# cptsv.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cptsv.f

## SYNOPSIS

### Functions/Subroutines

subroutine cptsv (N, NRHS, D, E, B, LDB, INFO)
CPTSV computes the solution to system of linear equations A * X = B for PT matrices

## Function/Subroutine 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 minor of order i is not
positive definite, and the solution has not been
computed.  The factorization has not been completed
unless i = N.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley