| trmv(3) | Library Functions Manual | trmv(3) |
NAME
trmv - trmv: triangular matrix-vector multiply
SYNOPSIS
Functions
subroutine ctrmv (uplo, trans, diag, n, a, lda, x, incx)
CTRMV subroutine dtrmv (uplo, trans, diag, n, a, lda, x, incx)
DTRMV subroutine strmv (uplo, trans, diag, n, a, lda, x, incx)
STRMV subroutine ztrmv (uplo, trans, diag, n, a, lda, x, incx)
ZTRMV
Detailed Description
Function Documentation
subroutine ctrmv (character uplo, character trans, character diag, integer n, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx)
CTRMV
Purpose:
CTRMV performs one of the matrix-vector operations
x := A*x, or x := A**T*x, or x := A**H*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A**T*x.
TRANS = 'C' or 'c' x := A**H*x.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
A
A is COMPLEX array, dimension ( 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.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
X
X is COMPLEX array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
transformed vector x.
INCX
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Definition at line 146 of file ctrmv.f.
subroutine dtrmv (character uplo, character trans, character diag, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx)
DTRMV
Purpose:
DTRMV performs one of the matrix-vector operations
x := A*x, or x := A**T*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A**T*x.
TRANS = 'C' or 'c' x := A**T*x.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
A
A is DOUBLE PRECISION array, dimension ( 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.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
X
X is DOUBLE PRECISION array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
transformed vector x.
INCX
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Definition at line 146 of file dtrmv.f.
subroutine strmv (character uplo, character trans, character diag, integer n, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx)
STRMV
Purpose:
STRMV performs one of the matrix-vector operations
x := A*x, or x := A**T*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A**T*x.
TRANS = 'C' or 'c' x := A**T*x.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
A
A is REAL array, dimension ( 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.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
X
X is REAL array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
transformed vector x.
INCX
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Definition at line 146 of file strmv.f.
subroutine ztrmv (character uplo, character trans, character diag, integer n, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)
ZTRMV
Purpose:
ZTRMV performs one of the matrix-vector operations
x := A*x, or x := A**T*x, or x := A**H*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Parameters
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A**T*x.
TRANS = 'C' or 'c' x := A**H*x.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
A
A is COMPLEX*16 array, dimension ( 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.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
X
X is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
transformed vector x.
INCX
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Definition at line 146 of file ztrmv.f.
Author
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