---
name: "pdpotrs"
section: "3"
platform: "linux"
package: "scalapack-doc"
version: "1.5-11"
release: "Debian 11 (Bullseye)"
platforms: ["linux"]
url: "https://new.carta.tech/pdpotrs"
---

# pdpotrs(3)

solve a system of linear equations sub( A ) \* X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)\*X = B(IB:IB+N-1,JB:JB+NRHS-1)

## NAME

PDPOTRS - solve a system of linear equations   sub( A ) \* X = sub( B )  A(IA:IA+N-1,JA:JA+N-1)\*X = B(IB:IB+N-1,JB:JB+NRHS-1)

## SYNOPSIS

- SUBROUTINE PDPOTRS(

  UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB, INFO )

- CHARACTER

  UPLO

- INTEGER

  IA, IB, INFO, JA, JB, N, NRHS

- INTEGER

  DESCA( \* ), DESCB( \* )

- DOUBLE

  PRECISION A( \* ), B( \* )

## PURPOSE

PDPOTRS solves a system of linear equations

where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a N-by-N symmetric positive definite distributed matrix using the Cholesky factorization sub( A ) = U\*\*T\*U or L\*L\*\*T computed by PDPOTRF. sub( B ) denotes the distributed matrix B(IB:IB+N-1,JB:JB+NRHS-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.\

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".\

NOTATION        STORED IN      EXPLANATION\
 \--------------- -------------- -------------------------------------- DTYPE\_A(global) DESCA( DTYPE\_ )The descriptor type.  In this case,\
                                DTYPE\_A = 1.\
 CTXT\_A (global) DESCA( CTXT\_ ) The BLACS context handle, indicating\
                                the BLACS process grid A is distribu-\
                                ted over. The context itself is glo-\
                                bal, but the handle (the integer\
                                value) may vary.\
 M\_A    (global) DESCA( M\_ )    The number of rows in the global\
                                array A.\
 N\_A    (global) DESCA( N\_ )    The number of columns in the global\
                                array A.\
 MB\_A   (global) DESCA( MB\_ )   The blocking factor used to distribute\
                                the rows of the array.\
 NB\_A   (global) DESCA( NB\_ )   The blocking factor used to distribute\
                                the columns of the array.\
 RSRC\_A (global) DESCA( RSRC\_ ) The process row over which the first\
                                row of the array A is distributed. CSRC\_A (global) DESCA( CSRC\_ ) The process column over which the\
                                first column of the array A is\
                                distributed.\
 LLD\_A  (local)  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\

This routine requires square block decomposition ( MB\_A = NB\_A ).

## ARGUMENTS

- UPLO (global input) CHARACTER

  \= 'U':  Upper triangle of sub( A ) is stored;\
   \= 'L':  Lower triangle of sub( A ) is stored.

- N (global input) INTEGER

  The number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub( A ). N \>= 0.

- NRHS (global input) INTEGER

  The number of right hand sides, i.e., the number of columns of the distributed submatrix sub( B ).  NRHS \>= 0.

- A (local input) DOUBLE PRECISION pointer into local memory to

  an array of dimension (LLD\_A, LOCc(JA+N-1)). On entry, this array contains the factors L or U from the Cholesky facto- rization sub( A ) = L\*L\*\*T or U\*\*T\*U, 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.

- B (local input/local output) DOUBLE PRECISION pointer into the

  local memory to an array of local dimension (LLD\_B,LOCc(JB+NRHS-1)).  On entry, this array contains the the local pieces of the right hand sides sub( B ). On exit, this array contains the local pieces of the solution distributed matrix X.

- IB (global input) INTEGER

  The row index in the global array B indicating the first row of sub( B ).

- JB (global input) INTEGER

  The column index in the global array B indicating the first column of sub( B ).

- DESCB (global and local input) INTEGER array of dimension DLEN\_.

  The array descriptor for the distributed matrix B.

- 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.