Visible to Intel only — GUID: GUID-2561C13C-7BA9-414B-8B43-1A915C4061EB
Visible to Intel only — GUID: GUID-2561C13C-7BA9-414B-8B43-1A915C4061EB
?tpsv
Solves a system of linear equations whose coefficients are in a triangular packed matrix.
Syntax
call stpsv(uplo, trans, diag, n, ap, x, incx)
call dtpsv(uplo, trans, diag, n, ap, x, incx)
call ctpsv(uplo, trans, diag, n, ap, x, incx)
call ztpsv(uplo, trans, diag, n, ap, x, incx)
call tpsv(ap, x [,uplo] [, trans] [,diag])
Include Files
- mkl.fi, blas.f90
Description
The ?tpsv routines solve one of the following 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, supplied in packed form.
This 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 system 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 conjg(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.
- ap
-
REAL for stpsv
DOUBLE PRECISION for dtpsv
COMPLEX for ctpsv
DOUBLE COMPLEX for ztpsv
Array, size at least ((n*(n + 1))/2).
Before entry with uplo = 'U' or 'u', the array ap must contain the upper triangular part of the triangular matrix packed sequentially, column-by-column, so that ap(1) contains a(1, 1), ap(2) and ap(3) contain a(1, 2) and a(2, 2) respectively, and so on.
Before entry with uplo = 'L' or 'l', the array ap must contain the lower triangular part of the triangular matrix packed sequentially, column-by-column, so that ap(1) contains a(1, 1), ap(2) and ap(3) contain a(2, 1) and a(3, 1) respectively, and so on.
When diag = 'U' or 'u', the diagonal elements of a are not referenced, but are assumed to be unity.
- x
-
REAL for stpsv
DOUBLE PRECISION for dtpsv
COMPLEX for ctpsv
DOUBLE COMPLEX for ztpsv
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 tpsv interface are the following:
- ap
-
Holds the array ap of size (n*(n+1)/2).
- 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'.