_SYR2,_HER2(3F) _SYR2,_HER2(3F)
dsyr2, ssyr2, zher2, cher2 - BLAS Level Two
(Symmetric/Hermitian)Matrix Rank 2 Update
FORTRAN 77 SYNOPSIS
subroutine dsyr2( uplo, n, alpha, x, incx, y, incy, a, lda )
character*1 uplo
integer n, incx, incy, lda
double precision alpha
double precision a( lda,*), x(*), y(*)
subroutine ssyr2( uplo, n, alpha, x, incx, y, incy, a, lda)
character*1 uplo
integer n, incx, incy, lda
real alpha
real a( lda,*), x(*), y(*)
subroutine zher2( uplo, n, alpha, x, incx, y, incy, a, lda)
character*1 uplo
integer n, incx, incy, lda
complex*16 alpha
complex*16 a( lda,*), x(*), y(*)
subroutine cher2( uplo, n, alpha, x, incx, y, incy, a, lda)
character*1 uplo
integer n, incx, incy, lda
complex alpha
complex a( lda,*), x(*), y(*)
void dsyr2( uplo, n, alpha, x, incx, y, incy, a, lda )
MatrixTriangle uplo;
Integer n, incx, incy, lda;
double alpha
double (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void ssyr2( uplo, n, alpha, x, incx, y, incy, a, lda )
MatrixTriangle uplo;
Integer n, incx, incy, lda;
float alpha
float (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void zher2( uplo, n, alpha, x, incx, y, incy, a, lda )
MatrixTriangle uplo;
Integer n, incx, incy, lda;
Zomplex alpha
Zomplex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
void cher2( uplo, n, alpha, x, incx, y, incy, a, lda )
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MatrixTriangle uplo;
Integer n, incx, incy, lda;
Complex alpha
Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
dsyr2 and ssyr2 perform the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
zher2 and cher2 perform the hermitian rank 2 operation
A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
where alpha is a scalar, x and y are n element vectors and A is an n by n
symmetric/hermitian matrix.
uplo On entry, uplo specifies whether the upper or lower triangular
part of the array A is to be referenced a follows:
FORTRAN
uplo = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
uplo = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
C
uplo = UpperTriangle Only the lower triangular part of A
is to be referenced.
uplo = LowerTriangle Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
n On entry, n specifies the the order of the matrix A. n must be
at least zero.
Unchanged on exit.
alpha specifies the scalar alpha.
Unchanged on exit.
x Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
entry, the incremented array x must contain the n element vector
x.
Unchanged on exit.
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incx On entry, incx specifies the increment for the elements of x.
incx must not be zero.
Unchanged on exit.
y Array of size at least ( 1 + ( n - 1 )*abs( incy ) ). Before
entry, the incremented array y must contain the n element vector
y. On exit, Y is overwritten by the updated vector y.
incy On entry, incy specifies the increment for the elements of y.
incy must not be zero.
Unchanged on exit.
a An array containing the matrix A.
FORTRAN
Array of dimension ( lda, n ).
C
A pointer to an array of size lda*n.
See note below about array storage convention for C.
Before entry with uplo = 'U' or 'u' or , the array elements
corresponding to the leading n by n upper triangular part of the
matrix A must contain the uppertriangular part of the
symmetric/hermitian matrix and the corresponding strictly lower
triangular part of A is not referenced. On exit, the array
elements corresponding to the upper triangular part of the matrix
A is overwritten by the upper triangular part of the updated
matrix.
Before entry with uplo = 'L' or 'l' or , the array elements
corresponding to the leading n by n lower triangular part of the
matrix A must contain the lower triangular part of the
symmetric/hermitian matrix and the corresponding strictly upper
triangular part of A is not referenced. On exit, the array
elements corresponding to the lower triangular part of the matrix
A is overwritten by the lower triangular part of the updated
matrix.
Note that the imaginary parts of the diagonal elements need not
be set and are assumed to be zero.
lda On entry, lda specifies the first dimension of A as declared in
the calling (sub) program. lda must be at least ( k + 1 ).
Unchanged on exit.
C ARRAY STORAGE CONVENTION
The matrices are assumed to be stored in a one dimensional C array
in an analogous fashion as a Fortran array (column major). Therefore,
the element A(i+1,j) of matrix A is stored immediately after the
element A(i,j), while A(i,j+1) is lda elements apart from A(i,j).
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The element A(i,j) of the matrix can be accessed directly by reference
to a[ (j-1)*lda + (i-1) ].
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
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