GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-08-13 12:19:12 +08:00
Code Issues Packages Projects Releases Wiki Activity

Merged in jdh8/eigen (pull request PR-17)

Browse Source
This commit is contained in:
Gael Guennebaud 2012-09-11 21:36:05 +02:00
commit 28528519e9
26 changed files with 602 additions and 4383 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
blas/CMakeLists.txt
View File

@ -18,10 +18,10 @@ if(EIGEN_Fortran_COMPILER_WORKS)
set(EigenBlas_SRCS ${EigenBlas_SRCS}
complexdots.f
srotm.f srotmg.f drotm.f drotmg.f
lsame.f chpr2.f dspmv.f dtpsv.f ssbmv.f sspr.f stpmv.f
zhpr2.f chbmv.f chpr.f ctpmv.f dspr2.f sspmv.f stpsv.f
zhbmv.f zhpr.f ztpmv.f chpmv.f ctpsv.f dsbmv.f dspr.f dtpmv.f sspr2.f
zhpmv.f ztpsv.f
lsame.f dspmv.f ssbmv.f
chbmv.f sspmv.f
zhbmv.f chpmv.f dsbmv.f
zhpmv.f
dtbmv.f stbmv.f ctbmv.f ztbmv.f
)
else()

24
blas/GeneralRank1Update.h
View File

@ -13,15 +13,29 @@
namespace internal {
/* Optimized matrix += alpha * uv' */
template<typename Scalar, typename Index, bool ConjRhs>
struct general_rank1_update
template<typename Scalar, typename Index, int StorageOrder, bool ConjLhs, bool ConjRhs>
struct general_rank1_update;
template<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>
struct general_rank1_update<Scalar,Index,ColMajor,ConjLhs,ConjRhs>
{
static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
{
typedef Matrix<Scalar,Dynamic,1> PlainVector;
internal::conj_if<ConjRhs> cj;
typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
conj_if<ConjRhs> cj;
for (Index i=0; i<cols; ++i)
Map<PlainVector>(mat+stride*i,rows) += alpha * cj(v[i]) * Map<const PlainVector>(u,rows);
Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i,rows) += alpha * cj(v[i]) * ConjRhsType(OtherMap(u,rows));
}
};
template<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>
struct general_rank1_update<Scalar,Index,RowMajor,ConjLhs,ConjRhs>
{
static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
{
general_rank1_update<Scalar,Index,ColMajor,ConjRhs,ConjRhs>::run(rows,cols,mat,stride,u,v,alpha);
}
};

54
blas/PackedSelfadjointProduct.h Normal file
View File

@ -0,0 +1,54 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SELFADJOINT_PACKED_PRODUCT_H
#define EIGEN_SELFADJOINT_PACKED_PRODUCT_H
namespace internal {
/* Optimized matrix += alpha * uv'
* The matrix is in packed form.
*/
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_packed_rank1_update;
template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
{
typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
conj_if<ConjRhs> cj;
for (Index i=0; i<size; ++i)
{
Map<Matrix<Scalar,Dynamic,1> >(mat, UpLo==Lower ? size-i : (i+1))
+= alpha * cj(vec[i]) * ConjRhsType(OtherMap(vec+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)));
//FIXME This should be handled outside.
mat[UpLo==Lower ? 0 : i] = real(mat[UpLo==Lower ? 0 : i]);
mat += UpLo==Lower ? size-i : (i+1);
}
}
};
template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
{
selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,vec,alpha);
}
};
} // end namespace internal
#endif // EIGEN_SELFADJOINT_PACKED_PRODUCT_H

79
blas/PackedTriangularMatrixVector.h Normal file
View File

@ -0,0 +1,79 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H
#define EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H
namespace internal {
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>
struct packed_triangular_matrix_vector_product;
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor>
{
typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
IsLower = (Mode & Lower) ==Lower,
HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
};
static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)
{
internal::conj_if<ConjRhs> cj;
typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;
typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;
for (Index i=0; i<size; ++i)
{
Index s = IsLower&&(HasUnitDiag||HasZeroDiag) ? 1 : 0;
Index r = IsLower ? size-i: i+1;
if (EIGEN_IMPLIES(HasUnitDiag||HasZeroDiag, (--r)>0))
ResMap(res+(IsLower ? s+i : 0),r) += alpha * cj(rhs[i]) * ConjLhsType(LhsMap(lhs+s,r));
if (HasUnitDiag)
res[i] += alpha * cj(rhs[i]);
lhs += IsLower ? size-i: i+1;
}
};
};
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor>
{
typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
IsLower = (Mode & Lower) ==Lower,
HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
};
static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)
{
internal::conj_if<ConjRhs> cj;
typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;
typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;
typedef typename conj_expr_if<ConjRhs,RhsMap>::type ConjRhsType;
for (Index i=0; i<size; ++i)
{
Index s = !IsLower&&(HasUnitDiag||HasZeroDiag) ? 1 : 0;
Index r = IsLower ? i+1 : size-i;
if (EIGEN_IMPLIES(HasUnitDiag||HasZeroDiag, (--r)>0))
res[i] += alpha * (ConjLhsType(LhsMap(lhs+s,r)).cwiseProduct(ConjRhsType(RhsMap(rhs+(IsLower ? 0 : s+i),r)))).sum();
if (HasUnitDiag)
res[i] += alpha * cj(rhs[i]);
lhs += IsLower ? i+1 : size-i;
}
};
};
} // end namespace internal
#endif // EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H

