# ptsv - Man Page

ptsv: factor and solve

## Synopsis

### Functions

subroutine cptsv (n, nrhs, d, e, b, ldb, info)
CPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine dptsv (n, nrhs, d, e, b, ldb, info)
DPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine sptsv (n, nrhs, d, e, b, ldb, info)
SPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine zptsv (n, nrhs, d, e, b, ldb, info)
ZPTSV computes the solution to system of linear equations A * X = B for PT matrices

## Function Documentation

### subroutine cptsv (integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

``` CPTSV computes the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.

A is factored as A = L*D*L**H, and the factored form of A is then
used to solve the system of equations.```
Parameters

N

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

NRHS

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

D

```          D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A.  On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**H.```

E

```          E is COMPLEX array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A.  On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of
A.  E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H*D*U factorization of A.```

B

```          B is COMPLEX 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 principal minor of order i
is not positive, and the solution has not been
computed.  The factorization has not been completed
unless i = N.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 114 of file cptsv.f.

### subroutine dptsv (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

``` DPTSV computes the solution to a real system of linear equations
A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.

A is factored as A = L*D*L**T, and the factored form of A is then
used to solve the system of equations.```
Parameters

N

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

NRHS

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

D

```          D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A.  On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**T.```

E

```          E is DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A.  On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of
A.  (E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.)```

B

```          B is DOUBLE PRECISION 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 principal minor of order i
is not positive, and the solution has not been
computed.  The factorization has not been completed
unless i = N.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 113 of file dptsv.f.

### subroutine sptsv (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)

SPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

``` SPTSV computes the solution to a real system of linear equations
A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.

A is factored as A = L*D*L**T, and the factored form of A is then
used to solve the system of equations.```
Parameters

N

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

NRHS

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

D

```          D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A.  On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**T.```

E

```          E is REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A.  On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of
A.  (E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.)```

B

```          B is REAL 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 principal minor of order i
is not positive, and the solution has not been
computed.  The factorization has not been completed
unless i = N.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 113 of file sptsv.f.

### subroutine zptsv (integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

``` ZPTSV computes the solution to a complex system of linear equations
A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
matrix, and X and B are N-by-NRHS matrices.

A is factored as A = L*D*L**H, and the factored form of A is then
used to solve the system of equations.```
Parameters

N

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

NRHS

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

D

```          D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A.  On exit, the n diagonal elements of the diagonal matrix
D from the factorization A = L*D*L**H.```

E

```          E is COMPLEX*16 array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A.  On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of
A.  E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H*D*U factorization of A.```

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 principal minor of order i
is not positive, and the solution has not been
computed.  The factorization has not been completed
unless i = N.```
Author

Univ. of Tennessee

Univ. of California Berkeley