PSGECON(l)

📦 version 1.5, in ubuntu jammy

💖 PSGECON 💖 — the LAPACK routine, bestie edition

okay so picture this: it's PSGECON(l), she's a LAPACK routine, she's version 1.5, and she is literally the moment. this is a ScaLAPACK page (that's the distributed-girlie branch of LAPACK), and she's here to tell you how sketchy your matrix is. buckle up. 🎀

🌸 NAME 🌸

PSGECON — she estimates the reciprocal of the condition number of a general distributed real matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm, using the LU factorization computed by PSGETRF. slay. 💅

✨ SYNOPSIS ✨

SUBROUTINE PSGECON( NORM, N, A, IA, JA, DESCA, ANORM, RCOND, WORK,
                    LWORK, IWORK, LIWORK, INFO )

    CHARACTER       NORM

    INTEGER         IA, INFO, JA, LIWORK, LWORK, N

    REAL            ANORM, RCOND

    INTEGER         DESCA( * ), IWORK( * )

    REAL            A( * ), WORK( * )

🦋 PURPOSE 🦋

so PSGECON estimates the reciprocal of the condition number of a general distributed real matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm, using the LU factorization computed by PSGETRF. no cap, that's the whole job.

an estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and the reciprocal of the condition number is computed as

RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
              norm( inv(A(IA:IA+N-1,JA:JA+N-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. it's giving glow-up for indices, fr fr.

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". iykyk. 👑

the notation situation, laid out all cute:

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. she's global but her handle is flexible, main character energy honestly.
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. see how that works? parallel besties. 🫶

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

🔥 ARGUMENTS 🔥

every single one of them, and yes we're doing all of them, because skipping the boring ones is not the vibe.

NORM (global input) CHARACTER — specifies whether the 1-norm condition number or the infinity-norm condition number is required:
- = '1' or 'O': 1-norm
- = 'I': Infinity-norm
N (global input) INTEGER — the order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1). N >= 0. (yes babe, non-negative, we don't do negative orders here 🙈)
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 A(IA:IA+N-1,JA:JA+N-1) = P*L*U; the unit diagonal elements of L are not stored. iconic, they simply didn't feel like storing them and honestly? valid.
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. she's the passport for your matrix, periodt.
ANORM (global input) REAL — if NORM = '1' or 'O', the 1-norm of the original distributed matrix A(IA:IA+N-1,JA:JA+N-1). if NORM = 'I', the infinity-norm of the original distributed matrix A(IA:IA+N-1,JA:JA+N-1). match her energy to your NORM, that's the rule. ✨
RCOND (global output) REAL — the reciprocal of the condition number of the distributed matrix A(IA:IA+N-1,JA:JA+N-1), computed as

RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).

WORK (local workspace/local output) REAL array, dimension (LWORK). on exit, WORK(1) returns the minimal and optimal LWORK. she reports back, as she should. 💅
LWORK (local or global input) INTEGER — the dimension of the array WORK. LWORK is local input and must be at least

LWORK >= 2*LOCr(N+MOD(IA-1,MB_A)) +
2*LOCc(N+MOD(JA-1,NB_A)) + MAX( 2, MAX( NB_A*MAX( 1,
CEIL(NPROW-1,NPCOL) ), LOCc(N+MOD(JA-1,NB_A)) + NB_A*MAX( 1,
CEIL(NPCOL-1,NPROW) ) ).

LOCr and LOCc values can be computed using the ScaLAPACK tool function NUMROC; NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.

if LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA. so like, don't come for PXERBLA, she's off duty for this one. 😭

IWORK (local workspace/local output) INTEGER array, dimension (LIWORK). on exit, IWORK(1) returns the minimal and optimal LIWORK.
LIWORK (local or global input) INTEGER — the dimension of the array IWORK. LIWORK is local input and must be at least LIWORK >= LOCr(N+MOD(IA-1,MB_A)).

if LIWORK = -1, then LIWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA. again! she's resting. 🍓

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.

and that's the whole page, bestie. she's PSGECON(l), she's a LAPACK routine, and this particular beauty is LAPACK version 1.5, dated 12 May 1997 — vintage, but she ate and left no crumbs. 🧚 stay distributed, stay conditioned, and go check your RCOND. 💖🌈⭐

📦 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