88
blas/PackedTriangularSolverVector.h Normal file
View File

@ -0,0 +1,88 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H
#define EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H
namespace internal {
template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
struct packed_triangular_solve_vector;
// forward and backward substitution, row-major, rhs is a vector
template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>
{
enum {
IsLower = (Mode&Lower)==Lower
};
static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
{
internal::conj_if<Conjugate> cj;
typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;
lhs += IsLower ? 0 : (size*(size+1)>>1)-1;
for(Index pi=0; pi<size; ++pi)
{
Index i = IsLower ? pi : size-pi-1;
Index s = IsLower ? 0 : 1;
if (pi>0)
rhs[i] -= (ConjLhsType(LhsMap(lhs+s,pi))
.cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower ? 0 : i+1),pi))).sum();
if (!(Mode & UnitDiag))
rhs[i] /= cj(lhs[IsLower ? i : 0]);
IsLower ? lhs += pi+1 : lhs -= pi+2;
}
}
};
// forward and backward substitution, column-major, rhs is a vector
template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>
{
enum {
IsLower = (Mode&Lower)==Lower
};
static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
{
internal::conj_if<Conjugate> cj;
typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;
lhs += IsLower ? 0 : size*(size-1)>>1;
for(Index pi=0; pi<size; ++pi)
{
Index i = IsLower ? pi : size-pi-1;
Index r = size - pi - 1;
if (!(Mode & UnitDiag))
rhs[i] /= cj(lhs[IsLower ? 0 : i]);
if (r>0)
Map<Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower? i+1 : 0),r) -=
rhs[i] * ConjLhsType(LhsMap(lhs+(IsLower? 1 : 0),r));
IsLower ? lhs += size-pi : lhs -= r;
}
}
};
template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>
{
static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
{
packed_triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,
((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
Conjugate,StorageOrder==RowMajor?ColMajor:RowMajor
>::run(size, lhs, rhs);
}
};
} // end namespace internal
#endif // EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H

40
blas/Rank2Update.h
View File

@ -16,38 +16,38 @@ namespace internal {
* This is the low-level version of SelfadjointRank2Update.h
*/
template<typename Scalar, typename Index, int UpLo>
struct rank2_update_selector;
template<typename Scalar, typename Index>
struct rank2_update_selector<Scalar,Index,Upper>
struct rank2_update_selector
{
static void run(Index size, Scalar* mat, Index stride, const Scalar* _u, const Scalar* _v, Scalar alpha)
static void run(Index size, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
{
typedef Matrix<Scalar,Dynamic,1> PlainVector;
Map<const PlainVector> u(_u, size), v(_v, size);
typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
for (Index i=0; i<size; ++i)
{
Map<PlainVector>(mat+stride*i, i+1) +=
conj(alpha) * conj(_u[i]) * v.head(i+1)
+ alpha * conj(_v[i]) * u.head(i+1);
Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)) +=
conj(alpha) * conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))
+ alpha * conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));
}
}
};
template<typename Scalar, typename Index>
struct rank2_update_selector<Scalar,Index,Lower>
/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
* The matrix is in packed form.
*/
template<typename Scalar, typename Index, int UpLo>
struct packed_rank2_update_selector
{
static void run(Index size, Scalar* mat, Index stride, const Scalar* _u, const Scalar* _v, Scalar alpha)
static void run(Index size, Scalar* mat, const Scalar* u, const Scalar* v, Scalar alpha)
{
typedef Matrix<Scalar,Dynamic,1> PlainVector;
Map<const PlainVector> u(_u, size), v(_v, size);
typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
Index offset = 0;
for (Index i=0; i<size; ++i)
{
Map<PlainVector>(mat+(stride+1)*i, size-i) +=
conj(alpha) * conj(_u[i]) * v.tail(size-i)
+ alpha * conj(_v[i]) * u.tail(size-i);
Map<Matrix<Scalar,Dynamic,1> >(mat+offset, UpLo==Lower ? size-i : (i+1)) +=
conj(alpha) * conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))
+ alpha * conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));
//FIXME This should be handled outside.
mat[offset+(UpLo==Lower ? 0 : i)] = real(mat[offset+(UpLo==Lower ? 0 : i)]);
offset += UpLo==Lower ? size-i : (i+1);
}
}
};

220
blas/chpr.f
View File

@ -1,220 +0,0 @@
SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
* .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
COMPLEX AP(*),X(*)
* ..
*
* Purpose
* =======
*
* CHPR 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 - REAL .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX 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 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 ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,REAL
* ..
*
* 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('CHPR ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(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*CONJG(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) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
ELSE
AP(KK+J-1) = REAL(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*CONJG(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) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
ELSE
AP(KK+J-1) = REAL(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*CONJG(X(J))
AP(KK) = REAL(AP(KK)) + REAL(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) = REAL(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*CONJG(X(JX))
AP(KK) = REAL(AP(KK)) + REAL(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) = REAL(AP(KK))
END IF
JX = JX + INCX
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHPR .
*
END

255
blas/chpr2.f
View File

@ -1,255 +0,0 @@
SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
* .. Scalar Arguments ..
COMPLEX ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
COMPLEX AP(*),X(*),Y(*)
* ..
*
* Purpose
* =======
*
* CHPR2 performs the hermitian rank 2 operation
*
* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
* where alpha is a scalar, x and y are n element vectors 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 - COMPLEX .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX 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.
*
* Y - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* AP - COMPLEX 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 ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,REAL
* ..
*
* 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
ELSE IF (INCY.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CHPR2 ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (N-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (N-1)*INCY
END IF
JX = KX
JY = KY
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) .AND. (INCY.EQ.1)) THEN
DO 20 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(J))
TEMP2 = CONJG(ALPHA*X(J))
K = KK
DO 10 I = 1,J - 1
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
10 CONTINUE
AP(KK+J-1) = REAL(AP(KK+J-1)) +
+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
ELSE
AP(KK+J-1) = REAL(AP(KK+J-1))
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(JY))
TEMP2 = CONJG(ALPHA*X(JX))
IX = KX
IY = KY
DO 30 K = KK,KK + J - 2
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
AP(KK+J-1) = REAL(AP(KK+J-1)) +
+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
ELSE
AP(KK+J-1) = REAL(AP(KK+J-1))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
DO 60 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(J))
TEMP2 = CONJG(ALPHA*X(J))
AP(KK) = REAL(AP(KK)) +
+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
K = KK + 1
DO 50 I = J + 1,N
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
50 CONTINUE
ELSE
AP(KK) = REAL(AP(KK))
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(JY))
TEMP2 = CONJG(ALPHA*X(JX))
AP(KK) = REAL(AP(KK)) +
+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
IX = JX
IY = JY
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
IY = IY + INCY
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
70 CONTINUE
ELSE
AP(KK) = REAL(AP(KK))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHPR2 .
*
END

