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https://gitlab.com/libeigen/eigen.git
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Fix rank-1 update for self-adjoint packed matrices.
This commit is contained in:
Chen-Pang He
parent
65caa40a3d
commit
04f315d692
@ -18,9 +18,9 @@ if(EIGEN_Fortran_COMPILER_WORKS)
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set(EigenBlas_SRCS ${EigenBlas_SRCS}
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set(EigenBlas_SRCS ${EigenBlas_SRCS}
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complexdots.f
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complexdots.f
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srotm.f srotmg.f drotm.f drotmg.f
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srotm.f srotmg.f drotm.f drotmg.f
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lsame.f dspmv.f ssbmv.f
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lsame.f dspmv.f ssbmv.f
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chbmv.f chpr.f sspmv.f
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chbmv.f sspmv.f
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zhbmv.f zhpr.f chpmv.f dsbmv.f
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zhbmv.f chpmv.f dsbmv.f
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zhpmv.f
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zhpmv.f
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dtbmv.f stbmv.f ctbmv.f ztbmv.f
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dtbmv.f stbmv.f ctbmv.f ztbmv.f
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)
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)
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@ -14,12 +14,6 @@ namespace internal {
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/* Optimized matrix += alpha * uv'
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/* Optimized matrix += alpha * uv'
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* The matrix is in packed form.
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* The matrix is in packed form.
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*
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* FIXME I always fail tests for complex self-adjoint matrices.
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*
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* ******* FATAL ERROR - PARAMETER NUMBER 6 WAS CHANGED INCORRECTLY *******
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* ******* xHPR FAILED ON CALL NUMBER:
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* 2: xHPR ('U', 1, 0.0, X, 1, AP)
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*/
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*/
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template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
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template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
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struct selfadjoint_packed_rank1_update;
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struct selfadjoint_packed_rank1_update;
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@ -27,20 +21,20 @@ struct selfadjoint_packed_rank1_update;
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template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
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template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
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struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
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struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
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{
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{
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static void run(Index size, Scalar* mat, const Scalar* vec, Scalar alpha)
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
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{
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{
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typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
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typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
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typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
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typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
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conj_if<ConjRhs> cj;
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conj_if<ConjRhs> cj;
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Index offset = 0;
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for (Index i=0; i<size; ++i)
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for (Index i=0; i<size; ++i)
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{
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{
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Map<Matrix<Scalar,Dynamic,1> >(mat+offset, UpLo==Lower ? size-i : (i+1))
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Map<Matrix<Scalar,Dynamic,1> >(mat, UpLo==Lower ? size-i : (i+1))
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+= alpha * cj(vec[i]) * ConjRhsType(OtherMap(vec+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)));
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+= alpha * cj(vec[i]) * ConjRhsType(OtherMap(vec+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)));
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//FIXME This should be handled outside.
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//FIXME This should be handled outside.
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mat[offset+(UpLo==Lower ? 0 : i)] = real(mat[offset+(UpLo==Lower ? 0 : i)]);
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mat[UpLo==Lower ? 0 : i] = real(mat[UpLo==Lower ? 0 : i]);
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offset += UpLo==Lower ? size-i : (i+1);
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mat += UpLo==Lower ? size-i : (i+1);
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}
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}
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}
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}
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};
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};
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@ -48,7 +42,8 @@ struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRh
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template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
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template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
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struct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
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struct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
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{
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{
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static void run(Index size, Scalar* mat, const Scalar* vec, Scalar alpha)
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
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{
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{
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selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,vec,alpha);
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selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,vec,alpha);
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}
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}
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220
blas/chpr.f
220
blas/chpr.f
@ -1,220 +0,0 @@
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SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
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* .. Scalar Arguments ..
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REAL ALPHA
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INTEGER INCX,N
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CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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COMPLEX AP(*),X(*)
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* ..
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*
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* Purpose
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* =======
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*
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* CHPR performs the hermitian rank 1 operation
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*
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* A := alpha*x*conjg( x' ) + A,
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*
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* where alpha is a real scalar, x is an n element vector and A is an
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* n by n hermitian matrix, supplied in packed form.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the matrix A is supplied in the packed
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* array AP as follows:
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*
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* UPLO = 'U' or 'u' The upper triangular part of A is
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* supplied in AP.
