?ptsv

Solve a system of linear equations, in which the coefficient matrix A is a real (conjugate) symmetric positive definite tridiagonal matrix.

Interface Definition

C interface:

void sptsv_(const int *N, const int *NRHS, float *D, float *E, float *B, const int *LDB, int *INFO);

void dptsv_(const int *N, const int *NRHS, double *D, double *E, double *B, const int *LDB, int *INFO);

void cptsv_(const int *N, const int *NRHS, float *D, float _Complex *E, float _Complex *B, const int *LDB, int *INFO);

void zptsv_(const int *N, const int *NRHS, double *D, double _Complex *E, double _Complex *B, const int *LDB, int *INFO);

Fortran interface:

SPTSV(N, NRHS, D, E, B, LDB, INFO);

DPTSV(N, NRHS, D, E, B, LDB, INFO);

CPTSV(N, NRHS, D, E, B, LDB, INFO);

ZPTSV(N, NRHS, D, E, B, LDB, INFO);

Parameters

Parameter	Type	Description	Input/Output
N	Integer	Number of dimensions in matrix A, N ≥ 0.	Input
NRHS	Integer	Number of columns in matrix B, NRHS ≥ 0.	Input
D	A single-precision floating-point array for sptsv/cptsv A double-precision floating-point array for dptsv/zptsv	When as an input value, it is a diagonal element of tridiagonal matrix A, and its dimension is N. When as an output value, it is a diagonal element D after factorization.	Input, output
E	A single-precision floating-point array for sptsv A double-precision floating-point array for dptsv A single-precision complex array for cptsv A double-precision complex array for zptsv	When as an input value, it is a sub-diagonal element of tridiagonal matrix A, and its dimension is N-1. When as an output value, it is a sub-diagonal element of matrix A after factorization.	Input, output
B	A single-precision floating-point array for sptsv A double-precision floating-point array for dptsv A single-precision complex array for cptsv A double-precision complex array for zptsv	When as an input value, it is a right-hand side matrix, and the dimension is (LDB, NRHS). When as an output value, it is the result X, and the dimension is (LDB, NRHS).	Input, output
LDB	Integer	Leading dimension of matrix B.	Input
INFO	Integer	0: The exit is successful. Smaller than 0: The value of the -info-th parameter is invalid. Greater than 0: The INFO-th order principal minor is not positive definite.	Output

Dependency

#include "klapack.h"

Examples

C interface:

    const int n = 4;
    const int ldb = n;
    const int nrhs = 1;
    double d[] = {7.608696,7.739130, 7.347826,4.652174};
    double e[] = {0.352941,0.000000,0.823529};
    double b[] = {0.300000,0.100000,0.700000,0.200000};
    int info = 0;
    
    dptsv_(&n, &nrhs, d, e, b, &ldb, &info);
/* 
* Output: 
*   d: 7.608696        7.722759        7.347826        4.559874
*   e: 0.046387        0.000000        0.112078
*   b: 0.038912        0.011147        0.092279        0.026655
*/

Fortran interface:

PARAMETER (n = 4) 
PARAMETER (ldb = 4)
PARAMETER (nrhs = 1) 
INTEGER :: info = 0 
REAL(8) :: d(n) 
REAL(8) :: e(n-1)
REAL(8) :: b(ldb, nrhs)  
  
DATA d / 7.608696,7.739130, 7.347826,4.652174 / 
DATA e / 0.352941,0.000000,0.823529 /
DATA b / 0.300000,0.100000,0.700000,0.200000 /
 EXTERNAL DPTSV 
 CALL DPTSV(n, nrhs, d, e, b, ldb, info);
* 
* Output: 
*   d: 7.608696        7.722759        7.347826        4.559874
*   e: 0.046387        0.000000        0.112078
*   b: 0.038912        0.011147        0.092279        0.026655

Parent topic: Functions for Solving a System of Linear Equations