_TRSM(3F) _TRSM(3F)
dtrsm, strsm, ztrsm, ctrsm - BLAS level three Solution of Systems of
Equations
FORTRAN 77 SYNOPSIS
subroutine dtrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
character*1 side,uplo,transa,diag
integer m, n, lda, ldb
double precision alpha
double precision a( lda,*), b(ldb,*)
subroutine strsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
character*1 side,uplo,transa,diag
integer m, n, lda, ldb
real alpha
real a( lda,*), b(ldb,*)
subroutine ztrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
character*1 side,uplo,transa,diag
integer m, n, lda, ldb
double complex alpha
double complex a( lda,*), b(ldb,*)
subroutine ctrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
character*1 side,uplo,transa,diag
integer m, n, lda, ldb
complex alpha
complex a( lda,*), b(ldb,*)
void dtrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
OperationSide side;
MatrixTriangle uplo;
MatrixTranspose transa;
MatrixUnitTriangular diag;
Integer m, n, tda, tdb;
double alpha;
double (*a)[lda*k], (*b)[lda*n];
void strsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
OperationSide side;
MatrixTriangle uplo;
MatrixTranspose transa;
MatrixUnitTriangular diag;
Integer m, n, lda, ldb;
float alpha;
float (*a)[lda*k], (*b)[lda*n];
void ztrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
OperationSide side;
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MatrixTriangle uplo;
MatrixTranspose transa;
MatrixUnitTriangular diag;
Integer m, n, lda, ldb;
Zomplex alpha;
Zomplex (*a)[lda*k], (*b)[lda*n];
void ctrsm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
OperationSide side;
MatrixTriangle uplo;
MatrixTranspose transa;
MatrixUnitTriangular diag;
Integer m, n, lda, ldb;
Complex alpha;
Complex (*a)[lda*k], (*b)[lda*n];
dtrsm, strsm, ztrsm and ctrsm solve 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 On entry, side specifies whether op( A ) appears on the left or
right of X as follows:
FORTRAN
side = 'L' or 'l' op( A )*X = alpha*B.
side = 'R' or 'r' X*op( A ) = alpha*B.
C
side = LeftSide op( A )*X = alpha*B.
side = RightSide X*op( A ) = alpha*B.
Unchanged on exit.
uplo On entry, uplo specifies whether the matrix A is an upper or
lower triangular matrix as follows:
FORTRAN
uplo = 'U' or 'u' A is an upper triangular matrix.
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uplo = 'L' or 'l' A is a lower triangular matrix.
C
uplo = UpperTriangle A is an upper triangular matrix.
uplo = LowerTriangle A is a lower triangular matrix.
Unchanged on exit.
transa On entry, transa specifies the form of op( A ) to be used in the
matrix multiplication as follows:
FORTRAN
transa = 'N' or 'n' op( A ) = A.
transa = 'T' or 't' op( A ) = A'.
transa = 'C' or 'c' op( A ) = conjg( A' ).
C
transa = NoTranspose op( A ) = A.
transa = Transpose op( A ) = A'.
transa = ConjugateTranspose op( A ) = conjg( A' ).
Unchanged on exit.
diag On entry, diag specifies whether or not A is unit triangular as
follows:
FORTRAN
diag = 'U' or 'u' A is assumed to be unit
triangular.
diag = 'N' or 'n' A is not assumed to be unit
triangular.
C
diag = UnitTriangular A is assumed to be unit
triangular.
diag = NotUnitTriangular A is not assumed to be unit
triangular.
Unchanged on exit.
m On entry, m specifies the number of rows of B. m must be at least
zero.
Unchanged on exit.
n On entry, n specifies the number of columns of B. n must be at
least zero.
Unchanged on exit.
alpha 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.
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a An array containing the matrix A.
FORTRAN
Array of dimension (lda, k).
C
A pointer to an array of size lda*k.
See note below about array storage convention for C.
k is m when side = 'L' or 'l' or LeftSide and is n when side =
'R' or 'r' or RightSide.
Before entry with uplo = 'U' or 'u' or , the elements
corresponding to the leading k by k upper triangular elements of
the matrix A must contain the upper triangular matrix and the
corresponding strictly lower triangular part of the matrix A is
not referenced.
Before entry with uplo = 'L' or 'l' or , the elements
corresponding to the leading k by k lower triangular elements of
the matrix A must contain the lower triangular matrix and the
corresponding strictly upper triangular part of the matrix A is
not referenced.
Note that when diag = 'U' or 'u' or , the elements corresponding
to the diagonal elements of the matrix A are not referenced
either, but are assumed to be unity.
Unchanged on exit.
lda 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 An array containing the matrix B.
FORTRAN
An array of dimension ( ldb, n ).
C
A pointer to an array of size ldb*n.
See note below about array storage convention for C.
Before entry it should contain the elements corresponding to the
m by n matrix B. On exit it overwritten by the transformed
matrix.
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ldb 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.
C ARRAY STORAGE CONVENTION
The matrices are assumed to be stored in a one dimensional C array
in an analogous fashion as a Fortran array (column major). Therefore,
the element A(i+1,j) of matrix A is stored immediately after the
element A(i,j), while A(i,j+1) is lda elements apart from A(i,j).
The element A(i,j) of the matrix can be accessed directly by reference
to a[ (j-1)*lda + (i-1) ].
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.
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