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*
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* UPLO = 'L' or 'l' The lower triangular part of A is
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* supplied in AP.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - REAL .
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* X - COMPLEX array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element vector x.
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* Unchanged on exit.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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* AP - COMPLEX array of DIMENSION at least
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* ( ( n*( n + 1 ) )/2 ).
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* Before entry with UPLO = 'U' or 'u', the array AP must
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* contain the upper triangular part of the hermitian matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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* and a( 2, 2 ) respectively, and so on. On exit, the array
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* AP is overwritten by the upper triangular part of the
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* updated matrix.
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* Before entry with UPLO = 'L' or 'l', the array AP must
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* contain the lower triangular part of the hermitian matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
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* and a( 3, 1 ) respectively, and so on. On exit, the array
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* AP is overwritten by the lower triangular part of the
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* updated matrix.
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* Note that the imaginary parts of the diagonal elements need
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* not be set, they are assumed to be zero, and on exit they
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* are set to zero.
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*
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* Further Details
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* ===============
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*
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* Level 2 Blas routine.
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*
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX ZERO
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PARAMETER (ZERO= (0.0E+0,0.0E+0))
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* ..
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* .. Local Scalars ..
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COMPLEX TEMP
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INTEGER I,INFO,IX,J,JX,K,KK,KX
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CONJG,REAL
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* ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (N.LT.0) THEN
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INFO = 2
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ELSE IF (INCX.EQ.0) THEN
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INFO = 5
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('CHPR ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
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*
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* Set the start point in X if the increment is not unity.
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*
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IF (INCX.LE.0) THEN
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KX = 1 - (N-1)*INCX
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ELSE IF (INCX.NE.1) THEN
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KX = 1
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END IF
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*
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* Start the operations. In this version the elements of the array AP
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* are accessed sequentially with one pass through AP.
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*
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KK = 1
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IF (LSAME(UPLO,'U')) THEN
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*
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* Form A when upper triangle is stored in AP.
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*
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IF (INCX.EQ.1) THEN
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DO 20 J = 1,N
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IF (X(J).NE.ZERO) THEN
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TEMP = ALPHA*CONJG(X(J))
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K = KK
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DO 10 I = 1,J - 1
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AP(K) = AP(K) + X(I)*TEMP
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K = K + 1
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10 CONTINUE
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AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
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ELSE
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AP(KK+J-1) = REAL(AP(KK+J-1))
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END IF
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KK = KK + J
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20 CONTINUE
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ELSE
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JX = KX
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DO 40 J = 1,N
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IF (X(JX).NE.ZERO) THEN
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TEMP = ALPHA*CONJG(X(JX))
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IX = KX
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DO 30 K = KK,KK + J - 2
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AP(K) = AP(K) + X(IX)*TEMP
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IX = IX + INCX
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30 CONTINUE
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AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
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ELSE
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AP(KK+J-1) = REAL(AP(KK+J-1))
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END IF
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JX = JX + INCX
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KK = KK + J
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40 CONTINUE
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END IF
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ELSE
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*
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* Form A when lower triangle is stored in AP.
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*
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IF (INCX.EQ.1) THEN
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DO 60 J = 1,N
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IF (X(J).NE.ZERO) THEN
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TEMP = ALPHA*CONJG(X(J))
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AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J))
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K = KK + 1
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DO 50 I = J + 1,N
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AP(K) = AP(K) + X(I)*TEMP
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K = K + 1
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50 CONTINUE
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ELSE
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AP(KK) = REAL(AP(KK))
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END IF
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KK = KK + N - J + 1
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60 CONTINUE
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ELSE
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JX = KX
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DO 80 J = 1,N
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IF (X(JX).NE.ZERO) THEN
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TEMP = ALPHA*CONJG(X(JX))
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AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX))
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IX = JX
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DO 70 K = KK + 1,KK + N - J
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IX = IX + INCX
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AP(K) = AP(K) + X(IX)*TEMP
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70 CONTINUE
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ELSE
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AP(KK) = REAL(AP(KK))
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END IF
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JX = JX + INCX
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KK = KK + N - J + 1
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80 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of CHPR .
