# zpbsv.f man page

zpbsv.f —

## Synopsis

### Functions/Subroutines

subroutinezpbsv(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

## Function/Subroutine Documentation

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

**ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices**

**Purpose:**

```
ZPBSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A. The factored form of A is then used to solve the
system of equations A * X = B.
```

**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 number of linear equations, i.e., 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)
On entry, the upper or lower triangle of the Hermitian 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).
See below for further details.
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H 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.
```

*B*

```
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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
> 0: if INFO = i, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed, and the solution has not been computed.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**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.
```

Definition at line 165 of file zpbsv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK