/home/abui...N/zlarot.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

ok so this is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/zlarot.f — like, the whole entire file path is the name, bestie. it's from the MATGEN testing folder of LAPACK, and it's a Library Functions Manual page, no cap. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine ZLAROT (lrows, lleft, lright, nl, c, s, a, lda, xleft, xright) — that's the one and only ZLAROT 🔥

🎀 Function/Subroutine Documentation 🎀

subroutine ZLAROT (logical lrows, logical lleft, logical lright, integer nl, complex*16 c, complex*16 s, complex*16, dimension( * ) a, integer lda, complex*16 xleft, complex*16 xright)

ok literally here's the whole signature, look at her, she's iconic 👑

subroutine ZLAROT (logical lrows, logical lleft, logical lright, integer nl,
    complex*16 c, complex*16 s, complex*16, dimension( * ) a, integer lda,
    complex*16 xleft, complex*16 xright)

💖 ZLAROT 💖

🦋 Purpose:

!>
!>    ZLAROT applies a (Givens) rotation to two adjacent rows or
!>    columns, where one element of the first and/or last column/row
!>    for use on matrices stored in some format other than GE, so
!>    that elements of the matrix may be used or modified for which
!>    no array element is provided.
!>
!>    One example is a symmetric matrix in SB format (bandwidth=4), for
!>    which UPLO='L':  Two adjacent rows will have the format:
!>
!>    row j:     C> C> C> C> C> .  .  .  .
!>    row j+1:      C> C> C> C> C> .  .  .  .
!>
!>    '*' indicates elements for which storage is provided,
!>    '.' indicates elements for which no storage is provided, but
!>    are not necessarily zero; their values are determined by
!>    symmetry.  ' ' indicates elements which are necessarily zero,
!>     and have no storage provided.
!>
!>    Those columns which have two '*'s can be handled by DROT.
!>    Those columns which have no '*'s can be ignored, since as long
!>    as the Givens rotations are carefully applied to preserve
!>    symmetry, their values are determined.
!>    Those columns which have one '*' have to be handled separately,
!>    by using separate variables  and :
!>
!>    row j:     C> C> C> C> C> p  .  .  .
!>    row j+1:   q  C> C> C> C> C> .  .  .  .
!>
!>    The element p would have to be set correctly, then that column
!>    is rotated, setting p to its new value.  The next call to
!>    ZLAROT would rotate columns j and j+1, using p, and restore
!>    symmetry.  The element q would start out being zero, and be
!>    made non-zero by the rotation.  Later, rotations would presumably
!>    be chosen to zero q out.
!>
!>    Typical Calling Sequences: rotating the i-th and (i+1)-st rows.
!>    ------- ------- ---------
!>
!>      General dense matrix:
!>
!>              CALL ZLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S,
!>                      A(i,1),LDA, DUMMY, DUMMY)
!>
!>      General banded matrix in GB format:
!>
!>              j = MAX(1, i-KL )
!>              NL = MIN( N, i+KU+1 ) + 1-j
!>              CALL ZLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S,
!>                      A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT )
!>
!>              [ note that i+1-j is just MIN(i,KL+1) ]
!>
!>      Symmetric banded matrix in SY format, bandwidth K,
!>      lower triangle only:
!>
!>              j = MAX(1, i-K )
!>              NL = MIN( K+1, i ) + 1
!>              CALL ZLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S,
!>                      A(i,j), LDA, XLEFT, XRIGHT )
!>
!>      Same, but upper triangle only:
!>
!>              NL = MIN( K+1, N-i ) + 1
!>              CALL ZLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S,
!>                      A(i,i), LDA, XLEFT, XRIGHT )
!>
!>      Symmetric banded matrix in SB format, bandwidth K,
!>      lower triangle only:
!>
!>              [ same as for SY, except:]
!>                  . . . .
!>                      A(i+1-j,j), LDA-1, XLEFT, XRIGHT )
!>
!>              [ note that i+1-j is just MIN(i,K+1) ]
!>
!>      Same, but upper triangle only:
!>                  . . .
!>                      A(K+1,i), LDA-1, XLEFT, XRIGHT )
!>
!>      Rotating columns is just the transpose of rotating rows, except
!>      for GB and SB: (rotating columns i and i+1)
!>
!>      GB:
!>              j = MAX(1, i-KU )
!>              NL = MIN( N, i+KL+1 ) + 1-j
!>              CALL ZLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S,
!>                      A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM )
!>
!>              [note that KU+j+1-i is just MAX(1,KU+2-i)]
!>
!>      SB: (upper triangle)
!>
!>                   . . . . . .
!>                      A(K+j+1-i,i),LDA-1, XTOP, XBOTTM )
!>
!>      SB: (lower triangle)
!>
!>                   . . . . . .
!>                      A(1,i),LDA-1, XTOP, XBOTTM )
!>

