*> \brief \b CAXPY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY)
*
* .. Scalar Arguments ..
* COMPLEX CA
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* COMPLEX CX(*),CY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CAXPY constant times a vector plus a vector.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] CA
*> \verbatim
*> CA is COMPLEX
*> On entry, CA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] CX
*> \verbatim
*> CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of CX
*> \endverbatim
*>
*> \param[in,out] CY
*> \verbatim
*> CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of CY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup axpy
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CAXPY(N,CA,CX,INCX,CY,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 ..
COMPLEX CA
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
COMPLEX CX(*),CY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,IX,IY
* ..
* .. External Functions ..
REAL SCABS1
EXTERNAL SCABS1
* ..
IF (N.LE.0) RETURN
IF (SCABS1(CA).EQ.0.0E+0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
CY(I) = CY(I) + CA*CX(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
CY(IY) = CY(IY) + CA*CX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
*
RETURN
*
* End of CAXPY
*
END
*> \brief \b CGEMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,LDA,M,N
* CHARACTER TRANS
* ..
* .. Array Arguments ..
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGEMV performs one of the matrix-vector operations
*>
*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
*>
*> y := alpha*A**H*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**H*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 COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX 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 COMPLEX 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 COMPLEX
*> 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 COMPLEX 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 CGEMV(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 ..
COMPLEX ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER TRANS
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE
PARAMETER (ONE= (1.0E+0,0.0E+0))
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
LOGICAL NOCONJ
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,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('CGEMV ',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
*
NOCONJ = LSAME(TRANS,'T')
*
* 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 or y := alpha*A**H*x + y.
*
JY = KY
IF (INCX.EQ.1) THEN
DO 110 J = 1,N
TEMP = ZERO
IF (NOCONJ) THEN
DO 90 I = 1,M
TEMP = TEMP + A(I,J)*X(I)
90 CONTINUE
ELSE
DO 100 I = 1,M
TEMP = TEMP + CONJG(A(I,J))*X(I)
100 CONTINUE
END IF
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
110 CONTINUE
ELSE
DO 140 J = 1,N
TEMP = ZERO
IX = KX
IF (NOCONJ) THEN
DO 120 I = 1,M
TEMP = TEMP + A(I,J)*X(IX)
IX = IX + INCX
120 CONTINUE
ELSE
DO 130 I = 1,M
TEMP = TEMP + CONJG(A(I,J))*X(IX)
IX = IX + INCX
130 CONTINUE
END IF
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
140 CONTINUE
END IF
END IF
*
RETURN
*
* End of CGEMV
*
END
*> \brief \b CGERC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* .. Scalar Arguments ..
* COMPLEX ALPHA
* INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGERC performs the rank 1 operation
*>
*> A := alpha*x*y**H + A,
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \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 COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is COMPLEX array, dimension at least
*> ( 1 + ( m - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the m
*> 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] Y
*> \verbatim
*> Y is COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y.
*> \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
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension ( LDA, N )
*> Before entry, the leading m by n part of the array A must
*> contain the matrix of coefficients. On exit, A is
*> overwritten by the updated matrix.
*> \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
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ger
*
*> \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 CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* -- 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 ..
COMPLEX ALPHA
INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,IX,J,JY,KX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,MAX
* ..
*
* Test the input parameters.
*
INFO = 0
IF (M.LT.0) THEN
INFO = 1
ELSE IF (N.LT.0) THEN
INFO = 2
ELSE IF (INCX.EQ.0) THEN
INFO = 5
ELSE IF (INCY.EQ.0) THEN
INFO = 7
ELSE IF (LDA.LT.MAX(1,M)) THEN
INFO = 9
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CGERC ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through A.
