Rechenzentrum  

Beschreibung der einzelnen Routinen

 


Level 1 BLAS

REAL*4 Level 1 BLAS


ISAMAX
Find the smallest index of the component of a real vector having maximum absolute value.
SASUM
Sum the absolute values of the components of a single precision vector.
SAXPY
Compute the scalar times a vector plus a vector, y = ax + y, all single precision.
SCASUM
Sum the absolute values of the real part together with the absolute values of the imaginary part of
the components of a complex vector.
SCNRM2
Compute the Euclidean length or L2 norm of a complex-precision vector.
SCOPY
Copy a vector X to a vector Y, both single precision.
SDOT
Compute the single-precision dot product x*y.
SDSDOT
Compute the sum of a single-precision scalar and a single-precision dot product, a + x*y, using a
double-precision accumulator.
SNRM2
Compute the Euclidean length or L2 norm of a single-precision vector.
SROT
Apply a Givens plane rotation in single precision.
SROTG
Construct a Givens plane rotation in single precision.
SROTM
Apply a modified Givens plane rotation in single precision.
SROTMG
Construct a modified Givens plane rotation in single precision.
SSCAL
Multiply a vector by a scalar, y = ay, both single precision.
SSWAP
Interchange vectors X and Y, both single precision.


REAL*8 Level 1 BLAS


IDAMAX
Find the smallest index of the component of a double-precision vector having maximum absolute
value.
DASUM
Sum the absolute values of the components of a double precision vector.
DAXPY
Compute the scalar times a vector plus a vector, y = ax + y, all double precision.
DCOPY
Copy a vector X to a vector Y, both double precision.
DDOT
Compute the double-precision dot product x*y.
DROT
Apply a Givens plane rotation in double precision.
DROTG
Construct a Givens plane rotation in double precision.
DROTM
Apply a modified Givens plane rotation in double precision.
DROTMG
Construct a modified Givens plane rotation in double precision.
DSCAL
Multiply a vector by a scalar, y = ay, both double precision.
DSWAP
Interchange vectors X and Y, both double precision.
DZASUM
Sum the absolute values of the real part together with the absolute values of the imaginary part of
the components of a double-complex vector.
DZNRM2
Compute the Euclidean length or L2 norm of a double complex-precision vector.


COMPLEX*8 Level 1 BLAS


ICAMAX
Find the smallest index of the component of a complex vector having maximum magnitude.
CAXPY
Compute the scalar times a vector plus a vector, y = ax + y, all complex.
CCOPY
Copy a vector X to a vector Y, both complex.
CDOTC
Compute the complex conjugate dot product, conjg(x)*y.
CDOTU
Compute the complex dot product x*y.
CSCAL
Multiply a vector by a scalar, y = ay, both complex.
CSSCAL
Multiply a complex vector by a single-precision scalar, y = ay.
CSWAP
Interchange vectors X and Y, both complex.


COMPLEX*16 Level 1 BLAS


IZAMAX
Find the smallest index of the component of a double-complex vector having maximum magnitude.
ZAXPY
Compute the scalar times a vector plus a vector, y = ax + y, all double complex.
ZCOPY
Copy a vector X to a vector Y, both double complex.
ZDOTC
Compute the double-complex conjugate dot product, conjg(x)*y.
ZDOTU
Compute the double-complex dot product x*y.
ZDSCAL
Multiply a double-complex vector by a double-precision scalar, y = ay.
ZSCAL
Multiply a vector by a scalar, y = ay, both double complex.
ZSWAP
Interchange vectors X and Y, both double complex.



