Level 3 BLAS
SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
SGEMM 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',
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.
TRANSA - 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'.
TRANSA = 'C' or 'c', op( A ) = A'.
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( B ) = B.
TRANSA = 'T' or 't', op( B ) = B'.
TRANSA = 'C' or 'c', op( B ) = B'.
Unchanged on exit.
M - 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.
Unchanged on exit.
N - 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.
Unchanged on exit.
K - 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.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - REAL array of 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.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE SSYMM(SIDE,UPLO,TRANSB,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
SSYMM performs one of the matrix-matrix operations
C := alpha*A*op( B ) + beta*C,
or
C := alpha*op( B )*A + beta*C,
where op( B ) is one of
op( B ) = B or op( B ) = B',
alpha and beta are scalars, A is a symmetric matrix, op( B ) is an
m by n matrix and C is an m by n matrix.
SIDE - 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*op( B ) + beta*C,
SIDE = 'R' or 'r' C := alpha*op( B )*A + beta*C,
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper of 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.
Unchanged on exit.
TRANSB - 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'.
TRANSB = 'C' or 'c' op( B ) = B'.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n' and is m otherwise.
Before entry with TRANSB = 'N' or 'n', the leading m by n
part of the array B must contain the matrix B. Before entry
with TRANSB = 'T' or 't' or 'C' or 'c', the leading n by m
part of the array B must contain the matrix B.
Unchanged on exit.
LDB - 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, m ), otherwise LDB must
be at least max( 1, n ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE SSYRK(UPLO,TRANSA,N,K,ALPHA,A,LDA,BETA,C,LDC)
SSYRK performs one of the symmetric rank k operations
C := alpha*A*A' + beta*C,
or
C := alpha*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.
UPLO - 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.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the operation to be performed as
follows:
TRANSA = 'N' or 'n' C := alpha*A*A' + beta*C.
TRANSA = 'T' or 't' C := alpha*A'*A + beta*C.
TRANSA = 'C' or 'c' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANSA = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANSA = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is n otherwise.
Before entry with TRANSA = '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.
Unchanged on exit.
LDA - 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, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE SSYR2K(UPLO,TRANSA,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
SSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B' + alpha*B*A' + beta*C,
or
C := alpha*A'*B + alpha*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.
UPLO - 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.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the operation to be performed as
follows:
TRANSA = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
beta*C.
TRANSA = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
beta*C.
TRANSA = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANSA = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANSA = '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.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is n otherwise.
Before entry with TRANSA = '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.
Unchanged on exit.
LDA - 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, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, kb ), where kb is
k when TRANSA = 'N' or 'n', and is n otherwise.
Before entry with TRANSA = '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.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSA = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE STRMM(SIDE,UPLO,TRANS,DIAG,M,N,A,LDA,B,LDB)
STRMM performs one of the matrix-matrix operations
B := op( A )*B, or B := B*op( A )
where 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'.
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := op( A )*B.
SIDE = 'R' or 'r' B := B*op( A ).
Unchanged on exit.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANS = 'N' or 'n' op( A ) = A.
TRANS = 'T' or 't' op( A ) = A'.
TRANS = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
A - REAL array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE STRSM(SIDE,UPLO,TRANS,DIAG,M,N,A,LDA,B,LDB)
STRSM solves one of the matrix equations
op( A )*X = B, or X*op( A ) = B,
where 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'.
The matrix X is overwritten on B.
SIDE - 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 = B.
SIDE = 'R' or 'r' X*op( A ) = B.
Unchanged on exit.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANS = 'N' or 'n' op( A ) = A.
TRANS = 'T' or 't' op( A ) = A'.
TRANS = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
A - REAL array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - REAL array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
CGEMM 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' or op( X ) = conjg( X' ),
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.
TRANSA - 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'.
TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
Unchanged on exit.
TRANSB - 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'.
TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
Unchanged on exit.
M - 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.
Unchanged on exit.
N - 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.
Unchanged on exit.
K - 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.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of 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.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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.
SIDE - 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,
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper of 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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.
SIDE - 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,
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper of 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
CSYRK performs one of the symmetric rank k operations
C := alpha*A*A' + beta*C,
or
C := alpha*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.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - 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', K specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
CHERK performs one of the hermitian rank k operations
C := alpha*A*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*A + beta*C,
where alpha and beta are real 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.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of 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 hermitian 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 hermitian 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.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - 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 ).
Unchanged on exit.
SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
CSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B' + alpha*B*A' + beta*C,
or
C := alpha*A'*B + alpha*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.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
beta*C.
TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - 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', K specifies the number of rows of the
matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of 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.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
CHER2K performs one of the hermitian rank 2k operations
C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
where alpha and beta are scalars with beta real, 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.
UPLO - 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.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - 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 = 'C' or 'c', K specifies the number of rows of the
matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of 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.
Unchanged on exit.
LDB - 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 ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of 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 hermitian 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 hermitian 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.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - 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 ).
Unchanged on exit.
SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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 or op( A ) = A' or op( A ) = conjg( A' ).
SIDE - 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 ).
Unchanged on exit.
UPLO - 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.
Unchanged on exit.
TRANSA - 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'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of 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 - 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 ).
Unchanged on exit.
SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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 or op( A ) = A' or op( A ) = conjg( A' ).
The matrix X is overwritten on B.
SIDE - 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.
Unchanged on exit.
UPLO - 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.
Unchanged on exit.
TRANSA - 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'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX array of 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.
Unchanged on exit.
LDA - 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 ).
Unchanged on exit.
B - COMPLEX array of 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 - 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 ).
Unchanged on exit.
This material was reproduced for educational use only from
the Pittsburgh Supercomputing Center and is copyrighted
© by the PSC.