ger(3)

Library Functions Manual

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

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

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

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

!>          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 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 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 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, complex16 alpha, complex16, dimension() x, integer incx, complex16, dimension() y, integer incy, complex16, 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 is INTEGER
!>           On entry, M specifies the number of rows of the matrix A.
!>           M must be at least zero.
!>

!>          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 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 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 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, complex16 alpha, complex16, dimension() x, integer incx, complex16, dimension() y, integer incy, complex16, 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 is INTEGER
!>           On entry, M specifies the number of rows of the matrix A.
!>           M must be at least zero.
!>

!>          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 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 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 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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