Level 2 BLAS

REAL*4 Level 2 BLAS


SGBMV
Perform one of the matrix-vector operations:
y = alpha*A*x + beta*y
or
y = alpha*trans(A)*x + beta*y
where A is a matrix stored in band storage mode, and trans(A) is the transpose of the matrix.
SGEMV
Perform one of the matrix-vector multiplications:
y = alpha*A*x + beta*y
y = alpha*trans(A)*x + beta*y
Here trans(A) is the transpose of the matrix.
SGER
Perform the rank-one matrix update:
A = alpha*x*trans(y) + A,
where trans(y) is the transpose of the vector.
SSBMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a symmetric matrix in band
symmetric storage mode.
SSPMV
Perform the matrix-vector multiplication: y = alpha*A*x + beta*y, where A is a symmetric and packed
matrix.
SSPR
Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where A is a symmetric and
packed matrix, and trans(x) represents the transpose of the vector.
SSPR2
Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) + alpha*y*trans(x), where A
is a symmetric and packed matrix, and trans( ) represents the transpose of the vectors.
SSYMV
Perform the matrix-vector multiplication: y = alpha*A*x + beta*y, where A is a symmetric and matrix.
SSYR
Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where A is a symmetric
matrix, and trans(x) represents the transpose of the vector.
SSYR2
Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) + alpha*y*trans(x), where A
is a symmetric matrix, and trans( ) represents the transpose of the vectors.
STBMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix in band storage mode, and trans(A) is the transpose of the matrix.
STBSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix in band storage mode, and trans(A) is the transpose of the matrix.
STPMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix in packed storage mode, and trans(A) is the transpose of the matrix.
STPSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix in packed storage mode, and trans(A) is the transpose of the matrix.
STRMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix, and trans(A) is the transpose of the matrix.
STRSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix, and trans(A) is the transpose of the matrix.

REAL*8 Level 2 BLAS


DGBMV
Perform one of the matrix-vector operations:
y = alpha*A*x + beta*y
or
y = alpha*trans(A)*x + beta*y
where A is a matrix stored in band storage mode, and trans(A) is the transpose of the matrix.
DGEMV
Perform one of the matrix-vector multiplications:
y = alpha*A*x + beta*y
y = alpha*trans(A)*x + beta*y
Here trans(A) is the transpose of the matrix.
DGER
Perform the rank-one matrix update:
A = alpha*x*trans(y) + A,
where trans(y) is the transpose of the vector.
DSBMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a symmetric matrix in band
symmetric storage mode.
DSPMV
Perform the matrix-vector multiplication: y = alpha*A*x + beta*y, where A is a symmetric and packed
matrix.
DSPR
Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where A is a symmetric and
packed matrix, and trans(x) represents the transpose of the vector.
DSPR2
Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) + alpha*y*trans(x), where A
is a symmetric and packed matrix, and trans( ) represents the transpose of the vectors.
DSYMV
Perform the matrix-vector multiplication y = alpha*A*x + beta*y, where A is a symmetric matrix.
DSYR
Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where A is a symmetric
matrix, and trans(x) represents the transpose of the vector.
DSYR2
Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) + alpha*y*trans(x), where A
is a symmetric matrix, and trans( ) represents the transpose of the vectors.
DTBMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix in band storage mode, and trans(A) is the transpose of the matrix.
DTBSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix in band storage mode, and trans(A) is the transpose of the matrix.
DTPMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix in packed storage mode, and trans(A) is the transpose of the matrix.
DTPSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix in packed storage mode, and trans(A) is the transpose of the matrix.
DTRMV
Perform one of the matrix-vector operations:
x = A*x,
or
x = trans(A)*x,
where A is a triangular matrix, and trans(A) is the transpose of the matrix.
DTRSV
Solve one of the triangular systems,
x = inv(A)*x,
or
x = inv(trans(A))*x,
where A is a triangular matrix, and trans(A) is the transpose of the matrix.

