cuBLAS Level-1 Function

Level-1 BLAS函數(shù)進行的是標(biāo)量，向量的基本操作。僅為學(xué)習(xí)記錄，具體內(nèi)容請以nvidia官方文檔為準(zhǔn)：
https://docs.nvidia.com/cuda/cublas/index.html#cublas-level-1-function-reference

函數(shù)命名中的一些字符的含義：

Screen Shot 2018-11-10 at 9.17.36 AM.png

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)

這些函數(shù)尋找最大長度元素的最小索引值。也就是說找到 $i$ 使得 $|Im(x[j])| + |Re(x[j])|$ 最大, 其中 $i\in [1,...,n], j=1+(i-1) * incx$
參數(shù)以及返回值如下圖：

參數(shù)以及返回值

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)

該函數(shù)找到擁有最小長度的元素的最小索引值。也就是說找到 $i$ 使得 $|Im(x[j])| + |Re(x[j])|$ 最小, 其中 $i\in [1,...,n], j=1+(i-1) * incx$

參數(shù)以及返回值如下圖：

參數(shù)以及返回值

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)

該函數(shù)計算向量 $x$ 的元素的絕對值的和。也就是說，計算結(jié)果為 $\sum_{i=1}^n |Im(x[j])|+Re|(x[j])||$ ，其中 $j=1+(i-1)*incx$

參數(shù)以及返回值

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)

該函數(shù)計算向量 $x$ 和標(biāo)量 $\alpha$ 的積，并將結(jié)果加到 $y$ 上，得到的結(jié)果覆蓋最后一個向量值。 $y[j]=\alpha * x[k]+y[j]$ ，其中 $i \in [1,...,n], k=1+(i-1)*incx, j=1+(i-1)*incy$

參數(shù)及返回值

參數(shù)以及返回值

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)

將向量 $x$ 復(fù)制到 $y$ 中， $y[j]=x[k]$ 其中 $i\in[1,...n], k=1+(i-1)*incx,j=1+(i-1)*incy$ 。

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)

計算兩個向量的點積。 $\sum_{i=1}^n(x[h]*y[j])$ ，其中 $k=1+(i-1)*incx,j=1+(i-1)*incy$

Screen Shot 2018-11-10 at 9.29.13 AM.png

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)

計算向量 $x$ 的歐式長度， $\sum_{i=1}^n (x[j]*x[j])$ ,其中 $j=1+(i-1)*incx$

Screen Shot 2018-11-10 at 9.32.21 AM.png

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)

該函數(shù)對向量進行旋轉(zhuǎn)變換，在向量 $x,y$ 所處的平面內(nèi)，逆時針旋轉(zhuǎn) $\alpha$ ，其中 $cos(\alpha)=c,sin(\alpha)=s$ 。
結(jié)果為 $x[k]=c*x[k]+s*y[j],y[j]=-s*x[k]+c*y[j]$ 其中 $k = 1 + ( i - 1 ) * incx$ , $j = 1 + ( i - 1 ) * incy$

Screen Shot 2018-11-10 at 9.36.37 AM.png

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)

該函數(shù)構(gòu)建旋轉(zhuǎn)矩陣： $G = \left\{ \begin{matrix} c & s \\ -s & c \end{matrix} \right\} \tag{2}$
然后令向量 $(a,b)^T$ 第二個元素為0，也就是：

Screen Shot 2018-11-10 at 9.44.32 AM.png

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)

Screen Shot 2018-11-10 at 9.46.01 AM.png

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)

標(biāo)量與向量相乘

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)

交換兩向量元素

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cuBLAS Level-1 Function