Provided by: liblapack-doc_3.11.0-2build1_all 
NAME
double_blas_level3 - double
SYNOPSIS
Functions
subroutine dgemm (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
subroutine dsymm (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
subroutine dsyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYR2K
subroutine dsyrk (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
subroutine dtrmm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
subroutine dtrsm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Detailed Description
This is the group of double LEVEL 3 BLAS routines.
Function Documentation
subroutine dgemm (character TRANSA, character TRANSB, integer M, integer N, integer K, 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)
DGEMM
Purpose:
DGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X**T,
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Parameters
TRANSA
TRANSA is CHARACTER*1
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A**T.
TRANSA = 'C' or 'c', op( A ) = A**T.
TRANSB
TRANSB is CHARACTER*1
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B**T.
TRANSB = 'C' or 'c', op( B ) = B**T.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix
op( A ) and 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
op( B ) and the number of columns of the matrix C. N must be
at least zero.
K
K is INTEGER
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K 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
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
B
B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k 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. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
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 matrix
( alpha*op( A )*op( B ) + beta*C ).
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 dsyr2k (character UPLO, character TRANS, integer N, integer K, 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)
DSYR2K
Purpose:
DSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B**T + alpha*B*A**T + beta*C,
or
C := alpha*A**T*B + alpha*B**T*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.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T +
beta*C.
TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
beta*C.
TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A +
beta*C.
N
N is INTEGER
On entry, N specifies the order of the matrix C. N must be
at least zero.
K
K is INTEGER
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrices A and B. K 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
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
B
B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k 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. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
BETA
BETA is DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
C
C is DOUBLE PRECISION array, dimension ( LDC, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the 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, n ).
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 dsyrk (character UPLO, character TRANS, integer N, integer K, double precision
ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision BETA, double
precision, dimension(ldc,*) C, integer LDC)
DSYRK
Purpose:
DSYRK performs one of the symmetric rank k operations
C := alpha*A*A**T + beta*C,
or
C := alpha*A**T*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.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C.
N
N is INTEGER
On entry, N specifies the order of the matrix C. N must be
at least zero.
K
K is INTEGER
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrix A. K 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
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
BETA
BETA is DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
C
C is DOUBLE PRECISION array, dimension ( LDC, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the 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, n ).
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 dtrmm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M,
integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA,
double precision, dimension(ldb,*) B, integer LDB)
DTRMM
Purpose:
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 ) = A**T.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANSA
TRANSA is CHARACTER*1
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A**T.
TRANSA = 'C' or 'c' op( A ) = A**T.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
M
M is INTEGER
On entry, M specifies the number of rows of B. M must be at
least zero.
N
N is INTEGER
On entry, N specifies the number of columns of B. N must be
at least zero.
ALPHA
ALPHA is DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
A
A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
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 ), when SIDE = 'R' or 'r'
then 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, and on exit is overwritten by the
transformed matrix.
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 ).
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 dtrsm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M,
integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA,
double precision, dimension(ldb,*) B, integer LDB)
DTRSM
Purpose:
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 ) = A**T.
The matrix X is overwritten on B.
Parameters
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANSA
TRANSA is CHARACTER*1
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A**T.
TRANSA = 'C' or 'c' op( A ) = A**T.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
M
M is INTEGER
On entry, M specifies the number of rows of B. M must be at
least zero.
N
N is INTEGER
On entry, N specifies the number of columns of B. N must be
at least zero.
ALPHA
ALPHA is DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
A
A is DOUBLE PRECISION array, dimension ( LDA, k ),
where k is m when SIDE = 'L' or 'l'
and k is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
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 ), when SIDE = 'R' or 'r'
then 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 right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
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 ).
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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