PSTRCON(l)

📦 version 1.5, in ubuntu jammy

💖 PSTRCON(l) — the LAPACK routine, but make it make sense 💖

okay so bestie, welcome to PSTRCON, a LAPACK routine, version 1.5. it estimates the reciprocal of the condition number of a triangular distributed matrix, and honestly? it's giving main character energy in the linear algebra world. no cap. 🦋

✨ NAME ✨

PSTRCON — 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. periodt. 💅

🌸 SYNOPSIS 🌸

SUBROUTINE PSTRCON( NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, WORK,
                    LWORK, IWORK, LIWORK, INFO )

    CHARACTER       DIAG, NORM, UPLO

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

    REAL            RCOND

    INTEGER         DESCA( * ), IWORK( * )

    REAL            A( * ), WORK( * )

like, look at her. she's doing SO much. 🫶

👑 PURPOSE 👑

PSTRCON 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.

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

like, that's the whole vibe. reciprocal of a product of norms. iconic. ⭐

📝 Notes 📝

each global data object is described by an associated description vector, bestie. this vector stores the information required to establish the mapping between an object element and its corresponding process and memory location. it's literally the group chat between your array elements and their homes. 💌

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. 💅

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

so like. that's your math. slay. 🧚

💅 ARGUMENTS 💅

okay bestie, here come all of them, one by one, no skipping, no summarising, we do NOT leave anyone on read in this house:

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.
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.
A (local input) REAL 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 distributed 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. (yes bestie, she said "ditributed" in the original and we are honoring that typo, it's part of her lore now. 🙈)
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)) ) ).

WORK (local workspace/local output) REAL 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)) + 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) ) ).

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. (workspace query mode is literally her "do not perceive me" era. 🔥)

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.

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 real talk, that negative-INFO thing is your bestie telling you exactly which argument you fumbled. don't ignore her. 😭

🌈 that's the whole page bestie 🌈

you now know everything PSTRCON has ever wanted to tell you, and you did not skip a single line. vibe check: passed. 💜

<div>— signed off from LAPACK version 1.5, dated 12 May 1997 ✨ ily, go estimate some condition numbers 💖🎀🦋</div>

📦 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