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80
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*> \brief \b DISNAN tests input for NaN.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DISNAN + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/disnan.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/disnan.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/disnan.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* LOGICAL FUNCTION DISNAN( DIN )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DIN
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
*> otherwise. To be replaced by the Fortran 2003 intrinsic in the
*> future.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DIN
*> \verbatim
*> DIN is DOUBLE PRECISION
*> Input to test for NaN.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
LOGICAL FUNCTION DISNAN( DIN )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
DOUBLE PRECISION DIN
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL DLAISNAN
EXTERNAL DLAISNAN
* ..
* .. Executable Statements ..
DISNAN = DLAISNAN(DIN,DIN)
RETURN
END

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*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAISNAN + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaisnan.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaisnan.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaisnan.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DIN1, DIN2
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> This routine is not for general use. It exists solely to avoid
*> over-optimization in DISNAN.
*>
*> DLAISNAN checks for NaNs by comparing its two arguments for
*> inequality. NaN is the only floating-point value where NaN != NaN
*> returns .TRUE. To check for NaNs, pass the same variable as both
*> arguments.
*>
*> A compiler must assume that the two arguments are
*> not the same variable, and the test will not be optimized away.
*> Interprocedural or whole-program optimization may delete this
*> test. The ISNAN functions will be replaced by the correct
*> Fortran 03 intrinsic once the intrinsic is widely available.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DIN1
*> \verbatim
*> DIN1 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] DIN2
*> \verbatim
*> DIN2 is DOUBLE PRECISION
*> Two numbers to compare for inequality.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
DOUBLE PRECISION DIN1, DIN2
* ..
*
* =====================================================================
*
* .. Executable Statements ..
DLAISNAN = (DIN1.NE.DIN2)
RETURN
END

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*> \brief \b ZDOTC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDOTC forms the dot product of a vector.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level1
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
COMPLEX*16 ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
COMPLEX*16 ZTEMP
INTEGER I,IX,IY
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG
* ..
ZTEMP = (0.0d0,0.0d0)
ZDOTC = (0.0d0,0.0d0)
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
ZTEMP = ZTEMP + DCONJG(ZX(I))*ZY(I)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZTEMP = ZTEMP + DCONJG(ZX(IX))*ZY(IY)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
ZDOTC = ZTEMP
RETURN
END

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*> \brief \b ZDSCAL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZDSCAL(N,DA,ZX,INCX)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DA
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* COMPLEX*16 ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDSCAL scales a vector by a constant.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level1
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZDSCAL(N,DA,ZX,INCX)
*
* -- Reference BLAS level1 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
DOUBLE PRECISION DA
INTEGER INCX,N
* ..
* .. Array Arguments ..
COMPLEX*16 ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,NINCX
* ..
* .. Intrinsic Functions ..
INTRINSIC DCMPLX
* ..
IF (N.LE.0 .OR. INCX.LE.0) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
ZX(I) = DCMPLX(DA,0.0d0)*ZX(I)
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
ZX(I) = DCMPLX(DA,0.0d0)*ZX(I)
END DO
END IF
RETURN
END

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*> \brief \b ZHPR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER INCX,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* COMPLEX*16 AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHPR performs the hermitian rank 1 operation
*>
*> A := alpha*x*x**H + 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* -- Reference BLAS level2 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
COMPLEX*16 AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
COMPLEX*16 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