*
IF (INCY.GT.0) THEN
JY = 1
ELSE
JY = 1 - (N-1)*INCY
END IF
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (Y(JY).NE.ZERO) THEN
TEMP = ALPHA*CONJG(Y(JY))
DO 10 I = 1,M
A(I,J) = A(I,J) + X(I)*TEMP
10 CONTINUE
END IF
JY = JY + INCY
20 CONTINUE
ELSE
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (M-1)*INCX
END IF
DO 40 J = 1,N
IF (Y(JY).NE.ZERO) THEN
TEMP = ALPHA*CONJG(Y(JY))
IX = KX
DO 30 I = 1,M
A(I,J) = A(I,J) + X(IX)*TEMP
IX = IX + INCX
30 CONTINUE
END IF
JY = JY + INCY
40 CONTINUE
END IF
*
RETURN
*
* End of CGERC
*
END
*> \brief \b CLARF1F applies an elementary reflector to a general rectangular
* matrix assuming v(1) = 1.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLARF1F + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLARF1F( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* .. Scalar Arguments ..
* CHARACTER SIDE
* INTEGER INCV, LDC, M, N
* COMPLEX TAU
* ..
* .. Array Arguments ..
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLARF1F applies a complex elementary reflector H to a complex m by n matrix
*> C, from either the left or the right. H is represented in the form
*>
*> H = I - tau * v * v**H
*>
*> where tau is a complex scalar and v is a complex vector assuming v(1) = 1.
*>
*> If tau = 0, then H is taken to be the unit matrix.
*>
*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
*> tau.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': form H * C
*> = 'R': form C * H
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is COMPLEX array, dimension
*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
*> The vector v in the representation of H. V is not used if
*> TAU = 0.
*> \endverbatim
*>
*> \param[in] INCV
*> \verbatim
*> INCV is INTEGER
*> The increment between elements of v. INCV <> 0.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX
*> The value tau in the representation of H.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX array, dimension (LDC,N)
*> On entry, the m by n matrix C.
*> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
*> or C * H if SIDE = 'R'.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup larf1f
*
* =====================================================================
SUBROUTINE CLARF1F( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, LDC, M, N
COMPLEX TAU
* ..
* .. Array Arguments ..
COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL APPLYLEFT
INTEGER I, LASTV, LASTC
* ..
* .. External Subroutines ..
EXTERNAL CGEMV, CGER, CSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILACLR, ILACLC
EXTERNAL LSAME, ILACLR, ILACLC
* ..
* .. Executable Statements ..
*
APPLYLEFT = LSAME( SIDE, 'L' )
LASTV = 1
LASTC = 0
IF( TAU.NE.ZERO ) THEN
! Set up variables for scanning V. LASTV begins pointing to the end
! of V up to V(1).
IF( APPLYLEFT ) THEN
LASTV = M
ELSE
LASTV = N
END IF
IF( INCV.GT.0 ) THEN
I = 1 + (LASTV-1) * INCV
ELSE
I = 1
END IF
! Look for the last non-zero row in V.
DO WHILE( LASTV.GT.1 .AND. V( I ).EQ.ZERO )
LASTV = LASTV - 1
I = I - INCV
END DO
IF( APPLYLEFT ) THEN
! Scan for the last non-zero column in C(1:lastv,:).
LASTC = ILACLC(LASTV, N, C, LDC)
ELSE
! Scan for the last non-zero row in C(:,1:lastv).
