---
name: "larz"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/larz"
---

# larz(3)

larz: apply reflector

## 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*

```
!>          M is INTEGER
!>          The number of rows of the matrix C.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C.
!>
```

*L*

```
!>          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*

```
!>          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*

```
!>          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*

```
!>          M is INTEGER
!>          The number of rows of the matrix C.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C.
!>
```

*L*

```
!>          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*

```
!>          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*

```
!>          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*

```
!>          M is INTEGER
!>          The number of rows of the matrix C.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C.
!>
```

*L*

```
!>          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*

```
!>          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*

```
!>          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, complex\*16, dimension( \* ) v, integer incv, complex\*16 tau, complex\*16, dimension( ldc, \* ) c, integer ldc, complex\*16, 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*

```
!>          M is INTEGER
!>          The number of rows of the matrix C.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C.
!>
```

*L*

```
!>          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*

```
!>          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*

```
!>          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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