GSL 系列 5 — 向量和矩阵 4 — 基本线性代数运算 (BLAS)
文章目录
- 写在前面
- 概述
- 层次 1 运算
- 层次 2 运算
- 层次 3 运算
写在前面
关于向量，矩阵的定义参考
-
GSL 系列 5 — 向量和矩阵 2 — 向量 (vector)
-
GSL 系列 5 — 向量和矩阵 3 — 矩阵 (matrix)
若无特别说明，本篇代码均来自头文件 gsl_blas.h
概述
将基本的线代运算分为三个层次：
- 层次1，向量运算，比如 α x + y \alpha x+y αx+y
- 层次2，矩阵和向量的运算，比如 α A x + β y \alpha Ax+\beta y αAx+βy
- 层次3，矩阵和矩阵的运算，比如 α A B + C \alpha AB+C αAB+C
将如下矩阵类型做名字简单的名字标记：
| 名字标记 | 矩阵类型 | 名字标记 | 矩阵类型 |
|---|---|---|---|
| GE | 一般矩阵 | GB | 一般带矩阵 |
| SY | 对称矩阵 | SB | 对称带矩阵 |
| SP | 对称矩阵包 | HE | 共轭矩阵 |
| HB | 共轭带矩阵 | HP | 共轭矩阵包 |
| TR | 三角矩阵 | TB | 三角带矩阵 |
| TP | 三角矩阵包 |
以下名字标记代表线代运算
| 名字标记 | 矩阵运算 |
|---|---|
| DOT | 标量乘 x T y x^Ty xTy |
| AXPY | 向量加 α x + y \alpha x+y αx+y |
| MV | 矩阵向量乘 A x Ax Ax |
| SV | 矩阵向量求解 A − 1 b A^{-1}b A−1b |
| MM | 矩阵矩阵乘 A A AA AA |
| SM | 矩阵矩阵求解 A − 1 B A^{-1}B A−1B |
以下名字标记代表数据类型
| 名字标记 | 数据类型 |
|---|---|
| S | 单精度实数 |
| D | 双精度实数 |
| C | 单精度复数 |
| Z | 双精度复数 |
层次 1 运算
α + x T y \alpha +x^Ty α+xTy
int gsl_blas_sdsdot (float alpha,
const gsl_vector_float * X,
const gsl_vector_float * Y,
float * result
);
x T y x^Ty xTy
int gsl_blas_dsdot (const gsl_vector_float * X,
const gsl_vector_float * Y,
double * result
);
int gsl_blas_sdot (const gsl_vector_float * X,
const gsl_vector_float * Y,
float * result
);
int gsl_blas_ddot (const gsl_vector * X,
const gsl_vector * Y,
double * result
);
int gsl_blas_cdotu (const gsl_vector_complex_float * X,
const gsl_vector_complex_float * Y,
gsl_complex_float * dotu);
int gsl_blas_zdotu (const gsl_vector_complex * X,
const gsl_vector_complex * Y,
gsl_complex * dotu);
x H y x^Hy xHy
int gsl_blas_cdotc (const gsl_vector_complex_float * X,
const gsl_vector_complex_float * Y,
gsl_complex_float * dotc);
int gsl_blas_zdotc (const gsl_vector_complex * X,
const gsl_vector_complex * Y,
gsl_complex * dotc);
∥ x ∥ 2 \|x\|_2 ∥x∥2
float gsl_blas_snrm2 (const gsl_vector_float * X);
double gsl_blas_dnrm2 (const gsl_vector * X);
float gsl_blas_scnrm2 (const gsl_vector_complex_float * X);
double gsl_blas_dznrm2 (const gsl_vector_complex * X);
∑ ∣ x i ∣ \sum|x_i| ∑∣xi∣
float gsl_blas_sasum (const gsl_vector_float * X);
double gsl_blas_dasum (const gsl_vector * X);
∑ ( ∣ ℜ ( x i ) ∣ + ∣ ℑ ( x i ) ∣ ) \sum\left(\left|\Re\left(x_{i}\right)\right|+\left|\Im\left(x_{i}\right)\right|\right) ∑(∣ℜ(xi)∣+∣ℑ(xi)∣)
float gsl_blas_scasum (const gsl_vector_complex_float * X);
double gsl_blas_dzasum (const gsl_vector_complex * X);
max i ∣ x i ∣ \max_i|x_i| maxi∣xi∣
CBLAS_INDEX_t gsl_blas_isamax (const gsl_vector_float * X);
CBLAS_INDEX_t gsl_blas_idamax (const gsl_vector * X);
// gsl_blas_types.h
typedef CBLAS_INDEX CBLAS_INDEX_t;
// gsl_cblas.h
#define CBLAS_INDEX size_t
max i ( ∣ ℜ ( x i ) ∣ + ∣ ℑ ( x i ) ∣ ) \max_i(\left|\Re\left(x_{i}\right)\right|+\left|\Im\left(x_{i}\right)\right|) maxi(∣ℜ(xi)∣+∣ℑ(xi)∣)
CBLAS_INDEX_t gsl_blas_icamax (const gsl_vector_complex_float * X);
CBLAS_INDEX_t gsl_blas_izamax (const gsl_vector_complex * X);
交换 x x x， y y y
int gsl_blas_sswap (gsl_vector_float * X,
gsl_vector_float * Y);
int gsl_blas_dswap (gsl_vector * X,
gsl_vector * Y);
int gsl_blas_cswap (gsl_vector_complex_float * X,
gsl_vector_complex_float * Y);
int gsl_blas_zswap (gsl_vector_complex * X,
gsl_vector_complex * Y);
复制 x x x 到 y y y
