?gttrs

Solve a system of linear equations with a tridiagonal matrix A * X = B, A^T * X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.

Interface Definition

C interface:

void sgttrs(const char *TRANS, const int *N, const int *NRHS, float *DL, float *D, float *DU, float *DU2, int *IPIV, float *B, const int *LDB, int *INFO);

void dgttrs(const char *TRANS, const int *N, const int *NRHS, double *DL, double *D, double *DU, double *DU2, int *IPIV, double *B, const int *LDB, int *INFO);

void cgttrs(const char *TRANS, const int *N, const int *NRHS, float _Complex *DL, float _Complex *D, float _Complex *DU, float _Complex *DU2, int *IPIV, float _Complex *B, const int *LDB, int *INFO);

void zgttrs(const char *TRANS, const int *N, const int *NRHS, double _Complex *DL, double _Complex *D, double _Complex *DU, double _Complex *DU2, int *IPIV, double _Complex *B, const int *LDB, int *INFO);

Fortran interface:

SGTTRS(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO);

DGTTRS(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO);

CGTTRS(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO);

ZGTTRS(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO);

Parameters

Parameter	Type	Description	Input/Output
TRANS	Character	If the value is 'N', A * X = B. If the value is 'T', A^T * X = B. If the value is 'C', A^T * X = B (conjugate transposition).	Input
N	Integer	Order of matrix A, N ≥ 0	Input
NRHS	Integer	Number of columns in matrix B, NRHS ≥ 0	Input
DL	For sgttrs, DL is a single-precision floating-point array For dgttrs, DL is a double-precision floating-point array. For cgttrs, DL is a single-precision complex number array. For zgttrs, DL is a double-precision complex number array.	Matrix L from the LU decomposition, with a dimension of N–1	Input
D	For sgttrs, D is a single-precision floating-point array. For dgttrs, D is a double-precision floating-point array. For cgttrs, D is a single-precision complex number array. For zgttrs, D is a double-precision complex number array.	Diagonal element of U, with a dimension of N	Input
DU	For sgttrs, DU is a single-precision floating-point array. For dgttrs, DU is a double-precision floating-point array. For cgttrs, DU is a single-precision complex number array. For zgttrs, DU is a double-precision complex number array.	First super-diagonal element of U	Input
DU2	For sgttrs, DU2 is a single-precision floating-point array. For dgttrs, DU2 is a double-precision floating-point array. For cgttrs, DU2 is a single-precision complex number array. For zgttrs, DU2 is a double-precision complex number array.	Second super-diagonal element of U	Input
IPIV	Integer array	Transposed array	Input
B	For sgttrs, B is a single-precision floating-point array. For dgttrs, B is a double-precision floating-point array. For cgttrs, B is a single-precision complex number array. For zgttrs, B is a double-precision complex number array.	Right-hand side matrix, with a dimension of (LDB, NRHS)	Input/Output
LDB	Integer	Leading dimension of matrix B	Input
INFO	Integer	0: The exit is successful. Smaller than 0: The -INFO-th parameter is invalid.	Output

Dependencies

include "klapack.h"

Examples

C interface:

const char trans = 'N';
const int n = 4;
const int ldb = n;
const int nrhs = 1;
double dl[] = {0.565217, 0.170949, 0.482378};
double d[] = {0.923077, 0.899954, 0.318932, -0.186088};
double du[] = {0.043478, -0.085316, 0.566038};
double du2[] = {0.150943, 0.000000};
double b[] = {0.301370, 0.835616, 0.109589, 0.041096};
int ipiv[] = {2,2,3,4};
int info = 0;
dgttrs_(&trans, &n, &nrhs, dl, d, du, du2, ipiv, b, &ldb, &info);
if (info != 0) {
    printf("ERROR, info = %d\n", info);
}

/* 
* Output: 
*   b:  0.882521        -0.172061       0.188567        0.138984
*/

Fortran interface:

CHARACTER :: trans = "N"
PARAMETER (n = 4) 
PARAMETER (ldb = 4)
PARAMETER (nrhs = 1) 
INTEGER :: info = 0 
REAL(8) :: d(n) 
REAL(8) :: dl(n-1)
REAL(8) :: du(n-1)
REAL(8) :: du2(n-2)
REAL(8) :: b(ldb, nrhs)  
INTEGER :: ipiv(n)
  
DATA d / 0.923077, 0.899954, 0.318932, -0.186088 / 
DATA dl / 0.565217, 0.170949, 0.482378/
DATA du / 0.043478, -0.085316, 0.566038 /
DATA du2 / 0.150943, 0.000000 /
DATA b / 0.301370, 0.835616, 0.109589, 0.041096 /
DATA ipiv / 2,2,3,4 /
 EXTERNAL DGTTRS 
 CALL DGTTRS(trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info);
* 
* Output: 
*   d:  0.882521        -0.172061       0.188567        0.138984

Parent topic: Back Substitution Solution