PCGETRS(l)

📦 version 1.5, in ubuntu jammy

💖 PCGETRS(l) 💖

okay so bestie, welcome to PCGETRS, straight outta section l of the manual. it solves 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 PCGETRF. and yes she's iconic, she's giving linear algebra main character energy. 🦋

✨ NAME ✨

PCGETRS — 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 PCGETRF. periodt. 💅

🌸 SYNOPSIS 🌸

SUBROUTINE PCGETRS( 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( * )

    COMPLEX         A( * ), B( * )

no cap, that's the whole vibe right there. 🎀

👑 PURPOSE 👑

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

🧚 Notes

Each global data object is described by an associated description vector. This vector stores the information required to establish 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".

ok so here's the little legend, and it is so important, do not skip it:

  • DTYPE_A (global) — stored in DESCA( DTYPE_ ). The descriptor type. In this case, DTYPE_A = 1.
  • CTXT_A (global) — stored in DESCA( CTXT_ ). The BLACS context handle, indicating the BLACS process grid A is distributed over. The context itself is global, but the handle (the integer value) may vary.
  • M_A (global) — stored in DESCA( M_ ). The number of rows in the global array A.
  • N_A (global) — stored in DESCA( N_ ). The number of columns in the global array A.
  • MB_A (global) — stored in DESCA( MB_ ). The blocking factor used to distribute the rows of the array.
  • NB_A (global) — stored in DESCA( NB_ ). The blocking factor used to distribute the columns of the array.
  • RSRC_A (global) — stored in DESCA( RSRC_ ). The process row over which the first row of the array A is distributed.
  • CSRC_A (global) — stored in DESCA( CSRC_ ). The process column over which the first column of the array A is distributed.
  • LLD_A (local) — stored in 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
⚠️ bestie listen — this routine requires square block data decomposition ( MB_A=NB_A ). it's not optional, it's the law. 💀

🔥 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 )**H * X = sub( B ) (Conjugate 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) COMPLEX 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) COMPLEX 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. 👑
  • 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
    • = 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.

and that's the whole page, bestie!! 🫶 this lil legend came to you from LAPACK version 1.5, dated 12 May 1997 — yeah she's vintage, she's an heirloom, and she still eats. mwah 💋✨

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