COMPLEX*8 Level 2 BLAS


CGBMV
Perform one of the matrix-vector operations:
y = alpha*A*x + beta*y,
y = alpha*trans(A)*x + beta*y,
y = alpha*ctrans(A)*x + beta*y,
where A is a matrix stored in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
CGEMV
Perform one of the matrix-vector multiplications:
y = alpha*A*x + beta*y
y = alpha*trans(A)*x + beta*y
y = alpha*ctrans(A)*x + beta*y
Here trans(A) is the transpose of the matrix, and ctrans(A) is the conjugate transpose of the matrix.
CGERC
Perform the rank-one matrix update:
A = A + alpha*x*ctrans(y),
where ctrans(y) is the conjugate transpose of the vector.
CGERU
Perform the rank-one matrix update:
A = A + alpha*x*trans(y),
where trans(y) is the transpose of the vector.
CHBMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a Hermitian band matrix in
band Hermitian storage.
CHEMV
Perform the matrix-vector multiplication y = alpha*A*x + beta*y, where A is a Hermitian matrix.
CHER
Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitian matrix A, with A and x
complex and alpha real. The vector ctrans(x) is the conjugate transpose of x.
CHER2
Perform a rank-two matrix update to the Hermitian matrix A, A = A + alpha*x*ctrans(y) + conjg(alpha)
*y*ctrans(x). Here ctrans( ) represents the conjugate transpose of the vectors.
CHPMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a Hermitian matrix in packed
mode.
CHPR
Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitian matrix A (stored in
packed storage mode), with A and x complex and alpha real. The vector ctrans(x) is the conjugate
transpose of x.
CHPR2
Perform a rank-two matrix update to the Hermitian matrix A, A = A + alpha*x*ctrans(y) + conjg(alpha)
*y*ctrans(x). Here ctrans( ) represents the conjugate transpose of the vectors. A is stored in packed
storage mode.
CTBMV
Perform one of the matrix-vector operations:
x = A*x,
x = trans(A)*x,
x = ctrans(A)*x,
where A is a triangular matrix in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
CTBSV
Solve one of the triangular systems,
x = inv(A)*x,
x = inv(trans(A))*x,
x = inv(ctrans(A))*x,
where A is a triangular matrix in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
CTRMV
Perform one of the matrix-vector operations:
x = A*x,
x = trans(A)*x,
or
x = ctrans(A)*x,
where A is a triangular matrix, trans(A) is the transpose of the matrix, and ctrans(A) is the conjugate
transpose of the matrix.
CTRSV
Solve one of the triangular systems,
x = inv(A)*x,
x = inv(trans(A))*x,
or
x = inv(ctrans(A))*x,
where A is a triangular matrix, trans(A) is the transpose of the matrix, and ctrans(A) is the conjugate
transpose of the matrix.

COMPLEX*8 Level 2 BLAS


ZGBMV
Perform one of the matrix-vector operations:
y = alpha*A*x + beta*y,
y = alpha*trans(A)*x + beta*y,
y = alpha*ctrans(A)*x + beta*y,
where A is a matrix stored in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
ZGEMV
Perform one of the matrix-vector multiplications:
y = alpha*A*x + beta*y
y = alpha*trans(A)*x + beta*y
y = alpha*ctrans(A)*x + beta*y
Here trans(A) is the transpose of the matrix, and ctrans(A) is the conjugate transpose of the matrix.
ZGERC
Perform the rank-one matrix update:
A = A + alpha*x*ctrans(y),
where ctrans(y) is the conjugate transpose of the vector.
ZGERU
Perform the rank-one matrix update:
A = A + alpha*x*trans(y),
where trans(y) is the transpose of the vector.
ZHBMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a Hermitian band matrix in
band Hermitian storage.
ZHEMV
Perform the matrix-vector multiplication y = alpha*A*x + beta*y, where A is a Hermitian matrix.
ZHER
Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitian matrix A. The vector
ctrans(x) is the conjugate transpose of x.
ZHER2
Perform a rank-two matrix update to the Hermitian matrix A, A = A + alpha*x*ctrans(y) + conjg(alpha)
*y*ctrans(x). Here ctrans( ) represents the conjugate transpose of the vectors.
ZHERK
Performs one of the Hermitian rank k operations
C = alpha*A*ctrans( A ) + beta*C,
or
C = alpha*ctrans( A )*A + beta*C,
where alpha and beta are scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. The name 'ctrans' represents the conjugate
transpose of the matrix.
ZHPMV
Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is a Hermitian matrix in packed
mode.
ZHPR
Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitian matrix A (stored in
packed storage mode), with A and x complex and alpha real. The vector ctrans(x) is the conjugate
transpose of x.
ZHPR2
Perform a rank-two matrix update to the Hermitian matrix A, A = A + alpha*x*ctrans(y) + conjg(alpha)
*y*ctrans(x). Here ctrans( ) represents the conjugate transpose of the vectors. A is stored in packed
storage mode.
ZTBMV
Perform one of the matrix-vector operations:
x = A*x,
x = trans(A)*x,
x = ctrans(A)*x,
where A is a triangular matrix in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
ZTBSV
Solve one of the triangular systems,
x = inv(A)*x,
x = inv(trans(A))*x,
x = inv(ctrans(A))*x,
where A is a triangular matrix in band storage mode, trans(A) is the transpose of the matrix, and
ctrans(A) is the conjugate transpose of the matrix.
ZTPMV
Perform one of the matrix-vector operations:
x = A*x,
x = trans(A)*x,
x = ctrans(A)*x,
where A is a triangular matrix in packed storage mode, trans(A) is the transpose of the matrix,
and ctrans(A) is the conjugate transpose of the matrix.
ZTPSV
Solve one of the triangular systems,
x = inv(A)*x, x = inv(trans(A))*x, x = inv(ctrans(A))*x,
where A is a triangular matrix in packed storage mode, trans(A) is the transpose of the matrix,
and ctrans(A) is the conjugate transpose of the matrix.
ZTRMV
Perform one of the matrix-vector operations:
x = A*x,
x = trans(A)*x,
or
x = ctrans(A)*x,
where A is a triangular matrix, trans(A) is the transpose of the matrix, and ctrans(A) is the
conjugate transpose of the matrix.
ZTRSV
Solve one of the triangular systems,
x = inv(A)*x,
x = inv(trans(A))*x,
or
x = inv(ctrans(A))*x,
where A is a triangular matrix, trans(A) is the transpose of the matrix, and ctrans(A) is the conjugate
transpose of the matrix.



