ger(3)

NAME
ger - ger: general matrix rank-1 update

SYNOPSIS

  Functions

subroutine cgerc (m, n, alpha, x, incx, y, incy, a, lda)
CGERC
subroutine cgeru (m, n, alpha, x, incx, y, incy, a, lda)
CGERU
subroutine dger (m, n, alpha, x, incx, y, incy, a, lda)
DGER
subroutine sger (m, n, alpha, x, incx, y, incy, a, lda)
SGER
subroutine zgerc (m, n, alpha, x, incx, y, incy, a, lda)
ZGERC
subroutine zgeru (m, n, alpha, x, incx, y, incy, a, lda)
ZGERU

Detailed Description

Function Documentation

  subroutine cgerc (integer m, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)

CGERC

Purpose:

    !>
    !> 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is COMPLEX
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          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.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          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.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          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.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

  subroutine cgeru (integer m, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)

CGERU

Purpose:

    !>
    !> CGERU  performs the rank 1 operation
    !>
    !>    A := alpha*x*y**T + 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is COMPLEX
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          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.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          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.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          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.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

  subroutine dger (integer m, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(lda,*) a, integer lda)

DGER

Purpose:

    !>
    !> DGER   performs the rank 1 operation
    !>
    !>    A := alpha*x*y**T + 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is DOUBLE PRECISION.
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the m
    !>           element vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          Y is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          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. On exit, A is
    !>           overwritten by the updated matrix.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

  subroutine sger (integer m, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(lda,*) a, integer lda)

SGER

Purpose:

    !>
    !> SGER   performs the rank 1 operation
    !>
    !>    A := alpha*x*y**T + 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is REAL
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          X is REAL array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the m
    !>           element vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          Y is REAL array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          A is REAL 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.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

  subroutine zgerc (integer m, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda)

ZGERC

Purpose:

    !>
    !> ZGERC  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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          X is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the m
    !>           element vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          Y is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          A is COMPLEX*16 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.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

  subroutine zgeru (integer m, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda)

ZGERU

Purpose:

    !>
    !> ZGERU  performs the rank 1 operation
    !>
    !>    A := alpha*x*y**T + 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    X

    !>          X is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the m
    !>           element vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    Y

    !>          Y is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

    A

    !>          A is COMPLEX*16 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.
    !>

    LDA

    !>          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 ).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  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.
    !>

Author

Generated automatically by Doxygen for LAPACK from the source code.