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*> \brief \b ZPPTRF
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZPPTRF + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptrf.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptrf.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptrf.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* COMPLEX*16 AP( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZPPTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A stored in packed format.
*>
*> The factorization has the form
*> A = U**H * U, if UPLO = 'U', or
*> A = L * L**H, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*> On entry, the upper or lower triangle of the Hermitian matrix
*> A, packed columnwise in a linear array. The j-th column of A
*> is stored in the array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*> See below for further details.
*>
*> On exit, if INFO = 0, the triangular factor U or L from the
*> Cholesky factorization A = U**H*U or A = L*L**H, in the same
*> storage format as A.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the leading minor of order i is not
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16OTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> when N = 4, UPLO = 'U':
*>
*> Two-dimensional storage of the Hermitian matrix A:
*>
*> a11 a12 a13 a14
*> a22 a23 a24
*> a33 a34 (aij = conjg(aji))
*> a44
*>
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
COMPLEX*16 AP( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JC, JJ
DOUBLE PRECISION AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
COMPLEX*16 ZDOTC
EXTERNAL LSAME, ZDOTC
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPSV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPPTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U**H * U.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
*
* Compute elements 1:J-1 of column J.
*
IF( J.GT.1 )
$ CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit',
$ J-1, AP, AP( JC ), 1 )
*
* Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = DBLE( AP( JJ ) ) - ZDOTC( J-1, AP( JC ), 1, AP( JC ),
$ 1 )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AP( JJ ) = SQRT( AJJ )
10 CONTINUE
ELSE
*
* Compute the Cholesky factorization A = L * L**H.
*
JJ = 1
DO 20 J = 1, N
*
* Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = DBLE( AP( JJ ) )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
AP( JJ ) = AJJ
*
* Compute elements J+1:N of column J and update the trailing
* submatrix.
*
IF( J.LT.N ) THEN
CALL ZDSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
CALL ZHPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
$ AP( JJ+N-J+1 ) )
JJ = JJ + N - J + 1
END IF
20 CONTINUE
END IF
GO TO 40
*
30 CONTINUE
INFO = J
*
40 CONTINUE
RETURN
*
* End of ZPPTRF
*
END

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*> \brief \b ZPPTRI
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZPPTRI + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptri.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptri.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptri.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* COMPLEX*16 AP( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZPPTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by ZPPTRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangular factor is stored in AP;
*> = 'L': Lower triangular factor is stored in AP.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*> On entry, the triangular factor U or L from the Cholesky
*> factorization A = U**H*U or A = L*L**H, packed columnwise as
*> a linear array. The j-th column of U or L is stored in the
*> array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
*>
*> On exit, the upper or lower triangle of the (Hermitian)
*> inverse of A, overwriting the input factor U or L.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16OTHERcomputational
*
* =====================================================================
SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
COMPLEX*16 AP( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JC, JJ, JJN
DOUBLE PRECISION AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
COMPLEX*16 ZDOTC
EXTERNAL LSAME, ZDOTC
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPMV, ZTPTRI
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPPTRI', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Invert the triangular Cholesky factor U or L.
*
CALL ZTPTRI( UPLO, 'Non-unit', N, AP, INFO )
IF( INFO.GT.0 )
$ RETURN
IF( UPPER ) THEN
*
* Compute the product inv(U) * inv(U)**H.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
IF( J.GT.1 )
$ CALL ZHPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
AJJ = AP( JJ )
CALL ZDSCAL( J, AJJ, AP( JC ), 1 )
10 CONTINUE
*
ELSE
*
* Compute the product inv(L)**H * inv(L).
*
JJ = 1
DO 20 J = 1, N
JJN = JJ + N - J + 1
AP( JJ ) = DBLE( ZDOTC( N-J+1, AP( JJ ), 1, AP( JJ ), 1 ) )
IF( J.LT.N )
$ CALL ZTPMV( 'Lower', 'Conjugate transpose', 'Non-unit',
$ N-J, AP( JJN ), AP( JJ+1 ), 1 )
JJ = JJN
20 CONTINUE
END IF
*
RETURN
*
* End of ZPPTRI
*
END

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*> \brief \b ZSCAL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSCAL(N,ZA,ZX,INCX)
*
* .. Scalar Arguments ..
* COMPLEX*16 ZA
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* COMPLEX*16 ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSCAL scales a vector by a constant.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level1
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSCAL(N,ZA,ZX,INCX)
*
* -- Reference BLAS level1 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
COMPLEX*16 ZA
INTEGER INCX,N
* ..
* .. Array Arguments ..
COMPLEX*16 ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,NINCX
* ..
IF (N.LE.0 .OR. INCX.LE.0) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
ZX(I) = ZA*ZX(I)
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
ZX(I) = ZA*ZX(I)
END DO
END IF
RETURN
END