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*
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END
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202
blas/dspr.f
202
blas/dspr.f
@ -1,202 +0,0 @@
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SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA
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INTEGER INCX,N
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CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AP(*),X(*)
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* ..
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*
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* Purpose
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* =======
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*
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* DSPR performs the symmetric rank 1 operation
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*
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* A := alpha*x*x' + A,
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*
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* where alpha is a real scalar, x is an n element vector and A is an
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* n by n symmetric matrix, supplied in packed form.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the matrix A is supplied in the packed
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* array AP as follows:
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*
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* UPLO = 'U' or 'u' The upper triangular part of A is
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* supplied in AP.
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*
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* UPLO = 'L' or 'l' The lower triangular part of A is
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* supplied in AP.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - DOUBLE PRECISION.
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* X - DOUBLE PRECISION array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element vector x.
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* Unchanged on exit.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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* AP - DOUBLE PRECISION array of DIMENSION at least
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* ( ( n*( n + 1 ) )/2 ).
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* Before entry with UPLO = 'U' or 'u', the array AP must
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* contain the upper triangular part of the symmetric matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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* and a( 2, 2 ) respectively, and so on. On exit, the array
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|
||||||
* AP is overwritten by the upper triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
* Before entry with UPLO = 'L' or 'l', the array AP must
|
|
||||||
* contain the lower triangular part of the symmetric matrix
|
|
||||||
* packed sequentially, column by column, so that AP( 1 )
|
|
||||||
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
|
|
||||||
* and a( 3, 1 ) respectively, and so on. On exit, the array
|
|
||||||
* AP is overwritten by the lower triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
*
|
|
||||||
* Further Details
|
|
||||||
* ===============
|
|
||||||
*
|
|
||||||
* Level 2 Blas routine.
|
|
||||||
*
|
|
||||||
* -- Written on 22-October-1986.
|
|
||||||
* Jack Dongarra, Argonne National Lab.
|
|
||||||
* Jeremy Du Croz, Nag Central Office.
|
|
||||||
* Sven Hammarling, Nag Central Office.
|
|
||||||
* Richard Hanson, Sandia National Labs.
|
|
||||||
*
|
|
||||||
* =====================================================================
|
|
||||||
*
|
|
||||||
* .. Parameters ..
|
|
||||||
DOUBLE PRECISION ZERO
|
|
||||||
PARAMETER (ZERO=0.0D+0)
|
|
||||||
* ..
|
|
||||||
* .. Local Scalars ..
|
|
||||||
DOUBLE PRECISION TEMP
|
|
||||||
INTEGER I,INFO,IX,J,JX,K,KK,KX
|
|
||||||
* ..
|
|
||||||
* .. External Functions ..
|
|
||||||
LOGICAL LSAME
|
|
||||||
EXTERNAL LSAME
|
|
||||||
* ..
|
|
||||||
* .. External Subroutines ..
|
|
||||||
EXTERNAL XERBLA
|
|
||||||
* ..
|
|
||||||
*
|
|
||||||
* Test the input parameters.
|
|
||||||
*
|
|
||||||
INFO = 0
|
|
||||||
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
|
|
||||||
INFO = 1
|
|
||||||
ELSE IF (N.LT.0) THEN
|
|
||||||
INFO = 2
|
|
||||||
ELSE IF (INCX.EQ.0) THEN
|
|
||||||
INFO = 5
|
|
||||||
END IF
|
|
||||||
IF (INFO.NE.0) THEN
|
|
||||||
CALL XERBLA('DSPR ',INFO)
|
|
||||||
RETURN
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Quick return if possible.
|
|
||||||
*
|
|
||||||
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
|
|
||||||
*
|
|
||||||
* Set the start point in X if the increment is not unity.
|
|
||||||
*
|
|
||||||
IF (INCX.LE.0) THEN
|
|
||||||
KX = 1 - (N-1)*INCX
|
|
||||||
ELSE IF (INCX.NE.1) THEN
|
|
||||||
KX = 1
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Start the operations. In this version the elements of the array AP
|
|
||||||
* are accessed sequentially with one pass through AP.
