*> \brief \b DCOPY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCOPY copies a vector, x, to a vector, y.
*> uses unrolled loops for increments equal to 1.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] DX
*> \verbatim
*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of DX
*> \endverbatim
*>
*> \param[out] DY
*> \verbatim
*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of DY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup copy
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE PRECISION DX(*),DY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,IX,IY,M,MP1
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* ..
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
*
* clean-up loop
*
M = MOD(N,7)
IF (M.NE.0) THEN
DO I = 1,M
DY(I) = DX(I)
END DO
IF (N.LT.7) RETURN
END IF
MP1 = M + 1
DO I = MP1,N,7
DY(I) = DX(I)
DY(I+1) = DX(I+1)
DY(I+2) = DX(I+2)
DY(I+3) = DX(I+3)
DY(I+4) = DX(I+4)
DY(I+5) = DX(I+5)
DY(I+6) = DX(I+6)
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
DY(IY) = DX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
*
* End of DCOPY
*
END
*> \brief \b DGEMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA,BETA
* INTEGER INCX,INCY,LDA,M,N
* CHARACTER TRANS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGEMV performs one of the matrix-vector operations
*>
*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
*>
*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
*>
*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns 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] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension ( LDA, N )
*> Before entry, the leading m by n part of the array A must
*> contain the matrix of coefficients.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*> and at least
*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*> Before entry, the incremented array X must contain the
*> 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] BETA
*> \verbatim
*> BETA is DOUBLE PRECISION.
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE PRECISION array, dimension at least
*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*> and at least
*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*> Before entry with BETA non-zero, the incremented array Y
*> must contain the vector y. On exit, Y is overwritten by the
*> updated vector y.
*> If either m or n is zero, then Y not referenced and the function
*> performs a quick return.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gemv
*
*> \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 DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER TRANS
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 1
ELSE IF (M.LT.0) THEN
INFO = 2
ELSE IF (N.LT.0) THEN
INFO = 3
ELSE IF (LDA.LT.MAX(1,M)) THEN
INFO = 6
ELSE IF (INCX.EQ.0) THEN
INFO = 8
ELSE IF (INCY.EQ.0) THEN
INFO = 11
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DGEMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
+ ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
*
* Set LENX and LENY, the lengths of the vectors x and y, and set
* up the start points in X and Y.
*
IF (LSAME(TRANS,'N')) THEN
LENX = N
LENY = M
ELSE
LENX = M
LENY = N
END IF
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (LENX-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (LENY-1)*INCY
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through A.
*
* First form y := beta*y.
*
IF (BETA.NE.ONE) THEN
IF (INCY.EQ.1) THEN
IF (BETA.EQ.ZERO) THEN
DO 10 I = 1,LENY
Y(I) = ZERO
10 CONTINUE
ELSE
DO 20 I = 1,LENY
Y(I) = BETA*Y(I)
20 CONTINUE
END IF
ELSE
IY = KY
IF (BETA.EQ.ZERO) THEN
DO 30 I = 1,LENY
Y(IY) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40 I = 1,LENY
Y(IY) = BETA*Y(IY)
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF (ALPHA.EQ.ZERO) RETURN
IF (LSAME(TRANS,'N')) THEN
*
* Form y := alpha*A*x + y.
*
JX = KX
IF (INCY.EQ.1) THEN
DO 60 J = 1,N
TEMP = ALPHA*X(JX)
DO 50 I = 1,M
Y(I) = Y(I) + TEMP*A(I,J)
50 CONTINUE
JX = JX + INCX
60 CONTINUE
ELSE
DO 80 J = 1,N
TEMP = ALPHA*X(JX)
IY = KY
DO 70 I = 1,M
Y(IY) = Y(IY) + TEMP*A(I,J)
IY = IY + INCY
70 CONTINUE
JX = JX + INCX
80 CONTINUE
END IF
ELSE
*
* Form y := alpha*A**T*x + y.
