--- name: "her" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/her" --- # her(3) {he,sy}r: Hermitian/symmetric rank-1 update ## NAME her - {he,sy}r: Hermitian/symmetric rank-1 update ## SYNOPSIS ### Functions subroutine **cher** (uplo, n, alpha, x, incx, a, lda)\ **CHER** subroutine **dsyr** (uplo, n, alpha, x, incx, a, lda)\ **DSYR** subroutine **ssyr** (uplo, n, alpha, x, incx, a, lda)\ **SSYR** subroutine **zher** (uplo, n, alpha, x, incx, a, lda)\ **ZHER** subroutine **csyr** (uplo, n, alpha, x, incx, a, lda)\ **CSYR** performs the symmetric rank-1 update of a complex symmetric matrix. subroutine **zsyr** (uplo, n, alpha, x, incx, a, lda)\ **ZSYR** performs the symmetric rank-1 update of a complex symmetric matrix. ## Detailed Description ## Function Documentation ### subroutine cher (character uplo, integer n, real alpha, complex, dimension(\*) x, integer incx, complex, dimension(lda,\*) a, integer lda) **CHER** **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> ``` *ALPHA* ``` !> ALPHA is REAL !> On entry, ALPHA specifies the scalar alpha. !> ``` *X* ``` !> 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. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *A* ``` !> 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. !> ``` *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, n ). !> ``` **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 **134** of file **cher.f**. ### subroutine csyr (character uplo, integer n, complex alpha, complex, dimension( \* ) x, integer incx, complex, dimension( lda, \* ) a, integer lda) **CSYR** performs the symmetric rank-1 update of a complex symmetric matrix. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !> ``` *ALPHA* ``` !> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !> ``` *X* ``` !> 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. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !> ``` *A* ``` !> 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. !> ``` *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, N ). !> Unchanged on exit. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **134** of file **csyr.f**. ### subroutine dsyr (character uplo, integer n, double precision alpha, double precision, dimension(\*) x, integer incx, double precision, dimension(lda,\*) a, integer lda) **DSYR** **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order 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 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *A* ``` !> 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. !> ``` *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, n ). !> ``` **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 **131** of file **dsyr.f**. ### subroutine ssyr (character uplo, integer n, real alpha, real, dimension(\*) x, integer incx, real, dimension(lda,\*) a, integer lda) **SSYR** **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order 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 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *A* ``` !> 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. !> ``` *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, n ). !> ``` **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 **131** of file **ssyr.f**. ### subroutine zher (character uplo, integer n, double precision alpha, complex\*16, dimension(\*) x, integer incx, complex\*16, dimension(lda,\*) a, integer lda) **ZHER** **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order 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 COMPLEX*16 array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *A* ``` !> 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. !> ``` *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, n ). !> ``` **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 **134** of file **zher.f**. ### subroutine zsyr (character uplo, integer n, complex\*16 alpha, complex\*16, dimension( \* ) x, integer incx, complex\*16, dimension( lda, \* ) a, integer lda) **ZSYR** performs the symmetric rank-1 update of a complex symmetric matrix. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *UPLO* ``` !> 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. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !> ``` *ALPHA* ``` !> ALPHA is COMPLEX*16 !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !> ``` *X* ``` !> 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. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !> ``` *A* ``` !> 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. !> ``` *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, N ). !> Unchanged on exit. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **134** of file **zsyr.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.