|
|
||||||
*
|
|
||||||
KK = 1
|
|
||||||
IF (LSAME(UPLO,'U')) THEN
|
|
||||||
*
|
|
||||||
* Form A when upper triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 20 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(J)
|
|
||||||
K = KK
|
|
||||||
DO 10 I = 1,J
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
10 CONTINUE
|
|
||||||
END IF
|
|
||||||
KK = KK + J
|
|
||||||
20 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 40 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(JX)
|
|
||||||
IX = KX
|
|
||||||
DO 30 K = KK,KK + J - 1
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
IX = IX + INCX
|
|
||||||
30 CONTINUE
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + J
|
|
||||||
40 CONTINUE
|
|
||||||
END IF
|
|
||||||
ELSE
|
|
||||||
*
|
|
||||||
* Form A when lower triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 60 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(J)
|
|
||||||
K = KK
|
|
||||||
DO 50 I = J,N
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
50 CONTINUE
|
|
||||||
END IF
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
60 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 80 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(JX)
|
|
||||||
IX = JX
|
|
||||||
DO 70 K = KK,KK + N - J
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
IX = IX + INCX
|
|
||||||
70 CONTINUE
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
80 CONTINUE
|
|
||||||
END IF
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
RETURN
|
|
||||||
*
|
|
||||||
* End of DSPR .
|
|
||||||
*
|
|
||||||
END
|
|
||||||
@ -108,10 +108,49 @@ int EIGEN_BLAS_FUNC(hemv)(char *uplo, int *n, RealScalar *palpha, RealScalar *pa
|
|||||||
* where alpha is a real scalar, x is an n element vector and A is an
|
* where alpha is a real scalar, x is an n element vector and A is an
|
||||||
* n by n hermitian matrix, supplied in packed form.
|
* n by n hermitian matrix, supplied in packed form.
|
||||||
*/
|
*/
|
||||||
// int EIGEN_BLAS_FUNC(hpr)(char *uplo, int *n, RealScalar *alpha, RealScalar *x, int *incx, RealScalar *ap)
|
int EIGEN_BLAS_FUNC(hpr)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pap)
|
||||||
// {
|
{
|
||||||
// return 1;
|
typedef void (*functype)(int, Scalar*, const Scalar*, RealScalar);
|
||||||
// }
|
static functype func[2];
|
||||||
|
|
||||||
|
static bool init = false;
|
||||||
|
if(!init)
|
||||||
|
{
|
||||||
|
for(int k=0; k<2; ++k)
|
||||||
|
func[k] = 0;
|
||||||
|
|
||||||
|
func[UP] = (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run);
|
||||||
|
func[LO] = (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run);
|
||||||
|
|
||||||
|
init = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
Scalar* x = reinterpret_cast<Scalar*>(px);
|
||||||
|
Scalar* ap = reinterpret_cast<Scalar*>(pap);
|
||||||
|
RealScalar alpha = *palpha;
|
||||||
|
|
||||||
|
int info = 0;
|
||||||
|
if(UPLO(*uplo)==INVALID) info = 1;
|
||||||
|
else if(*n<0) info = 2;
|
||||||
|
else if(*incx==0) info = 5;
|
||||||
|
if(info)
|
||||||
|
return xerbla_(SCALAR_SUFFIX_UP"HPR ",&info,6);
|
||||||
|
|
||||||
|
if(alpha==Scalar(0))
|
||||||
|
return 1;
|
||||||
|
|
||||||
|
Scalar* x_cpy = get_compact_vector(x, *n, *incx);
|
||||||
|
|
||||||
|
int code = UPLO(*uplo);
|
||||||
|
if(code>=2 || func[code]==0)
|
||||||
|
return 0;
|
||||||
|
|
||||||
|
func[code](*n, ap, x_cpy, alpha);
|
||||||
|
|
||||||
|
if(x_cpy!=x) delete[] x_cpy;
|
||||||
|
|
||||||
|
return 1;
|
||||||
|
}
|
||||||
|
|
||||||
/** ZHPR2 performs the hermitian rank 2 operation
|
/** ZHPR2 performs the hermitian rank 2 operation
|
||||||
*
|
*
|
||||||
|
|||||||
202
blas/sspr.f
202
blas/sspr.f
@ -1,202 +0,0 @@
|
|||||||
SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP)
|
|
||||||
* .. Scalar Arguments ..