🌸 The Arguments (yes, all of them, we're doing this) 🌸

  • LROWS — LOGICAL. if .TRUE., then ZLAROT rotates two rows; if .FALSE., it rotates two columns. not modified. 💫
  • LLEFT — LOGICAL. if .TRUE., then XLEFT gets used instead of the corresponding element of A for the first element in the second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.). if .FALSE., then the corresponding element of A is what gets used. not modified. 🫧
  • LRIGHT — LOGICAL. if .TRUE., then XRIGHT gets used instead of the corresponding element of A for the last element in the first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.). if .FALSE., then the corresponding element of A gets used. not modified. ⭐
  • NL — INTEGER. the length of the rows (if LROWS=.TRUE.) or columns (if LROWS=.FALSE.) to be rotated. if XLEFT and/or XRIGHT are used, the columns/rows they're in should be included in NL — like, if LLEFT = LRIGHT = .TRUE., then NL must be at least 2. the number of rows/columns to be rotated exclusive of those involving XLEFT and/or XRIGHT may not be negative, i.e. NL minus how many of LLEFT and LRIGHT are .TRUE. must be at least zero; if it isn't, XERBLA will be called 😤. not modified.
  • C, S — COMPLEX*16. these specify the Givens rotation to be applied. if LROWS is true, then the matrix
( c  s )
( _  _ )
(-s  c )

gets applied from the left; if false, then the transpose (not conjugated) thereof gets applied from the right. bestie, note that in contrast to the output of ZROTG or to most versions of ZROT, both C and S are complex. for a Givens rotation, |C|**2 + |S|**2 should be 1, but this is not checked 🙈. not modified.

  • A — COMPLEX*16 array. the array containing the rows/columns to be rotated. the first element of A should be the upper left element to be rotated. read and modified. 💅
  • LDA — INTEGER. the leading dimension of A. if A contains a matrix stored in GE, HE, or SY format, then this is just the leading dimension of A as dimensioned in the calling routine. if A contains a matrix stored in band (GB, HB, or SB) format, then this should be one less than the leading dimension used in the calling routine. so like, if A were dimensioned A(LDA,*) in ZLAROT, then A(1,j) would be the j-th element in the first of the two rows to be rotated, and A(2,j) would be the j-th in the second, regardless of how the array may be stored in the calling routine. (A cannot, however, actually be dimensioned thus, since for band format the row number may exceed LDA, which is not legal FORTRAN. 💀) if LROWS=.TRUE., then LDA must be at least 1, otherwise it must be at least NL minus the number of .TRUE. values in XLEFT and XRIGHT. not modified.
  • XLEFT — COMPLEX*16. if LLEFT is .TRUE., then XLEFT gets used and modified instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) (if LROWS=.FALSE.). read and modified. 🎀
  • XRIGHT — COMPLEX*16. if LRIGHT is .TRUE., then XRIGHT gets used and modified instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) (if LROWS=.FALSE.). read and modified. 🎀

👑 Author

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

🔥 Definition

definition at line 227 of file zlarot.f. periodt.

🌈 Author 🌈

this page was generated automatically by Doxygen for LAPACK, straight from the source code. yeah, a robot wrote the original, but I wrote this version, so. 🧚

fr fr bestie, that's the whole page. every flag, every .TRUE./.FALSE., every LDA-1 — all of it. nothing skipped, no cap. 💜

that's a wrap on LAPACK, Version 3.12.0, <pink>/home/abui...N/zlarot.f(3)</pink> — mwah 💋

📦 where this page comes from