---
name: "spbtrf"
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/spbtrf.f"
---

# spbtrf(3)

Part of [spbtrf.f(3)](/spbtrf.f/3.md).

## NAME

SRC/spbtrf.f

## SYNOPSIS

### Functions/Subroutines

subroutine **spbtrf** (uplo, n, kd, ab, ldab, info)\
 **SPBTRF**

## Function/Subroutine Documentation

### subroutine spbtrf (character uplo, integer n, integer kd, real, dimension( ldab, \* ) ab, integer ldab, integer info)

**SPBTRF**

**Purpose:**

```
!>
!> SPBTRF computes the Cholesky factorization of a real symmetric
!> positive definite band matrix A.
!>
!> The factorization has the form
!>    A = U**T * U,  if UPLO = 'U', or
!>    A = L  * L**T,  if UPLO = 'L',
!> where U is an upper triangular matrix and L is lower triangular.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*KD*

```
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>
```

*AB*

```
!>          AB is REAL array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**T*U or A = L*L**T of the band
!>          matrix A, in the same storage format as A.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the leading principal minor of order i
!>                is not positive, and the factorization could not be
!>                completed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The band storage scheme is illustrated by the following example, when
!>  N = 6, KD = 2, and UPLO = 'U':
!>
!>  On entry:                       On exit:
!>
!>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
!>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
!>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
!>
!>  Similarly, if UPLO = 'L' the format of A is as follows:
!>
!>  On entry:                       On exit:
!>
!>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
!>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
!>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
!>
!>  Array elements marked * are not used by the routine.
!>
```

**Contributors:**

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

Definition at line **141** of file **spbtrf.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.