--- rpl/lapack/lapack/zhesv.f 2010/01/26 15:22:46 1.1
+++ rpl/lapack/lapack/zhesv.f 2016/08/27 15:34:50 1.15
@@ -1,10 +1,180 @@
+*> \brief ZHESV computes the solution to system of linear equations A * X = B for HE matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHESV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHESV computes the solution to a complex system of linear equations
+*> A * X = B,
+*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> The diagonal pivoting method is used to factor A as
+*> A = U * D * U**H, if UPLO = 'U', or
+*> A = L * D * L**H, if UPLO = 'L',
+*> 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. The factored form of A is then
+*> used to solve the system of equations A * X = B.
+*> \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 number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 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, if INFO = 0, the block diagonal matrix D and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*D*U**H or A = L*D*L**H as computed by
+*> ZHETRF.
+*> \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, as
+*> determined by ZHETRF. 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[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \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, and for best performance
+*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*> ZHETRF.
+*> for LWORK < N, TRS will be done with Level BLAS 2
+*> for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*> 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.
+*> \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, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16HEsolve
+*
+* =====================================================================
SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ LWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver 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
@@ -15,92 +185,6 @@
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHESV computes the solution to a complex system of linear equations
-* A * X = B,
-* where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
-* matrices.
-*
-* The diagonal pivoting method is used to factor A as
-* A = U * D * U**H, if UPLO = 'U', or
-* A = L * D * L**H, if UPLO = 'L',
-* 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. The factored form of A is then
-* used to solve the system of equations A * X = B.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored;
-* = 'L': Lower triangle of A is stored.
-*
-* N (input) INTEGER
-* The number of linear equations, i.e., the order of the
-* matrix A. N >= 0.
-*
-* NRHS (input) INTEGER
-* The number of right hand sides, i.e., the number of columns
-* of the matrix B. NRHS >= 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, if INFO = 0, the block diagonal matrix D and the
-* multipliers used to obtain the factor U or L from the
-* factorization A = U*D*U**H or A = L*D*L**H as computed by
-* ZHETRF.
-*
-* 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, as
-* determined by ZHETRF. 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.
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
-* On entry, the N-by-NRHS right hand side matrix B.
-* On exit, if INFO = 0, the N-by-NRHS solution matrix X.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* 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, and for best performance
-* LWORK >= max(1,N*NB), where NB is the optimal blocksize for
-* ZHETRF.
-*
-* 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, so the solution could not be computed.
-*
* =====================================================================
*
* .. Local Scalars ..
@@ -113,7 +197,7 @@
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
- EXTERNAL XERBLA, ZHETRF, ZHETRS
+ EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
@@ -155,14 +239,26 @@
RETURN
END IF
*
-* Compute the factorization A = U*D*U' or A = L*D*L'.
+* Compute the factorization A = U*D*U**H or A = L*D*L**H.
*
CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
- CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+ IF ( LWORK.LT.N ) THEN
+*
+* Solve with TRS ( Use Level BLAS 2)
+*
+ CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+ ELSE
+*
+* Solve with TRS2 ( Use Level BLAS 3)
+*
+ CALL ZHETRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO )
+*
+ END IF
*
END IF
*