PCLANSY(l)

📦 version 1.5, in ubuntu jammy

PCLANSY 💅✨

ok bestie, sit down, hydrate, because today we're reading a LAPACK auxiliary routine and honestly? she's serving. this one lives in the l manual section, she's version 1.5 energy, and she's about to tell you the size of your matrix without ever touching the matrix. no cap.

✨ NAME ✨

PCLANSY — bestie, she returns the value of the one norm, or the Frobenius norm, …and more, keep reading, we're getting there 🫶

🌸 SYNOPSIS 🌸

REAL FUNCTION PCLANSY( NORM, UPLO, N, A, IA, JA, DESCA, WORK )

    CHARACTER NORM, UPLO

    INTEGER   IA, JA, N

    INTEGER   DESCA( * )

    REAL      WORK( * )

    COMPLEX   A( * )

she returns a REAL, she takes a COMPLEX array, and yes, the mismatch is intentional. it's giving "trust the process". 💀

🎀 PURPOSE 🎀

PCLANSY returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).

(yes, a real symmetric distributed matrix, that's what the original says, we do not editorialize, we only vibe. 💖)

so PCLANSY returns the value:

   ( max(abs(A(i,j))),  NORM = 'M' or 'm' with IA <= i <= IA+N-1,
   (                                      and  JA <= j <= JA+N-1,
   (
   ( norm1( sub( A ) ), NORM = '1', 'O' or 'o'
   (
   ( normI( sub( A ) ), NORM = 'I' or 'i'
   (
   ( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e'

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). 📐

⚠️ heads up bestie: note that max(abs(A(i,j))) is not a matrix norm. she's just built different. don't come for her. 💅

🌈 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. iykyk. 🧠✨

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".

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

periodt. 🎀

💖 ARGUMENTS 💖

NORM — (global input) CHARACTER — specifies the value to be returned in PCLANSY as described above. she decides which norm you're getting, so choose wisely bestie. ✨
UPLO — (global input) CHARACTER — specifies whether the upper or lower triangular part of the symmetric matrix sub( A ) is to be referenced. = 'U': upper triangular part of sub( A ) is referenced, = 'L': lower triangular part of sub( A ) is referenced. pick a side, we love that for you. 🦋
N — (global input) INTEGER — the number of rows and columns to be operated on, i.e. the number of rows and columns of the distributed submatrix sub( A ). when N = 0, PCLANSY is set to zero. N >= 0. zero means zero, no drama.
A — (local input) COMPLEX pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the local pieces of the symmetric distributed matrix sub( A ). if UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular matrix which norm is to be computed, and the strictly lower triangular part of this matrix is not referenced. if UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular matrix which norm is to be computed, and the strictly upper triangular part of sub( A ) is not referenced. 👑
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 whole personality of this operation, honestly. 💜
WORK — (local workspace) REAL array dimension (LWORK). listen, this is the part with the formulas, stay with me:

LWORK >= 0 if NORM = 'M' or 'm' (not referenced), 2*Nq0+Np0+LDW if NORM = '1', 'O', 'o', 'I' or 'i', where LDW is given by:

IF( NPROW.NE.NPCOL ) THEN
   LDW = MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW))
ELSE
   LDW = 0
END IF

0 if NORM = 'F', 'f', 'E' or 'e' (not referenced),

where LCM is the least common multiple of NPROW and NPCOL, LCM = ILCM( NPROW, NPCOL ), and CEIL denotes the ceiling operation (ICEIL).

IROFFA = MOD( IA-1, MB_A ),
ICOFFA = MOD( JA-1, NB_A ),
IAROW  = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
IACOL  = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
Np0    = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ),
Nq0    = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),

ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO. 🛠️✨

🌟 reminder bestie: she's an auxiliary routine, she doesn't factorize, she doesn't solve, she just measures. main character energy, minimal responsibilities. we respect it. 💅

and that's the whole page, fr fr. this was LAPACK version 1.5, dated 12 May 1997 — yes she's vintage, yes she still slays, no further questions. 🫶💖✨ 🎀

📦 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