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Visible to Intel only — GUID: GUID-ADA1769F-627E-4311-BBE8-3D931729D4FE
?trmv
Computes a matrix-vector product using a triangular matrix.
Syntax
call strmv(uplo, trans, diag, n, a, lda, x, incx)
call dtrmv(uplo, trans, diag, n, a, lda, x, incx)
call ctrmv(uplo, trans, diag, n, a, lda, x, incx)
call ztrmv(uplo, trans, diag, n, a, lda, x, incx)
call trmv(a, x [,uplo] [, trans] [,diag])
Include Files
- mkl.fi, blas.f90
Description
The ?trmv routines perform one of the following matrix-vector operations defined as
x := A*x, or x := A'*x, or x := conjg(A')*x,
where:
x is an n-element vector,
A is an n-by-n unit, or non-unit, upper or lower triangular matrix.
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 operation:
if trans= 'N' or 'n', then x := A*x;
if trans= 'T' or 't', then x := A'*x;
if trans= 'C' or 'c', then x := conjg(A')*x.
- 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 strmv
DOUBLE PRECISION for dtrmv
COMPLEX for ctrmv
DOUBLE COMPLEX for ztrmv
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 strmv
DOUBLE PRECISION for dtrmv
COMPLEX for ctrmv
DOUBLE COMPLEX for ztrmv
Array, size at least (1 + (n - 1)*abs(incx)). Before entry, the incremented array x must contain the n-element vector x.
- incx
-
INTEGER. Specifies the increment for the elements of x.
The value of incx must not be zero.
Output Parameters
- x
-
Overwritten with the transformed 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 trmv 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'.