Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by ?pttrf.

Syntax

call spttrs( n, nrhs, d, e, b, ldb, info )

call dpttrs( n, nrhs, d, e, b, ldb, info )

call cpttrs( uplo, n, nrhs, d, e, b, ldb, info )

call zpttrs( uplo, n, nrhs, d, e, b, ldb, info )

call pttrs( d, e, b [,info] )

call pttrs( d, e, b [,uplo] [,info] )

Include Files
  • mkl.fi, lapack.f90
Description

The routine solves for X a system of linear equations A*X = B with a symmetric (Hermitian) positive-definite tridiagonal matrix A. Before calling this routine, call ?pttrf to compute the L*D*LT or UT*D*Ufor real data and the L*D*LH or UH*D*Ufactorization of A for complex data.

Input Parameters

uplo

CHARACTER*1. Used for cpttrs/zpttrs only. Must be 'U' or 'L'.

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and how A is factored:

If uplo = 'U', the array e stores the conjugated values of the superdiagonal of U, and A is factored as UH*D*U.

If uplo = 'L', the array e stores the subdiagonal of L, and A is factored as L*D*LH.

n

INTEGER. The order of A; n 0.

nrhs

INTEGER. The number of right-hand sides, that is, the number of columns of the matrix B; nrhs 0.

d

REAL for spttrs, cpttrs

DOUBLE PRECISION for dpttrs, zpttrs.

Array, dimension (n). Contains the diagonal elements of the diagonal matrix D from the factorization computed by ?pttrf.

e, b

REAL for spttrs

DOUBLE PRECISION for dpttrs

COMPLEX for cpttrs

DOUBLE COMPLEX for zpttrs.

Arrays: e(n -1), b(ldb, nrhs).

The array e contains the (n - 1) sub-diagonal elements of the unit bidiagonal factor L or the conjugated values of the superdiagonal of U from the factorization computed by ?pttrf (see uplo).

The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

ldb

INTEGER. The leading dimension of b; ldb max(1, n).

Output Parameters

b

Overwritten by the solution matrix X.

info

INTEGER. If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine pttrs interface are as follows:

d

Holds the vector of length n.

e

Holds the vector of length (n-1).

b

Holds the matrix B of size (n, nrhs).

uplo

Used in complex flavors only. Must be 'U' or 'L'. The default value is 'U'.