table of contents
| larfy(3) | LAPACK | larfy(3) |
NAME¶
larfy - larfy: apply Householder reflector symmetrically (2-sided)
SYNOPSIS¶
Functions¶
subroutine clarfy (uplo, n, v, incv, tau, c, ldc, work)
CLARFY subroutine dlarfy (uplo, n, v, incv, tau, c, ldc, work)
DLARFY subroutine slarfy (uplo, n, v, incv, tau, c, ldc, work)
SLARFY subroutine zlarfy (uplo, n, v, incv, tau, c, ldc, work)
ZLARFY
Detailed Description¶
Function Documentation¶
subroutine clarfy (character uplo, integer n, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)¶
CLARFY
Purpose:
CLARFY applies an elementary reflector, or Householder matrix, H,
to an n x n Hermitian matrix C, from both the left and the right.
H is represented in the form
H = I - tau * v * v'
where tau is a scalar and v is a vector.
If tau is zero, then H is taken to be the unit matrix.
Parameters
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix C is stored.
= 'U': Upper triangle
= 'L': Lower triangle
N
N is INTEGER
The number of rows and columns of the matrix C. N >= 0.
V
V is COMPLEX array, dimension
(1 + (N-1)*abs(INCV))
The vector v as described above.
INCV
INCV is INTEGER
The increment between successive elements of v. INCV must
not be zero.
TAU
TAU is COMPLEX
The value tau as described above.
C
C is COMPLEX array, dimension (LDC, N)
On entry, the matrix C.
On exit, C is overwritten by H * C * H'.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max( 1, N ).
WORK
WORK is COMPLEX array, dimension (N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dlarfy (character uplo, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)¶
DLARFY
Purpose:
DLARFY applies an elementary reflector, or Householder matrix, H,
to an n x n symmetric matrix C, from both the left and the right.
H is represented in the form
H = I - tau * v * v'
where tau is a scalar and v is a vector.
If tau is zero, then H is taken to be the unit matrix.
Parameters
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix C is stored.
= 'U': Upper triangle
= 'L': Lower triangle
N
N is INTEGER
The number of rows and columns of the matrix C. N >= 0.
V
V is DOUBLE PRECISION array, dimension
(1 + (N-1)*abs(INCV))
The vector v as described above.
INCV
INCV is INTEGER
The increment between successive elements of v. INCV must
not be zero.
TAU
TAU is DOUBLE PRECISION
The value tau as described above.
C
C is DOUBLE PRECISION array, dimension (LDC, N)
On entry, the matrix C.
On exit, C is overwritten by H * C * H'.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max( 1, N ).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine slarfy (character uplo, integer n, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)¶
SLARFY
Purpose:
SLARFY applies an elementary reflector, or Householder matrix, H,
to an n x n symmetric matrix C, from both the left and the right.
H is represented in the form
H = I - tau * v * v'
where tau is a scalar and v is a vector.
If tau is zero, then H is taken to be the unit matrix.
Parameters
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix C is stored.
= 'U': Upper triangle
= 'L': Lower triangle
N
N is INTEGER
The number of rows and columns of the matrix C. N >= 0.
V
V is REAL array, dimension
(1 + (N-1)*abs(INCV))
The vector v as described above.
INCV
INCV is INTEGER
The increment between successive elements of v. INCV must
not be zero.
TAU
TAU is REAL
The value tau as described above.
C
C is REAL array, dimension (LDC, N)
On entry, the matrix C.
On exit, C is overwritten by H * C * H'.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max( 1, N ).
WORK
WORK is REAL array, dimension (N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zlarfy (character uplo, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)¶
ZLARFY
Purpose:
ZLARFY applies an elementary reflector, or Householder matrix, H,
to an n x n Hermitian matrix C, from both the left and the right.
H is represented in the form
H = I - tau * v * v'
where tau is a scalar and v is a vector.
If tau is zero, then H is taken to be the unit matrix.
Parameters
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix C is stored.
= 'U': Upper triangle
= 'L': Lower triangle
N
N is INTEGER
The number of rows and columns of the matrix C. N >= 0.
V
V is COMPLEX*16 array, dimension
(1 + (N-1)*abs(INCV))
The vector v as described above.
INCV
INCV is INTEGER
The increment between successive elements of v. INCV must
not be zero.
TAU
TAU is COMPLEX*16
The value tau as described above.
C
C is COMPLEX*16 array, dimension (LDC, N)
On entry, the matrix C.
On exit, C is overwritten by H * C * H'.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max( 1, N ).
WORK
WORK is COMPLEX*16 array, dimension (N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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