PSGETRS(l)

💖 PSGETRS 💖

okay bestie, welcome to PSGETRS from the LAPACK fam, routine version 1.5, sitting pretty in section l of the manual. she solves distributed linear systems and she does it flawlessly — let's get into it ✨

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✨ NAME ✨

PSGETRS — solve a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PSGETRF. 🫶

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🌸 SYNOPSIS 🌸

SUBROUTINE PSGETRS( TRANS, N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB,
                    DESCB, INFO )

    CHARACTER       TRANS

    INTEGER         IA, IB, INFO, JA, JB, N, NRHS

    INTEGER         DESCA( * ), DESCB( * ), IPIV( * )

    REAL            A( * ), B( * )

like... look at her. no cap, that's the whole signature. 💅

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🦋 PURPOSE 🦋

PSGETRS solves a system of distributed linear equations where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A or A**T, and sub( B ) denotes B(IB:IB+N-1,JB:JB+NRHS-1). ✨

💜 Notes 💜

every global data object is described by an associated description vector. this vector stores the info you need to establish the mapping between an object element and its corresponding process and memory location. iykyk.

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

💀 heads up bestie: this routine requires square block data decomposition (MB_A=NB_A). not optional, that's the vibe check.

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🎀 ARGUMENTS 🎀

• TRANS — (global input) CHARACTER. specifies the form of the system of equations:
  • = 'N': sub( A ) * X = sub( B ) (No transpose)
  • = 'T': sub( A )**T * X = sub( B ) (Transpose)
  • = 'C': sub( A )**T * X = sub( B ) (Transpose)
• N — (global input) INTEGER. the number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub( A ). N >= 0.
• NRHS — (global input) INTEGER. the number of right hand sides, i.e., the number of columns of the distributed submatrix sub( B ). NRHS >= 0.
• A — (local input) REAL pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). on entry, this array contains the local pieces of the factors L and U from the factorization sub( A ) = P*L*U; the unit diagonal elements of L are not stored. 🙈
• IA — (global input) INTEGER. the row index in the global array A indicating the first row of sub( A ).
• JA — (global input) INTEGER. the column index in the global array A indicating the first column of sub( A ).
• DESCA — (global and local input) INTEGER array of dimension DLEN_. the array descriptor for the distributed matrix A.
• IPIV — (local input) INTEGER array, dimension ( LOCr(M_A)+MB_A ). this array contains the pivoting information. IPIV(i) -> The global row local row i was swapped with. this array is tied to the distributed matrix A.
• B — (local input/local output) REAL pointer into the local memory to an array of dimension (LLD_B,LOCc(JB+NRHS-1)). on entry, the right hand sides sub( B ). on exit, sub( B ) is overwritten by the solution distributed matrix X. ✨ main character transformation honestly.
• IB — (global input) INTEGER. the row index in the global array B indicating the first row of sub( B ).
• JB — (global input) INTEGER. the column index in the global array B indicating the first column of sub( B ).
• DESCB — (global and local input) INTEGER array of dimension DLEN_. the array descriptor for the distributed matrix B.
• INFO — (global output) INTEGER. the receipts 📋:
  • = 0: successful exit 👑
  • < 0: If the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i.

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and that's the whole page, bestie 💖 this was LAPACK version 1.5, dated 12 May 1997 — iconic behavior, truly a classic. mwah. 💅🎀🦋