LASTC = ILACLR(M, LASTV, C, LDC)
END IF
END IF
IF( LASTC.EQ.0 ) THEN
RETURN
END IF
IF( APPLYLEFT ) THEN
*
* Form H * C
*
IF( LASTV.EQ.1 ) THEN
*
* C(1,1:lastc) := ( 1 - tau ) * C(1,1:lastc)
*
CALL CSCAL( LASTC, ONE - TAU, C, LDC )
ELSE
*
* w(1:lastc,1) := C(2:lastv,1:lastc)**H * v(2:lastv,1)
*
CALL CGEMV( 'Conjugate transpose', LASTV - 1, LASTC, ONE,
$ C( 2, 1 ), LDC, V( 1 + INCV ), INCV, ZERO,
$ WORK, 1 )
*
* w(1:lastc,1) += v(1,1) * C(1,1:lastc)**H
*
DO I = 1, LASTC
WORK( I ) = WORK( I ) + CONJG( C( 1, I ) )
END DO
*
* C(1, 1:lastc) += - tau * v(1,1) * w(1:lastc,1)**H
*
DO I = 1, LASTC
C( 1, I ) = C( 1, I ) - TAU * CONJG( WORK( I ) )
END DO
*
* C(2:lastv,1:lastc) += - tau * v(2:lastv,1) * w(1:lastc,1)**H
*
CALL CGERC( LASTV - 1, LASTC, -TAU, V( 1 + INCV ), INCV,
$ WORK, 1, C( 2, 1 ), LDC )
END IF
ELSE
*
* Form C * H
*
IF( LASTV.EQ.1 ) THEN
*
* C(1:lastc,1) := ( 1 - tau ) * C(1:lastc,1)
*
CALL CSCAL( LASTC, ONE - TAU, C, 1 )
ELSE
*
* w(1:lastc,1) := C(1:lastc,2:lastv) * v(2:lastv,1)
*
CALL CGEMV( 'No transpose', LASTC, LASTV - 1, ONE,
$ C( 1, 2 ), LDC, V( 1 + INCV ), INCV, ZERO,
$ WORK, 1 )
*
* w(1:lastc,1) += v(1,1) * C(1:lastc,1)
*
CALL CAXPY( LASTC, ONE, C, 1, WORK, 1 )
*
* C(1:lastc,1) += - tau * v(1,1) * w(1:lastc,1)
*
CALL CAXPY( LASTC, -TAU, WORK, 1, C, 1 )
*
* C(1:lastc,2:lastv) += - tau * w(1:lastc,1) * v(2:lastv)**H
*
CALL CGERC( LASTC, LASTV - 1, -TAU, WORK, 1,
$ V( 1 + INCV ), INCV, C( 1, 2 ), LDC )
END IF
END IF
RETURN
*
* End of CLARF1F
*
END
*> \brief \b CSCAL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CSCAL(N,CA,CX,INCX)
*
* .. Scalar Arguments ..
* COMPLEX CA
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* COMPLEX CX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CSCAL scales a vector by a constant.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] CA
*> \verbatim
*> CA is COMPLEX
*> On entry, CA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in,out] CX
*> \verbatim
*> CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of CX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup scal
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CSCAL(N,CA,CX,INCX)
*
* -- 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 ..
COMPLEX CA
INTEGER INCX,N
* ..
* .. Array Arguments ..
COMPLEX CX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,NINCX
* ..
* .. Parameters ..
COMPLEX ONE
PARAMETER (ONE= (1.0E+0,0.0E+0))
* ..
IF (N.LE.0 .OR. INCX.LE.0 .OR. CA.EQ.ONE) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
CX(I) = CA*CX(I)
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
CX(I) = CA*CX(I)
END DO
END IF
RETURN
*
* End of CSCAL
*
END
*> \brief \b CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CUNM2R + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS
* INTEGER INFO, K, LDA, LDC, M, N
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CUNM2R overwrites the general complex m-by-n matrix C with
*>
*> Q * C if SIDE = 'L' and TRANS = 'N', or
*>
*> Q**H* C if SIDE = 'L' and TRANS = 'C', or
*>
*> C * Q if SIDE = 'R' and TRANS = 'N', or
*>
*> C * Q**H if SIDE = 'R' and TRANS = 'C',
*>
*> where Q is a complex unitary matrix defined as the product of k
*> elementary reflectors
*>
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by CGEQRF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply Q or Q**H from the Left
*> = 'R': apply Q or Q**H from the Right
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': apply Q (No transpose)
*> = 'C': apply Q**H (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines
*> the matrix Q.
*> If SIDE = 'L', M >= K >= 0;
*> if SIDE = 'R', N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,K)
*> The i-th column must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> CGEQRF in the first k columns of its array argument A.
*> A is modified by the routine but restored on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A.
*> If SIDE = 'L', LDA >= max(1,M);
*> if SIDE = 'R', LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (K)
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by CGEQRF.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX array, dimension (LDC,N)
*> On entry, the m-by-n matrix C.