3
blas/common.h
View File

@ -75,6 +75,9 @@ inline bool check_uplo(const char* uplo)
namespace Eigen {
#include "BandTriangularSolver.h"
#include "GeneralRank1Update.h"
#include "PackedSelfadjointProduct.h"
#include "PackedTriangularMatrixVector.h"
#include "PackedTriangularSolverVector.h"
#include "Rank2Update.h"
}

329
blas/ctpmv.f
View File

@ -1,329 +0,0 @@
SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX AP(*),X(*)
* ..
*
* Purpose
* =======
*
* CTPMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix, supplied in packed form.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' x := A*x.
*
* TRANS = 'T' or 't' x := A'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - COMPLEX array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* Unchanged on exit.
*
* X - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x. On exit, X is overwritten with the
* tranformed vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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 ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CTPMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOCONJ = LSAME(TRANS,'T')
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x:= A*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 10 I = 1,J - 1
X(I) = X(I) + TEMP*AP(K)
K = K + 1
10 CONTINUE
IF (NOUNIT) X(J) = X(J)*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 = X(JX)
IX = KX
DO 30 K = KK,KK + J - 2
X(IX) = X(IX) + TEMP*AP(K)
IX = IX + INCX
30 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 50 I = N,J + 1,-1
X(I) = X(I) + TEMP*AP(K)
K = K - 1
50 CONTINUE
IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
END IF
KK = KK - (N-J+1)
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 70 K = KK,KK - (N- (J+1)),-1
X(IX) = X(IX) + TEMP*AP(K)
IX = IX - INCX
70 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
END IF
JX = JX - INCX
KK = KK - (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A'*x or x := conjg( A' )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 110 J = N,1,-1
TEMP = X(J)
K = KK - 1
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 90 I = J - 1,1,-1
TEMP = TEMP + AP(K)*X(I)
K = K - 1
90 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
DO 100 I = J - 1,1,-1
TEMP = TEMP + CONJG(AP(K))*X(I)
K = K - 1
100 CONTINUE
END IF
X(J) = TEMP
KK = KK - J
110 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 140 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 120 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + AP(K)*X(IX)
120 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
DO 130 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + CONJG(AP(K))*X(IX)
130 CONTINUE
END IF
X(JX) = TEMP
JX = JX - INCX
KK = KK - J
140 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 170 J = 1,N
TEMP = X(J)
K = KK + 1
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 150 I = J + 1,N
TEMP = TEMP + AP(K)*X(I)
K = K + 1
150 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
DO 160 I = J + 1,N
TEMP = TEMP + CONJG(AP(K))*X(I)
K = K + 1
160 CONTINUE
END IF
X(J) = TEMP
KK = KK + (N-J+1)
170 CONTINUE
ELSE
JX = KX
DO 200 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 180 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + AP(K)*X(IX)
180 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
DO 190 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + CONJG(AP(K))*X(IX)
190 CONTINUE
END IF
X(JX) = TEMP
JX = JX + INCX
KK = KK + (N-J+1)
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTPMV .
*
END

332
blas/ctpsv.f
View File

@ -1,332 +0,0 @@
SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX AP(*),X(*)
* ..
*
* Purpose
* =======
*
* CTPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular matrix, supplied in packed form.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - COMPLEX array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* Unchanged on exit.
*
* X - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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 ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CTPSV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOCONJ = LSAME(TRANS,'T')
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK - 1
DO 10 I = J - 1,1,-1
X(I) = X(I) - TEMP*AP(K)
K = K - 1
10 CONTINUE
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 30 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
X(IX) = X(IX) - TEMP*AP(K)
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK + 1
DO 50 I = J + 1,N
X(I) = X(I) - TEMP*AP(K)
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
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
X(IX) = X(IX) - TEMP*AP(K)
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 110 J = 1,N
TEMP = X(J)
K = KK
IF (NOCONJ) THEN
DO 90 I = 1,J - 1
TEMP = TEMP - AP(K)*X(I)
K = K + 1
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
ELSE
DO 100 I = 1,J - 1
TEMP = TEMP - CONJG(AP(K))*X(I)
K = K + 1
100 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
END IF
X(J) = TEMP
KK = KK + J
110 CONTINUE
ELSE
JX = KX
DO 140 J = 1,N
TEMP = X(JX)
IX = KX
IF (NOCONJ) THEN
DO 120 K = KK,KK + J - 2
TEMP = TEMP - AP(K)*X(IX)
IX = IX + INCX
120 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
ELSE
DO 130 K = KK,KK + J - 2
TEMP = TEMP - CONJG(AP(K))*X(IX)
IX = IX + INCX
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
END IF
X(JX) = TEMP
JX = JX + INCX
KK = KK + J
140 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 170 J = N,1,-1
TEMP = X(J)
K = KK
IF (NOCONJ) THEN
DO 150 I = N,J + 1,-1
TEMP = TEMP - AP(K)*X(I)
K = K - 1
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
ELSE
DO 160 I = N,J + 1,-1
TEMP = TEMP - CONJG(AP(K))*X(I)
K = K - 1
160 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
END IF
X(J) = TEMP
KK = KK - (N-J+1)
170 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 200 J = N,1,-1
TEMP = X(JX)
IX = KX
IF (NOCONJ) THEN
DO 180 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - AP(K)*X(IX)
IX = IX - INCX
180 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
ELSE
DO 190 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - CONJG(AP(K))*X(IX)
IX = IX - INCX
190 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
END IF
X(JX) = TEMP
JX = JX - INCX
KK = KK - (N-J+1)
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTPSV .
*
END

202
blas/dspr.f
View File

@ -1,202 +0,0 @@
SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
* ..
*
* Purpose
* =======
*
* DSPR 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 - DOUBLE PRECISION.
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 ..
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

