Man page - tpmv(3)

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Manual

tpmv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctpmv (character uplo, character trans, character diag, integern, complex, dimension(*) ap, complex, dimension(*) x, integer incx)
subroutine dtpmv (character uplo, character trans, character diag, integern, double precision, dimension(*) ap, double precision, dimension(*) x,integer incx)
subroutine stpmv (character uplo, character trans, character diag, integern, real, dimension(*) ap, real, dimension(*) x, integer incx)
subroutine ztpmv (character uplo, character trans, character diag, integern, complex*16, dimension(*) ap, complex*16, dimension(*) x, integerincx)
Author

NAME

tpmv - tpmv: triangular matrix-vector multiply

SYNOPSIS

Functions

subroutine ctpmv (uplo, trans, diag, n, ap, x, incx)
CTPMV
subroutine dtpmv (uplo, trans, diag, n, ap, x, incx)
DTPMV
subroutine stpmv (uplo, trans, diag, n, ap, x, incx)
STPMV
subroutine ztpmv (uplo, trans, diag, n, ap, x, incx)
ZTPMV

Detailed Description

Function Documentation

subroutine ctpmv (character uplo, character trans, character diag, integern, complex, dimension(*) ap, complex, dimension(*) x, integer incx)

CTPMV

Purpose:

CTPMV 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, supplied in packed form.

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.

AP

AP is COMPLEX array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ’U’ or ’u’, the array AP must
contain the upper 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 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.
Note that when DIAG = ’U’ or ’u’, the diagonal elements of
A are not referenced, but are assumed to be unity.

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.

subroutine dtpmv (character uplo, character trans, character diag, integern, double precision, dimension(*) ap, double precision, dimension(*) x,integer incx)

DTPMV

Purpose:

DTPMV 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, supplied in packed form.

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.

AP

AP is DOUBLE PRECISION array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ’U’ or ’u’, the array AP must
contain the upper 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 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.
Note that when DIAG = ’U’ or ’u’, the diagonal elements of
A are not referenced, but are assumed to be unity.

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.

subroutine stpmv (character uplo, character trans, character diag, integern, real, dimension(*) ap, real, dimension(*) x, integer incx)

STPMV

Purpose:

STPMV 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, supplied in packed form.

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.

AP

AP is REAL array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ’U’ or ’u’, the array AP must
contain the upper 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 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.
Note that when DIAG = ’U’ or ’u’, the diagonal elements of
A are not referenced, but are assumed to be unity.

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.

subroutine ztpmv (character uplo, character trans, character diag, integern, complex*16, dimension(*) ap, complex*16, dimension(*) x, integerincx)

ZTPMV

Purpose:

ZTPMV 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, supplied in packed form.

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.

AP

AP is COMPLEX*16 array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ’U’ or ’u’, the array AP must
contain the upper 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 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.
Note that when DIAG = ’U’ or ’u’, the diagonal elements of
A are not referenced, but are assumed to be unity.

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.

Author

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