Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
p?trsv
Solves a system of linear equations whose coefficients are in a distributed triangular matrix.
Syntax
call pstrsv ( uplo , trans , diag , n , a , ia , ja , desca , x , ix , jx , descx , incx )
call pdtrsv ( uplo , trans , diag , n , a , ia , ja , desca , x , ix , jx , descx , incx )
call pctrsv ( uplo , trans , diag , n , a , ia , ja , desca , x , ix , jx , descx , incx )
call pztrsv ( uplo , trans , diag , n , a , ia , ja , desca , x , ix , jx , descx , incx )
Include Files
mkl_pblas.h
Description
The p?trsv routines solve one of the systems of equations:
sub(A)*sub(x) = b , or sub(A)'*sub(x) = b , or conjg(sub(A)')*sub(x) = b ,
where:
sub(A) is a n -by- n unit, or non-unit, upper or lower triangular distributed matrix, sub(A) = A(ia:ia+n-1, ja:ja+n-1) ,
b and sub(x) are n -element distributed vectors,
sub(x) denotes X(ix, jx:jx+n-1) if incx = m_x , and X(ix: ix+n-1, jx) if incx = 1, .
The routine does not test for singularity or near-singularity. Such tests must be performed before calling this routine.
Input Parameters
uplo
(global) CHARACTER*1 . Specifies whether the distributed matrix sub(A) is upper or lower triangular:
if uplo = 'U' or ‘u’ , then the matrix is upper triangular; if uplo = 'L' or ‘l’ , then the matrix is low triangular.
trans
(global) CHARACTER*1 . Specifies the form of the system of equations:
if transa = 'N' or 'n' , then sub(A)*sub(x) = b ; if transa = 'T' or 't' , then sub(A)'*sub(x) = b ; if transa = 'C' or 'c' , then conjg(sub(A)')*sub(x) = b .
diag
(global) CHARACTER*1 . Specifies whether the matrix sub(A) is unit triangular:
if diag = 'U' or ‘u’ then the matrix is unit triangular; if diag = 'N' or ‘n’ , then the matrix is not unit triangular.
n
(global) INTEGER . Specifies the order of the distributed matrix sub(A) , n ≥ 0.
a
(local) REAL for pstrsv
DOUBLE PRECISION for pdtrsv COMPLEX for pctrsv DOUBLE COMPLEX for pztrsv Array, size at least (lld_a, LOCq(1, ja+n-1)) . Before entry with uplo = 'U' or ‘u’ , this array contains the local entries corresponding to the entries of the upper triangular distributed matrix sub(A) , and the local entries corresponding to the entries of the strictly lower triangular part of the distributed matrix sub(A) is not referenced. Before entry with uplo = 'L' or ‘l’ , this array contains the local entries corresponding to the entries of the lower triangular distributed matrix sub(A) , and the local entries corresponding to the entries of the strictly upper triangular part of the distributed matrix sub(A) is not referenced . When diag = 'U' or ‘u’ , the local entries corresponding to the diagonal elements of the submatrix sub(A) are not referenced either, but are assumed to be unity.
ia , ja
(global) INTEGER . The row and column indices in the distributed matrix A indicating the first row and the first column of the submatrix sub(A) , respectively.
desca
(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix A .
x
(local) REAL for pstrsv
DOUBLE PRECISION for pdtrsv COMPLEX for pctrsv DOUBLE COMPLEX for pztrsv Array, size at least (jx-1)*m_x + ix+(n-1)*abs(incx)) . This array contains the entries of the distributed vector sub(x) . Before entry, sub(x) must contain the n -element right-hand side distributed vector b .
ix , jx
(global) INTEGER . The row and column indices in the distributed matrix X indicating the first row and the first column of the submatrix sub(x) , respectively.
descx
(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix X .
incx
(global) INTEGER . Specifies the increment for the elements of sub(x) . Only two values are supported, namely 1 and m_x . incx must not be zero.
Output Parameters
- x
-
Overwritten with the solution vector.