blas.texi

开放gsl矩阵运算

@deftypefunx int gsl_blas_zaxpy (const gsl_complex @var{alpha}, const gsl_vector_complex * @var{x}, gsl_vector_complex * @var{y})
@cindex AXPY, Level-1 BLAS
These functions compute the sum @math{y = \alpha x + y} for the vectors
@var{x} and @var{y}.
@end deftypefun

@deftypefun void gsl_blas_sscal (float @var{alpha}, gsl_vector_float * @var{x})
@deftypefunx void gsl_blas_dscal (double @var{alpha}, gsl_vector * @var{x})
@deftypefunx void gsl_blas_cscal (const gsl_complex_float @var{alpha}, gsl_vector_complex_float * @var{x})
@deftypefunx void gsl_blas_zscal (const gsl_complex @var{alpha}, gsl_vector_complex * @var{x})
@deftypefunx void gsl_blas_csscal (float @var{alpha}, gsl_vector_complex_float * @var{x})
@deftypefunx void gsl_blas_zdscal (double @var{alpha}, gsl_vector_complex * @var{x})
@cindex SCAL, Level-1 BLAS
These functions rescale the vector @var{x} by the multiplicative factor
@var{alpha}.
@end deftypefun

@deftypefun int gsl_blas_srotg (float a[], float b[], float c[], float s[])
@deftypefunx int gsl_blas_drotg (double a[], double b[], double c[], double s[])
@cindex ROTG, Level-1 BLAS
@cindex Givens Rotation, BLAS
These functions compute a Givens rotation @math{(c,s)} which zeroes the
vector @math{(a,b)},

@tex
\beforedisplay
$$
\left(
\matrix{c&s\cr
-s&c\cr}
\right)
\left(
\matrix{a\cr
b\cr}
\right)
=
\left(
\matrix{r'\cr
0\cr}
\right)
$$
\afterdisplay
@end tex
@ifinfo
@example
[  c  s ] [ a ] = [ r ]
[ -s  c ] [ b ]   [ 0 ]
@end example
@end ifinfo
@noindent
The variables @var{a} and @var{b} are overwritten by the routine.
@end deftypefun

@deftypefun int gsl_blas_srot (gsl_vector_float * @var{x}, gsl_vector_float * @var{y}, float @var{c}, float @var{s})
@deftypefunx int gsl_blas_drot (gsl_vector * @var{x}, gsl_vector * @var{y}, const double @var{c}, const double @var{s})
These functions apply a Givens rotation @math{(x', y') = (c x + s y, -s
x + c y)} to the vectors @var{x}, @var{y}.
@end deftypefun

@deftypefun int gsl_blas_srotmg (float d1[], float d2[], float b1[], float @var{b2}, float P[])
@deftypefunx int gsl_blas_drotmg (double d1[], double d2[], double b1[], double @var{b2}, double P[])
@cindex Modified Givens Rotation, BLAS
@cindex Givens Rotation, Modified, BLAS
These functions compute a modified Given's transformation.
@end deftypefun

@deftypefun int gsl_blas_srotm (gsl_vector_float * @var{x}, gsl_vector_float * @var{y}, const float P[])
@deftypefunx int gsl_blas_drotm (gsl_vector * @var{x}, gsl_vector * @var{y}, const double P[])
These functions apply a modified Given's transformation.
@end deftypefun

@node Level 2 GSL BLAS Interface
@subsection Level 2 

@deftypefun int gsl_blas_sgemv (CBLAS_TRANSPOSE_t @var{TransA}, float @var{alpha}, const gsl_matrix_float * @var{A}, const gsl_vector_float * @var{x}, float @var{beta}, gsl_vector_float * @var{y})
@deftypefunx int gsl_blas_dgemv (CBLAS_TRANSPOSE_t @var{TransA}, double @var{alpha}, const gsl_matrix * @var{A}, const gsl_vector * @var{x}, double @var{beta}, gsl_vector * @var{y})
@deftypefunx int gsl_blas_cgemv (CBLAS_TRANSPOSE_t @var{TransA}, const gsl_complex_float @var{alpha}, const gsl_matrix_complex_float * @var{A}, const gsl_vector_complex_float * @var{x}, const gsl_complex_float @var{beta}, gsl_vector_complex_float * @var{y})
@deftypefunx int gsl_blas_zgemv (CBLAS_TRANSPOSE_t @var{TransA}, const gsl_complex @var{alpha}, const gsl_matrix_complex * @var{A}, const gsl_vector_complex * @var{x}, const gsl_complex @var{beta}, gsl_vector_complex * @var{y})
@cindex GEMV, Level-2 BLAS
These functions compute the matrix-vector product and sum @math{y =
\alpha op(A) x + \beta y}, where @math{op(A) = A},
@math{A^T}, @math{A^H} for @var{TransA} = @code{CblasNoTrans},
@code{CblasTrans}, @code{CblasConjTrans}.
@end deftypefun


