# larf - Man Page

larf: apply Householder reflector

## Synopsis

### Functions

subroutine **clarf** (side, m, n, v, incv, tau, c, ldc, work)**CLARF** applies an elementary reflector to a general rectangular matrix.

subroutine **dlarf** (side, m, n, v, incv, tau, c, ldc, work)**DLARF** applies an elementary reflector to a general rectangular matrix.

subroutine **slarf** (side, m, n, v, incv, tau, c, ldc, work)**SLARF** applies an elementary reflector to a general rectangular matrix.

subroutine **zlarf** (side, m, n, v, incv, tau, c, ldc, work)**ZLARF** applies an elementary reflector to a general rectangular matrix.

## Detailed Description

## Function Documentation

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

**CLARF** applies an elementary reflector to a general rectangular matrix.

**Purpose:**

CLARF 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.

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H

*M*M is INTEGER The number of rows of the matrix C.

*N*N is INTEGER The number of columns of the matrix C.

*V*V is COMPLEX array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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*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.

Definition at line **127** of file **clarf.f**.

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

**DLARF** applies an elementary reflector to a general rectangular matrix.

**Purpose:**

DLARF 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.

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H

*M*M is INTEGER The number of rows of the matrix C.

*N*N is INTEGER The number of columns of the matrix C.

*V*V is DOUBLE PRECISION array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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*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.

Definition at line **123** of file **dlarf.f**.

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

**SLARF** applies an elementary reflector to a general rectangular matrix.

**Purpose:**

SLARF 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.

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H

*M*M is INTEGER The number of rows of the matrix C.

*N*N is INTEGER The number of columns of the matrix C.

*V*V is REAL array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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*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.

Definition at line **123** of file **slarf.f**.

### subroutine zlarf (character side, integer m, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

**ZLARF** applies an elementary reflector to a general rectangular matrix.

**Purpose:**

ZLARF 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, supply conjg(tau) instead tau.

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H

*M*M is INTEGER The number of rows of the matrix C.

*N*N is INTEGER The number of columns of the matrix C.

*V*V is COMPLEX*16 array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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*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.

Definition at line **127** of file **zlarf.f**.

## Author

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