PDPOCON(l)

📦 version 1.5, in ubuntu jammy

✨ PDPOCON — the vibe check for your Cholesky factorization 💅

okay bestie, welcome to PDPOCON(l), a LAPACK routine (she's version 1.5, vintage, iconic) and she is literally here to tell you how sketchy your matrix is. 🎀

🌸 NAME 🌸

PDPOCON — she estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matrix, using the Cholesky factorization A = U**T*U or A = L*L**T that PDPOTRF already computed for you. periodt.

🦋 SYNOPSIS 🦋

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

    CHARACTER       UPLO

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

    DOUBLE          PRECISION ANORM, RCOND

    INTEGER         DESCA( * ), IWORK( * )

    DOUBLE          PRECISION A( * ), WORK( * )

👑 PURPOSE 👑

So PDPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matrix, using the Cholesky factorization A = U**T*U or A = L*L**T computed by PDPOTRF. she's not doing the factorization herself, she's reading the receipts 💅

An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and then the reciprocal of the condition number gets 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 personality. one number, zero chill.

📓 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".

okay so here's the descriptor lore, in bullet form 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)).

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

🎀 ARGUMENTS 🎀

UPLO — (global input) CHARACTER. Specifies whether the factor stored in A(IA:IA+N-1,JA:JA+N-1) is upper or lower triangular.
- = 'U': Upper triangular ✨
- = 'L': Lower 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) DOUBLE PRECISION 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 or U from the Cholesky factorization A(IA:IA+N-1,JA:JA+N-1) = U'*U or L*L', as computed by PDPOTRF.
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.
ANORM — (global input) DOUBLE PRECISION. The 1-norm (or infinity-norm) of the symmetric distributed matrix A(IA:IA+N-1,JA:JA+N-1).
RCOND — (global output) DOUBLE PRECISION. 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) DOUBLE PRECISION 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)) +
2*LOCc(N+MOD(JA-1,NB_A)) + MAX( 2,
MAX(NB_A*CEIL(NPROW-1,NPCOL),LOCc(N+MOD(JA-1,NB_A)) +
NB_A*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. 🕵️‍♀️

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.

bestie, if INFO comes back negative, that's not a vibe — go re-read which argument you fumbled. 😭

and that's the whole page, you ate it, no crumbs 🫶

this lil legend came straight out of LAPACK version 1.5, dated 12 May 1997 — so yeah, she's older than most of us and still serving, lowkey iconic, fr fr. 💖✨🌸

📦 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