org.netlib.lapack
Class SSYTRF
java.lang.Object
org.netlib.lapack.SSYTRF
public class SSYTRF
- extends java.lang.Object
SSYTRF is a simplified interface to the JLAPACK routine ssytrf.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SSYTRF computes the factorization of a real symmetric matrix A using
* the Bunch-Kaufman diagonal pivoting method. The form of the
* factorization is
*
* 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.
*
* This is the blocked version of the algorithm, calling Level 3 BLAS.
*
* 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.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the symmetric matrix A. If UPLO = 'U', the leading
* N-by-N upper triangular part of A contains the upper
* triangular part of the matrix A, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading N-by-N lower triangular part of A contains the lower
* triangular part of the matrix A, and the strictly upper
* triangular part of A is not referenced.
*
* On exit, the block diagonal matrix D and the multipliers used
* to obtain the factor U or L (see below for further details).
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* 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.
*
* WORK (workspace/output) REAL array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The length of WORK. LWORK >=1. For best performance
* LWORK >= N*NB, where NB is the block size returned by ILAENV.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* 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
* ===============
*
* 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).
*
* =====================================================================
*
* .. Local Scalars ..
|
Method Summary |
static void |
SSYTRF(java.lang.String uplo,
int n,
float[][] a,
int[] ipiv,
float[] work,
int lwork,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SSYTRF
public SSYTRF()
SSYTRF
public static void SSYTRF(java.lang.String uplo,
int n,
float[][] a,
int[] ipiv,
float[] work,
int lwork,
intW info)