Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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

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