*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (N) if SIDE = 'L',
*> (M) if SIDE = 'R'
*> \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 unm2r
*
* =====================================================================
SUBROUTINE CUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
$ WORK, 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 ..
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDA, LDC, M, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL LEFT, NOTRAN
INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ
COMPLEX TAUI
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLARF1F, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
*
* NQ is the order of Q
*
IF( LEFT ) THEN
NQ = M
ELSE
NQ = N
END IF
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
INFO = -7
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CUNM2R', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
$ RETURN
*
IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
I1 = 1
I2 = K
I3 = 1
ELSE
I1 = K
I2 = 1
I3 = -1
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
ELSE
MI = M
IC = 1
END IF
*
DO 10 I = I1, I2, I3
IF( LEFT ) THEN
*
* H(i) or H(i)**H is applied to C(i:m,1:n)
*
MI = M - I + 1
IC = I
ELSE
*
* H(i) or H(i)**H is applied to C(1:m,i:n)
*
NI = N - I + 1
JC = I
END IF
*
* Apply H(i) or H(i)**H
*
IF( NOTRAN ) THEN
TAUI = TAU( I )
ELSE
TAUI = CONJG( TAU( I ) )
END IF
CALL CLARF1F( SIDE, MI, NI, A( I, I ), 1, TAUI, C( IC, JC ),
$ LDC, WORK )
10 CONTINUE
RETURN
*
* End of CUNM2R
*
END
*> \brief \b ILACLC scans a matrix for its last non-zero column.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ILACLC + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* INTEGER FUNCTION ILACLC( M, N, A, LDA )
*
* .. Scalar Arguments ..
* INTEGER M, N, LDA
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ILACLC scans A for its last non-zero column.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> The m by n matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ilalc
*
* =====================================================================
INTEGER FUNCTION ILACLC( M, N, A, LDA )
*
* -- LAPACK auxiliary 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 M, N, LDA
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER ( ZERO = (0.0E+0, 0.0E+0) )
* ..
* .. Local Scalars ..
INTEGER I
* ..
* .. Executable Statements ..
*
* Quick test for the common case where one corner is non-zero.
IF( N.EQ.0 ) THEN
ILACLC = N
ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN
ILACLC = N
ELSE
* Now scan each column from the end, returning with the first non-zero.
DO ILACLC = N, 1, -1
DO I = 1, M
IF( A(I, ILACLC).NE.ZERO ) RETURN
END DO
END DO
END IF
RETURN
END
*> \brief \b ILACLR scans a matrix for its last non-zero row.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ILACLR + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* INTEGER FUNCTION ILACLR( M, N, A, LDA )
*
* .. Scalar Arguments ..
* INTEGER M, N, LDA
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ILACLR scans A for its last non-zero row.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> The m by n matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ilalr
*
* =====================================================================
INTEGER FUNCTION ILACLR( M, N, A, LDA )
*
* -- LAPACK auxiliary 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 M, N, LDA
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER ( ZERO = (0.0E+0, 0.0E+0) )
* ..
* .. Local Scalars ..
INTEGER I, J
* ..
* .. Executable Statements ..
*
* Quick test for the common case where one corner is non-zero.
IF( M.EQ.0 ) THEN
ILACLR = M
ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN
ILACLR = M
ELSE
* Scan up each column tracking the last zero row seen.
ILACLR = 0
DO J = 1, N
I=M
DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1))
I=I-1
ENDDO
ILACLR = MAX( ILACLR, I )
END DO
END IF
RETURN
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 SCABS1
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* REAL FUNCTION SCABS1(Z)
*
* .. Scalar Arguments ..
* COMPLEX Z
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SCABS1 computes |Re(.)| + |Im(.)| of a complex number
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] Z
*> \verbatim
*> Z is COMPLEX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup abs1
*
* =====================================================================
REAL FUNCTION SCABS1(Z)
*
* -- 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 ..
COMPLEX Z
* ..
*
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC ABS,AIMAG,REAL
* ..
SCABS1 = ABS(REAL(Z)) + ABS(AIMAG(Z))
RETURN
*
* End of SCABS1
*
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