower or upper part is stored, the other symmetric part is not referenced and is inferred from the stored elements.

n

input

Number of rows and columns of matrix A.

alpha

host or device

input

<type> scalar used for multiplication.

x

device

input

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

y

device

input

<type> vector with n elements.

incy

input

Stride between consecutive elements of y.

A

device

in/out

<type> array of dimensions lda x n, with lda>=max(1,n).

lda

input

Leading dimension of two-dimensional array used to store matrix A.

The possible error values returned by this function and their meanings are listed in the following table:

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or

• if incx = 0 or incy = 0 or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• if alpha == NULL or

• lda < max(1, n)

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.11. cublas<t>tbmv()

cublasStatus_t cublasStbmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const float           *A, int lda,
float           *x, int incx)
cublasStatus_t cublasDtbmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const double          *A, int lda,
double          *x, int incx)
cublasStatus_t cublasCtbmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const cuComplex       *A, int lda,
cuComplex       *x, int incx)
cublasStatus_t cublasZtbmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const cuDoubleComplex *A, int lda,
cuDoubleComplex *x, int incx)

This function performs the triangular banded matrix-vector multiplication

$\mathbf{\text{x}}=\text{op}\left(A\right)\mathbf{\text{x}}$

where $A$ is a triangular banded matrix, and $\mathbf{x}$ is a vector. Also, for matrix $A$

If uplo == CUBLAS_FILL_MODE_LOWER then the triangular banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row 1, the first subdiagonal in row 2 (starting at first position), the second subdiagonal in row 3 (starting at first position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+i-j,j) for $j=1,\dots ,n$ and $i\in \left[j,min\left(m,j+k\right)\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the bottom right $k×k$ triangle) are not referenced.

If uplo == CUBLAS_FILL_MODE_UPPER then the triangular banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row k+1, the first superdiagonal in row k (starting at second position), the second superdiagonal in row k-1 (starting at third position), and so on. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+k+i-j,j) for $j=1,\dots ,n$ and $i\in \left[max\left(1,j-k,j\right)\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the top left $k×k$ triangle) are not referenced.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix A lower or upper part is stored, the other part is not referenced and is inferred from the stored elements.

trans

input

Operation op(A) that is non- or (conj.) transpose.

diag

input

Indicates if the elements on the main diagonal of matrix A are unity and should not be accessed.

n

input

Number of rows and columns of matrix A.

k

input

Number of sub- and super-diagonals of matrix .

A

device

input

<type> array of dimension lda x n, with lda>=k+1.

lda

input

Leading dimension of two-dimensional array used to store matrix A.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or k < 0 or

• if incx = 0 or

• if trans != CUBLAS_OP_N, CUBLAS_OP_C, CUBLAS_OP_T or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• if diag != CUBLAS_DIAG_UNIT, CUBLAS_DIAG_NON_UNIT or

• lda < (1 + k)

CUBLAS_STATUS_ALLOC_FAILED

The allocation of internal scratch memory failed.

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.12. cublas<t>tbsv()

cublasStatus_t cublasStbsv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const float           *A, int lda,
float           *x, int incx)
cublasStatus_t cublasDtbsv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const double          *A, int lda,
double          *x, int incx)
cublasStatus_t cublasCtbsv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const cuComplex       *A, int lda,
cuComplex       *x, int incx)
cublasStatus_t cublasZtbsv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, int k, const cuDoubleComplex *A, int lda,
cuDoubleComplex *x, int incx)

This function solves the triangular banded linear system with a single right-hand-side

$\text{op}\left(A\right)\mathbf{\text{x}}=\mathbf{\text{b}}$

where $A$ is a triangular banded matrix, and $\mathbf{x}$ and $\mathbf{b}$ are vectors. Also, for matrix $A$

The solution $\mathbf{x}$ overwrites the right-hand-sides $\mathbf{b}$ on exit.

No test for singularity or near-singularity is included in this function.

If uplo == CUBLAS_FILL_MODE_LOWER then the triangular banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row 1, the first subdiagonal in row 2 (starting at first position), the second subdiagonal in row 3 (starting at first position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+i-j,j) for $j=1,\dots ,n$ and $i\in \left[j,min\left(m,j+k\right)\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the bottom right $k×k$ triangle) are not referenced.

If uplo == CUBLAS_FILL_MODE_UPPER then the triangular banded matrix $A$ is stored column by column, with the main diagonal of the matrix stored in row k+1, the first superdiagonal in row k (starting at second position), the second superdiagonal in row k-1 (starting at third position), etc. So that in general, the element $A\left(i,j\right)$ is stored in the memory location A(1+k+i-j,j) for $j=1,\dots ,n$ and $i\in \left[max\left(1,j-k,j\right)\right]$ . Also, the elements in the array A that do not conceptually correspond to the elements in the banded matrix (the top left $k×k$ triangle) are not referenced.

Param. Memory In/out Meaning

handle

input

Handle to the cuBLAS library context.

uplo

input

Indicates if matrix A lower or upper part is stored, the other part is not referenced and is inferred from the stored elements.

trans

input

Operation op(A) that is non- or (conj.) transpose.

diag

input

Indicates if the elements on the main diagonal of matrix A are unity and should not be accessed.

n

input

Number of rows and columns of matrix A.

k

input

Number of sub- and super-diagonals of matrix A.

A

device

input

<type> array of dimension lda x n, with lda >= k+1.

lda

input

Leading dimension of two-dimensional array used to store matrix A.

x

device

in/out

<type> vector with n elements.

incx

input

Stride between consecutive elements of x.

The possible error values returned by this function and their meanings are listed below.

Error Value Meaning

CUBLAS_STATUS_SUCCESS

The operation completed successfully.

CUBLAS_STATUS_NOT_INITIALIZED

The library was not initialized.

CUBLAS_STATUS_INVALID_VALUE

• If n < 0 or k < 0 or

• if incx = 0 or

• if trans != CUBLAS_OP_N, CUBLAS_OP_C, CUBLAS_OP_T or

• if uplo != CUBLAS_FILL_MODE_LOWER, CUBLAS_FILL_MODE_UPPER or

• if diag != CUBLAS_DIAG_UNIT, CUBLAS_DIAG_NON_UNIT or

• lda < (1 + k)

CUBLAS_STATUS_EXECUTION_FAILED

The function failed to launch on the GPU.

2.6.13. cublas<t>tpmv()

cublasStatus_t cublasStpmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, const float           *AP,
float           *x, int incx)
cublasStatus_t cublasDtpmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, const double          *AP,
double          *x, int incx)
cublasStatus_t cublasCtpmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, const cuComplex       *AP,
cuComplex       *x, int incx)
cublasStatus_t cublasZtpmv(cublasHandle_t handle, cublasFillMode_t uplo,
cublasOperation_t trans, cublasDiagType_t diag,
int n, const cuDoubleComplex *AP,
cuDoubleComplex *x, int incx)

This function performs the triangular packed matrix-vector multiplication

$\mathbf{\text{x}}=\text{op}\left(A\right)\mathbf{\text{x}}$

where $A$ is a triangular matrix stored in packed format, and $\mathbf{x}$ is a vector. Also, for matrix $A$

If uplo == CUBLAS_FILL_MODE_LOWER then the elements in the lower triangular part of the triangular matrix $A$