DPFTRF(3)

💖 DPFTRF(3) — like, the Cholesky factorization of a real symmetric positive definite matrix, bestie 💖

okay so this page lives in the LAPACK manual (Version 3.12.0, iykyk ✨), and the actual file it's documenting is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpftrf.f

that's the whole NAME section, no cap — it's literally just the path 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine DPFTRF (transr, uplo, n, a, info)

DPFTRF — that's the vibe 💅

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🌸 Function/Subroutine Documentation 🌸

subroutine DPFTRF (character transr, character uplo, integer n, double
    precision, dimension( 0: * ) a, integer info)

DPFTRF 👑

🦋 Purpose 🦋

!> !> DPFTRF computes the Cholesky factorization of a real symmetric !> positive definite matrix A. !> !> The factorization has the form !> A = U**T * U, if UPLO = 'U', or !> A = L * L**T, if UPLO = 'L', !> where U is an upper triangular matrix and L is lower triangular. !> !> This is the block version of the algorithm, calling Level 3 BLAS. !>

so like, this is the block version of the algorithm and it calls Level 3 BLAS — highkey efficient, we love to see it 🔥

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💜 Parameters 💜

• TRANSR — TRANSR is CHARACTER*1, and it decides which flavour of TRANSR we're doing:
  • = 'N': the Normal TRANSR of RFP A is stored;
  • = 'T': the Transpose TRANSR of RFP A is stored.
• UPLO — UPLO is CHARACTER*1, pick your triangle bestie:
  • = 'U': Upper triangle of RFP A is stored;
  • = 'L': Lower triangle of RFP A is stored.
• N — N is INTEGER: the order of the matrix A. Constraint is N >= 0. periodt ✨
• A — A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). okay so this one's a whole paragraph, buckle up 🎢:
  • On entry, the symmetric matrix A in RFP format. RFP format is described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is the transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the NT elements of upper packed A. If UPLO = 'L' the RFP A contains the elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N is odd. See the Note below for more details.
  • On exit, if INFO = 0, the factor U or L from the Cholesky factorization RFP A = U**T*U or RFP A = L*L**T.
• INFO — INFO is INTEGER, the receipts 📋:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the leading principal minor of order i is not positive, and the factorization could not be completed.

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👑 Author 👑

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

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🌈 Further Details: 🌈

!> !> We first consider Rectangular Full Packed (RFP) Format when N is !> even. We give an example where N = 6. !> !> AP is Upper AP is Lower !> !> 00 01 02 03 04 05 00 !> 11 12 13 14 15 10 11 !> 22 23 24 25 20 21 22 !> 33 34 35 30 31 32 33 !> 44 45 40 41 42 43 44 !> 55 50 51 52 53 54 55 !> !> !> Let TRANSR = 'N'. RFP holds AP as follows: !> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last !> three columns of AP upper. The lower triangle A(4:6,0:2) consists of !> the transpose of the first three columns of AP upper. !> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first !> three columns of AP lower. The upper triangle A(0:2,0:2) consists of !> the transpose of the last three columns of AP lower. !> This covers the case N even and TRANSR = 'N'. !> !> RFP A RFP A !> !> 03 04 05 33 43 53 !> 13 14 15 00 44 54 !> 23 24 25 10 11 55 !> 33 34 35 20 21 22 !> 00 44 45 30 31 32 !> 01 11 55 40 41 42 !> 02 12 22 50 51 52 !> !> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the !> transpose of RFP A above. One therefore gets: !> !> !> RFP A RFP A !> !> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 !> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 !> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 !> !> !> We then consider Rectangular Full Packed (RFP) Format when N is !> odd. We give an example where N = 5. !> !> AP is Upper AP is Lower !> !> 00 01 02 03 04 00 !> 11 12 13 14 10 11 !> 22 23 24 20 21 22 !> 33 34 30 31 32 33 !> 44 40 41 42 43 44 !> !> !> Let TRANSR = 'N'. RFP holds AP as follows: !> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last !> three columns of AP upper. The lower triangle A(3:4,0:1) consists of !> the transpose of the first two columns of AP upper. !> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first !> three columns of AP lower. The upper triangle A(0:1,1:2) consists of !> the transpose of the last two columns of AP lower. !> This covers the case N odd and TRANSR = 'N'. !> !> RFP A RFP A !> !> 02 03 04 00 33 43 !> 12 13 14 10 11 44 !> 22 23 24 20 21 22 !> 00 33 34 30 31 32 !> 01 11 44 40 41 42 !> !> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the !> transpose of RFP A above. One therefore gets: !> !> RFP A RFP A !> !> 02 12 22 00 01 00 10 20 30 40 50 !> 03 13 23 33 11 33 11 21 31 41 51 !> 04 14 24 34 44 43 44 22 32 42 52 !>

like, the way those matrices line up?? obsESSED 😭💖

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⭐ Definition at line 197 of file dpftrf.f. ⭐

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole thing bestie, you ate that 🫶✨ this page is LAPACK Version 3.12.0, footer path /home/abui...RC/dpftrf.f(3) — and that's the group chat, signing off 💅🎀🦋