table of contents
| hemm(3) | LAPACK | hemm(3) |
NAME¶
hemm - {he,sy}mm: Hermitian/symmetric matrix-matrix multiply
SYNOPSIS¶
Functions¶
subroutine chemm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
CHEMM subroutine csymm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
CSYMM subroutine dsymm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
DSYMM subroutine ssymm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
SSYMM subroutine zhemm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
ZHEMM subroutine zsymm (side, uplo, m, n, alpha, a, lda, b, ldb,
beta, c, ldc)
ZSYMM
Detailed Description¶
Function Documentation¶
subroutine chemm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)¶
CHEMM
Purpose:
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 an hermitian matrix and B and
C are m by n matrices.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the hermitian matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the hermitian matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
hermitian matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
hermitian matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is COMPLEX
On entry, ALPHA specifies the scalar alpha.
A
A is COMPLEX array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the hermitian matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the hermitian matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the hermitian
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the hermitian matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the hermitian matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the hermitian
matrix and the strictly upper triangular part of A is not
referenced.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is COMPLEX array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is COMPLEX
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is COMPLEX array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
subroutine csymm (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)¶
CSYMM
Purpose:
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.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the symmetric matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
symmetric matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is COMPLEX
On entry, ALPHA specifies the scalar alpha.
A
A is COMPLEX array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is COMPLEX array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is COMPLEX
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is COMPLEX array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
subroutine dsymm (character side, character uplo, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)¶
DSYMM
Purpose:
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.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the symmetric matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
symmetric matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
A
A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is DOUBLE PRECISION array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is DOUBLE PRECISION array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
subroutine ssymm (character side, character uplo, integer m, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)¶
SSYMM
Purpose:
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.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the symmetric matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
symmetric matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is REAL
On entry, ALPHA specifies the scalar alpha.
A
A is REAL array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is REAL array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is REAL
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is REAL array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
subroutine zhemm (character side, character uplo, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)¶
ZHEMM
Purpose:
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 an hermitian matrix and B and
C are m by n matrices.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the hermitian matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the hermitian matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
hermitian matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
hermitian matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
A
A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the hermitian matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the hermitian matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the hermitian
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the hermitian matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the hermitian matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the hermitian
matrix and the strictly upper triangular part of A is not
referenced.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is COMPLEX*16 array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is COMPLEX*16 array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
subroutine zsymm (character side, character uplo, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)¶
ZSYMM
Purpose:
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.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the symmetric matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
symmetric matrix is to be referenced.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
ALPHA
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
A
A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
B
B is COMPLEX*16 array, dimension ( LDB, N )
Before entry, the leading m by n part of the array B must
contain the matrix B.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
BETA
BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
C
C is COMPLEX*16 array, dimension ( LDC, N )
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Author¶
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