?pttrsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?pttrsv

Solves a symmetric (Hermitian) positive-definite tridiagonal system of linear equations, using the L*D*L ^:code:`H` factorization computed by ?pttrf .

Syntax

call spttrsv ( trans , n , nrhs , d , e , b , ldb , info )

call dpttrsv ( trans , n , nrhs , d , e , b , ldb , info )

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

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

Include Files

mkl_scalapack.h

Description

spttrsv dpttrsv cpttrsv zpttrsv The ?pttrsv routine function solves one of the triangular systems:

L^{T}*X = B , or L*X = B for real flavors,

L*X = B , or L^{H}*X = B ,

U*X = B , or U^{H}*X = B for complex flavors,

where L (or U for complex flavors) is the Cholesky factor of a Hermitian positive-definite tridiagonal matrix A such that

A = L*D*L^{H} (computed by spttrf/dpttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) )

A = U^{H}*D*U or A = L*D*L^{H} (computed by cpttrf/zpttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) ).

Input Parameters

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization: If uplo = 'U' , e is the superdiagonal of U , and A = U^{H}*D*U or A = L*D*L^{H} ; if uplo = 'L' , e is the subdiagonal of L , and A = L*D*L^{H} . The two forms are equivalent, if A is real.

trans

CHARACTER .

Specifies the form of the system of equations: for real flavors: if trans = 'N' : L*X = B (no transpose) if trans = 'T' : L^{T}*X = B (transpose) for complex flavors: if trans = 'N' : U*X = B or L*X = B (no transpose) if trans = 'C' : U^{H}*X = B or L^{H}*X = B (conjugate transpose).

n

INTEGER . The order of the tridiagonal matrix 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 array of size n . The n diagonal elements of the diagonal matrix D from the factorization computed by GUID-C5723D71-924B-49FF-9FD4-9BDE2B3EB682.xml#GUID-C5723D71-924B-49FF-9FD4-9BDE2B3EB682 .

e

COMPLEX array of size (n-1) . The ( n -1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by GUID-C5723D71-924B-49FF-9FD4-9BDE2B3EB682.xml#GUID-C5723D71-924B-49FF-9FD4-9BDE2B3EB682 . See uplo .

b

COMPLEX array of size ldb by nrhs .

On entry, the right hand side matrix B .

ldb

INTEGER .

The leading dimension of the array b . ldb ≥ max(1, n) .

Output Parameters

b: On exit, the solution matrix X .

info

INTEGER .

= 0 : successful exit < 0 : if info = -i , the i- th argument had an illegal value.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pttrsv

Syntax

Include Files

Description

Input Parameters

Output Parameters