DSYTF2 (3)  Linux Manuals
NAME
dsytf2.f 
SYNOPSIS
Functions/Subroutines
subroutine dsytf2 (UPLO, N, A, LDA, IPIV, INFO)
DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
Function/Subroutine Documentation
subroutine dsytf2 (characterUPLO, integerN, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, integerINFO)
DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
Purpose:

DSYTF2 computes the factorization of a real symmetric matrix A using the BunchKaufman 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, U**T is the transpose of U, and D is symmetric and block diagonal with 1by1 and 2by2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.
Parameters:

UPLO
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
NN is INTEGER The order of the matrix A. N >= 0.
AA is DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading nbyn 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 nbyn 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).
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIVIPIV is 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 1by1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 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 2by2 diagonal block.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = k, the kth argument had an illegal value > 0: if INFO = k, D(k,k) 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.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Further Details:

If UPLO = 'U', then A = U*D*U**T, where U = H(n)*H(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 1by1 and 2by2 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 ) ks U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1:k). If UPLO = 'L', then A = L*D*L**T, 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 1by1 and 2by2 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 ) k1 L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+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).
Contributors:

092906  patch from Bobby Cheng, MathWorks Replace l.204 and l.372 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN by IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN 010196  Based on modifications by J. Lewis, Boeing Computer Services Company A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 196  Based on modifications by J. Lewis, Boeing Computer Services Company
Definition at line 186 of file dsytf2.f.
Author
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