numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/cgbmv.f | 11202B | -rw-r--r-- |
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*> \brief \b CGBMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * COMPLEX ALPHA,BETA * INTEGER INCX,INCY,KL,KU,LDA,M,N * CHARACTER TRANS * .. * .. Array Arguments .. * COMPLEX A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. *> \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] KL *> \verbatim *> KL is INTEGER *> On entry, KL specifies the number of sub-diagonals of the *> matrix A. KL must satisfy 0 .le. KL. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> On entry, KU specifies the number of super-diagonals of the *> matrix A. KU must satisfy 0 .le. KU. *> \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 ( kl + ku + 1 ) by n part of the *> array A must contain the matrix of coefficients, supplied *> column by column, with the leading diagonal of the matrix in *> row ( ku + 1 ) of the array, the first super-diagonal *> starting at position 2 in row ku, the first sub-diagonal *> starting at position 1 in row ( ku + 2 ), and so on. *> Elements in the array A that do not correspond to elements *> in the band matrix (such as the top left ku by ku triangle) *> are not referenced. *> The following program segment will transfer a band matrix *> from conventional full matrix storage to band storage: *> *> DO 20, J = 1, N *> K = KU + 1 - J *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) *> A( K + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE *> \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 *> ( kl + ku + 1 ). *> \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, 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 gbmv * *> \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 CGBMV(TRANS,M,N,KL,KU,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,KL,KU,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,K,KUP1,KX,KY,LENX,LENY LOGICAL NOCONJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,MAX,MIN * .. * * 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 (KL.LT.0) THEN INFO = 4 ELSE IF (KU.LT.0) THEN INFO = 5 ELSE IF (LDA.LT. (KL+KU+1)) THEN INFO = 8 ELSE IF (INCX.EQ.0) THEN INFO = 10 ELSE IF (INCY.EQ.0) THEN INFO = 13 END IF IF (INFO.NE.0) THEN CALL XERBLA('CGBMV ',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 the band part of 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 KUP1 = KU + 1 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) K = KUP1 - J DO 50 I = MAX(1,J-KU),MIN(M,J+KL) Y(I) = Y(I) + TEMP*A(K+I,J) 50 CONTINUE JX = JX + INCX 60 CONTINUE ELSE DO 80 J = 1,N TEMP = ALPHA*X(JX) IY = KY K = KUP1 - J DO 70 I = MAX(1,J-KU),MIN(M,J+KL) Y(IY) = Y(IY) + TEMP*A(K+I,J) IY = IY + INCY 70 CONTINUE JX = JX + INCX IF (J.GT.KU) KY = KY + INCY 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 K = KUP1 - J IF (NOCONJ) THEN DO 90 I = MAX(1,J-KU),MIN(M,J+KL) TEMP = TEMP + A(K+I,J)*X(I) 90 CONTINUE ELSE DO 100 I = MAX(1,J-KU),MIN(M,J+KL) TEMP = TEMP + CONJG(A(K+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 K = KUP1 - J IF (NOCONJ) THEN DO 120 I = MAX(1,J-KU),MIN(M,J+KL) TEMP = TEMP + A(K+I,J)*X(IX) IX = IX + INCX 120 CONTINUE ELSE DO 130 I = MAX(1,J-KU),MIN(M,J+KL) TEMP = TEMP + CONJG(A(K+I,J))*X(IX) IX = IX + INCX 130 CONTINUE END IF Y(JY) = Y(JY) + ALPHA*TEMP JY = JY + INCY IF (J.GT.KU) KX = KX + INCX 140 CONTINUE END IF END IF * RETURN * * End of CGBMV * END