@deftypefun int gsl_blas_strmv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_float * @var{A}, gsl_vector_float * @var{x})
@deftypefunx int gsl_blas_dtrmv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix * @var{A}, gsl_vector * @var{x})
@deftypefunx int gsl_blas_ctrmv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_complex_float * @var{A}, gsl_vector_complex_float * @var{x})
@deftypefunx int gsl_blas_ztrmv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_complex * @var{A}, gsl_vector_complex * @var{x})
@cindex TRMV, Level-2 BLAS
These functions compute the matrix-vector product and sum 
@math{y =\alpha op(A) x + \beta y} for the triangular matrix @var{A}, where
@math{op(A) = A}, @math{A^T}, @math{A^H} for @var{TransA} =
@code{CblasNoTrans}, @code{CblasTrans}, @code{CblasConjTrans}.  When
@var{Uplo} is @code{CblasUpper} then the upper triangle of @var{A} is
used, and when @var{Uplo} is @code{CblasLower} then the lower triangle
of @var{A} is used.  If @var{Diag} is @code{CblasNonUnit} then the
diagonal of the matrix is used, but if @var{Diag} is @code{CblasUnit}
then the diagonal elements of the matrix @var{A} are taken as unity and
are not referenced.
@end deftypefun


@deftypefun int gsl_blas_strsv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_float * @var{A}, gsl_vector_float * @var{x})
@deftypefunx int gsl_blas_dtrsv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix * @var{A}, gsl_vector * @var{x})
@deftypefunx int gsl_blas_ctrsv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_complex_float * @var{A}, gsl_vector_complex_float * @var{x})
@deftypefunx int gsl_blas_ztrsv (CBLAS_UPLO_t @var{Uplo}, CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_DIAG_t @var{Diag}, const gsl_matrix_complex * @var{A}, gsl_vector_complex *@var{x})
@cindex TRSV, Level-2 BLAS
These functions compute @math{inv(op(A)) x} for @var{x}, where
@math{op(A) = A}, @math{A^T}, @math{A^H} for @var{TransA} =
@code{CblasNoTrans}, @code{CblasTrans}, @code{CblasConjTrans}.  When
@var{Uplo} is @code{CblasUpper} then the upper triangle of @var{A} is
used, and when @var{Uplo} is @code{CblasLower} then the lower triangle
of @var{A} is used.  If @var{Diag} is @code{CblasNonUnit} then the
diagonal of the matrix is used, but if @var{Diag} is @code{CblasUnit}
then the diagonal elements of the matrix @var{A} are taken as unity and
are not referenced.
@end deftypefun


@deftypefun int gsl_blas_ssymv (CBLAS_UPLO_t @var{Uplo}, float @var{alpha}, const gsl_matrix_float * @var{A}, const gsl_vector_float * @var{x}, float @var{beta}, gsl_vector_float * @var{y})
@deftypefunx int gsl_blas_dsymv (CBLAS_UPLO_t @var{Uplo}, double @var{alpha}, const gsl_matrix * @var{A}, const gsl_vector * @var{x}, double @var{beta}, gsl_vector * @var{y})
@cindex SYMV, Level-2 BLAS
These functions compute the matrix-vector product and sum @math{y =
\alpha A x + \beta y} for the symmetric matrix @var{A}.  Since the
matrix @var{A} is symmetric only its upper half or lower half need to be
stored.  When @var{Uplo} is @code{CblasUpper} then the upper triangle
and diagonal of @var{A} are used, and when @var{Uplo} is
@code{CblasLower} then the lower triangle and diagonal of @var{A} are
used.
@end deftypefun

@deftypefun int gsl_blas_chemv (CBLAS_UPLO_t @var{Uplo}, const gsl_complex_float @var{alpha}, const gsl_matrix_complex_float * @var{A}, const gsl_vector_complex_float * @var{x}, const gsl_complex_float @var{beta}, gsl_vector_complex_float * @var{y})
@deftypefunx int gsl_blas_zhemv (CBLAS_UPLO_t @var{Uplo}, const gsl_complex @var{alpha}, const gsl_matrix_complex * @var{A}, const gsl_vector_complex * @var{x}, const gsl_complex @var{beta}, gsl_vector_complex * @var{y})
@cindex HEMV, Level-2 BLAS
These functions compute the matrix-vector product and sum @math{y =
\alpha A x + \beta y} for the hermitian matrix @var{A}.  Since the
matrix @var{A} is hermitian only its upper half or lower half need to be
stored.  When @var{Uplo} is @code{CblasUpper} then the upper triangle
and diagonal of @var{A} are used, and when @var{Uplo} is
@code{CblasLower} then the lower triangle and diagonal of @var{A} are
used.  The imaginary elements of the diagonal are automatically assumed
to be zero and are not referenced.
@end deftypefun