|
|
||||||
REAL ALPHA
|
|
||||||
INTEGER INCX,N
|
|
||||||
CHARACTER UPLO
|
|
||||||
* ..
|
|
||||||
* .. Array Arguments ..
|
|
||||||
REAL AP(*),X(*)
|
|
||||||
* ..
|
|
||||||
*
|
|
||||||
* Purpose
|
|
||||||
* =======
|
|
||||||
*
|
|
||||||
* SSPR performs the symmetric rank 1 operation
|
|
||||||
*
|
|
||||||
* A := alpha*x*x' + A,
|
|
||||||
*
|
|
||||||
* where alpha is a real scalar, x is an n element vector and A is an
|
|
||||||
* n by n symmetric matrix, supplied in packed form.
|
|
||||||
*
|
|
||||||
* Arguments
|
|
||||||
* ==========
|
|
||||||
*
|
|
||||||
* UPLO - CHARACTER*1.
|
|
||||||
* On entry, UPLO specifies whether the upper or lower
|
|
||||||
* triangular part of the matrix A is supplied in the packed
|
|
||||||
* array AP as follows:
|
|
||||||
*
|
|
||||||
* UPLO = 'U' or 'u' The upper triangular part of A is
|
|
||||||
* supplied in AP.
|
|
||||||
*
|
|
||||||
* UPLO = 'L' or 'l' The lower triangular part of A is
|
|
||||||
* supplied in AP.
|
|
||||||
*
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* N - INTEGER.
|
|
||||||
* On entry, N specifies the order of the matrix A.
|
|
||||||
* N must be at least zero.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* ALPHA - REAL .
|
|
||||||
* On entry, ALPHA specifies the scalar alpha.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* X - REAL array of dimension at least
|
|
||||||
* ( 1 + ( n - 1 )*abs( INCX ) ).
|
|
||||||
* Before entry, the incremented array X must contain the n
|
|
||||||
* element vector x.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* INCX - INTEGER.
|
|
||||||
* On entry, INCX specifies the increment for the elements of
|
|
||||||
* X. INCX must not be zero.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* AP - REAL array of DIMENSION at least
|
|
||||||
* ( ( n*( n + 1 ) )/2 ).
|
|
||||||
* Before entry with UPLO = 'U' or 'u', the array AP must
|
|
||||||
* contain the upper triangular part of the symmetric matrix
|
|
||||||
* packed sequentially, column by column, so that AP( 1 )
|
|
||||||
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
|
|
||||||
* and a( 2, 2 ) respectively, and so on. On exit, the array
|
|
||||||
* AP is overwritten by the upper triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
* Before entry with UPLO = 'L' or 'l', the array AP must
|
|
||||||
* contain the lower triangular part of the symmetric matrix
|
|
||||||
* packed sequentially, column by column, so that AP( 1 )
|
|
||||||
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
|
|
||||||
* and a( 3, 1 ) respectively, and so on. On exit, the array
|
|
||||||
* AP is overwritten by the lower triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
*
|
|
||||||
* Further Details
|
|
||||||
* ===============
|
|
||||||
*
|
|
||||||
* Level 2 Blas routine.
|
|
||||||
*
|
|
||||||
* -- Written on 22-October-1986.
|
|
||||||
* Jack Dongarra, Argonne National Lab.
|
|
||||||
* Jeremy Du Croz, Nag Central Office.
|
|
||||||
* Sven Hammarling, Nag Central Office.
|
|
||||||
* Richard Hanson, Sandia National Labs.
|
|
||||||
*
|
|
||||||
* =====================================================================
|
|
||||||
*
|
|
||||||
* .. Parameters ..
|
|
||||||
REAL ZERO
|
|
||||||
PARAMETER (ZERO=0.0E+0)
|
|
||||||
* ..
