.TH "her" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
her \- {he,sy}r: Hermitian/symmetric rank-1 update
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcher\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBCHER\fP "
.ti -1c
.RI "subroutine \fBdsyr\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBDSYR\fP "
.ti -1c
.RI "subroutine \fBssyr\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBSSYR\fP "
.ti -1c
.RI "subroutine \fBzher\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBZHER\fP "
.ti -1c
.RI "subroutine \fBcsyr\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBCSYR\fP performs the symmetric rank-1 update of a complex symmetric matrix\&. "
.ti -1c
.RI "subroutine \fBzsyr\fP (uplo, n, alpha, x, incx, a, lda)"
.br
.RI "\fBZSYR\fP performs the symmetric rank-1 update of a complex symmetric matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cher (character uplo, integer n, real alpha, complex, dimension(*) x, integer incx, complex, dimension(lda,*) a, integer lda)"

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

.PP
.nf
!>
!> CHER   performs the hermitian rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a real scalar, x is an n element vector and A is an
!> n by n hermitian matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order 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 COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the hermitian matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the hermitian matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of the updated matrix\&.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero\&.
!> 
.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, n )\&.
!> 
.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

.PP
Definition at line \fB134\fP of file \fBcher\&.f\fP\&.
.SS "subroutine csyr (character uplo, integer n, complex alpha, complex, dimension( * ) x, integer incx, complex, dimension( lda, * ) a, integer lda)"

.PP
\fBCSYR\fP performs the symmetric rank-1 update of a complex symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CSYR   performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a complex scalar, x is an n element vector and A is an
!> n by n symmetric matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!>
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX array, dimension at least
!>           ( 1 + ( N - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the N-
!>           element vector x\&.
!>           Unchanged on exit\&.
!> 
.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\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension ( LDA, N )
!>           Before entry, with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the symmetric matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry, with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the symmetric matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of 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, N )\&.
!>           Unchanged on exit\&.
!> 
.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

.PP
Definition at line \fB134\fP of file \fBcsyr\&.f\fP\&.
.SS "subroutine dsyr (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(lda,*) a, integer lda)"

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

.PP
.nf
!>
!> DSYR   performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**T + A,
!>
!> where alpha is a real scalar, x is an n element vector and A is an
!> n by n symmetric matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order 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 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           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
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the symmetric matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the symmetric matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of 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, n )\&.
!> 
.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

.PP
Definition at line \fB131\fP of file \fBdsyr\&.f\fP\&.
.SS "subroutine ssyr (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(lda,*) a, integer lda)"

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

.PP
.nf
!>
!> SSYR   performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**T + A,
!>
!> where alpha is a real scalar, x is an n element vector and A is an
!> n by n symmetric matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order 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 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           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
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the symmetric matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the symmetric matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of 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, n )\&.
!> 
.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

.PP
Definition at line \fB131\fP of file \fBssyr\&.f\fP\&.
.SS "subroutine zher (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*) a, integer lda)"

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

.PP
.nf
!>
!> ZHER   performs the hermitian rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a real scalar, x is an n element vector and A is an
!> n by n hermitian matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order 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 COMPLEX*16 array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the hermitian matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the hermitian matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of the updated matrix\&.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero\&.
!> 
.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, n )\&.
!> 
.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

.PP
Definition at line \fB134\fP of file \fBzher\&.f\fP\&.
.SS "subroutine zsyr (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16, dimension( lda, * ) a, integer lda)"

.PP
\fBZSYR\fP performs the symmetric rank-1 update of a complex symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZSYR   performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a complex scalar, x is an n element vector and A is an
!> n by n symmetric matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced\&.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced\&.
!>
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX*16 array, dimension at least
!>           ( 1 + ( N - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the N-
!>           element vector x\&.
!>           Unchanged on exit\&.
!> 
.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\&.
!>           Unchanged on exit\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension ( LDA, N )
!>           Before entry, with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the symmetric matrix and the strictly
!>           lower triangular part of A is not referenced\&. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix\&.
!>           Before entry, with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the symmetric matrix and the strictly
!>           upper triangular part of A is not referenced\&. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of 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, N )\&.
!>           Unchanged on exit\&.
!> 
.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

.PP
Definition at line \fB134\fP of file \fBzsyr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.