SRC/dsytri_3.f(3)

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version 3.12.1 · 4 versions
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💜 SRC/dsytri_3.f(3) — like, the manual page bestie 💜

okay so this is from the Library Functions Manual, and it's literally all about DSYTRI_3, which is giving "main character BLAS energy" ngl.

✨ NAME ✨

SRC/dsytri_3.f — that's the file, that's the vibe. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine dsytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)

DSYTRI_3 👑

🦋 Function/Subroutine Documentation 🦋

subroutine dsytri_3 (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
    dimension( * ) ipiv, double precision, dimension( * ) work, integer
    lwork, integer info)

DSYTRI_3 ✨ (yes, again, she contains multitudes)

🎀 Purpose 🎀

!> DSYTRI_3 computes the inverse of a real symmetric indefinite !> matrix A using the factorization computed by DSYTRF_RK or DSYTRF_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. !> !> DSYTRI_3 sets the leading dimension of the workspace before calling !> DSYTRI_3X that actually computes the inverse. This is the blocked !> version of the algorithm, calling Level 3 BLAS. !>

so like, she inverts your symmetric indefinite matrix 💅 but only after DSYTRF_RK or DSYTRF_BK already did the factorization. and yeah, she's the blocked version that calls Level 3 BLAS — icon behavior, fr fr 🔥

💖 Parameters 💖

  • UPLO
!> UPLO is CHARACTER*1 !> 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. !>

literally just "which triangle are we even talking about" — 'U' for upper, 'L' for lower. pick one bestie 💫

  • N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>

the order of the matrix A. and she said N >= 0, so no negative nonsense 🙈

  • A
!> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by DSYTRF_RK and 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 !> 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. !>

okay this one's the main character of the whole page, lowkey. on entry she holds the diagonal of D (only D(k,k) = A(k,k) on the diagonal of A, and the superdiagonal/subdiagonal bits of D go live in array E instead) plus factor U in the superdiagonal part or factor L in the subdiagonal part depending on UPLO. on exit, if INFO = 0, you get the symmetric inverse of the original matrix — upper triangular part if UPLO = 'U' (and everything below the diagonal is not referenced, so don't come for her), or lower triangular part if UPLO = 'L' (and above the diagonal is not referenced either). slay 💅

  • LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>

leading dimension of A. she needs LDA >= max(1,N), no cap 🎀

  • E
!> E is DOUBLE PRECISION 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. !>

the off-diagonal bestie of the block diagonal matrix D (which has 1-by-1 or 2-by-2 diagonal blocks, periodt). with UPLO = 'U' you get E(i) = D(i-1,i),i=2:N and E(1) is not referenced; with UPLO = 'L' you get E(i) = D(i+1,i),i=1:N-1 and E(N) is not referenced. 📌 NOTE: for a 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. iykyk 😌

  • IPIV
!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by DSYTRF_RK or DSYTRF_BK. !>

the receipts 🧾 — all the interchange details and the block structure of D, exactly as DSYTRF_RK or DSYTRF_BK determined them. don't argue with IPIV, she was there.

  • WORK
!> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>

workspace array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) hands you back the optimal LWORK 🫶

  • LWORK
!> LWORK is INTEGER !> The length of WORK. !> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3). !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA. !>

the length of WORK. if N = 0, then LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3). and if LWORK = -1 it's a workspace query — the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and XERBLA issues no error message related to LWORK. so like, -1 is the "just tell me how much room i need" vibe check 🔍

  • 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. !>

the report card 📋 — = 0 means successful exit (we ate 💅), < 0 means if INFO = -i the i-th argument had an illegal value (rude), and > 0 means if INFO = i, D(i,i) = 0 — the matrix is singular and its inverse could not be computed 😭💀

👑 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 !> !>

shoutout Igor, November 2017, Computer Science Division, University of California, Berkeley 🌈

⭐ Definition at line 169 of file dsytri_3.f. ⭐

🌸 Author 🌸

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