# pbtrs - Man Page

pbtrs: triangular solve using factor

## Synopsis

### Functions

subroutine cpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
CPBTRS
subroutine dpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
DPBTRS
subroutine spbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
SPBTRS
subroutine zpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
ZPBTRS

## Function Documentation

### subroutine cpbtrs (character uplo, integer n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPBTRS

Purpose:

``` CPBTRS 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 CPBTRF.```
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 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 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

NAG Ltd.

Definition at line 120 of file cpbtrs.f.

### subroutine dpbtrs (character uplo, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPBTRS

Purpose:

``` DPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U**T*U or A = L*L**T computed by DPBTRF.```
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 DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T 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 DOUBLE PRECISION 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

NAG Ltd.

Definition at line 120 of file dpbtrs.f.

### subroutine spbtrs (character uplo, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, integer info)

SPBTRS

Purpose:

``` SPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U**T*U or A = L*L**T computed by SPBTRF.```
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 REAL array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T 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 REAL 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

NAG Ltd.

Definition at line 120 of file spbtrs.f.

### subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

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