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Fix rank-1 update for self-adjoint packed matrices.

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This commit is contained in:
Chen-Pang He 2012-09-10 18:25:30 +08:00
parent 65caa40a3d
commit 04f315d692
7 changed files with 53 additions and 863 deletions
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4
blas/CMakeLists.txt
View File

@ -19,8 +19,8 @@ set(EigenBlas_SRCS ${EigenBlas_SRCS}
complexdots.f
srotm.f srotmg.f drotm.f drotmg.f
lsame.f dspmv.f ssbmv.f
chbmv.f chpr.f sspmv.f
zhbmv.f zhpr.f chpmv.f dsbmv.f
chbmv.f sspmv.f
zhbmv.f chpmv.f dsbmv.f
zhpmv.f
dtbmv.f stbmv.f ctbmv.f ztbmv.f
)

19
blas/PackedSelfadjointProduct.h
View File

@ -14,12 +14,6 @@ namespace internal {
/* Optimized matrix += alpha * uv'
* The matrix is in packed form.
*
* FIXME I always fail tests for complex self-adjoint matrices.
*
* ******* FATAL ERROR - PARAMETER NUMBER 6 WAS CHANGED INCORRECTLY *******
* ******* xHPR FAILED ON CALL NUMBER:
* 2: xHPR ('U', 1, 0.0, X, 1, AP)
*/
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_packed_rank1_update;
@ -27,20 +21,20 @@ 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>
{
static void run(Index size, Scalar* mat, const Scalar* vec, Scalar alpha)
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;
Index offset = 0;
for (Index i=0; i<size; ++i)
{
Map<Matrix<Scalar,Dynamic,1> >(mat+offset, UpLo==Lower ? size-i : (i+1))
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[offset+(UpLo==Lower ? 0 : i)] = real(mat[offset+(UpLo==Lower ? 0 : i)]);
offset += UpLo==Lower ? size-i : (i+1);
mat[UpLo==Lower ? 0 : i] = real(mat[UpLo==Lower ? 0 : i]);
mat += UpLo==Lower ? size-i : (i+1);
}
}
};
@ -48,7 +42,8 @@ struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRh
template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
{
static void run(Index size, Scalar* mat, const Scalar* vec, Scalar alpha)
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);
}

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

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

47
blas/level2_cplx_impl.h
View File

@ -108,10 +108,49 @@ int EIGEN_BLAS_FUNC(hemv)(char *uplo, int *n, RealScalar *palpha, RealScalar *pa
* where alpha is a real scalar, x is an n element vector and A is an
* 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
*

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

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