*
JY = KY
IF (INCX.EQ.1) THEN
DO 100 J = 1,N
TEMP = ZERO
DO 90 I = 1,M
TEMP = TEMP + A(I,J)*X(I)
90 CONTINUE
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
100 CONTINUE
ELSE
DO 120 J = 1,N
TEMP = ZERO
IX = KX
DO 110 I = 1,M
TEMP = TEMP + A(I,J)*X(IX)
IX = IX + INCX
110 CONTINUE
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
120 CONTINUE
END IF
END IF
*
RETURN
*
* End of DGEMV
*
END
*> \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAEDA + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
* .. Scalar Arguments ..
* INTEGER CURLVL, CURPBM, INFO, N, TLVLS
* ..
* .. Array Arguments ..
* INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ),
* $ PRMPTR( * ), QPTR( * )
* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAEDA computes the Z vector corresponding to the merge step in the
*> CURLVLth step of the merge process with TLVLS steps for the CURPBMth
*> problem.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The dimension of the symmetric tridiagonal matrix. N >= 0.
*> \endverbatim
*>
*> \param[in] TLVLS
*> \verbatim
*> TLVLS is INTEGER
*> The total number of merging levels in the overall divide and
*> conquer tree.
*> \endverbatim
*>
*> \param[in] CURLVL
*> \verbatim
*> CURLVL is INTEGER
*> The current level in the overall merge routine,
*> 0 <= curlvl <= tlvls.
*> \endverbatim
*>
*> \param[in] CURPBM
*> \verbatim
*> CURPBM is INTEGER
*> The current problem in the current level in the overall
*> merge routine (counting from upper left to lower right).
*> \endverbatim
*>
*> \param[in] PRMPTR
*> \verbatim
*> PRMPTR is INTEGER array, dimension (N lg N)
*> Contains a list of pointers which indicate where in PERM a
*> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
*> indicates the size of the permutation and incidentally the
*> size of the full, non-deflated problem.
*> \endverbatim
*>
*> \param[in] PERM
*> \verbatim
*> PERM is INTEGER array, dimension (N lg N)
*> Contains the permutations (from deflation and sorting) to be
*> applied to each eigenblock.
*> \endverbatim
*>
*> \param[in] GIVPTR
*> \verbatim
*> GIVPTR is INTEGER array, dimension (N lg N)
*> Contains a list of pointers which indicate where in GIVCOL a
*> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
*> indicates the number of Givens rotations.
*> \endverbatim
*>
*> \param[in] GIVCOL
*> \verbatim
*> GIVCOL is INTEGER array, dimension (2, N lg N)
*> Each pair of numbers indicates a pair of columns to take place
*> in a Givens rotation.
*> \endverbatim
*>
*> \param[in] GIVNUM
*> \verbatim
*> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N)
*> Each number indicates the S value to be used in the
*> corresponding Givens rotation.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*> Q is DOUBLE PRECISION array, dimension (N**2)
*> Contains the square eigenblocks from previous levels, the
*> starting positions for blocks are given by QPTR.
*> \endverbatim
*>
*> \param[in] QPTR
*> \verbatim
*> QPTR is INTEGER array, dimension (N+2)
*> Contains a list of pointers which indicate where in Q an
*> eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates
*> the size of the block.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension (N)
*> On output this vector contains the updating vector (the last
*> row of the first sub-eigenvector matrix and the first row of
*> the second sub-eigenvector matrix).
*> \endverbatim
*>
*> \param[out] ZTEMP
*> \verbatim
*> ZTEMP is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup laeda
*
*> \par Contributors:
* ==================
*>
*> Jeff Rutter, Computer Science Division, University of California
*> at Berkeley, USA
*
* =====================================================================
SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM,
$ GIVPTR,
$ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER CURLVL, CURPBM, INFO, N, TLVLS
* ..
* .. Array Arguments ..
INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ),
$ PRMPTR( * ), QPTR( * )
DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2,
$ PTR, ZPTR1
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMV, DROT, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, INT, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
*
IF( N.LT.0 ) THEN
INFO = -1
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLAEDA', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine location of first number in second half.
*
MID = N / 2 + 1
*
* Gather last/first rows of appropriate eigenblocks into center of Z
*
PTR = 1
*
* Determine location of lowest level subproblem in the full storage
* scheme
*
CURR = PTR + CURPBM*2**CURLVL + 2**( CURLVL-1 ) - 1
*
* Determine size of these matrices. We add HALF to the value of
* the SQRT in case the machine underestimates one of these square
* roots.
