# csytrs_3.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

csytrs_3.f

## SYNOPSIS

### Functions/Subroutines

subroutine csytrs_3 (UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
CSYTRS_3

## Function/Subroutine Documentation

### subroutine csytrs_3 (character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) E, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CSYTRS_3

Purpose:

``` CSYTRS_3 solves a system of linear equations A * X = B with a complex
symmetric matrix A using the factorization computed
by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix:
= 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
= 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).
```

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.
```

A

```          A is COMPLEX array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CSYTRF_RK and CSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = 'U': factor U in the superdiagonal part of A.
If UPLO = 'L': factor L in the subdiagonal part of A.
```

LDA

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

E

```          E is COMPLEX array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = 'U' or UPLO = 'L' cases.
```

IPIV

```          IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF_RK or CSYTRF_BK.
```

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.

Date:

June 2017

Contributors:

```  June 2017,  Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester
```

Definition at line 167 of file csytrs_3.f.

## Author

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