---
name: "dlansp.f"
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/dlansp.f"
---

# dlansp.f(3)

## NAME

SRC/dlansp.f

## SYNOPSIS

### Functions/Subroutines

double precision function **dlansp** (norm, uplo, n, ap, work)\
 **DLANSP** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

## Function/Subroutine Documentation

### double precision function dlansp (character norm, character uplo, integer n, double precision, dimension( \* ) ap, double precision, dimension( \* ) work)

**DLANSP** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

**Purpose:**

```
!>
!> DLANSP  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real symmetric matrix A,  supplied in packed form.
!>
```

**Returns**

DLANSP

```
!>
!>    DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
!>             (
!>             ( norm1(A),         NORM = '1', 'O' or 'o'
!>             (
!>             ( normI(A),         NORM = 'I' or 'i'
!>             (
!>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
!>
!> where  norm1  denotes the  one norm of a matrix (maximum column sum),
!> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
!> normF  denotes the  Frobenius norm of a matrix (square root of sum of
!> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>
```

**Parameters**

*NORM*

```
!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in DLANSP as described
!>          above.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is supplied.
!>          = 'U':  Upper triangular part of A is supplied
!>          = 'L':  Lower triangular part of A is supplied
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, DLANSP is
!>          set to zero.
!>
```

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The upper or lower triangle of the symmetric matrix A, packed
!>          columnwise in a linear array.  The j-th column of A is stored
!>          in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
!>          WORK is not referenced.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **113** of file **dlansp.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.