PCTRCON(l)

📦 version 1.5, in ubuntu jammy

💖 NAME 💖

okay bestie, gather round, because PCTRCON is here to estimate the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm. that's it. that's the whole job. she's a specialist, she's booked, she's thriving. 💅

✨ SYNOPSIS ✨

SUBROUTINE PCTRCON( NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, WORK,
                    LWORK, RWORK, LRWORK, INFO )

    CHARACTER       DIAG, NORM, UPLO

    INTEGER         IA, JA, INFO, LRWORK, LWORK, N

    REAL            RCOND

    INTEGER         DESCA( * )

    REAL            RWORK( * )

    COMPLEX         A( * ), WORK( * )

look at her. thirteen arguments. she's got range. 🦋

🎀 PURPOSE 🎀

PCTRCON estimates the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm.

here's the recipe, no cap:

the norm of A(IA:IA+N-1,JA:JA+N-1) gets computed
then an estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1)))
then 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)) ) ).

it's giving math girl summer. 🧚

📝 Notes 📝

okay so this part is the "how does a distributed array even work" lore drop. every 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. iconic behaviour honestly.

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". 🌸

here's the whole vibe chart, as bullets because tables are not the moment:

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)).

now. 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

there. now you can flex at parties. iykyk. 💜

👑 ARGUMENTS 👑

`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.

pick your fighter. 💅

`UPLO`

(global input) CHARACTER —

= 'U': A(IA:IA+N-1,JA:JA+N-1) is upper triangular;
= 'L': A(IA:IA+N-1,JA:JA+N-1) is lower triangular.

`DIAG`

(global input) CHARACTER —

= 'N': A(IA:IA+N-1,JA:JA+N-1) is non-unit triangular;
= 'U': A(IA:IA+N-1,JA:JA+N-1) is unit triangular.

`N`

(global input) INTEGER — the order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1). N >= 0. (yes bestie, zero is allowed, we love a boundary case. 🫶)

`A`

(local input) COMPLEX pointer into the local memory to an array of dimension ( LLD_A, LOCc(JA+N-1) ). this array contains the local pieces of the triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1).

if UPLO = 'U', the leading N-by-N upper triangular part of this distributed matrix contains the upper triangular matrix, and its strictly lower triangular part is not referenced.
if UPLO = 'L', the leading N-by-N lower triangular part of this ditributed matrix contains the lower triangular matrix, and the strictly upper triangular part is not referenced.
if DIAG = 'U', the diagonal elements of A(IA:IA+N-1,JA:JA+N-1) are also not referenced and are assumed to be 1.

so half of her is literally just vibes. not read. ignored. main character only. ✨

`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.

`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)) ) ).

she's the whole point of the function, and she knows it. 👑

`WORK`

(local workspace/local output) COMPLEX array, dimension (LWORK). on exit, WORK(1) returns the minimal and optimal LWORK.

`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)) + MAX( 2, MAX(NB_A*CEIL(P-1,Q),LOCc(N+MOD(JA-1,NB_A)) + NB_A*CEIL(Q-1,P)) ).

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. sneaky little query mode, we love her. 🙈

`RWORK`

(local workspace/local output) REAL array, dimension (LRWORK). on exit, RWORK(1) returns the minimal and optimal LRWORK.

`LRWORK`

(local or global input) INTEGER — the dimension of the array RWORK. LRWORK is local input and must be at least

LRWORK >= LOCc(N+MOD(JA-1,NB_A)).

if LRWORK = -1, then LRWORK 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. same trick, different array. 💅

`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.

okay so if INFO comes back negative, something you handed her was illegal — she will literally encode the exact argument index in the number. read it carefully. do not ignore her. she is not being dramatic, she is being precise. 😭

and that's the whole page, bestie. this one is from LAPACK version 1.5, dated 12 May 1997 — yes she's vintage, yes she still eats, no we are not taking questions. 🌈 go forth, pass LWORK = -1, do your workspace query, and slay. 💖✨🎀🦋

📦 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