|
|
||||||
* .. Local Scalars ..
|
|
||||||
REAL TEMP
|
|
||||||
INTEGER I,INFO,IX,J,JX,K,KK,KX
|
|
||||||
* ..
|
|
||||||
* .. External Functions ..
|
|
||||||
LOGICAL LSAME
|
|
||||||
EXTERNAL LSAME
|
|
||||||
* ..
|
|
||||||
* .. External Subroutines ..
|
|
||||||
EXTERNAL XERBLA
|
|
||||||
* ..
|
|
||||||
*
|
|
||||||
* Test the input parameters.
|
|
||||||
*
|
|
||||||
INFO = 0
|
|
||||||
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
|
|
||||||
INFO = 1
|
|
||||||
ELSE IF (N.LT.0) THEN
|
|
||||||
INFO = 2
|
|
||||||
ELSE IF (INCX.EQ.0) THEN
|
|
||||||
INFO = 5
|
|
||||||
END IF
|
|
||||||
IF (INFO.NE.0) THEN
|
|
||||||
CALL XERBLA('SSPR ',INFO)
|
|
||||||
RETURN
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Quick return if possible.
|
|
||||||
*
|
|
||||||
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
|
|
||||||
*
|
|
||||||
* Set the start point in X if the increment is not unity.
|
|
||||||
*
|
|
||||||
IF (INCX.LE.0) THEN
|
|
||||||
KX = 1 - (N-1)*INCX
|
|
||||||
ELSE IF (INCX.NE.1) THEN
|
|
||||||
KX = 1
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Start the operations. In this version the elements of the array AP
|
|
||||||
* are accessed sequentially with one pass through AP.
|
|
||||||
*
|
|
||||||
KK = 1
|
|
||||||
IF (LSAME(UPLO,'U')) THEN
|
|
||||||
*
|
|
||||||
* Form A when upper triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 20 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(J)
|
|
||||||
K = KK
|
|
||||||
DO 10 I = 1,J
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
10 CONTINUE
|
|
||||||
END IF
|
|
||||||
KK = KK + J
|
|
||||||
20 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 40 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(JX)
|
|
||||||
IX = KX
|
|
||||||
DO 30 K = KK,KK + J - 1
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
IX = IX + INCX
|
|
||||||
30 CONTINUE
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + J
|
|
||||||
40 CONTINUE
|
|
||||||
END IF
|
|
||||||
ELSE
|
|
||||||
*
|
|
||||||
* Form A when lower triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 60 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(J)
|
|
||||||
K = KK
|
|
||||||
DO 50 I = J,N
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
50 CONTINUE
|
|
||||||
END IF
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
60 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 80 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*X(JX)
|
|
||||||
IX = JX
|
|
||||||
DO 70 K = KK,KK + N - J
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
IX = IX + INCX
|
|
||||||
70 CONTINUE
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
80 CONTINUE
|
|
||||||
END IF
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
RETURN
|
|
||||||
*
|
|
||||||
* End of SSPR .
|
|
||||||
*
|
|
||||||
END
|
|
||||||
220
blas/zhpr.f
220
blas/zhpr.f
@ -1,220 +0,0 @@
|
|||||||
SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
|
|
||||||
* .. Scalar Arguments ..
|
|
||||||
DOUBLE PRECISION ALPHA
|
|
||||||
INTEGER INCX,N
|
|
||||||
CHARACTER UPLO
|
|
||||||
* ..
|
|
||||||
* .. Array Arguments ..
|
|
||||||
DOUBLE COMPLEX AP(*),X(*)
|
|
||||||
* ..
|
|
||||||
*
|
|
||||||
* Purpose
|
|
||||||
* =======
|
|
||||||
*
|
|
||||||
* ZHPR performs the hermitian rank 1 operation
|
|
||||||
*
|
|
||||||
* A := alpha*x*conjg( x' ) + A,
|
|
||||||
*
|
|
||||||
* where alpha is a real scalar, x is an n element vector and A is an
|
|
||||||
* n by n hermitian matrix, supplied in packed form.