233
blas/dspr2.f
View File

@ -1,233 +0,0 @@
SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*),Y(*)
* ..
*
* Purpose
* =======
*
* DSPR2 performs the symmetric rank 2 operation
*
* A := alpha*x*y' + alpha*y*x' + A,
*
* where alpha is a scalar, x and y are n element vectors 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 - DOUBLE PRECISION.
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - DOUBLE PRECISION 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.
*
* Y - DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* AP - DOUBLE PRECISION 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 ..
DOUBLE PRECISION ZERO
PARAMETER (ZERO=0.0D+0)
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
* ..
* .. 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
ELSE IF (INCY.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DSPR2 ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (N-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (N-1)*INCY
END IF
JX = KX
JY = KY
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) .AND. (INCY.EQ.1)) THEN
DO 20 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(J)
TEMP2 = ALPHA*X(J)
K = KK
DO 10 I = 1,J
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
10 CONTINUE
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(JY)
TEMP2 = ALPHA*X(JX)
IX = KX
IY = KY
DO 30 K = KK,KK + J - 1
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
DO 60 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(J)
TEMP2 = ALPHA*X(J)
K = KK
DO 50 I = J,N
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
50 CONTINUE
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(JY)
TEMP2 = ALPHA*X(JX)
IX = JX
IY = JY
DO 70 K = KK,KK + N - J
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of DSPR2 .
*
END

293
blas/dtpmv.f
View File

@ -1,293 +0,0 @@
SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
* ..
*
* Purpose
* =======
*
* DTPMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix, supplied in packed form.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' x := A*x.
*
* TRANS = 'T' or 't' x := A'*x.
*
* TRANS = 'C' or 'c' x := A'*x.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - DOUBLE PRECISION array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* Unchanged on exit.
*
* X - DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x. On exit, X is overwritten with the
* tranformed vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOUNIT
* ..
* .. 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 (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTPMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x:= A*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 10 I = 1,J - 1
X(I) = X(I) + TEMP*AP(K)
K = K + 1
10 CONTINUE
IF (NOUNIT) X(J) = X(J)*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 = X(JX)
IX = KX
DO 30 K = KK,KK + J - 2
X(IX) = X(IX) + TEMP*AP(K)
IX = IX + INCX
30 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 50 I = N,J + 1,-1
X(I) = X(I) + TEMP*AP(K)
K = K - 1
50 CONTINUE
IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
END IF
KK = KK - (N-J+1)
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 70 K = KK,KK - (N- (J+1)),-1
X(IX) = X(IX) + TEMP*AP(K)
IX = IX - INCX
70 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
END IF
JX = JX - INCX
KK = KK - (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A'*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 100 J = N,1,-1
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*AP(KK)
K = KK - 1
DO 90 I = J - 1,1,-1
TEMP = TEMP + AP(K)*X(I)
K = K - 1
90 CONTINUE
X(J) = TEMP
KK = KK - J
100 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 120 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 110 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + AP(K)*X(IX)
110 CONTINUE
X(JX) = TEMP
JX = JX - INCX
KK = KK - J
120 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 140 J = 1,N
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*AP(KK)
K = KK + 1
DO 130 I = J + 1,N
TEMP = TEMP + AP(K)*X(I)
K = K + 1
130 CONTINUE
X(J) = TEMP
KK = KK + (N-J+1)
140 CONTINUE
ELSE
JX = KX
DO 160 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 150 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + AP(K)*X(IX)
150 CONTINUE
X(JX) = TEMP
JX = JX + INCX
KK = KK + (N-J+1)
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTPMV .
*
END

296
blas/dtpsv.f
View File

@ -1,296 +0,0 @@
SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
* ..
*
* Purpose
* =======
*
* DTPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular matrix, supplied in packed form.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x = b.
*
* TRANS = 'C' or 'c' A'*x = b.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - DOUBLE PRECISION array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* Unchanged on exit.
*
* X - DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOUNIT
* ..
* .. 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 (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTPSV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK - 1
DO 10 I = J - 1,1,-1
X(I) = X(I) - TEMP*AP(K)
K = K - 1
10 CONTINUE
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 30 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
X(IX) = X(IX) - TEMP*AP(K)
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK + 1
DO 50 I = J + 1,N
X(I) = X(I) - TEMP*AP(K)
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
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
X(IX) = X(IX) - TEMP*AP(K)
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A' )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 100 J = 1,N
TEMP = X(J)
K = KK
DO 90 I = 1,J - 1
TEMP = TEMP - AP(K)*X(I)
K = K + 1
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(J) = TEMP
KK = KK + J
100 CONTINUE
ELSE
JX = KX
DO 120 J = 1,N
TEMP = X(JX)
IX = KX
DO 110 K = KK,KK + J - 2
TEMP = TEMP - AP(K)*X(IX)
IX = IX + INCX
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(JX) = TEMP
JX = JX + INCX
KK = KK + J
120 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 140 J = N,1,-1
TEMP = X(J)
K = KK
DO 130 I = N,J + 1,-1
TEMP = TEMP - AP(K)*X(I)
K = K - 1
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(J) = TEMP
KK = KK - (N-J+1)
140 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 160 J = N,1,-1
TEMP = X(JX)
IX = KX
DO 150 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - AP(K)*X(IX)
IX = IX - INCX
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(JX) = TEMP
JX = JX - INCX
KK = KK - (N-J+1)
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTPSV .
*
END

