## Syntax

Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations.

void psptsv (MKL_INT *n , MKL_INT *nrhs , float *d , float *e , MKL_INT *ja , MKL_INT *desca , float *b , MKL_INT *ib , MKL_INT *descb , float *work , MKL_INT *lwork , MKL_INT *info );

void pdptsv (MKL_INT *n , MKL_INT *nrhs , double *d , double *e , MKL_INT *ja , MKL_INT *desca , double *b , MKL_INT *ib , MKL_INT *descb , double *work , MKL_INT *lwork , MKL_INT *info );

void pcptsv (char *uplo , MKL_INT *n , MKL_INT *nrhs , float *d , MKL_Complex8 *e , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *b , MKL_INT *ib , MKL_INT *descb , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *info );

void pzptsv (char *uplo , MKL_INT *n , MKL_INT *nrhs , double *d , MKL_Complex16 *e , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *b , MKL_INT *ib , MKL_INT *descb , MKL_Complex16 *work , MKL_INT *lwork , MKL_INT *info );

## Include Files

• mkl_scalapack.h

## Description

The p?ptsvfunction solves a system of linear equations

A(1:n, ja:ja+n-1)*X = B(ib:ib+n-1, 1:nrhs),

where A(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distributed matrix.

Cholesky factorization is used to factor a reordering of the matrix into L*L'.

Optimization Notice

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804

## Input Parameters

n

(global) The order of matrix A(n 0).

nrhs

(global) The number of right-hand sides; the number of columns of the distributed submatrix B(nrhs 0).

d

(local)

Pointer to local part of global vector storing the main diagonal of the matrix.

e

(local)

Pointer to local part of global vector storing the upper diagonal of the matrix. Globally, du(n) is not referenced, and du must be aligned with d.

ja

(global) The index in the global matrix A indicating the start of the matrix to be operated on (which may be either all of A or a submatrix of A).

desca

(global and local) array of size dlen.

If 1d type (dtype_a=501 or 502), dlen ≥ 7;

If 2d type (dtype_a=1), dlen ≥ 9.

The array descriptor for the distributed matrix A.

Contains information of mapping of A to memory.

b

(local)

Pointer into the local memory to an array of local lead size lld_bnb.

On entry, this array contains the local pieces of the right hand sides B(ib:ib+n-1, 1:nrhs).

ib

(global) The row index in the global matrix B indicating the first row of the matrix to be operated on (which may be either all of b or a submatrix of B).

descb

(global and local) array of size dlen.

If 1d type (dtype_b = 502), dlen ≥ 7;

If 2d type (dtype_b = 1), dlen ≥ 9.

The array descriptor for the distributed matrix B.

Contains information of mapping of B to memory.

work

(local).

Temporary workspace. This space may be overwritten in between calls to functions. work must be the size given in lwork.

lwork

(local or global) Size of user-input workspace work. If lwork is too small, the minimal acceptable size will be returned in work[0] and an error code is returned. lwork > (12*NPCOL+3*nb)+max((10+2*min(100, nrhs))*NPCOL+4*nrhs, 8*NPCOL).

## Output Parameters

d

On exit, this array contains information containing the factors of the matrix. Must be of size greater than or equal to desca[nb_ - 1].

e

On exit, this array contains information containing the factors of the matrix. Must be of size greater than or equal to desca[nb_ - 1].

b

On exit, this contains the local piece of the solutions distributed matrix X.

work

On exit, work[0] contains the minimal lwork.

info

(local) If info=0, the execution is successful.

< 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.

> 0: If info = kNPROCS, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.

If info = k > NPROCS, the submatrix stored on processor info-NPROCS representing interactions with other processors was not positive definite, and the factorization was not completed.