|
|
||||||
*
|
|
||||||
* Arguments
|
|
||||||
* ==========
|
|
||||||
*
|
|
||||||
* UPLO - CHARACTER*1.
|
|
||||||
* On entry, UPLO specifies whether the upper or lower
|
|
||||||
* triangular part of the matrix A is supplied in the packed
|
|
||||||
* array AP as follows:
|
|
||||||
*
|
|
||||||
* UPLO = 'U' or 'u' The upper triangular part of A is
|
|
||||||
* supplied in AP.
|
|
||||||
*
|
|
||||||
* UPLO = 'L' or 'l' The lower triangular part of A is
|
|
||||||
* supplied in AP.
|
|
||||||
*
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* N - INTEGER.
|
|
||||||
* On entry, N specifies the order of the matrix A.
|
|
||||||
* N must be at least zero.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* ALPHA - DOUBLE PRECISION.
|
|
||||||
* On entry, ALPHA specifies the scalar alpha.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* X - COMPLEX*16 array of dimension at least
|
|
||||||
* ( 1 + ( n - 1 )*abs( INCX ) ).
|
|
||||||
* Before entry, the incremented array X must contain the n
|
|
||||||
* element vector x.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* INCX - INTEGER.
|
|
||||||
* On entry, INCX specifies the increment for the elements of
|
|
||||||
* X. INCX must not be zero.
|
|
||||||
* Unchanged on exit.
|
|
||||||
*
|
|
||||||
* AP - COMPLEX*16 array of DIMENSION at least
|
|
||||||
* ( ( n*( n + 1 ) )/2 ).
|
|
||||||
* Before entry with UPLO = 'U' or 'u', the array AP must
|
|
||||||
* contain the upper triangular part of the hermitian matrix
|
|
||||||
* packed sequentially, column by column, so that AP( 1 )
|
|
||||||
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
|
|
||||||
* and a( 2, 2 ) respectively, and so on. On exit, the array
|
|
||||||
* AP is overwritten by the upper triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
* Before entry with UPLO = 'L' or 'l', the array AP must
|
|
||||||
* contain the lower triangular part of the hermitian matrix
|
|
||||||
* packed sequentially, column by column, so that AP( 1 )
|
|
||||||
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
|
|
||||||
* and a( 3, 1 ) respectively, and so on. On exit, the array
|
|
||||||
* AP is overwritten by the lower triangular part of the
|
|
||||||
* updated matrix.
|
|
||||||
* Note that the imaginary parts of the diagonal elements need
|
|
||||||
* not be set, they are assumed to be zero, and on exit they
|
|
||||||
* are set to zero.
|
|
||||||
*
|
|
||||||
* Further Details
|
|
||||||
* ===============
|
|
||||||
*
|
|
||||||
* Level 2 Blas routine.
|
|
||||||
*
|
|
||||||
* -- Written on 22-October-1986.
|
|
||||||
* Jack Dongarra, Argonne National Lab.
|
|
||||||
* Jeremy Du Croz, Nag Central Office.
|
|
||||||
* Sven Hammarling, Nag Central Office.
|
|
||||||
* Richard Hanson, Sandia National Labs.
|
|
||||||
*
|
|
||||||
* =====================================================================
|
|
||||||
*
|
|
||||||
* .. Parameters ..
|
|
||||||
DOUBLE COMPLEX ZERO
|
|
||||||
PARAMETER (ZERO= (0.0D+0,0.0D+0))
|
|
||||||
* ..
|
|
||||||
* .. Local Scalars ..
|
|
||||||
DOUBLE COMPLEX TEMP
|
|
||||||
INTEGER I,INFO,IX,J,JX,K,KK,KX
|
|
||||||
* ..
|
|
||||||
* .. External Functions ..
|
|
||||||
LOGICAL LSAME
|
|
||||||
EXTERNAL LSAME
|
|
||||||
* ..
|
|
||||||
* .. External Subroutines ..
|
|
||||||
EXTERNAL XERBLA
|
|
||||||
* ..
|
|
||||||
* .. Intrinsic Functions ..
|
|
||||||
INTRINSIC DBLE,DCONJG
|
|
||||||
* ..