125
blas/level2_cplx_impl.h
View File

@ -18,6 +18,21 @@
*/
int EIGEN_BLAS_FUNC(hemv)(char *uplo, int *n, RealScalar *palpha, RealScalar *pa, int *lda, RealScalar *px, int *incx, RealScalar *pbeta, RealScalar *py, int *incy)
{
typedef void (*functype)(int, const Scalar*, int, const Scalar*, int, Scalar*, Scalar);
static functype func[2];
static bool init = false;
if(!init)
{
for(int k=0; k<2; ++k)
func[k] = 0;
func[UP] = (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run);
func[LO] = (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run);
init = true;
}
Scalar* a = reinterpret_cast<Scalar*>(pa);
Scalar* x = reinterpret_cast<Scalar*>(px);
Scalar* y = reinterpret_cast<Scalar*>(py);
@ -48,9 +63,11 @@ int EIGEN_BLAS_FUNC(hemv)(char *uplo, int *n, RealScalar *palpha, RealScalar *pa
if(alpha!=Scalar(0))
{
// TODO performs a direct call to the underlying implementation function
if(UPLO(*uplo)==UP) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Upper>() * (alpha * vector(actual_x,*n));
else if(UPLO(*uplo)==LO) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Lower>() * (alpha * vector(actual_x,*n));
int code = UPLO(*uplo);
if(code>=2 || func[code]==0)
return 0;
func[code](*n, a, *lda, actual_x, 1, actual_y, alpha);
}
if(actual_x!=x) delete[] actual_x;
@ -91,10 +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
* 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)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(hpr)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pap)
{
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
*
@ -103,10 +159,53 @@ int EIGEN_BLAS_FUNC(hemv)(char *uplo, int *n, RealScalar *palpha, RealScalar *pa
* where alpha is a scalar, x and y are n element vectors and A is an
* n by n hermitian matrix, supplied in packed form.
*/
// int EIGEN_BLAS_FUNC(hpr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *x, int *incx, RealScalar *y, int *incy, RealScalar *ap)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(hpr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)
{
typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);
static functype func[2];
static bool init = false;
if(!init)
{
for(int k=0; k<2; ++k)
func[k] = 0;
func[UP] = (internal::packed_rank2_update_selector<Scalar,int,Upper>::run);
func[LO] = (internal::packed_rank2_update_selector<Scalar,int,Lower>::run);
init = true;
}
Scalar* x = reinterpret_cast<Scalar*>(px);
Scalar* y = reinterpret_cast<Scalar*>(py);
Scalar* ap = reinterpret_cast<Scalar*>(pap);
Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
int info = 0;
if(UPLO(*uplo)==INVALID) info = 1;
else if(*n<0) info = 2;
else if(*incx==0) info = 5;
else if(*incy==0) info = 7;
if(info)
return xerbla_(SCALAR_SUFFIX_UP"HPR2 ",&info,6);
if(alpha==Scalar(0))
return 1;
Scalar* x_cpy = get_compact_vector(x, *n, *incx);
Scalar* y_cpy = get_compact_vector(y, *n, *incy);
int code = UPLO(*uplo);
if(code>=2 || func[code]==0)
return 0;
func[code](*n, ap, x_cpy, y_cpy, alpha);
if(x_cpy!=x) delete[] x_cpy;
if(y_cpy!=y) delete[] y_cpy;
return 1;
}
/** ZHER performs the hermitian rank 1 operation
*
@ -249,7 +348,7 @@ int EIGEN_BLAS_FUNC(geru)(int *m, int *n, RealScalar *palpha, RealScalar *px, in
Scalar* x_cpy = get_compact_vector(x,*m,*incx);
Scalar* y_cpy = get_compact_vector(y,*n,*incy);
internal::general_rank1_update<Scalar,int,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
if(x_cpy!=x) delete[] x_cpy;
if(y_cpy!=y) delete[] y_cpy;
@ -286,7 +385,7 @@ int EIGEN_BLAS_FUNC(gerc)(int *m, int *n, RealScalar *palpha, RealScalar *px, in
Scalar* x_cpy = get_compact_vector(x,*m,*incx);
Scalar* y_cpy = get_compact_vector(y,*n,*incy);
internal::general_rank1_update<Scalar,int,Conj>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
internal::general_rank1_update<Scalar,int,ColMajor,false,Conj>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
if(x_cpy!=x) delete[] x_cpy;
if(y_cpy!=y) delete[] y_cpy;

121
blas/level2_impl.h
View File

@ -187,7 +187,7 @@ int EIGEN_BLAS_FUNC(trmv)(char *uplo, char *opa, char *diag, int *n, RealScalar
copy_back(res.data(),b,*n,*incb);
if(actual_b!=b) delete[] actual_b;
return 0;
return 1;
}
/** GBMV performs one of the matrix-vector operations
@ -399,10 +399,66 @@ int EIGEN_BLAS_FUNC(tbsv)(char *uplo, char *op, char *diag, int *n, int *k, Real
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix, supplied in packed form.
*/
// int EIGEN_BLAS_FUNC(tpmv)(char *uplo, char *trans, char *diag, int *n, RealScalar *ap, RealScalar *x, int *incx)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(tpmv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)
{
typedef void (*functype)(int, const Scalar*, const Scalar*, Scalar*, Scalar);
static functype func[16];
static bool init = false;
if(!init)
{
for(int k=0; k<16; ++k)
func[k] = 0;
func[NOTR | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,ColMajor>::run);
func[TR | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,RowMajor>::run);
func[ADJ | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,Conj, Scalar,false,RowMajor>::run);
func[NOTR | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,ColMajor>::run);
func[TR | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,RowMajor>::run);
func[ADJ | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,Conj, Scalar,false,RowMajor>::run);
func[NOTR | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run);
func[TR | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run);
func[ADJ | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run);
func[NOTR | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run);
func[TR | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run);
func[ADJ | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run);
init = true;
}
Scalar* ap = reinterpret_cast<Scalar*>(pap);
Scalar* x = reinterpret_cast<Scalar*>(px);
int info = 0;
if(UPLO(*uplo)==INVALID) info = 1;
else if(OP(*opa)==INVALID) info = 2;
else if(DIAG(*diag)==INVALID) info = 3;
else if(*n<0) info = 4;
else if(*incx==0) info = 7;
if(info)
return xerbla_(SCALAR_SUFFIX_UP"TPMV ",&info,6);
if(*n==0)
return 1;
Scalar* actual_x = get_compact_vector(x,*n,*incx);
Matrix<Scalar,Dynamic,1> res(*n);
res.setZero();
int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
if(code>=16 || func[code]==0)
return 0;
func[code](*n, ap, actual_x, res.data(), Scalar(1));
copy_back(res.data(),x,*n,*incx);
if(actual_x!=x) delete[] actual_x;
return 1;
}
/** DTPSV solves one of the systems of equations
*
@ -414,8 +470,55 @@ int EIGEN_BLAS_FUNC(tbsv)(char *uplo, char *op, char *diag, int *n, int *k, Real
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*/
// int EIGEN_BLAS_FUNC(tpsv)(char *uplo, char *trans, char *diag, int *n, RealScalar *ap, RealScalar *x, int *incx)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(tpsv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)
{
typedef void (*functype)(int, const Scalar*, Scalar*);
static functype func[16];
static bool init = false;
if(!init)
{
for(int k=0; k<16; ++k)
func[k] = 0;
func[NOTR | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,ColMajor>::run);
func[TR | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,RowMajor>::run);
func[ADJ | (UP << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, Conj, RowMajor>::run);
func[NOTR | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,ColMajor>::run);
func[TR | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,RowMajor>::run);
func[ADJ | (LO << 2) | (NUNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, Conj, RowMajor>::run);
func[NOTR | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,ColMajor>::run);
func[TR | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,RowMajor>::run);
func[ADJ | (UP << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,Conj, RowMajor>::run);
func[NOTR | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,ColMajor>::run);
func[TR | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,RowMajor>::run);
func[ADJ | (LO << 2) | (UNIT << 3)] = (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,Conj, RowMajor>::run);
init = true;
}
Scalar* ap = reinterpret_cast<Scalar*>(pap);
Scalar* x = reinterpret_cast<Scalar*>(px);
int info = 0;
if(UPLO(*uplo)==INVALID) info = 1;
else if(OP(*opa)==INVALID) info = 2;
else if(DIAG(*diag)==INVALID) info = 3;
else if(*n<0) info = 4;
else if(*incx==0) info = 7;
if(info)
return xerbla_(SCALAR_SUFFIX_UP"TPSV ",&info,6);
Scalar* actual_x = get_compact_vector(x,*n,*incx);
int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
func[code](*n, ap, actual_x);
if(actual_x!=x) delete[] copy_back(actual_x,x,*n,*incx);
return 1;
}