Level 3 BLAS

REAL*4 Level 3 BLAS


SGEMM
Perform one of the following matrix-matrix multiplications:
C = alpha*A*B + beta*C
C = alpha*trans(A)*B + beta*C
C = alpha*A*trans(B) + beta*C
C = alpha*trans(A)*trans(B) + beta*C
trans represents the transpose of the matrix.
SSYMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.
SSYRK
Performs one of the symmetric rank k operations
C = alpha*A*trans(A) + beta*C,
or
C = alpha*trans(A)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. Trans represents the transpose of the
matrix.
SSYR2K
Performs one of the symmetric rank 2k operations
C = alpha*A*trans(B) + alpha*B*trans(A) + beta*C,
or
C = alpha*trans(A)*B + alpha*trans(B)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. Trans represents the transpose of the
matrix.
STRMM
Performs one of the matrix-matrix operations:
B = alpha*op( A )*B,
or
B = alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular
matrix and op( A ) is one of
op( A ) = A
or
op( A ) = trans(A)
where trans represents the transpose of the matrix.
STRSM
Solves one of the matrix equations:
op( A )*X = alpha*B,
or
X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of:
op( A ) = A
or
op( A ) = trans(A).
Trans represents the transpose of the matrix. The matrix X is overwriBRen on B.


REAL*8 Level 3 BLAS


DGEMM
Perform one of the following matrix-matrix multiplications:
C = alpha*A*B + beta*C
C = alpha*trans(A)*B + beta*C
C = alpha*A*trans(B) + beta*C
C = alpha*trans(A)*trans(B) + beta*C
trans represents the transpose of the matrix.
DSYMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.
DSYRK
Performs one of the symmetric rank k operations
C = alpha*A*trans(A) + beta*C,
or
C = alpha*trans(A)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. Trans represents the transpose of the matrix.
DSYR2K
Performs one of the symmetric rank 2k operations
C = alpha*A*trans(B) + alpha*B*trans(A) + beta*C,
or
C = alpha*trans(A)*B + alpha*trans(B)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. Trans represents the transpose of the
matrix.
DTRMM
Performs one of the matrix-matrix operations:
B = alpha*op( A )*B,
or
B = alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular
matrix and op( A ) is one of
op( A ) = A
or
op( A ) = trans(A)
where trans represents the transpose of the matrix.
DTRSM
Solves one of the matrix equations:
op( A )*X = alpha*B,
or
X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of:
op( A ) = A
or
op( A ) = trans(A).
Trans represents the transpose of the matrix. The matrix X is overwriBRen on B.