@deftypefun int gsl_blas_sger (float @var{alpha}, const gsl_vector_float * @var{x}, const gsl_vector_float * @var{y}, gsl_matrix_float * @var{A})
@deftypefunx int gsl_blas_dger (double @var{alpha}, const gsl_vector * @var{x}, const gsl_vector * @var{y}, gsl_matrix * @var{A})
@deftypefunx int gsl_blas_cgeru (const gsl_complex_float @var{alpha}, const gsl_vector_complex_float * @var{x}, const gsl_vector_complex_float * @var{y}, gsl_matrix_complex_float * @var{A})
@deftypefunx int gsl_blas_zgeru (const gsl_complex @var{alpha}, const gsl_vector_complex * @var{x}, const gsl_vector_complex * @var{y}, gsl_matrix_complex * @var{A})
@cindex GER, Level-2 BLAS
@cindex GERU, Level-2 BLAS
These functions compute the rank-1 update @math{A = \alpha x y^T + A} of
the matrix @var{A}.
@end deftypefun

@deftypefun int gsl_blas_cgerc (const gsl_complex_float @var{alpha}, const gsl_vector_complex_float * @var{x}, const gsl_vector_complex_float * @var{y}, gsl_matrix_complex_float * @var{A})
@deftypefunx int gsl_blas_zgerc (const gsl_complex @var{alpha}, const gsl_vector_complex * @var{x}, const gsl_vector_complex * @var{y}, gsl_matrix_complex * @var{A})
@cindex GERC, Level-2 BLAS
These functions compute the conjugate rank-1 update @math{A = \alpha x
y^H + A} of the matrix @var{A}.
@end deftypefun

@deftypefun int gsl_blas_ssyr (CBLAS_UPLO_t @var{Uplo}, float @var{alpha}, const gsl_vector_float * @var{x}, gsl_matrix_float * @var{A})
@deftypefunx int gsl_blas_dsyr (CBLAS_UPLO_t @var{Uplo}, double @var{alpha}, const gsl_vector * @var{x}, gsl_matrix * @var{A})
@cindex SYR, Level-2 BLAS
These functions compute the symmetric rank-1 update @math{A = \alpha x
x^T + A} of the symmetric matrix @var{A}.  Since the matrix @var{A} is
symmetric only its upper half or lower half need to be stored.  When
@var{Uplo} is @code{CblasUpper} then the upper triangle and diagonal of
@var{A} are used, and when @var{Uplo} is @code{CblasLower} then the
lower triangle and diagonal of @var{A} are used.
@end deftypefun

@deftypefun int gsl_blas_cher (CBLAS_UPLO_t @var{Uplo}, float @var{alpha}, const gsl_vector_complex_float * @var{x}, gsl_matrix_complex_float * @var{A})
@deftypefunx int gsl_blas_zher (CBLAS_UPLO_t @var{Uplo}, double @var{alpha}, const gsl_vector_complex * @var{x}, gsl_matrix_complex * @var{A})
@cindex HER, Level-2 BLAS
These functions compute the hermitian rank-1 update @math{A = \alpha x
x^H + A} of the hermitian matrix @var{A}.  Since the matrix @var{A} is
hermitian only its upper half or lower half need to be stored.  When
@var{Uplo} is @code{CblasUpper} then the upper triangle and diagonal of
@var{A} are used, and when @var{Uplo} is @code{CblasLower} then the
lower triangle and diagonal of @var{A} are used.  The imaginary elements
of the diagonal are automatically set to zero.
@end deftypefun

@deftypefun int gsl_blas_ssyr2 (CBLAS_UPLO_t @var{Uplo}, float @var{alpha}, const gsl_vector_float * @var{x}, const gsl_vector_float * @var{y}, gsl_matrix_float * @var{A})
@deftypefunx int gsl_blas_dsyr2 (CBLAS_UPLO_t @var{Uplo}, double @var{alpha}, const gsl_vector * @var{x}, const gsl_vector * @var{y}, gsl_matrix * @var{A})
@cindex SYR2, Level-2 BLAS
These functions compute the symmetric rank-2 update @math{A = \alpha x
y^T + \alpha y x^T + A} of the symmetric matrix @var{A}.  Since the
matrix @var{A} is symmetric only its upper half or lower half need to be
stored.  When @var{Uplo} is @code{CblasUpper} then the upper triangle
and diagonal of @var{A} are used, and when @var{Uplo} is
@code{CblasLower} then the lower triangle and diagonal of @var{A} are
used.
@end deftypefun

