---
name: "ssptrf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/ssptrf/3lapack"
---

# ssptrf(3lapack)

computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

## NAME

SSPTRF - computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

## SYNOPSIS

- SUBROUTINE SSPTRF(

  UPLO, N, AP, IPIV, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, N

- INTEGER

  IPIV( \* )

- REAL

  AP( \* )

## PURPOSE

SSPTRF computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:\
    A = U\*D\*U\*\*T  or  A = L\*D\*L\*\*T\
 where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.\

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- AP (input/output) REAL array, dimension (N\*(N+1)/2)

  On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)\*j/2) = A(i,j) for 1\<=i\<=j; if UPLO = 'L', AP(i + (j-1)\*(2n-j)/2) = A(i,j) for j\<=i\<=n. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix overwriting A (see below for further details).

- IPIV (output) INTEGER array, dimension (N)

  Details of the interchanges and the block structure of D. If IPIV(k) \> 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) \< 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) \< 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

- INFO (output) INTEGER

  \= 0: successful exit\
   \< 0: if INFO = -i, the i-th argument had an illegal value\
   \> 0: if INFO = i, D(i,i) is exactly zero.  The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

## FURTHER DETAILS

5-96 - Based on modifications by J. Lewis, Boeing Computer Services\
        Company\
 If UPLO = 'U', then A = U\*D\*U', where\
\
    U = P(n)\*U(n)\* ... \*P(k)U(k)\* ...,\
 i.e., U is a product of terms P(k)\*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then\
            (   I    v    0   )   k-s\
\
    U(k) =  (   0    I    0   )   s\
\
            (   0    0    I   )   n-k\
\
               k-s   s   n-k\
 If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).\
 If UPLO = 'L', then A = L\*D\*L', where\
\
    L = P(1)\*L(1)\* ... \*P(k)\*L(k)\* ...,\
 i.e., L is a product of terms P(k)\*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then\
            (   I    0     0   )  k-1\
\
    L(k) =  (   0    I     0   )  s\
\
            (   0    v     I   )  n-k-s+1\
\
               k-1   s  n-k-s+1\
 If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).\