COMPLEX*8 Level 3 BLAS


CGEMM
Perform one of the following matrix-matrix multiplications:
C = alpha*A*B + beta*C
C = alpha*trans(A)*B + beta*C
C = alpha*A*trans(B) + beta*C
C = alpha*trans(A)*trans(B) + beta*C
C = alpha*A*ctrans(B) + beta*C
C = alpha*ctrans(A)*B + beta*C
C = alpha*trans(A)*ctrans(B) + beta*C
C = alpha*ctrans(A)*trans(B) + beta*C
C = alpha*ctrans(A)*ctrans(B) + beta*C
trans represents the transpose of the matrix. The name 'ctrans' represents the conjugate transpose
of the matrix.
CHEMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a Hermitian matrix, and B and C are m by n matrices.
CHER2K
Performs one of the Hermitian rank 2k operations
C = alpha*A*ctrans( B ) + conjg( alpha )*B*ctrans( A )
+ beta*C,
or
C = alpha*ctrans( A )*B + conjg( alpha )*ctrans( B )*A
+ beta*C,
where alpha and beta are scalars, C is an n by n Hermitian matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. The name 'ctrans' represents the
conjugate transpose of the matrix.
CHERK
Performs one of the Hermitian rank k operations
C = alpha*A*ctrans( A ) + beta*C,
or
C = alpha*ctrans( A )*A + beta*C,
where alpha and beta are scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. The name 'ctrans' represents the conjugate
transpose of the matrix.
CSYMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.
CSYRK
Performs one of the symmetric rank k operations
C = alpha*A*trans(A) + beta*C,
or
C = alpha*trans(A)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. Trans represents the transpose of the matrix.
CSYR2K
Performs one of the symmetric rank 2k operations
C = alpha*A*trans(B) + alpha*B*trans(A) + beta*C,
or
C = alpha*trans(A)*B + alpha*trans(B)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. Trans represents the transpose of the
matrix.
CTRMM
Performs one of the matrix-matrix operations:
B = alpha*op( A )*B,
or
B = alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular
matrix and op( A ) is one of:
op( A ) = A
op( A ) = trans(A)
op( A ) = ctrans(A)
where trans represents the transpose of the matrix and The name 'ctrans' represents the conjugate
transpose of the matrix.
CTRSM
Solves one of the matrix equations:
op( A )*X = alpha*B,
or
X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of:
op( A ) = A
op( A ) = trans(A)
op( A ) = ctrans(A)
Trans represents the transpose of the matrix. The name 'ctrans' represents the conjugate
transpose of the matrix. The matrix X is overwritten on B.


COMPLEX*16 Level 3 BLAS


ZGEMM
Perform one of the following matrix-matrix multiplications:
C = alpha*A*B + beta*C
C = alpha*trans(A)*B + beta*C
C = alpha*A*trans(B) + beta*C
C = alpha*trans(A)*trans(B) + beta*C
C = alpha*A*ctrans(B) + beta*C
C = alpha*ctrans(A)*B + beta*C
C = alpha*trans(A)*ctrans(B) + beta*C
C = alpha*ctrans(A)*trans(B) + beta*C
C = alpha*ctrans(A)*ctrans(B) + beta*C
trans represents the transpose of the matrix. The name 'ctrans' represents the conjugate transpose
of the matrix.
ZHEMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a Hermitian matrix, and B and C are m by n matrices.
ZHER2K
Performs one of the Hermitian rank 2k operations
C = alpha*A*ctrans( B ) + conjg( alpha )*B*ctrans( A )
+ beta*C,
or
C = alpha*ctrans( A )*B + conjg( alpha )*ctrans( B )*A
+ beta*C,
where alpha and beta are scalars, C is an n by n Hermitian matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. The name 'ctrans' represents the
conjugate transpose of the matrix.
ZSYMM
Performs one of the matrix-matrix operations:
C = alpha*A*B + beta*C,
or
C = alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.
ZSYRK
Performs one of the symmetric rank k operations
C = alpha*A*trans(A) + beta*C,
or
C = alpha*trans(A)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the
first case and a k by n matrix in the second case. Trans represents the transpose of the matrix.
ZSYR2K
Performs one of the symmetric rank 2k operations
C = alpha*A*trans(B) + alpha*B*trans(A) + beta*C,
or
C = alpha*trans(A)*B + alpha*trans(B)*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices
in the first case and k by n matrices in the second case. Trans represents the transpose of the
matrix.
ZTRMM
Performs one of the matrix-matrix operations:
B = alpha*op( A )*B,
or
B = alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular
matrix and op( A ) is one of:
op( A ) = A
op( A ) = trans(A)
op( A ) = ctrans(A)
where trans represents the transpose of the matrix and The name 'ctrans' represents the conjugate
transpose of the matrix.
ZTRSM
Solves one of the matrix equations:
op( A )*X = alpha*B,
or
X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower
triangular matrix and op( A ) is one of:
op( A ) = A
op( A ) = trans(A)
op( A ) = ctrans(A)
Trans represents the transpose of the matrix. The name 'ctrans' represents the conjugate
transpose of the matrix. The matrix X is overwritten on B.
Letzte Änderung: 30.09.2008 14:25