# csytrs_3.f - Man Page

## 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

Univ. of Colorado Denver

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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page csytrs_3(3) is an alias of csytrs_3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK