PZPOSV(l)

📦 version 1.5, in ubuntu jammy

✨ PZPOSV ✨

okay so bestie, welcome to PZPOSV, a routine from the LAPACK family (version 1.5, we're talking vintage but still slaying 💅). It's here to compute the solution to a complex system of linear equations sub( A ) * X = sub( B ). Yes. That's the whole vibe. Let's get into it 🫶

NAME

PZPOSV — compute the solution to a complex system of linear equations sub( A ) * X = sub( B ), 🎀

SYNOPSIS

SUBROUTINE PZPOSV( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB,
                   INFO )

    CHARACTER      UPLO

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

    INTEGER        DESCA( * ), DESCB( * )

    COMPLEX*16     A( * ), B( * )

look at those arguments. iconic. no notes. ✨

PURPOSE

So like, what does PZPOSV actually do? It computes the solution to a complex system of linear equations

sub( A ) * X = sub( B ),

where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is an N-by-N hermitian distributed positive definite matrix 🌸 and X and sub( B ) — denoting B(IB:IB+N-1,JB:JB+NRHS-1) — are N-by-NRHS distributed matrices ✨.

The Cholesky decomposition is used to factor sub( A ) as

                   sub( A ) = U**H * U,  if UPLO = 'U', or

                   sub( A ) = L * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of sub( A ) is then used to solve the system of equations. factorize, then solve — the two-step, the main character arc, we love to see it 💖

Notes 🦋

Okay bestie, this part is the descriptor lore, and it's lowkey important, so pay attention 📚

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".

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 distributed over. The context itself is global, 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 decomposition ( MB_A = NB_A ). no exceptions, that's the rule 🌈

ARGUMENTS

okay now the moment you've all been waiting for: the arguments. every single one. we are NOT skipping anybody 💅

UPLO — (global input) CHARACTER = 'U': Upper triangle of sub( A ) is stored; = 'L': Lower triangle of sub( A ) is stored. 🎀
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/local output) COMPLEX*16 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 N-by-N symmetric distributed matrix sub( A ) to be factored. If UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular part of the distributed matrix, and its strictly upper triangular part is not referenced. On exit, if INFO = 0, this array contains the local pieces of the factor U or L from the Cholesky factorization sub( A ) = U**H*U or L*L**H. in and out, like a revolving door, love that for it 🚪💖
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. 🎀
B — (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_B,LOC(JB+NRHS-1)). On entry, the local pieces of the right hand sides distributed matrix sub( B ). On exit, if INFO = 0, sub( B ) is overwritten with the solution distributed matrix X. bestie, it gets overwritten, do not expect your original B to survive. that's just how it is 🙈
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. > 0: If INFO = K, the leading minor of order K, A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and the factorization could not be completed, and the solution has not been computed. 💀

💀 the INFO > 0 case is the "it's not positive definite bestie, we can't do it" moment. factorization incomplete, solution not computed. the math said no.

and that's the whole page, no cap. you now know PZPOSV better than it knows itself 🫶✨

signing off with the receipts: this is LAPACK version 1.5, dated 12 May 1997, and it goes by PZPOSV(l) on the official record. mwah, bye bestie 💖💅🎀🦋

📦 where this page comes from

ubuntu jammy: scalapack-doc 1.5-11
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms