.TH "her" 3 "Wed Feb 7 2024 11:30:40" "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 .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 .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 .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 .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 .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.