?sfrk

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?sfrk

Performs a symmetric rank-k operation for matrix in RFP format.

Syntax

lapack_int LAPACKE_ssfrk (int matrix_layout , char transr , char uplo , char trans , lapack_int n , lapack_int k , float alpha , const float * a , lapack_int lda , float beta , float * c );

lapack_int LAPACKE_dsfrk (int matrix_layout , char transr , char uplo , char trans , lapack_int n , lapack_int k , double alpha , const double * a , lapack_int lda , double beta , double * c );

Include Files

mkl.h

Description

The ?sfrk routines perform a matrix-matrix operation using symmetric matrices. The operation is defined as

C := alpha*A*A^T + beta*C,

C := alpha*A^T*A + beta*C,

where:

alpha and beta are scalars,

C is an n-by-n symmetric matrix in rectangular full packed (RFP) format,

A is an n-by-k matrix in the first case and a k-by-n matrix in the second case.

Input Parameters

matrix_layout

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

transr

if transr = 'N' or 'n', the normal form of RFP C is stored;

if transr= 'T' or 't', the transpose form of RFP C is stored.

uplo

Specifies whether the upper or lower triangular part of the array c is used.

If uplo = 'U' or 'u', then the upper triangular part of the array c is used.

If uplo = 'L' or 'l', then the low triangular part of the array c is used.

trans

Specifies the operation:

if trans = 'N' or 'n', then C := alpha*A*A^T + beta*C;

if trans = 'T' or 't', then C := alpha*A^T*A + beta*C;

n

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

k

On entry with trans = 'N' or 'n', k specifies the number of columns of the matrix A, and on entry with trans = 'T' or 't', k specifies the number of rows of the matrix A.

The value of k must be at least zero.

alpha

Specifies the scalar alpha.

a

Array, size max(1,lda*ka), where ka is in the following table:

	Col_major	Row_major
`trans` = 'N'	`k`	`n`
`trans` = 'T'	`n`	`k`

Before entry with trans = 'N' or 'n', the leading n-by-k part of the array a must contain the matrix A, otherwise the leading k-by-n part of the array a must contain the matrix A.

lda

Specifies the leading dimension of a as declared in the calling (sub)program. lda is defined by the following table:

	Col_major	Row_major
`trans` = 'N'	`max(1,n)`	`max(1,k)`
`trans` = 'T'	`max(1,k)`	`max(1,n)`

beta

Specifies the scalar beta.

c

Array, size (n*(n+1)/2 ). Before entry contains the symmetric matrix C in RFP format.

Output Parameters

c

If trans = 'N' or 'n', then c contains C := alpha*A*A' + beta*C;

if trans = 'T' or 't', then c contains C := alpha*A'*A + beta*C;

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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?sfrk