int gsl_blas_scopy (const gsl_vector_float * X,
gsl_vector_float * Y);
int gsl_blas_dcopy (const gsl_vector * X,
gsl_vector * Y);
int gsl_blas_ccopy (const gsl_vector_complex_float * X,
gsl_vector_complex_float * Y);
int gsl_blas_zcopy (const gsl_vector_complex * X,
gsl_vector_complex * Y);
y = α x + y y=\alpha x+y y=αx+y
int gsl_blas_saxpy (float alpha,
const gsl_vector_float * X,
gsl_vector_float * Y);
int gsl_blas_daxpy (double alpha,
const gsl_vector * X,
gsl_vector * Y);
int gsl_blas_caxpy (const gsl_complex_float alpha,
const gsl_vector_complex_float * X,
gsl_vector_complex_float * Y);
int gsl_blas_zaxpy (const gsl_complex alpha,
const gsl_vector_complex * X,
gsl_vector_complex * Y);
α x \alpha x αx
void gsl_blas_sscal (float alpha, gsl_vector_float * X);
void gsl_blas_dscal (double alpha, gsl_vector * X);
void gsl_blas_cscal (const gsl_complex_float alpha, gsl_vector_complex_float * X);
void gsl_blas_zscal (const gsl_complex alpha, gsl_vector_complex * X);
void gsl_blas_csscal (float alpha, gsl_vector_complex_float * X);
void gsl_blas_zdscal (double alpha, gsl_vector_complex * X);
计算满足如下旋转:
( c s − s c ) ( a b ) = ( r ′ 0 ) \left(\begin{array}{cc}c & s \\ -s & c\end{array}\right)\left(\begin{array}{l}a \\ b\end{array}\right)=\left(\begin{array}{l}r^{\prime} \\ 0\end{array}\right) (c−ssc)(ab)=(r′0)
计算得到 c, s，同时，a, b 也进行重写
int gsl_blas_srotg (float a[], float b[], float c[], float s[]);
int gsl_blas_drotg (double a[], double b[], double c[], double s[]);
应用旋转，计算 ( x , y ) = ( c x + s y , − s x + c y ) (x,y) = (cx+sy,-sx+cy) (x,y)=(cx+sy,−sx+cy)
int gsl_blas_srot (gsl_vector_float * X,
gsl_vector_float * Y,
float c, float s);
int gsl_blas_drot (gsl_vector * X,
gsl_vector * Y,
const double c, const double s);
计算修正旋转
int gsl_blas_srotmg (float d1[], float d2[], float b1[], float b2, float P[]);
int gsl_blas_drotmg (double d1[], double d2[], double b1[],
double b2, double P[]);
应用修正旋转
int gsl_blas_srotm (gsl_vector_float * X,
gsl_vector_float * Y,
const float P[]);
int gsl_blas_drotm (gsl_vector * X,
gsl_vector * Y,
const double P[]);
层次 2 运算
y = α op ( A ) x + β y y=\alpha \operatorname{op}(A)x+\beta y y=αop(A)x+βy
当 TransA 等于 CblasNoTrans，CblasTrans，CblasConjTrans 时， op ( A ) \operatorname{op}(A) op(A) 分别等于 A A A， A T A^T AT， A H A^H AH
int gsl_blas_sgemv (CBLAS_TRANSPOSE_t TransA,
float alpha,
const gsl_matrix_float * A,
const gsl_vector_float * X,
float beta,
gsl_vector_float * Y);
int gsl_blas_dgemv (CBLAS_TRANSPOSE_t TransA,
double alpha,
const gsl_matrix * A,
const gsl_vector * X,
double beta,
gsl_vector * Y);
int gsl_blas_cgemv (CBLAS_TRANSPOSE_t TransA,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_vector_complex_float * X,
const gsl_complex_float beta,
gsl_vector_complex_float * Y);
int gsl_blas_zgemv (CBLAS_TRANSPOSE_t TransA,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_vector_complex * X,
const gsl_complex beta,
gsl_vector_complex * Y);
// gsl_blas_types.h
typedef enum CBLAS_TRANSPOSE CBLAS_TRANSPOSE_t;
// gsl_cblas.h
enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113};
三角矩阵， op ( A ) x \operatorname{op}(A)x op(A)x
当 Uplo 为 CblasUpper，CblasLower 时，分别使用 A 的上三角，下三角部分
当 Diag 为 CblasNonUnit，CblasUnit 时，分别使用 A 的对角线，为 1 的对角线
