Visible to Intel only — GUID: GUID-13DB003B-72CE-4F87-8952-9A6914F51337
Visible to Intel only — GUID: GUID-13DB003B-72CE-4F87-8952-9A6914F51337
?trsv
Solves a system of linear equations whose coefficients are in a triangular matrix.
Syntax
call strsv(uplo, trans, diag, n, a, lda, x, incx)
call dtrsv(uplo, trans, diag, n, a, lda, x, incx)
call ctrsv(uplo, trans, diag, n, a, lda, x, incx)
call ztrsv(uplo, trans, diag, n, a, lda, x, incx)
call trsv(a, x [,uplo] [, trans] [,diag])
Include Files
- mkl.fi, blas.f90
Description
The ?trsv routines solve one of the systems of equations:
A*x = b, or A'*x = b, or conjg(A')*x = b,
where:
b and x are n-element vectors,
A is an n-by-n unit, or non-unit, upper or lower triangular matrix.
The routine does not test for singularity or near-singularity.
Such tests must be performed before calling this routine.
Input Parameters
- uplo
-
CHARACTER*1. Specifies whether the matrix A is upper or lower triangular:
uplo = 'U' or 'u'if uplo = 'L' or 'l', then the matrix is low triangular.
- trans
-
CHARACTER*1. Specifies the systems of equations:
if trans= 'N' or 'n', then A*x = b;
if trans= 'T' or 't', then A'*x = b;
if trans= 'C' or 'c', then oconjg(A')*x = b.
- diag
-
CHARACTER*1. Specifies whether the matrix 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
-
INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.
- a
-
REAL for strsv
DOUBLE PRECISION for dtrsv
COMPLEX for ctrsv
DOUBLE COMPLEX for ztrsv
Array, size (lda, n) . Before entry with uplo = 'U' or 'u', the leading n-by-n 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 n-by-n lower triangular part of the array a must contain the lower triangular matrix and the strictly upper triangular part of a is not referenced.
When diag = 'U' or 'u', the diagonal elements of a are not referenced either, but are assumed to be unity.
- lda
-
INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least max(1, n).
- x
-
REAL for strsv
DOUBLE PRECISION for dtrsv
COMPLEX for ctrsv
DOUBLE COMPLEX for ztrsv
Array, size at least (1 + (n - 1)*abs(incx)). Before entry, the incremented array x must contain the n-element right-hand side vector b.
- incx
-
INTEGER. Specifies the increment for the elements of x.
The value of incx must not be zero.
Output Parameters
- x
-
Overwritten with the solution vector x.
BLAS 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions.
Specific details for the routine trsv interface are the following:
- a
-
Holds the matrix a of size (n,n).
- x
-
Holds the vector with the number of elements n.
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
- trans
-
Must be 'N', 'C', or 'T'.
The default value is 'N'.
- diag
-
Must be 'N' or 'U'. The default value is 'N'.