p?pttrsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 6/24/2024

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p?pttrsv

Solves a single triangular linear system via frontsolve or backsolve where the triangular matrix is a factor of a tridiagonal matrix computed by p?pttrf .

Syntax

void pspttrsv (char *uplo , 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 *af , MKL_INT *laf , float *work , MKL_INT *lwork , MKL_INT *info );

void pdpttrsv (char *uplo , 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 *af , MKL_INT *laf , double *work , MKL_INT *lwork , MKL_INT *info );

void pcpttrsv (char *uplo , char *trans , 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 *af , MKL_INT *laf , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *info );

void pzpttrsv (char *uplo , char *trans , 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 *af , MKL_INT *laf , MKL_Complex16 *work , MKL_INT *lwork , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?pttrsvfunction solves a tridiagonal triangular system of linear equations

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

A(1:n, ja:ja+n-1)^T*X = B(jb:jb+n-1, 1:nrhs) for real flavors,

A(1:n, ja:ja+n-1)^H*X = B(jb:jb+n-1, 1:nrhs) for complex flavors,

where A(1:n, ja:ja+n-1) is a tridiagonal triangular matrix factor produced by the Cholesky factorization code p?pttrf and is stored in A(1:n, ja:ja+n-1) and af. The matrix stored in A(1:n, ja:ja+n-1) is either upper or lower triangular according to uplo.

The function p?pttrf must be called first.

Input Parameters

uplo

(global) Must be 'U' or 'L'.

If uplo = 'U', upper triangle of A(1:n, ja:ja+n-1) is stored;

If uplo = 'L', lower triangle of A(1:n, ja:ja+n-1) is stored.

trans

(global) Must be 'N' or 'C'.

If trans = 'N', solve with A(1:n, ja:ja+n-1);

If trans = 'C' (for complex flavors), solve with conjugate transpose (A(1:n, ja:ja+n-1))^H.

n

(global)

The number of rows and columns to be operated on, that is, the order of the distributed submatrix A(1:n, ja:ja+n-1). n ≥ 0.

nrhs

(global)

The number of right hand sides; the number of columns of the distributed submatrix B(jb:jb+n-1, 1:nrhs); nrhs ≥ 0.

d

(local)

Pointer to the local part of the global vector storing the main diagonal of the matrix; must be of size ≥nb_a.

e

(local)

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

ja

(global) The index in the global matrix A that points to 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_. The array descriptor for the distributed matrix A.

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

If 2D type (dtype_a = 1), then dlen ≥ 9.

Contains information on mapping of A to memory. See ScaLAPACK manual for full description and options.

b

(local)

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(jb:jb+n-1, 1:nrhs).

ib

(global) The row index in the global matrix B that points to 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_. The array descriptor for the distributed matrix B.

If 1D type (dtype_b = 502), then dlen ≥ 7;

If 2D type (dtype_b = 1), then dlen ≥ 9.

Contains information on mapping of B to memory. See ScaLAPACK manual for full description and options.

laf

(local)

The size of user-input auxiliary fill-in space af. Must be laf ≥ (nb+2*bw)*bw.

If laf is not large enough, an error code will be returned and the minimum acceptable size will be returned in af[0].

work

(local)

The array work is a temporary workspace array of size lwork. This space may be overwritten in between function calls.

lwork

(local or global) The size of the user-input workspace work, must be at least lwork ≥(10+2*min(100, nrhs))*npcol+4*nrhs. If lwork is too small, the minimal acceptable size will be returned in work[0] and an error code is returned.

Output Parameters

d, e

(local).

On exit, these arrays contain information on the factors of the matrix.

af

(local)

The array af is of size laf. It contains auxiliary fill-in space. The fill-in space is created in a call to the factorization function p?pbtrf and is stored in af. If a linear system is to be solved using p?pttrs after the factorization function, af must not be altered after the factorization.

b

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

work[0]

On exit, work[0] contains the minimum value of lwork.

info

(local)

= 0: successful exit

< 0: if the i-th argument is an array and the j-th entry, indexed j-1, 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.

Parent topic: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?pttrsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also