TESTING/LIN/zlavsp.f(3)

💖 TESTING/LIN/zlavsp.f(3) 💖

okay so bestie, we're looking at the zlavsp page from the TESTING/LIN corner of the LAPACK universe — it's a Fortran subroutine docs page, manual-page style, and it's lowkey iconic. Let's get into it. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zlavsp (uplo, trans, diag, n, nrhs, a, ipiv, b, ldb, info)

ZLAVSP — that's the name, and yes it's all caps because Fortran is dramatic like that. 💅

Function/Subroutine Documentation

subroutine zlavsp (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) a, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZLAVSP

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🌸 DESCRIPTION 🌸

Purpose:

!> !> ZLAVSP performs one of the matrix-vector operations !> x := A*x or x := A^T*x, !> where x is an N element vector and A is one of the factors !> from the symmetric factorization computed by ZSPTRF. !> ZSPTRF produces a factorization of the form !> U * D * U^T or L * D * L^T, !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, U^T (or L^T) is the transpose of !> U (or L), and D is symmetric and block diagonal with 1 x 1 and !> 2 x 2 diagonal blocks. The multipliers for the transformations !> and the upper or lower triangular parts of the diagonal blocks !> are stored columnwise in packed format in the linear array A. !> !> If TRANS = 'N' or 'n', ZLAVSP multiplies either by U or U * D !> (or L or L * D). !> If TRANS = 'C' or 'c', ZLAVSP multiplies either by U^T or D * U^T !> (or L^T or D * L^T ). !>

so basically, ZLAVSP is the vibe-check enforcer for multiplying a vector by one of the factors from a symmetric factorization. It's giving "I know what ZSPTRF did last summer" and it's ready to apply those transformations. The packed format in A is doing the most, but that's the assignment. 😭

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🌈 PARAMETERS 🌈

• UPLO — CHARACTER*1 on entry, UPLO specifies whether the triangular matrix stored in A is upper or lower triangular.
  • UPLO = 'U' or 'u' — the matrix is upper triangular. 👑
  • UPLO = 'L' or 'l' — the matrix is lower triangular. 🧚 unchanged on exit.
• TRANS — CHARACTER*1 on entry, TRANS specifies the operation to be performed, and it's honestly straightforward:
  • TRANS = 'N' or 'n' — x := A*x. ✨
  • TRANS = 'T' or 't' — x := A^T*x. 🔥 unchanged on exit.
• DIAG — CHARACTER*1 on entry, DIAG specifies whether the diagonal blocks are assumed to be unit matrices:
  • DIAG = 'U' or 'u' — diagonal blocks are unit matrices. 💅
  • DIAG = 'N' or 'n' — diagonal blocks are non-unit. 🌸 unchanged on exit.
• N — INTEGER on entry, N specifies the order of the matrix A. N must be at least zero. (no negatives, bestie, it's not that kind of party) unchanged on exit.
• NRHS — INTEGER on entry, NRHS specifies the number of right hand sides — i.e., the number of vectors x to be multiplied by A. NRHS must be at least zero. unchanged on exit.
• A — COMPLEX*16 array, dimension( N*(N+1)/2 ) on entry, A contains a block diagonal matrix and the multipliers of the transformations used to obtain it, stored as a packed triangular matrix. unchanged on exit. (she's just here to be read, not rewritten, periodt)
• IPIV — INTEGER array, dimension( N ) on entry, IPIV contains the vector of pivot indices as determined by ZSPTRF.
  • If IPIV( K ) = K, no interchange was done. 😌
  • If IPIV( K ) <> K but IPIV( K ) > 0, then row K was interchanged with row IPIV( K ) and a 1 x 1 pivot block was used.
  • If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used.
  • If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used.
• B — COMPLEX*16 array, dimension( LDB, NRHS ) on entry, B contains NRHS vectors of length N. on exit, B is overwritten with the product A * B. 🔥 (she ate and left no crumbs, but also she left the result in B)
• LDB — INTEGER on entry, LDB contains the leading dimension of B as declared in the calling program. LDB must be at least max( 1, N ). unchanged on exit.
• INFO — INTEGER INFO is the error flag.
  • On exit, a value of 0 indicates a successful exit. 🎉
  • A negative value, say -K, indicates that the K-th argument has an illegal value. 💀 (so check your inputs, bestie, INFO will absolutely call you out)

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🎀 AUTHOR 🎀

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

Definition at line 129 of file zlavsp.f. 📍

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⭐ AUTHOR (the meta one) ⭐

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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LAPACK — Version 3.12.0 — TESTING/LIN/zlavsp.f(3) that's the whole page, bestie. no cap, every flag and every pivot rule is here. now go slay those symmetric factorizations. 💜🦋