*
BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) )
BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+1 ) ) ) )
DO 10 K = 1, MID - BSIZ1 - 1
Z( K ) = ZERO
10 CONTINUE
CALL DCOPY( BSIZ1, Q( QPTR( CURR )+BSIZ1-1 ), BSIZ1,
$ Z( MID-BSIZ1 ), 1 )
CALL DCOPY( BSIZ2, Q( QPTR( CURR+1 ) ), BSIZ2, Z( MID ), 1 )
DO 20 K = MID + BSIZ2, N
Z( K ) = ZERO
20 CONTINUE
*
* Loop through remaining levels 1 -> CURLVL applying the Givens
* rotations and permutation and then multiplying the center matrices
* against the current Z.
*
PTR = 2**TLVLS + 1
DO 70 K = 1, CURLVL - 1
CURR = PTR + CURPBM*2**( CURLVL-K ) + 2**( CURLVL-K-1 ) - 1
PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR )
PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 )
ZPTR1 = MID - PSIZ1
*
* Apply Givens at CURR and CURR+1
*
DO 30 I = GIVPTR( CURR ), GIVPTR( CURR+1 ) - 1
CALL DROT( 1, Z( ZPTR1+GIVCOL( 1, I )-1 ), 1,
$ Z( ZPTR1+GIVCOL( 2, I )-1 ), 1, GIVNUM( 1, I ),
$ GIVNUM( 2, I ) )
30 CONTINUE
DO 40 I = GIVPTR( CURR+1 ), GIVPTR( CURR+2 ) - 1
CALL DROT( 1, Z( MID-1+GIVCOL( 1, I ) ), 1,
$ Z( MID-1+GIVCOL( 2, I ) ), 1, GIVNUM( 1, I ),
$ GIVNUM( 2, I ) )
40 CONTINUE
PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR )
PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 )
DO 50 I = 0, PSIZ1 - 1
ZTEMP( I+1 ) = Z( ZPTR1+PERM( PRMPTR( CURR )+I )-1 )
50 CONTINUE
DO 60 I = 0, PSIZ2 - 1
ZTEMP( PSIZ1+I+1 ) = Z( MID+PERM( PRMPTR( CURR+1 )+I )-1 )
60 CONTINUE
*
* Multiply Blocks at CURR and CURR+1
*
* Determine size of these matrices. We add HALF to the value of
* the SQRT in case the machine underestimates one of these
* square roots.
*
BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) )
BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+
$ 1 ) ) ) )
IF( BSIZ1.GT.0 ) THEN
CALL DGEMV( 'T', BSIZ1, BSIZ1, ONE, Q( QPTR( CURR ) ),
$ BSIZ1, ZTEMP( 1 ), 1, ZERO, Z( ZPTR1 ), 1 )
END IF
CALL DCOPY( PSIZ1-BSIZ1, ZTEMP( BSIZ1+1 ), 1,
$ Z( ZPTR1+BSIZ1 ),
$ 1 )
IF( BSIZ2.GT.0 ) THEN
CALL DGEMV( 'T', BSIZ2, BSIZ2, ONE, Q( QPTR( CURR+1 ) ),
$ BSIZ2, ZTEMP( PSIZ1+1 ), 1, ZERO, Z( MID ), 1 )
END IF
CALL DCOPY( PSIZ2-BSIZ2, ZTEMP( PSIZ1+BSIZ2+1 ), 1,
$ Z( MID+BSIZ2 ), 1 )
*
PTR = PTR + 2**( TLVLS-K )
70 CONTINUE
*
RETURN
*
* End of DLAEDA
*
END
*> \brief \b DROT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION C,S
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DROT applies a plane rotation.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in,out] DX
*> \verbatim
*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of DX
*> \endverbatim
*>
*> \param[in,out] DY
*> \verbatim
*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of DY
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is DOUBLE PRECISION
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup rot
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION C,S
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE PRECISION DX(*),DY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE PRECISION DTEMP
INTEGER I,IX,IY
* ..
