PZLACGV(l)

📦 version 1.5, in ubuntu jammy

✨ PZLACGV 💅 the aux routine that conjugates your complex vector ✨

okay so bestie, welcome to PZLACGV from LAPACK, a LAPACK auxiliary routine, sitting pretty at version 1.5. It's a ScaLAPACK-flavoured little icon and it does exactly one thing and does it gorgeously. Sit down, grab a strawberry 🍓, and let's get into it.

🌸 NAME 🌸

PZLACGV — conjugate a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and Notes ===== Each global data object is described by an associated description vector.

yeah that's a lot in one breath, but it's all facts, no filler. 💖

🦋 SYNOPSIS 🦋

SUBROUTINE PZLACGV( N, X, IX, JX, DESCX, INCX )

    INTEGER         INCX, IX, JX, N

    INTEGER         DESCX( * )

    COMPLEX*16      X( * )

👑 PURPOSE 👑

PZLACGV conjugates a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and the mapping between an object element and its corresponding process and memory location.

Let A be a generic term for any 2D block cyclicly distributed array. Such a global array has an associated description vector DESCA. In the following comments, the character _ should be read as "of the global array".

NOTATION        STORED IN      EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                               DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                               the BLACS process grid A is distribu-
                               ted over. The context itself is glo-
                               bal, but the handle (the integer
                               value) may vary.
M_A    (global) DESCA( M_ )    The number of rows in the global
                               array A.
N_A    (global) DESCA( N_ )    The number of columns in the global
                               array A.
MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                               the rows of the array.
NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                               the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                               row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                               first column of the array A is
                               distributed.
LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                               array.  LLD_A >= MAX(1,LOCr(M_A)).

Let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.

LOCr( K ) denotes the number of elements of K that a process would receive if K were distributed over the p processes of its process column.

Similarly, LOCc( K ) denotes the number of elements of K that a process would receive if K were distributed over the q processes of its process row.

The values of LOCr() and LOCc() may be determined via a call to the ScaLAPACK tool function, NUMROC:

LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).

An upper bound for these quantities may be computed by:

LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

Because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a distributed matrix. 🫶 yes, vectors are just matrices living their best life.

💜 ARGUMENTS 💜

  • N — (global input) INTEGER — The length of the distributed vector sub( X ). it's the vibe count, the how-many-elements-we-talking-about 💫
  • X — (local input/local output) COMPLEX16 pointer into the local memory to an array of dimension (LLD_X,*).* — On entry the vector to be conjugated x( i ) = X(IX+(JX-1)*M_X +(i-1)*INCX ), 1 <= i <= N. On exit the conjugated vector. so it comes in all normal and leaves all conjugated 💅
  • IX — (global input) INTEGER — The row index in the global array X indicating the first row of sub( X ).
  • JX — (global input) INTEGER — The column index in the global array X indicating the first column of sub( X ).
  • DESCX — (global and local input) INTEGER array of dimension DLEN_. — The array descriptor for the distributed matrix X. the little ID card that tells everyone where X actually lives 🎀
  • INCX — (global input) INTEGER — The global increment for the elements of X. Only two values of INCX are supported in this version, namely 1 and M_X. INCX must not be zero.
🚨 bestie listen: only 1 and M_X are supported for INCX in this version, and INCX must not be zero. no cap. don't try it, she will not be nice about it.

and that's the whole page, gorgeous. go conjugate something responsibly. 🦋✨

with love from the LAPACK gang — this page is from LAPACK version 1.5, dated 12 May 1997, and it's filed under PZLACGV(l). 💖

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