*> \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