.TH "ger" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ger \- ger: general matrix rank-1 update
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgerc\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBCGERC\fP "
.ti -1c
.RI "subroutine \fBcgeru\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBCGERU\fP "
.ti -1c
.RI "subroutine \fBdger\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBDGER\fP "
.ti -1c
.RI "subroutine \fBsger\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBSGER\fP "
.ti -1c
.RI "subroutine \fBzgerc\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBZGERC\fP "
.ti -1c
.RI "subroutine \fBzgeru\fP (m, n, alpha, x, incx, y, incy, a, lda)"
.br
.RI "\fBZGERU\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgerc (integer m, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)"

.PP
\fBCGERC\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

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

.PP
\fBCGERU\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fBDGER\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is DOUBLE PRECISION\&.
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

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

.PP
\fBSGER\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is REAL
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fBZGERC\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fBZGERU\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A\&.
           M must be at least zero\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y\&. INCY must not be zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.