123
blas/level2_real_impl.h
View File

@ -12,6 +12,21 @@
// y = alpha*A*x + beta*y
int EIGEN_BLAS_FUNC(symv) (char *uplo, int *n, RealScalar *palpha, RealScalar *pa, int *lda, RealScalar *px, int *incx, RealScalar *pbeta, RealScalar *py, int *incy)
{
typedef void (*functype)(int, const Scalar*, int, const Scalar*, int, Scalar*, Scalar);
static functype func[2];
static bool init = false;
if(!init)
{
for(int k=0; k<2; ++k)
func[k] = 0;
func[UP] = (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run);
func[LO] = (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run);
init = true;
}
Scalar* a = reinterpret_cast<Scalar*>(pa);
Scalar* x = reinterpret_cast<Scalar*>(px);
Scalar* y = reinterpret_cast<Scalar*>(py);
@ -40,9 +55,11 @@ int EIGEN_BLAS_FUNC(symv) (char *uplo, int *n, RealScalar *palpha, RealScalar *p
else vector(actual_y, *n) *= beta;
}
// TODO performs a direct call to the underlying implementation function
if(UPLO(*uplo)==UP) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Upper>() * (alpha * vector(actual_x,*n));
else if(UPLO(*uplo)==LO) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Lower>() * (alpha * vector(actual_x,*n));
int code = UPLO(*uplo);
if(code>=2 || func[code]==0)
return 0;
func[code](*n, a, *lda, actual_x, 1, actual_y, alpha);
if(actual_x!=x) delete[] actual_x;
if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);
@ -214,10 +231,49 @@ int EIGEN_BLAS_FUNC(syr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px
* 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.
*/
// int EIGEN_BLAS_FUNC(spr)(char *uplo, int *n, Scalar *alpha, Scalar *x, int *incx, Scalar *ap)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(spr)(char *uplo, int *n, Scalar *palpha, Scalar *px, int *incx, Scalar *pap)
{
typedef void (*functype)(int, Scalar*, const Scalar*, Scalar);
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,false>::run);
func[LO] = (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,false>::run);
init = true;
}
Scalar* x = reinterpret_cast<Scalar*>(px);
Scalar* ap = reinterpret_cast<Scalar*>(pap);
Scalar alpha = *reinterpret_cast<Scalar*>(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"SPR ",&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;
}
/** DSPR2 performs the symmetric rank 2 operation
*
@ -226,10 +282,53 @@ int EIGEN_BLAS_FUNC(syr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px
* where alpha is a scalar, x and y are n element vectors and A is an
* n by n symmetric matrix, supplied in packed form.
*/
// int EIGEN_BLAS_FUNC(spr2)(char *uplo, int *n, RealScalar *alpha, RealScalar *x, int *incx, RealScalar *y, int *incy, RealScalar *ap)
// {
// return 1;
// }
int EIGEN_BLAS_FUNC(spr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)
{
typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);
static functype func[2];
static bool init = false;
if(!init)
{
for(int k=0; k<2; ++k)
func[k] = 0;
func[UP] = (internal::packed_rank2_update_selector<Scalar,int,Upper>::run);
func[LO] = (internal::packed_rank2_update_selector<Scalar,int,Lower>::run);
init = true;
}
Scalar* x = reinterpret_cast<Scalar*>(px);
Scalar* y = reinterpret_cast<Scalar*>(py);
Scalar* ap = reinterpret_cast<Scalar*>(pap);
Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
int info = 0;
if(UPLO(*uplo)==INVALID) info = 1;
else if(*n<0) info = 2;
else if(*incx==0) info = 5;
else if(*incy==0) info = 7;
if(info)
return xerbla_(SCALAR_SUFFIX_UP"SPR2 ",&info,6);
if(alpha==Scalar(0))
return 1;
Scalar* x_cpy = get_compact_vector(x, *n, *incx);
Scalar* y_cpy = get_compact_vector(y, *n, *incy);
int code = UPLO(*uplo);
if(code>=2 || func[code]==0)
return 0;
func[code](*n, ap, x_cpy, y_cpy, alpha);
if(x_cpy!=x) delete[] x_cpy;
if(y_cpy!=y) delete[] y_cpy;
return 1;
}
/** DGER performs the rank 1 operation
*
@ -260,7 +359,7 @@ int EIGEN_BLAS_FUNC(ger)(int *m, int *n, Scalar *palpha, Scalar *px, int *incx,
Scalar* x_cpy = get_compact_vector(x,*m,*incx);
Scalar* y_cpy = get_compact_vector(y,*n,*incy);
internal::general_rank1_update<Scalar,int,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
if(x_cpy!=x) delete[] x_cpy;
if(y_cpy!=y) delete[] y_cpy;

