p?ptsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 11/07/2023

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p?ptsv

Syntax

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

call psptsv(n, nrhs, d, e, ja, desca, b, ib, descb, work, lwork, info)

call pdptsv(n, nrhs, d, e, ja, desca, b, ib, descb, work, lwork, info)

call pcptsv(n, nrhs, d, e, ja, desca, b, ib, descb, work, lwork, info)

call pzptsv(n, nrhs, d, e, ja, desca, b, ib, descb, work, lwork, info)

Include Files

Description

The p?ptsvroutine 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'.

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

Input Parameters

n

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

nrhs

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

d

(local)

REAL for psptsv

DOUBLE PRECISON for pdptsv

COMPLEX for pcptsv

DOUBLE COMPLEX for pzptsv.

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

e

(local)

REAL for psptsv

DOUBLE PRECISON for pdptsv

COMPLEX for pcptsv

DOUBLE COMPLEX for pzptsv.

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) INTEGER. 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) INTEGER 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)

REAL for psptsv

DOUBLE PRECISON for pdptsv

COMPLEX for pcptsv

DOUBLE COMPLEX for pzptsv.

Pointer into the local memory to an array of local lead size lld_b ≥ nb.

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

ib

(global) INTEGER. 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) INTEGER 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).

REAL for psptsv

DOUBLE PRECISON for pdptsv

COMPLEX for pcptsv

DOUBLE COMPLEX for pzptsv.

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

lwork

(local or global) INTEGER. Size of user-input workspace work. If lwork is too small, the minimal acceptable size will be returned in work(1) 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_).

e

On exit, this array contains information containing the factors of the matrix. Must be of size greater than or equal to desca(nb_).

b

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

work

On exit, work(1) contains the minimal lwork.

info

(local) INTEGER. 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 = k ≤ NPROCS, 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.

Parent topic: ScaLAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?ptsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also