|
|
||||||
*
|
|
||||||
* Test the input parameters.
|
|
||||||
*
|
|
||||||
INFO = 0
|
|
||||||
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
|
|
||||||
INFO = 1
|
|
||||||
ELSE IF (N.LT.0) THEN
|
|
||||||
INFO = 2
|
|
||||||
ELSE IF (INCX.EQ.0) THEN
|
|
||||||
INFO = 5
|
|
||||||
END IF
|
|
||||||
IF (INFO.NE.0) THEN
|
|
||||||
CALL XERBLA('ZHPR ',INFO)
|
|
||||||
RETURN
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Quick return if possible.
|
|
||||||
*
|
|
||||||
IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
|
|
||||||
*
|
|
||||||
* Set the start point in X if the increment is not unity.
|
|
||||||
*
|
|
||||||
IF (INCX.LE.0) THEN
|
|
||||||
KX = 1 - (N-1)*INCX
|
|
||||||
ELSE IF (INCX.NE.1) THEN
|
|
||||||
KX = 1
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
* Start the operations. In this version the elements of the array AP
|
|
||||||
* are accessed sequentially with one pass through AP.
|
|
||||||
*
|
|
||||||
KK = 1
|
|
||||||
IF (LSAME(UPLO,'U')) THEN
|
|
||||||
*
|
|
||||||
* Form A when upper triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 20 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*DCONJG(X(J))
|
|
||||||
K = KK
|
|
||||||
DO 10 I = 1,J - 1
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
10 CONTINUE
|
|
||||||
AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP)
|
|
||||||
ELSE
|
|
||||||
AP(KK+J-1) = DBLE(AP(KK+J-1))
|
|
||||||
END IF
|
|
||||||
KK = KK + J
|
|
||||||
20 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 40 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*DCONJG(X(JX))
|
|
||||||
IX = KX
|
|
||||||
DO 30 K = KK,KK + J - 2
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
IX = IX + INCX
|
|
||||||
30 CONTINUE
|
|
||||||
AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP)
|
|
||||||
ELSE
|
|
||||||
AP(KK+J-1) = DBLE(AP(KK+J-1))
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + J
|
|
||||||
40 CONTINUE
|
|
||||||
END IF
|
|
||||||
ELSE
|
|
||||||
*
|
|
||||||
* Form A when lower triangle is stored in AP.
|
|
||||||
*
|
|
||||||
IF (INCX.EQ.1) THEN
|
|
||||||
DO 60 J = 1,N
|
|
||||||
IF (X(J).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*DCONJG(X(J))
|
|
||||||
AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J))
|
|
||||||
K = KK + 1
|
|
||||||
DO 50 I = J + 1,N
|
|
||||||
AP(K) = AP(K) + X(I)*TEMP
|
|
||||||
K = K + 1
|
|
||||||
50 CONTINUE
|
|
||||||
ELSE
|
|
||||||
AP(KK) = DBLE(AP(KK))
|
|
||||||
END IF
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
60 CONTINUE
|
|
||||||
ELSE
|
|
||||||
JX = KX
|
|
||||||
DO 80 J = 1,N
|
|
||||||
IF (X(JX).NE.ZERO) THEN
|
|
||||||
TEMP = ALPHA*DCONJG(X(JX))
|
|
||||||
AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX))
|
|
||||||
IX = JX
|
|
||||||
DO 70 K = KK + 1,KK + N - J
|
|
||||||
IX = IX + INCX
|
|
||||||
AP(K) = AP(K) + X(IX)*TEMP
|
|
||||||
70 CONTINUE
|
|
||||||
ELSE
|
|
||||||
AP(KK) = DBLE(AP(KK))
|
|
||||||
END IF
|
|
||||||
JX = JX + INCX
|
|
||||||
KK = KK + N - J + 1
|
|
||||||
80 CONTINUE
|
|
||||||
END IF
|
|
||||||
END IF
|
|
||||||
*
|
|
||||||
RETURN
|
|
||||||
*
|
|
||||||
* End of ZHPR .
|
|
||||||
*
|
|
||||||
END
|
|
||||||
Loading…
x
Reference in New Issue
Block a user