SRC/csyconvf_rook.f(3)

💅 SRC/csyconvf_rook.f(3) 💅

okay bestie, welcome to the SRC/csyconvf_rook.f(3) page from the Library Functions Manual. this is the CSYCONVF_ROOK lore, and we’re keeping every single detail because that’s the whole point. 💖✨

💖 NAME 💖

SRC/csyconvf_rook.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine csyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
     CSYCONVF_ROOK

🌸 Function/Subroutine Documentation 🌸

subroutine csyconvf_rook (character uplo, character way, integer n, complex,
     dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,
     dimension( * ) ipiv, integer info)
     CSYCONVF_ROOK

🎯 Purpose 🎯

okay so if parameter WAY = 'C': CSYCONVF_ROOK converts the factorization output format used in CSYTRF_ROOK provided on entry in parameter A into the factorization output format used in CSYTRF_RK (or CSYTRF_BK) that is stored on exit in parameters A and E. the IPIV format for CSYTRF_ROOK and CSYTRF_RK (or CSYTRF_BK) is the same and is not converted. no cap. 🫶

if parameter WAY = 'R': CSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in CSYTRF_RK (or CSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in CSYTRF_ROOK that is stored on exit in parameter A. again, the IPIV format for CSYTRF_ROOK and CSYTRF_RK (or CSYTRF_BK) is the same and is not converted. 🔁

CSYCONVF_ROOK can also convert in Hermitian matrix case, i.e. between formats used in CHETRF_ROOK and CHETRF_RK (or CHETRF_BK). iconic. 💅

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix A. = 'U': Upper triangular. = 'L': Lower triangular. 🦋
• WAY — WAY is CHARACTER*1. = 'C': Convert. = 'R': Revert. 🌈
• N — N is INTEGER. the order of the matrix A. N >= 0. ⭐
• A — A is COMPLEX array, dimension (LDA,N).
  • 1) If WAY ='C': On entry, contains factorization details in format used in CSYTRF_ROOK:
    • a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and
    • b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal part of A. On exit, contains factorization details in format used in CSYTRF_RK or 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 are stored on exit 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.
  • 2) If WAY = 'R': On entry, contains factorization details in format used in CSYTRF_RK or 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 are stored on exit 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, contains factorization details in format used in CSYTRF_ROOK:
    • a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and
    • b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal 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).
  • 1) If WAY ='C': On entry, just a workspace. On exit, 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) is set to 0; If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
  • 2) If WAY = 'R': 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. On exit, is not changed.
• IPIV — IPIV is INTEGER array, dimension (N). On entry, details of the interchanges and the block structure of D as determined: 1) by CSYTRF_ROOK, if WAY ='C'; 2) by CSYTRF_RK (or CSYTRF_BK), if WAY ='R'. the IPIV format is the same for all these routines. On exit, is not changed. 🙈
• 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.

🫶 Contributors 🫶

• November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley.

Definition at line 199 of file csyconvf_rook.f. 📌

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🌈 Author 🌈

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