Solves a system of linear equations with a diagonally dominant tridiagonal coefficient matrix using the LU factorization computed by ?dttrfb.

## Syntax

void sdttrsb (const char * trans, const MKL_INT * n, const MKL_INT * nrhs, const float * dl, const float * d, const float * du, float * b, const MKL_INT * ldb, MKL_INT * info );

void ddttrsb (const char * trans, const MKL_INT * n, const MKL_INT * nrhs, const double * dl, const double * d, const double * du, double * b, const MKL_INT * ldb, MKL_INT * info );

void cdttrsb (const char * trans, const MKL_INT * n, const MKL_INT * nrhs, const MKL_Complex8 * dl, const MKL_Complex8 * d, const MKL_Complex8 * du, MKL_Complex8 * b, const MKL_INT * ldb, MKL_INT * info );

void zdttrsb (const char * trans, const MKL_INT * n, const MKL_INT * nrhs, const MKL_Complex16 * dl, const MKL_Complex16 * d, const MKL_Complex16 * du, MKL_Complex16 * b, const MKL_INT * ldb, MKL_INT * info );

• mkl.h

## Description

The ?dttrsb routine solves the following systems of linear equations with multiple right hand sides for X:

 A*X = B if trans='N', AT*X = B if trans='T', AH*X = B if trans='C' (for complex matrices only).

Before calling this routine, call ?dttrfb to compute the factorization of A.

## Input Parameters

 trans Must be 'N' or 'T' or 'C'. Indicates the form of the equations solved for X: If trans = 'N', then A*X = B. If trans = 'T', then AT*X = B. If trans = 'C', then AH*X = B. n The order of A; n≥ 0. nrhs The number of right-hand sides, that is, the number of columns in B; nrhs≥ 0. dl, d, du Arrays: dl(n -1), d(n), du(n -1). The array dl contains the (n - 1) multipliers that define the matrices L1, L2 from the factorization of A. The array d contains the n diagonal elements of the upper triangular matrix U from the factorization of A. The array du contains the (n - 1) elements of the superdiagonal of U. b Array of size max(1, ldb*nrhs). Contains the matrix B whose columns are the right-hand sides for the systems of equations. ldb The leading dimension of b; ldb≥ max(1, n).

## Output Parameters

 b Overwritten by the solution matrix X. info If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value.
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