--- rpl/lapack/lapack/zhetrf.f 2010/12/21 13:53:46 1.7
+++ rpl/lapack/lapack/zhetrf.f 2011/11/21 20:43:12 1.9
@@ -1,9 +1,186 @@
+*> \brief \b ZHETRF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETRF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETRF computes the factorization of a complex Hermitian matrix A
+*> using the Bunch-Kaufman diagonal pivoting method. The form of the
+*> factorization is
+*>
+*> A = U*D*U**H or A = L*D*L**H
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is Hermitian 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.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the Hermitian 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).
+*> \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] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >=1. For best performance
+*> LWORK >= N*NB, where NB is the block size returned by ILAENV.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is 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.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16HEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> If UPLO = 'U', then A = U*D*U**H, 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**H, 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 ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -14,108 +191,6 @@
COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHETRF computes the factorization of a complex Hermitian matrix A
-* using the Bunch-Kaufman diagonal pivoting method. The form of the
-* factorization is
-*
-* A = U*D*U**H or A = L*D*L**H
-*
-* where U (or L) is a product of permutation and unit upper (lower)
-* triangular matrices, and D is Hermitian 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) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the Hermitian 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) COMPLEX*16 array, dimension (MAX(1,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.
-*
-* 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 ..
@@ -182,7 +257,7 @@
*
IF( UPPER ) THEN
*
-* Factorize A as U*D*U' using the upper triangle of A
+* Factorize A as U*D*U**H using the upper triangle of A
*
* K is the main loop index, decreasing from N to 1 in steps of
* KB, where KB is the number of columns factorized by ZLAHEF;
@@ -222,7 +297,7 @@
*
ELSE
*
-* Factorize A as L*D*L' using the lower triangle of A
+* Factorize A as L*D*L**H using the lower triangle of A
*
* K is the main loop index, increasing from 1 to N in steps of
* KB, where KB is the number of columns factorized by ZLAHEF;