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.

Definition at line 129 of file cgerc.f.

  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.

Definition at line 129 of file cgeru.f.

  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.

Definition at line 129 of file dger.f.

  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.

Definition at line 129 of file sger.f.

  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.

Definition at line 129 of file zgerc.f.

  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.

Definition at line 129 of file zgeru.f.

Author

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