SRC/csytrs_3.f(3)

💖 SRC/csytrs_3.f(3) — Library Functions Manual 💖

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💖 NAME 💖

SRC/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 🎯

Okay so 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.

And this algorithm is using Level 3 BLAS — iconic, no cap 🔥

🌸 Parameters 🌸

• 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 — is INTEGER. The order of the matrix A. N >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 — is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF_RK or CSYTRF_BK.
• B — is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

💅 Author 💅

Brought to you by:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌈 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 163 of file csytrs_3.f.

👑 Author 👑

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