---
name: "lauum"
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/lauum"
---

# lauum(3)

lauum: triangular multiply: U^H U

## NAME

lauum - lauum: triangular multiply: U^H U

## SYNOPSIS

### Functions

subroutine **clauum** (uplo, n, a, lda, info)\
 **CLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).  subroutine **dlauum** (uplo, n, a, lda, info)\
 **DLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).  subroutine **slauum** (uplo, n, a, lda, info)\
 **SLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).  subroutine **zlauum** (uplo, n, a, lda, info)\
 **ZLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

## Detailed Description

## Function Documentation

### subroutine clauum (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer info)

**CLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

**Purpose:**

```
!>
!> CLAUUM computes the product U * U**H or L**H * L, where the triangular
!> factor U or L is stored in the upper or lower triangular part of
!> the array A.
!>
!> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
!> overwriting the factor U in A.
!> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
!> overwriting the factor L in A.
!>
!> This is the blocked form of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the triangular factor stored in the array A
!>          is upper or lower triangular:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the triangular factor U or L.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the triangular factor U or L.
!>          On exit, if UPLO = 'U', the upper triangle of A is
!>          overwritten with the upper triangle of the product U * U**H;
!>          if UPLO = 'L', the lower triangle of A is overwritten with
!>          the lower triangle of the product L**H * L.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **clauum.f**.

### subroutine dlauum (character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, integer info)

**DLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

**Purpose:**

```
!>
!> DLAUUM computes the product U * U**T or L**T * L, where the triangular
!> factor U or L is stored in the upper or lower triangular part of
!> the array A.
!>
!> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
!> overwriting the factor U in A.
!> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
!> overwriting the factor L in A.
!>
!> This is the blocked form of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the triangular factor stored in the array A
!>          is upper or lower triangular:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the triangular factor U or L.  N >= 0.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the triangular factor U or L.
!>          On exit, if UPLO = 'U', the upper triangle of A is
!>          overwritten with the upper triangle of the product U * U**T;
!>          if UPLO = 'L', the lower triangle of A is overwritten with
!>          the lower triangle of the product L**T * L.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **dlauum.f**.

### subroutine slauum (character uplo, integer n, real, dimension( lda, \* ) a, integer lda, integer info)

**SLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

**Purpose:**

```
!>
!> SLAUUM computes the product U * U**T or L**T * L, where the triangular
!> factor U or L is stored in the upper or lower triangular part of
!> the array A.
!>
!> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
!> overwriting the factor U in A.
!> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
!> overwriting the factor L in A.
!>
!> This is the blocked form of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the triangular factor stored in the array A
!>          is upper or lower triangular:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the triangular factor U or L.  N >= 0.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the triangular factor U or L.
!>          On exit, if UPLO = 'U', the upper triangle of A is
!>          overwritten with the upper triangle of the product U * U**T;
!>          if UPLO = 'L', the lower triangle of A is overwritten with
!>          the lower triangle of the product L**T * L.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **slauum.f**.

### subroutine zlauum (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer info)

**ZLAUUM** computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

**Purpose:**

```
!>
!> ZLAUUM computes the product U * U**H or L**H * L, where the triangular
!> factor U or L is stored in the upper or lower triangular part of
!> the array A.
!>
!> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
!> overwriting the factor U in A.
!> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
!> overwriting the factor L in A.
!>
!> This is the blocked form of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the triangular factor stored in the array A
!>          is upper or lower triangular:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the triangular factor U or L.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the triangular factor U or L.
!>          On exit, if UPLO = 'U', the upper triangle of A is
!>          overwritten with the upper triangle of the product U * U**H;
!>          if UPLO = 'L', the lower triangle of A is overwritten with
!>          the lower triangle of the product L**H * L.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **zlauum.f**.

## Author

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