202
blas/sspr.f
View File

@ -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

233
blas/sspr2.f
View File

@ -1,233 +0,0 @@
SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
* .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
REAL AP(*),X(*),Y(*)
* ..
*
* Purpose
* =======
*
* SSPR2 performs the symmetric rank 2 operation
*
* A := alpha*x*y' + alpha*y*x' + A,
*
* where alpha is a scalar, x and y are n element vectors 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.
*
* Y - REAL array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY 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 TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
* ..
* .. 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
ELSE IF (INCY.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('SSPR2 ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (N-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (N-1)*INCY
END IF
JX = KX
JY = KY
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) .AND. (INCY.EQ.1)) THEN
DO 20 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(J)
TEMP2 = ALPHA*X(J)
K = KK
DO 10 I = 1,J
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
10 CONTINUE
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(JY)
TEMP2 = ALPHA*X(JX)
IX = KX
IY = KY
DO 30 K = KK,KK + J - 1
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
DO 60 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(J)
TEMP2 = ALPHA*X(J)
K = KK
DO 50 I = J,N
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
50 CONTINUE
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*Y(JY)
TEMP2 = ALPHA*X(JX)
IX = JX
IY = JY
DO 70 K = KK,KK + N - J
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of SSPR2 .
*
END

293
blas/stpmv.f
View File

@ -1,293 +0,0 @@
SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
REAL AP(*),X(*)
* ..
*
* Purpose
* =======
*
* STPMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix, supplied in packed form.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' x := A*x.
*
* TRANS = 'T' or 't' x := A'*x.
*
* TRANS = 'C' or 'c' x := A'*x.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least 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 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* 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. On exit, X is overwritten with the
* tranformed vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOUNIT
* ..
* .. 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 (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('STPMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x:= A*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 10 I = 1,J - 1
X(I) = X(I) + TEMP*AP(K)
K = K + 1
10 CONTINUE
IF (NOUNIT) X(J) = X(J)*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 = X(JX)
IX = KX
DO 30 K = KK,KK + J - 2
X(IX) = X(IX) + TEMP*AP(K)
IX = IX + INCX
30 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 50 I = N,J + 1,-1
X(I) = X(I) + TEMP*AP(K)
K = K - 1
50 CONTINUE
IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
END IF
KK = KK - (N-J+1)
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 70 K = KK,KK - (N- (J+1)),-1
X(IX) = X(IX) + TEMP*AP(K)
IX = IX - INCX
70 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
END IF
JX = JX - INCX
KK = KK - (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A'*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 100 J = N,1,-1
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*AP(KK)
K = KK - 1
DO 90 I = J - 1,1,-1
TEMP = TEMP + AP(K)*X(I)
K = K - 1
90 CONTINUE
X(J) = TEMP
KK = KK - J
100 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 120 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 110 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + AP(K)*X(IX)
110 CONTINUE
X(JX) = TEMP
JX = JX - INCX
KK = KK - J
120 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 140 J = 1,N
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*AP(KK)
K = KK + 1
DO 130 I = J + 1,N
TEMP = TEMP + AP(K)*X(I)
K = K + 1
130 CONTINUE
X(J) = TEMP
KK = KK + (N-J+1)
140 CONTINUE
ELSE
JX = KX
DO 160 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 150 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + AP(K)*X(IX)
150 CONTINUE
X(JX) = TEMP
JX = JX + INCX
KK = KK + (N-J+1)
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of STPMV .
*
END

296
blas/stpsv.f
View File

@ -1,296 +0,0 @@
SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
REAL AP(*),X(*)
* ..
*
* Purpose
* =======
*
* STPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular matrix, supplied in packed form.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x = b.
*
* TRANS = 'C' or 'c' A'*x = b.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least 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 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* 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 right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOUNIT
* ..
* .. 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 (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('STPSV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK - 1
DO 10 I = J - 1,1,-1
X(I) = X(I) - TEMP*AP(K)
K = K - 1
10 CONTINUE
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 30 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
X(IX) = X(IX) - TEMP*AP(K)
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK + 1
DO 50 I = J + 1,N
X(I) = X(I) - TEMP*AP(K)
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
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
X(IX) = X(IX) - TEMP*AP(K)
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A' )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 100 J = 1,N
TEMP = X(J)
K = KK
DO 90 I = 1,J - 1
TEMP = TEMP - AP(K)*X(I)
K = K + 1
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(J) = TEMP
KK = KK + J
100 CONTINUE
ELSE
JX = KX
DO 120 J = 1,N
TEMP = X(JX)
IX = KX
DO 110 K = KK,KK + J - 2
TEMP = TEMP - AP(K)*X(IX)
IX = IX + INCX
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(JX) = TEMP
JX = JX + INCX
KK = KK + J
120 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 140 J = N,1,-1
TEMP = X(J)
K = KK
DO 130 I = N,J + 1,-1
TEMP = TEMP - AP(K)*X(I)
K = K - 1
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(J) = TEMP
KK = KK - (N-J+1)
140 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 160 J = N,1,-1
TEMP = X(JX)
IX = KX
DO 150 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - AP(K)*X(IX)
IX = IX - INCX
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(JX) = TEMP
JX = JX - INCX
KK = KK - (N-J+1)
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of STPSV .
*
END

220
blas/zhpr.f
View File

@ -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

255
blas/zhpr2.f
View File

@ -1,255 +0,0 @@
SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*),Y(*)
* ..
*
* Purpose
* =======
*
* ZHPR2 performs the hermitian rank 2 operation
*
* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
* where alpha is a scalar, x and y are n element vectors 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 - COMPLEX*16 .
* 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.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY 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 TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
* ..
* .. 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
ELSE IF (INCY.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZHPR2 ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (N-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (N-1)*INCY
END IF
JX = KX
JY = KY
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) .AND. (INCY.EQ.1)) THEN
DO 20 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(Y(J))
TEMP2 = DCONJG(ALPHA*X(J))
K = KK
DO 10 I = 1,J - 1
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
10 CONTINUE
AP(KK+J-1) = DBLE(AP(KK+J-1)) +
+ DBLE(X(J)*TEMP1+Y(J)*TEMP2)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(Y(JY))
TEMP2 = DCONJG(ALPHA*X(JX))
IX = KX
IY = KY
DO 30 K = KK,KK + J - 2
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
AP(KK+J-1) = DBLE(AP(KK+J-1)) +
+ DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
DO 60 J = 1,N
IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(Y(J))
TEMP2 = DCONJG(ALPHA*X(J))
AP(KK) = DBLE(AP(KK)) +
+ DBLE(X(J)*TEMP1+Y(J)*TEMP2)
K = KK + 1
DO 50 I = J + 1,N
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
50 CONTINUE
ELSE
AP(KK) = DBLE(AP(KK))
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*DCONJG(Y(JY))
TEMP2 = DCONJG(ALPHA*X(JX))
AP(KK) = DBLE(AP(KK)) +
+ DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
IX = JX
IY = JY
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
IY = IY + INCY
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
70 CONTINUE
ELSE
AP(KK) = DBLE(AP(KK))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHPR2 .
*
END

