# zpbtrs.f man page

zpbtrs.f —

## Synopsis

### Functions/Subroutines

subroutinezpbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)ZPBTRS

## Function/Subroutine Documentation

### subroutine zpbtrs (characterUPLO, integerN, integerKD, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)

**ZPBTRS**

**Purpose:**

```
ZPBTRS solves a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factorization
A = U**H *U or A = L*L**H computed by ZPBTRF.
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
```

*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.
```

*NRHS*

```
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
```

*AB*

```
AB is COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H *U or A = L*L**H of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
```

*LDAB*

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

*B*

```
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
```

*LDB*

```
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
```

*INFO*

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

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 122 of file zpbtrs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zpbtrs(3) is an alias of zpbtrs.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK