NAME

larz - larz: apply reflector

SYNOPSIS

Functions

subroutine clarz (side, m, n, l, v, incv, tau, c, ldc, work)
CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine dlarz (side, m, n, l, v, incv, tau, c, ldc, work)
DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine slarz (side, m, n, l, v, incv, tau, c, ldc, work)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. subroutine zlarz (side, m, n, l, v, incv, tau, c, ldc, work)
ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Detailed Description

Function Documentation

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

CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:



 CLARZ 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.


 To apply H**H (the conjugate transpose of H), supply conjg(tau) instead


 tau.


 H is a product of k elementary reflectors as returned by CTZRZF.

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.



          L is INTEGER


          The number of entries of the vector V containing


          the meaningful part of the Householder vectors.


          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.



          V is COMPLEX array, dimension (1+(L-1)*abs(INCV))


          The vector v in the representation of H as returned by


          CTZRZF. V is not used if TAU = 0.

INCV



          INCV is INTEGER


          The increment between elements of v. INCV <> 0.

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'

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 146 of file clarz.f.

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

DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:



 DLARZ 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.


 H is a product of k elementary reflectors as returned by DTZRZF.

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.



          L is INTEGER


          The number of entries of the vector V containing


          the meaningful part of the Householder vectors.


          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.



          V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))


          The vector v in the representation of H as returned by


          DTZRZF. V is not used if TAU = 0.

INCV



          INCV is INTEGER


          The increment between elements of v. INCV <> 0.

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 >= max(1,M).

WORK



          WORK is DOUBLE PRECISION array, dimension


                         (N) if SIDE = 'L'


                      or (M) if SIDE = 'R'

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 144 of file dlarz.f.

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

SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:



 SLARZ 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.


 H is a product of k elementary reflectors as returned by STZRZF.

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.



          L is INTEGER


          The number of entries of the vector V containing


          the meaningful part of the Householder vectors.


          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.



          V is REAL array, dimension (1+(L-1)*abs(INCV))


          The vector v in the representation of H as returned by


          STZRZF. V is not used if TAU = 0.

INCV



          INCV is INTEGER


          The increment between elements of v. INCV <> 0.

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 >= max(1,M).

WORK



          WORK is REAL array, dimension


                         (N) if SIDE = 'L'


                      or (M) if SIDE = 'R'

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 144 of file slarz.f.

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

ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:



 ZLARZ 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.


 To apply H**H (the conjugate transpose of H), supply conjg(tau) instead


 tau.


 H is a product of k elementary reflectors as returned by ZTZRZF.

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.



          L is INTEGER


          The number of entries of the vector V containing


          the meaningful part of the Householder vectors.


          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.



          V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))


          The vector v in the representation of H as returned by


          ZTZRZF. V is not used if TAU = 0.

INCV



          INCV is INTEGER


          The increment between elements of v. INCV <> 0.

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'

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 146 of file zlarz.f.

Author

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