int gsl_blas_strmv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_float * A,
gsl_vector_float * X);
int gsl_blas_dtrmv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix * A,
gsl_vector * X);
int gsl_blas_ctrmv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_complex_float * A,
gsl_vector_complex_float * X);
int gsl_blas_ztrmv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_complex * A,
gsl_vector_complex * X);
// gsl_blas_types.h
typedef enum CBLAS_UPLO CBLAS_UPLO_t;
typedef enum CBLAS_DIAG CBLAS_DIAG_t;
// gsl_cblas.h
enum CBLAS_UPLO {CblasUpper=121, CblasLower=122};
enum CBLAS_DIAG {CblasNonUnit=131, CblasUnit=132};
三角矩阵， i n v ( op ( A ) ) x inv(\operatorname{op}(A))x inv(op(A))x
int gsl_blas_strsv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_float * A,
gsl_vector_float * X);
int gsl_blas_dtrsv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix * A,
gsl_vector * X);
int gsl_blas_ctrsv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_complex_float * A,
gsl_vector_complex_float * X);
int gsl_blas_ztrsv (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag,
const gsl_matrix_complex * A,
gsl_vector_complex *X);
对称矩阵， y = α A x + β y y=\alpha Ax+\beta y y=αAx+βy
int gsl_blas_ssymv (CBLAS_UPLO_t Uplo,
float alpha,
const gsl_matrix_float * A,
const gsl_vector_float * X,
float beta,
gsl_vector_float * Y);
int gsl_blas_dsymv (CBLAS_UPLO_t Uplo,
double alpha,
const gsl_matrix * A,
const gsl_vector * X,
double beta,
gsl_vector * Y);
共轭矩阵， y = α A x + β y y=\alpha Ax+\beta y y=αAx+βy
int gsl_blas_chemv (CBLAS_UPLO_t Uplo,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_vector_complex_float * X,
const gsl_complex_float beta,
gsl_vector_complex_float * Y);
int gsl_blas_zhemv (CBLAS_UPLO_t Uplo,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_vector_complex * X,
const gsl_complex beta,
gsl_vector_complex * Y);
A = α x y T + A A=\alpha xy^T+A A=αxyT+A
int gsl_blas_sger (float alpha,
const gsl_vector_float * X,
const gsl_vector_float * Y,
gsl_matrix_float * A);
int gsl_blas_dger (double alpha,
const gsl_vector * X,
const gsl_vector * Y,
gsl_matrix * A);
int gsl_blas_cgeru (const gsl_complex_float alpha,
const gsl_vector_complex_float * X,
const gsl_vector_complex_float * Y,
gsl_matrix_complex_float * A);
int gsl_blas_zgeru (const gsl_complex alpha,
const gsl_vector_complex * X,
const gsl_vector_complex * Y,
gsl_matrix_complex * A);
A = α x y H + A A=\alpha xy^H+A A=αxyH+A
int gsl_blas_cgerc (const gsl_complex_float alpha,
const gsl_vector_complex_float * X,
const gsl_vector_complex_float * Y,
gsl_matrix_complex_float * A);
int gsl_blas_zgerc (const gsl_complex alpha,
const gsl_vector_complex * X,
const gsl_vector_complex * Y,
gsl_matrix_complex * A);
对称矩阵， A = α x x T + A A=\alpha xx^T+A A=αxxT+A
int gsl_blas_ssyr (CBLAS_UPLO_t Uplo,
float alpha,
const gsl_vector_float * X,
gsl_matrix_float * A);
int gsl_blas_dsyr (CBLAS_UPLO_t Uplo,
double alpha,
const gsl_vector * X,
gsl_matrix * A);
共轭矩阵， A = α x x H + A A=\alpha xx^H+A A=αxxH+A
int gsl_blas_cher (CBLAS_UPLO_t Uplo,
float alpha,
const gsl_vector_complex_float * X,
gsl_matrix_complex_float * A);
int gsl_blas_zher (CBLAS_UPLO_t Uplo,
double alpha,
const gsl_vector_complex * X,
gsl_matrix_complex * A);