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*> \brief \b ZTPMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* COMPLEX*16 AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x, or x := A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x.
*>
*> TRANS = 'C' or 'c' x := A**H*x.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is 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.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is (input/output) 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* -- Reference BLAS level2 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX*16 AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
COMPLEX*16 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**T*x or x := A**H*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

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*> \brief \b ZTPSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* COMPLEX*16 AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPSV solves one of the systems of equations
*>
*> A*x = b, or A**T*x = b, or A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x = b.
*>
*> TRANS = 'C' or 'c' A**H*x = b.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is 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.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* -- Reference BLAS level2 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX*16 AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
COMPLEX*16 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**T )*x or x := inv( A**H )*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

242
lib/linalg/ztptri.f Normal file
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@ -0,0 +1,242 @@
*> \brief \b ZTPTRI
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZTPTRI + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztptri.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztptri.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztptri.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* COMPLEX*16 AP( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPTRI computes the inverse of a complex upper or lower triangular
*> matrix A stored in packed format.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': A is upper triangular;
*> = 'L': A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> = 'N': A is non-unit triangular;
*> = 'U': A is unit triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*> On entry, the upper or lower triangular matrix A, stored
*> columnwise in a linear array. The j-th column of A is stored
*> in the array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
*> See below for further details.
*> On exit, the (triangular) inverse of the original matrix, in
*> the same packed storage format.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16OTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> A triangular matrix A can be transferred to packed storage using one
*> of the following program segments:
*>
*> UPLO = 'U': UPLO = 'L':
*>
*> JC = 1 JC = 1
*> DO 2 J = 1, N DO 2 J = 1, N
*> DO 1 I = 1, J DO 1 I = J, N
*> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
*> 1 CONTINUE 1 CONTINUE
*> JC = JC + J JC = JC + N - J + 1
*> 2 CONTINUE 2 CONTINUE
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
COMPLEX*16 AP( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE, ZERO
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J, JC, JCLAST, JJ
COMPLEX*16 AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZSCAL, ZTPMV
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTPTRI', -INFO )
RETURN
END IF
*
* Check for singularity if non-unit.
*
IF( NOUNIT ) THEN
IF( UPPER ) THEN
JJ = 0
DO 10 INFO = 1, N
JJ = JJ + INFO
IF( AP( JJ ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
JJ = 1
DO 20 INFO = 1, N
IF( AP( JJ ).EQ.ZERO )
$ RETURN
JJ = JJ + N - INFO + 1
20 CONTINUE
END IF
INFO = 0
END IF
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix.
*
JC = 1
DO 30 J = 1, N
IF( NOUNIT ) THEN
AP( JC+J-1 ) = ONE / AP( JC+J-1 )
AJJ = -AP( JC+J-1 )
ELSE
AJJ = -ONE
END IF
*
* Compute elements 1:j-1 of j-th column.
*
CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
$ AP( JC ), 1 )
CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
JC = JC + J
30 CONTINUE
*
ELSE
*
* Compute inverse of lower triangular matrix.
*
JC = N*( N+1 ) / 2
DO 40 J = N, 1, -1
IF( NOUNIT ) THEN
AP( JC ) = ONE / AP( JC )
AJJ = -AP( JC )
ELSE
AJJ = -ONE
END IF
IF( J.LT.N ) THEN
*
* Compute elements j+1:n of j-th column.
*
CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
$ AP( JCLAST ), AP( JC+1 ), 1 )
CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
END IF
JCLAST = JC
JC = JC - N + J - 2
40 CONTINUE
END IF
*
RETURN
*
* End of ZTPTRI
*
END