@deftypefun int gsl_blas_cher2 (CBLAS_UPLO_t @var{Uplo}, const gsl_complex_float @var{alpha}, const gsl_vector_complex_float * @var{x}, const gsl_vector_complex_float * @var{y}, gsl_matrix_complex_float * @var{A})
@deftypefunx int gsl_blas_zher2 (CBLAS_UPLO_t @var{Uplo}, const gsl_complex @var{alpha}, const gsl_vector_complex * @var{x}, const gsl_vector_complex * @var{y}, gsl_matrix_complex * @var{A})
@cindex HER2, Level-2 BLAS
These functions compute the hermitian rank-2 update @math{A = \alpha x
y^H + \alpha^* y x^H A} of the hermitian matrix @var{A}.  Since the
matrix @var{A} is hermitian only its upper half or lower half need to be
stored.  When @var{Uplo} is @code{CblasUpper} then the upper triangle
and diagonal of @var{A} are used, and when @var{Uplo} is
@code{CblasLower} then the lower triangle and diagonal of @var{A} are
used.  The imaginary elements of the diagonal are automatically set to zero.
@end deftypefun

@node Level 3 GSL BLAS Interface
@subsection Level 3


@deftypefun int gsl_blas_sgemm (CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_TRANSPOSE_t @var{TransB}, float @var{alpha}, const gsl_matrix_float * @var{A}, const gsl_matrix_float * @var{B}, float @var{beta}, gsl_matrix_float * @var{C})
@deftypefunx int gsl_blas_dgemm (CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_TRANSPOSE_t @var{TransB}, double @var{alpha}, const gsl_matrix * @var{A}, const gsl_matrix * @var{B}, double @var{beta}, gsl_matrix * @var{C})
@deftypefunx int gsl_blas_cgemm (CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_TRANSPOSE_t @var{TransB}, const gsl_complex_float @var{alpha}, const gsl_matrix_complex_float * @var{A}, const gsl_matrix_complex_float * @var{B}, const gsl_complex_float @var{beta}, gsl_matrix_complex_float * @var{C})
@deftypefunx int gsl_blas_zgemm (CBLAS_TRANSPOSE_t @var{TransA}, CBLAS_TRANSPOSE_t @var{TransB}, const gsl_complex @var{alpha}, const gsl_matrix_complex * @var{A}, const gsl_matrix_complex * @var{B}, const gsl_complex @var{beta}, gsl_matrix_complex * @var{C})
@cindex GEMM, Level-3 BLAS
These functions compute the matrix-matrix product and sum @math{C =
\alpha op(A) op(B) + \beta C} where @math{op(A) = A}, @math{A^T},
@math{A^H} for @var{TransA} = @code{CblasNoTrans}, @code{CblasTrans},
@code{CblasConjTrans} and similarly for the parameter @var{TransB}.
@end deftypefun


@deftypefun int gsl_blas_ssymm (CBLAS_SIDE_t @var{Side}, CBLAS_UPLO_t @var{Uplo}, float @var{alpha}, const gsl_matrix_float * @var{A}, const gsl_matrix_float * @var{B}, float @var{beta}, gsl_matrix_float * @var{C})
@deftypefunx int gsl_blas_dsymm (CBLAS_SIDE_t @var{Side}, CBLAS_UPLO_t @var{Uplo}, double @var{alpha}, const gsl_matrix * @var{A}, const gsl_matrix * @var{B}, double @var{beta}, gsl_matrix * @var{C})
@deftypefunx int gsl_blas_csymm (CBLAS_SIDE_t @var{Side}, CBLAS_UPLO_t @var{Uplo}, const gsl_complex_float @var{alpha}, const gsl_matrix_complex_float * @var{A}, const gsl_matrix_complex_float * @var{B}, const gsl_complex_float @var{beta}, gsl_matrix_complex_float * @var{C})
@deftypefunx int gsl_blas_zsymm (CBLAS_SIDE_t @var{Side}, CBLAS_UPLO_t @var{Uplo}, const gsl_complex @var{alpha}, const gsl_matrix_complex * @var{A}, const gsl_matrix_complex * @var{B}, const gsl_complex @var{beta}, gsl_matrix_complex * @var{C})
@cindex SYMM, Level-3 BLAS
These functions compute the matrix-matrix product and sum @math{C =
\alpha A B + \beta C} for @var{Side} is @code{CblasLeft} and @math{C =
\alpha B A + \beta C} for @var{Side} is @code{CblasRight}, where the