SRC/dsyconvf_rook.f(3)

💖 SRC/dsyconvf_rook.f 💖

okay bestie, this page is living in the Library Functions Manual, and it's all about dsyconvf_rook — a literal format-conversion icon in LAPACK. let's get into it 💅

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🌸 NAME 🌸

SRC/dsyconvf_rook.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine dsyconvf_rook (uplo, way, n, a, lda, e, ipiv, info) — DSYCONVF_ROOK

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💖 Function/Subroutine Documentation 💖

subroutine dsyconvf_rook (character uplo, character way, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) e, integer, dimension( * ) ipiv, integer info)

DSYCONVF_ROOK

🌟 Purpose 🌟

okay so if parameter WAY = 'C':

DSYCONVF_ROOK converts the factorization output format used in DSYTRF_ROOK, provided on entry in parameter A, into the factorization output format used in DSYTRF_RK (or DSYTRF_BK) that is stored on exit in parameters A and E. the IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted. periodt ✨

if parameter WAY = 'R':

DSYCONVF_ROOK performs the conversion in reverse direction, i.e. it converts the factorization output format used in DSYTRF_RK (or DSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in DSYTRF_ROOK that is stored on exit in parameter A. and again, the IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted 🫶

🧚 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 DOUBLE PRECISION array, dimension (LDA,N).
  1. if WAY ='C':

on entry, contains factorization details in format used in DSYTRF_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 DSYTRF_RK or DSYTRF_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 DSYTRF_RK or DSYTRF_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 DSYTRF_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 DOUBLE PRECISION 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 DSYTRF_ROOK, if WAY ='C';
2. by DSYTRF_RK (or DSYTRF_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 196 of file dsyconvf_rook.f.

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💌 Author 💌

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