对称矩阵， A = α x y T + α y x T + A A=\alpha xy^T+\alpha yx^T + A A=αxyT+αyxT+A
int gsl_blas_ssyr2 (CBLAS_UPLO_t Uplo,
float alpha,
const gsl_vector_float * X,
const gsl_vector_float * Y,
gsl_matrix_float * A);
int gsl_blas_dsyr2 (CBLAS_UPLO_t Uplo,
double alpha,
const gsl_vector * X,
const gsl_vector * Y,
gsl_matrix * A);
共轭矩阵， A = α x y H + α ∗ y x H + A A=\alpha xy^H+\alpha^{*} yx^H + A A=αxyH+α∗yxH+A
int gsl_blas_cher2 (CBLAS_UPLO_t Uplo,
const gsl_complex_float alpha,
const gsl_vector_complex_float * X,
const gsl_vector_complex_float * Y,
gsl_matrix_complex_float * A);
int gsl_blas_zher2 (CBLAS_UPLO_t Uplo,
const gsl_complex alpha,
const gsl_vector_complex * X,
const gsl_vector_complex * Y,
gsl_matrix_complex * A);
层次 3 运算
C = α op ( A ) op ( B ) + β C C=\alpha\operatorname{op}(A)\operatorname{op}(B)+\beta C C=αop(A)op(B)+βC
int gsl_blas_sgemm (CBLAS_TRANSPOSE_t TransA,
CBLAS_TRANSPOSE_t TransB,
float alpha,
const gsl_matrix_float * A,
const gsl_matrix_float * B,
float beta,
gsl_matrix_float * C);
int gsl_blas_dgemm (CBLAS_TRANSPOSE_t TransA,
CBLAS_TRANSPOSE_t TransB,
double alpha,
const gsl_matrix * A,
const gsl_matrix * B,
double beta,
gsl_matrix * C);
int gsl_blas_cgemm (CBLAS_TRANSPOSE_t TransA,
CBLAS_TRANSPOSE_t TransB,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_matrix_complex_float * B,
const gsl_complex_float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zgemm (CBLAS_TRANSPOSE_t TransA,
CBLAS_TRANSPOSE_t TransB,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
const gsl_complex beta,
gsl_matrix_complex * C);
对称矩阵 A A A； C = α A B + β C C=\alpha AB+\beta C C=αAB+βC 或 C = α B A + β C C=\alpha BA+\beta C C=αBA+βC
当 Side 为 CblasLeft，CblasRight 时，分别计算 C = α A B + β C C=\alpha AB+\beta C C=αAB+βC， C = α B A + β C C=\alpha BA+\beta C C=αBA+βC
int gsl_blas_ssymm (CBLAS_SIDE_t Side, CBLAS_UPLO_t Uplo,
float alpha,
const gsl_matrix_float * A,
const gsl_matrix_float * B,
float beta,
gsl_matrix_float * C);
int gsl_blas_dsymm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo,
double alpha,
const gsl_matrix * A,
const gsl_matrix * B,
double beta,
gsl_matrix * C);
int gsl_blas_csymm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_matrix_complex_float * B,
const gsl_complex_float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zsymm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
const gsl_complex beta,
gsl_matrix_complex * C);
// gsl_blas_types.h
typedef enum CBLAS_SIDE CBLAS_SIDE_t;
// gsl_cblas.h
enum CBLAS_SIDE {CblasLeft=141, CblasRight=142};
共轭矩阵 A A A； C = α A B + β C C=\alpha AB+\beta C C=αAB+βC 或 C = α B A + β C C=\alpha BA+\beta C C=αBA+βC
int gsl_blas_chemm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_matrix_complex_float * B,
const gsl_complex_float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zhemm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
const gsl_complex beta,
gsl_matrix_complex * C);
三角矩阵 A A A； B = α op ( A ) B B=\alpha\operatorname{op}(A)B B=αop(A)B 或 B = α B op ( A ) B=\alpha B\operatorname{op}(A) B=αBop(A)
int gsl_blas_strmm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
float alpha,
const gsl_matrix_float * A,
gsl_matrix_float * B);
int gsl_blas_dtrmm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