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
DTEMP = C*DX(I) + S*DY(I)
DY(I) = C*DY(I) - S*DX(I)
DX(I) = DTEMP
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
DTEMP = C*DX(IX) + S*DY(IY)
DY(IY) = C*DY(IY) - S*DX(IX)
DX(IX) = DTEMP
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
*
* End of DROT
*
END
*> \brief \b LSAME
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* LOGICAL FUNCTION LSAME(CA,CB)
*
* .. Scalar Arguments ..
* CHARACTER CA,CB
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
*> case.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] CA
*> \verbatim
*> CA is CHARACTER*1
*> \endverbatim
*>
*> \param[in] CB
*> \verbatim
*> CB is CHARACTER*1
*> CA and CB specify the single characters to be compared.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup lsame
*
* =====================================================================
LOGICAL FUNCTION LSAME(CA,CB)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER CA,CB
* ..
*
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC ICHAR
* ..
* .. Local Scalars ..
INTEGER INTA,INTB,ZCODE
* ..
*
* Test if the characters are equal
*
LSAME = CA .EQ. CB
IF (LSAME) RETURN
*
* Now test for equivalence if both characters are alphabetic.
*
ZCODE = ICHAR('Z')
*
* Use 'Z' rather than 'A' so that ASCII can be detected on Prime
* machines, on which ICHAR returns a value with bit 8 set.
* ICHAR('A') on Prime machines returns 193 which is the same as
* ICHAR('A') on an EBCDIC machine.
*
INTA = ICHAR(CA)
INTB = ICHAR(CB)
*
IF (ZCODE.EQ.90 .OR. ZCODE.EQ.122) THEN
*
* ASCII is assumed - ZCODE is the ASCII code of either lower or
* upper case 'Z'.
*
IF (INTA.GE.97 .AND. INTA.LE.122) INTA = INTA - 32
IF (INTB.GE.97 .AND. INTB.LE.122) INTB = INTB - 32
*
ELSE IF (ZCODE.EQ.233 .OR. ZCODE.EQ.169) THEN
*
* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
* upper case 'Z'.
*
IF (INTA.GE.129 .AND. INTA.LE.137 .OR.
+ INTA.GE.145 .AND. INTA.LE.153 .OR.
+ INTA.GE.162 .AND. INTA.LE.169) INTA = INTA + 64
IF (INTB.GE.129 .AND. INTB.LE.137 .OR.
+ INTB.GE.145 .AND. INTB.LE.153 .OR.
+ INTB.GE.162 .AND. INTB.LE.169) INTB = INTB + 64
*
ELSE IF (ZCODE.EQ.218 .OR. ZCODE.EQ.250) THEN
*
* ASCII is assumed, on Prime machines - ZCODE is the ASCII code
* plus 128 of either lower or upper case 'Z'.
*
IF (INTA.GE.225 .AND. INTA.LE.250) INTA = INTA - 32
IF (INTB.GE.225 .AND. INTB.LE.250) INTB = INTB - 32
END IF
LSAME = INTA .EQ. INTB
*
* RETURN
*
* End of LSAME
*
END
*> \brief \b XERBLA
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* .. Scalar Arguments ..
* CHARACTER*(*) SRNAME
* INTEGER INFO
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> XERBLA is an error handler for the LAPACK routines.
*> It is called by an LAPACK routine if an input parameter has an
*> invalid value. A message is printed and execution stops.
*>
*> Installers may consider modifying the STOP statement in order to
*> call system-specific exception-handling facilities.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> SRNAME is CHARACTER*(*)
*> The name of the routine which called XERBLA.
*> \endverbatim
*>
*> \param[in] INFO
*> \verbatim
*> INFO is INTEGER
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup xerbla
*
* =====================================================================
SUBROUTINE XERBLA( SRNAME, INFO )
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER*(*) SRNAME
INTEGER INFO
* ..
*
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC LEN_TRIM
* ..
* .. Executable Statements ..
*
WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO
*
STOP
*
9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ',
$ 'an illegal value' )
*
* End of XERBLA
*
END