LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

subroutine sgetrf  (  integer  M, 
integer  N,  
real, dimension( lda, * )  A,  
integer  LDA,  
integer, dimension( * )  IPIV,  
integer  INFO  
) 
SGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
SGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm
SGETRF VARIANT: leftlooking Level 3 BLAS version of the algorithm.
Purpose:
SGETRF computes an LU factorization of a general MbyN matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the Crout Level 3 BLAS version of the algorithm.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the MbyN matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  IPIV  IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 
Purpose:
SGETRF computes an LU factorization of a general MbyN matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the leftlooking Level 3 BLAS version of the algorithm.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the MbyN matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  IPIV  IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 
Purpose:
SGETRF computes an LU factorization of a general MbyN matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This code implements an iterative version of Sivan Toledo's recursive LU algorithm[1]. For square matrices, this iterative versions should be within a factor of two of the optimum number of memory transfers. The pattern is as follows, with the large blocks of U being updated in one call to STRSM, and the dotted lines denoting sections that have had all pending permutations applied: 1 2 3 4 5 6 7 8 +++++  1   .++ 2        ..+++ 4     1    .++        ....++++ 8      1      .++ 2              ..+++        1       .++          ........+          The 12141218... pattern is the position of the last 1 bit in the binary expansion of the current column. Each Schur update is applied as soon as the necessary portion of U is available. [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997), 10651081. http://dx.doi.org/10.1137/S0895479896297744
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the MbyN matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  IPIV  IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 
Definition at line 101 of file sgetrf.f.