double alpha,
const gsl_matrix * A,
gsl_matrix * B);
int gsl_blas_ctrmm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
gsl_matrix_complex_float * B);
int gsl_blas_ztrmm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
const gsl_complex alpha,
const gsl_matrix_complex * A,
gsl_matrix_complex * B);
三角矩阵 A A A； B = α op ( i n v ( A ) ) B B=\alpha\operatorname{op}(inv(A))B B=αop(inv(A))B 或 B = α B op ( i n v ( A ) ) B=\alpha B\operatorname{op}(inv(A)) B=αBop(inv(A))
int gsl_blas_strsm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
float alpha,
const gsl_matrix_float * A,
gsl_matrix_float * B);
int gsl_blas_dtrsm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
double alpha,
const gsl_matrix * A,
gsl_matrix * B);
int gsl_blas_ctrsm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
gsl_matrix_complex_float * B);
int gsl_blas_ztrsm (CBLAS_SIDE_t Side,
CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA,
CBLAS_DIAG_t Diag,
const gsl_complex alpha,
const gsl_matrix_complex * A,
gsl_matrix_complex * B);
对称矩阵 C C C； C = α A A T + β C C=\alpha AA^T+\beta C C=αAAT+βC
int gsl_blas_ssyrk (CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t Trans,
float alpha,
const gsl_matrix_float * A,
float beta,
gsl_matrix_float * C);
int gsl_blas_dsyrk (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
double alpha,
const gsl_matrix * A,
double beta,
gsl_matrix * C);
int gsl_blas_csyrk (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_complex_float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zsyrk (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_complex beta,
gsl_matrix_complex * C);
共轭矩阵 C C C； C = α A A H + β C C=\alpha AA^H+\beta C C=αAAH+βC
int gsl_blas_cherk (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
float alpha,
const gsl_matrix_complex_float * A,
float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zherk (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
double alpha,
const gsl_matrix_complex * A,
double beta,
gsl_matrix_complex * C);
对称矩阵 C C C； C = α A T B + α B T A + β C C=\alpha A^TB+\alpha B^TA+\beta C C=αATB+αBTA+βC
int gsl_blas_ssyr2k (CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t Trans,
float alpha,
const gsl_matrix_float * A,
const gsl_matrix_float * B,
float beta,
gsl_matrix_float * C);
int gsl_blas_dsyr2k (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
double alpha,
const gsl_matrix * A,
const gsl_matrix * B,
double beta,
gsl_matrix * C);
int gsl_blas_csyr2k (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_matrix_complex_float * B,
const gsl_complex_float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zsyr2k (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
const gsl_complex beta,
gsl_matrix_complex *C);
共轭矩阵 C C C； C = α A H B + α ∗ B H A + β C C=\alpha A^HB+\alpha^* B^HA+\beta C C=αAHB+α∗BHA+βC
int gsl_blas_cher2k (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex_float alpha,
const gsl_matrix_complex_float * A,
const gsl_matrix_complex_float * B,
float beta,
gsl_matrix_complex_float * C);
int gsl_blas_zher2k (CBLAS_UPLO_t Uplo,
CBLAS_TRANSPOSE_t Trans,
const gsl_complex alpha,
const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
double beta,
gsl_matrix_complex * C);