329
blas/ztpmv.f
View File

@ -1,329 +0,0 @@
SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*)
* ..
*
* Purpose
* =======
*
* ZTPMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix, supplied in packed form.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' x := A*x.
*
* TRANS = 'T' or 't' x := A'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least 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 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* 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. On exit, X is overwritten with the
* tranformed vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZTPMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOCONJ = LSAME(TRANS,'T')
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x:= A*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 10 I = 1,J - 1
X(I) = X(I) + TEMP*AP(K)
K = K + 1
10 CONTINUE
IF (NOUNIT) X(J) = X(J)*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 = X(JX)
IX = KX
DO 30 K = KK,KK + J - 2
X(IX) = X(IX) + TEMP*AP(K)
IX = IX + INCX
30 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
K = KK
DO 50 I = N,J + 1,-1
X(I) = X(I) + TEMP*AP(K)
K = K - 1
50 CONTINUE
IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
END IF
KK = KK - (N-J+1)
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 70 K = KK,KK - (N- (J+1)),-1
X(IX) = X(IX) + TEMP*AP(K)
IX = IX - INCX
70 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
END IF
JX = JX - INCX
KK = KK - (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A'*x or x := conjg( A' )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 110 J = N,1,-1
TEMP = X(J)
K = KK - 1
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 90 I = J - 1,1,-1
TEMP = TEMP + AP(K)*X(I)
K = K - 1
90 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
DO 100 I = J - 1,1,-1
TEMP = TEMP + DCONJG(AP(K))*X(I)
K = K - 1
100 CONTINUE
END IF
X(J) = TEMP
KK = KK - J
110 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 140 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 120 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + AP(K)*X(IX)
120 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
DO 130 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
TEMP = TEMP + DCONJG(AP(K))*X(IX)
130 CONTINUE
END IF
X(JX) = TEMP
JX = JX - INCX
KK = KK - J
140 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 170 J = 1,N
TEMP = X(J)
K = KK + 1
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 150 I = J + 1,N
TEMP = TEMP + AP(K)*X(I)
K = K + 1
150 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
DO 160 I = J + 1,N
TEMP = TEMP + DCONJG(AP(K))*X(I)
K = K + 1
160 CONTINUE
END IF
X(J) = TEMP
KK = KK + (N-J+1)
170 CONTINUE
ELSE
JX = KX
DO 200 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*AP(KK)
DO 180 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + AP(K)*X(IX)
180 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
DO 190 K = KK + 1,KK + N - J
IX = IX + INCX
TEMP = TEMP + DCONJG(AP(K))*X(IX)
190 CONTINUE
END IF
X(JX) = TEMP
JX = JX + INCX
KK = KK + (N-J+1)
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of ZTPMV .
*
END

332
blas/ztpsv.f
View File

@ -1,332 +0,0 @@
SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*)
* ..
*
* Purpose
* =======
*
* ZTPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular matrix, supplied in packed form.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least 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 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.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular 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.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* 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 right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* 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
LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZTPSV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOCONJ = LSAME(TRANS,'T')
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK - 1
DO 10 I = J - 1,1,-1
X(I) = X(I) - TEMP*AP(K)
K = K - 1
10 CONTINUE
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 30 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
X(IX) = X(IX) - TEMP*AP(K)
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK + 1
DO 50 I = J + 1,N
X(I) = X(I) - TEMP*AP(K)
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
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
X(IX) = X(IX) - TEMP*AP(K)
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 110 J = 1,N
TEMP = X(J)
K = KK
IF (NOCONJ) THEN
DO 90 I = 1,J - 1
TEMP = TEMP - AP(K)*X(I)
K = K + 1
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
ELSE
DO 100 I = 1,J - 1
TEMP = TEMP - DCONJG(AP(K))*X(I)
K = K + 1
100 CONTINUE
IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
END IF
X(J) = TEMP
KK = KK + J
110 CONTINUE
ELSE
JX = KX
DO 140 J = 1,N
TEMP = X(JX)
IX = KX
IF (NOCONJ) THEN
DO 120 K = KK,KK + J - 2
TEMP = TEMP - AP(K)*X(IX)
IX = IX + INCX
120 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
ELSE
DO 130 K = KK,KK + J - 2
TEMP = TEMP - DCONJG(AP(K))*X(IX)
IX = IX + INCX
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
END IF
X(JX) = TEMP
JX = JX + INCX
KK = KK + J
140 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 170 J = N,1,-1
TEMP = X(J)
K = KK
IF (NOCONJ) THEN
DO 150 I = N,J + 1,-1
TEMP = TEMP - AP(K)*X(I)
K = K - 1
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
ELSE
DO 160 I = N,J + 1,-1
TEMP = TEMP - DCONJG(AP(K))*X(I)
K = K - 1
160 CONTINUE
IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
END IF
X(J) = TEMP
KK = KK - (N-J+1)
170 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 200 J = N,1,-1
TEMP = X(JX)
IX = KX
IF (NOCONJ) THEN
DO 180 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - AP(K)*X(IX)
IX = IX - INCX
180 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
ELSE
DO 190 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - DCONJG(AP(K))*X(IX)
IX = IX - INCX
190 CONTINUE
IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
END IF
X(JX) = TEMP
JX = JX - INCX
KK = KK - (N-J+1)
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of ZTPSV .
*
END