?syr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?syr

Performs the symmetric rank-1 update of a complex symmetric matrix.

Syntax

lapack_intLAPACKE_csyr ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_floatalpha , constlapack_complex_float*x , lapack_intincx , lapack_complex_float*a , lapack_intlda );

lapack_intLAPACKE_zsyr ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_doublealpha , constlapack_complex_double*x , lapack_intincx , lapack_complex_double*a , lapack_intlda );

Include Files

mkl.h

Description

csyr zsyr

The routine performs the symmetric rank 1 operation defined as

a := alpha*x*x^{H} + a ,

where:

alpha is a complex scalar. x is an n -element complex vector. a is an n -by- n complex symmetric matrix.

These routines have their real equivalents in BLAS (see ?syr (Performs a rank-1 update of a symmetric matrix.) in Chapter “BLAS and Sparse BLAS Routines” ).

Input Parameters

matrix_layout: Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

uplo

Specifies whether the upper or lower triangular part of the array a is used:

If uplo = 'U' or ‘u’ , then the upper triangular part of the array a is used. If uplo = 'L' or ‘l’ , then the lower triangular part of the array a is used.

n

Specifies the order of the matrix a . The value of n must be at least zero.

alpha: COMPLEX for csyr DOUBLE COMPLEX for zsyr Specifies the scalar alpha .
x: COMPLEX for csyr DOUBLE COMPLEX for zsyr Array, size at least (1 + (n - 1)*abs(incx)) . Before entry, the incremented array x must contain the n -element vector x .

incx

Specifies the increment for the elements of x . The value of incx must not be zero.

a: COMPLEX for csyr DOUBLE COMPLEX for zsyr 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.

lda

Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least max(1,n) .

Output Parameters

a: With uplo = 'U' or ‘u’ , the upper triangular part of the array a is overwritten by the upper triangular part of the updated matrix. With uplo = 'L' or ‘l’ , the lower triangular part of the array a is overwritten by the lower triangular part of the updated matrix.

Return Values

This function returns a value info .

If info = 0 , the execution is successful.
If info < 0 , the i -th parameter had an illegal value.
If info = -1011 , memory allocation error occurred.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?syr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values