NAME

larfx - larfx: apply Householder reflector, unrolled

SYNOPSIS

Functions

subroutine clarfx (side, m, n, v, tau, c, ldc, work)
CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. subroutine dlarfx (side, m, n, v, tau, c, ldc, work)
DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. subroutine slarfx (side, m, n, v, tau, c, ldc, work)
SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. subroutine zlarfx (side, m, n, v, tau, c, ldc, work)
ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Detailed Description

Function Documentation

subroutine clarfx (character side, integer m, integer n, complex, dimension( * ) v, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)

CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:



 CLARFX applies a complex elementary reflector H to a complex m by n


 matrix C, from either the left or the right. H is represented in the


 form


       H = I - tau * v * v**H


 where tau is a complex scalar and v is a complex vector.


 If tau = 0, then H is taken to be the unit matrix


 This version uses inline code if H has order < 11.

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': form  H * C


          = 'R': form  C * H



          M is INTEGER


          The number of rows of the matrix C.



          N is INTEGER


          The number of columns of the matrix C.



          V is COMPLEX array, dimension (M) if SIDE = 'L'


                                        or (N) if SIDE = 'R'


          The vector v in the representation of H.

TAU



          TAU is COMPLEX


          The value tau in the representation of H.



          C is COMPLEX array, dimension (LDC,N)


          On entry, the m by n matrix C.


          On exit, C is overwritten by the matrix H * C if SIDE = 'L',


          or C * H if SIDE = 'R'.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is COMPLEX array, dimension (N) if SIDE = 'L'


                                            or (M) if SIDE = 'R'


          WORK is not referenced if H has order < 11.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 118 of file clarfx.f.

subroutine dlarfx (character side, integer m, integer n, double precision, dimension( * ) v, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:



 DLARFX applies a real elementary reflector H to a real m by n


 matrix C, from either the left or the right. H is represented in the


 form


       H = I - tau * v * v**T


 where tau is a real scalar and v is a real vector.


 If tau = 0, then H is taken to be the unit matrix


 This version uses inline code if H has order < 11.

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': form  H * C


          = 'R': form  C * H



          M is INTEGER


          The number of rows of the matrix C.



          N is INTEGER


          The number of columns of the matrix C.



          V is DOUBLE PRECISION array, dimension (M) if SIDE = 'L'


                                     or (N) if SIDE = 'R'


          The vector v in the representation of H.

TAU



          TAU is DOUBLE PRECISION


          The value tau in the representation of H.



          C is DOUBLE PRECISION array, dimension (LDC,N)


          On entry, the m by n matrix C.


          On exit, C is overwritten by the matrix H * C if SIDE = 'L',


          or C * H if SIDE = 'R'.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= (1,M).

WORK



          WORK is DOUBLE PRECISION array, dimension


                      (N) if SIDE = 'L'


                      or (M) if SIDE = 'R'


          WORK is not referenced if H has order < 11.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 119 of file dlarfx.f.

subroutine slarfx (character side, integer m, integer n, real, dimension( * ) v, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:



 SLARFX applies a real elementary reflector H to a real m by n


 matrix C, from either the left or the right. H is represented in the


 form


       H = I - tau * v * v**T


 where tau is a real scalar and v is a real vector.


 If tau = 0, then H is taken to be the unit matrix


 This version uses inline code if H has order < 11.

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': form  H * C


          = 'R': form  C * H



          M is INTEGER


          The number of rows of the matrix C.



          N is INTEGER


          The number of columns of the matrix C.



          V is REAL array, dimension (M) if SIDE = 'L'


                                     or (N) if SIDE = 'R'


          The vector v in the representation of H.

TAU



          TAU is REAL


          The value tau in the representation of H.



          C is REAL array, dimension (LDC,N)


          On entry, the m by n matrix C.


          On exit, C is overwritten by the matrix H * C if SIDE = 'L',


          or C * H if SIDE = 'R'.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= (1,M).

WORK



          WORK is REAL array, dimension


                      (N) if SIDE = 'L'


                      or (M) if SIDE = 'R'


          WORK is not referenced if H has order < 11.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 119 of file slarfx.f.

subroutine zlarfx (character side, integer m, integer n, complex16, dimension( ) v, complex16 tau, complex16, dimension( ldc, * ) c, integer ldc, complex16, dimension( ) work)

ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:



 ZLARFX applies a complex elementary reflector H to a complex m by n


 matrix C, from either the left or the right. H is represented in the


 form


       H = I - tau * v * v**H


 where tau is a complex scalar and v is a complex vector.


 If tau = 0, then H is taken to be the unit matrix


 This version uses inline code if H has order < 11.

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': form  H * C


          = 'R': form  C * H



          M is INTEGER


          The number of rows of the matrix C.



          N is INTEGER


          The number of columns of the matrix C.



          V is COMPLEX*16 array, dimension (M) if SIDE = 'L'


                                        or (N) if SIDE = 'R'


          The vector v in the representation of H.

TAU



          TAU is COMPLEX*16


          The value tau in the representation of H.



          C is COMPLEX*16 array, dimension (LDC,N)


          On entry, the m by n matrix C.


          On exit, C is overwritten by the matrix H * C if SIDE = 'L',


          or C * H if SIDE = 'R'.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L'


                                            or (M) if SIDE = 'R'


          WORK is not referenced if H has order < 11.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 118 of file zlarfx.f.

Author

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