Visible to Intel only — GUID: GUID-FE593312-5EA4-4914-BEF9-682D5DB72416
Visible to Intel only — GUID: GUID-FE593312-5EA4-4914-BEF9-682D5DB72416
?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'. |