?pttrf

Compute the LDL^* or U^*DU factorization of a real (conjugate) symmetric positive definite tridiagonal matrix A, where D is a diagonal block matrix, L is a lower triangular matrix, and U is an upper triangular matrix.

Interface Definition

C interface:

void spttrf_(const int *N, float *D, float *E, int *INFO);

void dpttrf_(const int *N, double *D, double *E, int *INFO);

void cpttrf_(const int *N, float *D, float _Complex *E, int *INFO);

void zpttrf_(const int *N, double *D, double _Complex *E, int *INFO);

Fortran interface:

SPTTRF(N, D, E, INFO);

DPTTRF(N, D, E, INFO);

CPTTRF(N, D, E, INFO);

ZPTTRF(N, D, E, INFO);

Parameters

Parameter	Type	Description	Input/Output
N	Integer	Number of dimensions in matrix A, N ≥ 0.	Input
D	A single-precision floating-point array for spttrf/cpttrf A double-precision floating-point array for dpttrf/zpttrf	As an input value, it represents a diagonal element of tridiagonal matrix A, with a dimension of N. As an output value, it represents a diagonal element D after factorization.	Input, output
E	A single-precision floating-point array for spttrf A double-precision floating-point array for dpttrf A single-precision complex array for cpttrf A double-precision complex array for zpttrf	As an input value, it represents a sub-diagonal element of tridiagonal matrix A, with a dimension of N-1. As an output value, it represents a sub-diagonal element of matrix A after factorization.	Input, output
INFO	Integer	0: The exit is successful. Smaller than 0: The -INFO-th parameter is invalid. Greater than 0: The INFO-th principal minor is not positive definite.	Output

Dependency

#include "klapack.h"

Examples

C interface:

const int n = 4;
double d[] = {103.608696, 103.739130, 103.347826, 100.652174};
double e[] = {0.352941, 0.000000, 0.823529};
int info = 0;
dpttrf_(&n, d, e, &info);
/* 
* Output: 
*  d: 103.608696      103.737928      103.347826      100.645612
*  e:  0.003406        0.000000        0.007969
*/

Fortran interface:

PARAMETER (n = 4) 
INTEGER :: info = 0 
REAL(8) :: d(n) 
REAL(8) :: e(n-1)  
  
DATA d / 103.608696, 103.739130, 103.347826, 100.652174 /
DATA e / 0.352941,0.000000,0.823529/ 
 EXTERNAL DPTTRF 
 CALL DPTTRF (n, d, e, info)
* Output: 
*  d: 103.608696      103.737928      103.347826      100.645612
*  e:  0.003406        0.000000        0.007969

Parent topic: Matrix Decomposition Functions