SRC/csytri_3x.f(3)

💖 NAME 💖

Okay bestie, this page is SRC/csytri_3x.f — and it comes from the Library Functions Manual, so you know it’s official.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine csytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
           CSYTRI_3X

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🎀 Function/Subroutine Documentation 🎀

✨ CSYTRI_3X ✨

subroutine csytri_3x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

💡 Purpose 💡

Okay so CSYTRI_3X computes the inverse of a complex symmetric indefinite 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 is the blocked version of the algorithm, calling Level 3 BLAS. It’s giving main character energy in the factorization department. 💅

🌸 Parameters 🌸

UPLO

UPLO is CHARACTER*1 — it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

N

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

A

A is COMPLEX array, dimension (LDA,N).

On entry, 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.

On exit, if INFO = 0, the symmetric inverse of the original matrix.

• If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
• If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

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.

WORK

WORK is COMPLEX array, dimension (N+NB+1,NB+3).

NB

NB is INTEGER — block size.

INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

Heads up bestie: if INFO > 0, the matrix is singular and the inverse could not be computed. No cap, that’s a real “oop” moment. 😭

👑 Author 👑

• 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

Definition at line 158 of file csytri_3x.f.

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👑 Author 👑

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