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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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+*> \brief \b SSYTF2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SSYTF2( UPLO, N, A, LDA, IPIV, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * )
+* ..
+*
+* Purpose
+* =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SSYTF2 computes the factorization of a real symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and
+*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*>
+*>\endverbatim
+*
+* Arguments
+* =========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> 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
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is 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.
+*> \endverbatim
+*> \verbatim
+*> On exit, the block diagonal matrix D and the multipliers used
+*> to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV 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 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.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th 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.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup realSYcomputational
+*
+*
+* Further Details
+* ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*> 09-29-06 - 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. SISNAN(ABSAKK) ) THEN
+*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
+*> Company
+*>
+*> If UPLO = 'U', then A = U*D*U**T, 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**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 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).
+*>
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE SSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -14,116 +188,6 @@
REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
-*
-* SSYTF2 computes the factorization of a real symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and
-* block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
-*
-* This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* symmetric matrix A is stored:
-* = 'U': Upper triangular
-* = 'L': Lower triangular
-*
-* 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.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -k, the k-th 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.
-*
-* Further Details
-* ===============
-*
-* 09-29-06 - 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. SISNAN(ABSAKK) ) THEN
-*
-* 01-01-96 - Based on modifications by
-* J. Lewis, Boeing Computer Services Company
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-* 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
-* Company
-*
-* If UPLO = 'U', then A = U*D*U**T, 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**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 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).
-*
* =====================================================================
*
* .. Parameters ..