LAPACK Auxiliary Routines

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

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LAPACK Auxiliary Routines

Routine naming conventions, mathematical notation, and matrix storage schemes used for LAPACK auxiliary routines are the same as for the driver and computational routines described in previous chapters.

The table below summarizes information about the available LAPACK auxiliary routines.

LAPACK Auxiliary Routines in C

Routine Name	Data Types	Description
?lacgv	c , z	Conjugates a complex vector.
?lacrm	c , z	Multiplies a complex matrix by a square real matrix.
?syconv	s , c , d , z	Converts a symmetric matrix given by a triangular matrix factorization into two matrices and vice versa.
?syr	c , z	Performs the symmetric rank-1 update of a complex symmetric matrix.
i?max1	c , z	Finds the index of the vector element whose real part has maximum absolute value.
?sum1	sc , dz	Forms the 1-norm of the complex vector using the true absolute value.
?gelq2	s , d , c , z	Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
?geqr2	s , d , c , z	Computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
?geqrt2	s , d , c , z	Computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
?geqrt3	s , d , c , z	Recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
?getf2	s , d , c , z	Computes the LU factorization of a general `m` -by- `n` matrix using partial pivoting with row interchanges (unblocked algorithm).
?lacn2	s , d , c , z	Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
?lacpy	s , d , c , z	Copies all or part of one two-dimensional array to another.
?lakf2	s , d , c , z	Forms a matrix containing Kronecker products between the given matrices.
?lange	s , d , c , z	Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
?lansy	s , d , c , z	Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real/complex symmetric matrix.
?lanhe	c , z	Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
?lantr	s , d , c , z	Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
LAPACKE_get_nancheck		Checks whether NaN-checking is enabled or disabled for LAPACKE functions.
LAPACKE_set_nancheck		Enables or disables NaN-checking for LAPACKE functions.
?lapmr	s , d , c , z	Rearranges rows of a matrix as specified by a permutation vector.
?lapmt	s , d , c , z	Performs a forward or backward permutation of the columns of a matrix.
?lapy2	s , d	Returns sqrt( `x`² + `y`² ).
?lapy3	s , d	Returns sqrt( `x`² + `y`² + `z`² ).
?laran	s , d	Returns a random real number from a uniform distribution.
?larfb	s , d , c , z	Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.
?larfg	s , d , c , z	Generates an elementary reflector (Householder matrix).
?larft	s , d , c , z	Forms the triangular factor `T` of a block reflector `H` = `I` - `vtv`^:code:`H`
?larfx	s , d , c , z	Applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.
?large	s , d , c , z	Pre- and post-multiplies a real general matrix with a random orthogonal matrix.
?larnd	s , d , c , z	Returns a random real number from a uniform or normal distribution.
?larnv	s , d , c , z	Returns a vector of random numbers from a uniform or normal distribution.
?laror	s , d , c , z	Pre- or post-multiplies an `m` -by- `n` matrix by a random orthogonal/unitary matrix.
?larot	s , d , c , z	Applies a Givens rotation to two adjacent rows or columns.
?lartgp	s , d	Generates a plane rotation so that the diagonal is nonnegative.
?lartgs	s , d	Generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.
?lascl	s , d , c , z	Multiplies a general rectangular matrix by a real scalar defined as `\(c_{to} / c_{from}\)`.
?lasd0	s , d	Computes the singular values of a real upper bidiagonal n-by-m matrix `B` with diagonal `d` and off-diagonal `e` . Used by `?bdsdc` .
?lasd1	s , d	Computes the SVD of an upper bidiagonal matrix `B` of the specified size. Used by `?bdsdc` .
?lasd2	s , d	Merges the two sets of singular values together into a single sorted set. Used by `?bdsdc` .
?lasd3	s , d	Finds all square roots of the roots of the secular equation, as defined by the values in `D` and `Z` , and then updates the singular vectors by matrix multiplication. Used by `?bdsdc` .
?lasd4	s , d	Computes the square root of the `i` -th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by `?bdsdc` .
?lasd5	s , d	Computes the square root of the `i` -th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by `?bdsdc` .
?lasd6	s , d	Computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by `?bdsdc` .
?lasd7	s , d	Merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by `?bdsdc` .
?lasd8	s , d	Finds the square roots of the roots of the secular equation, and stores, for each element in `D` , the distance to its two nearest poles. Used by `?bdsdc` .
?lasda	s , d	Computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal `d` and off-diagonal `e` . Used by `?bdsdc` .
?lasdq	s , d	Computes the SVD of a real bidiagonal matrix with diagonal `d` and off-diagonal `e` . Used by `?bdsdc` .
?lasdt	s , d	Creates a tree of subproblems for bidiagonal divide and conquer. Used by `?bdsdc` .
?laset	s , d , c , z	Initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
?lasrt	s , d	Sorts numbers in increasing or decreasing order.
?laswp	s , d , c , z	Performs a series of row interchanges on a general rectangular matrix.
?latm1	s , d , c , z	Computes the entries of a matrix as specified.
?latm2	s , d , c , z	Returns an entry of a random matrix.
?latm3	s , d , c , z	Returns set entry of a random matrix.
?latm5	s , d , c , z	Generates matrices involved in the Generalized Sylvester equation.
?latm6	s , d , c , z	Generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues.
?latme	s , d , c , z	Generates random non-symmetric square matrices with specified eigenvalues.
?latmr	s , d , c , z	Generates random matrices of various types.
?lauum	s , d , c , z	Computes the product `\(UU^{H}\)` or `\(L^{H}L\)` , where `\(U\)` and `\(L\)` are upper or lower triangular matrices (blocked algorithm).
?syswapr	s , d , c , z	Applies an elementary permutation on the rows and columns of a symmetric matrix.
?heswapr	c , z	Applies an elementary permutation on the rows and columns of a Hermitian matrix.
?sfrk	s , d	Performs a symmetric rank-k operation for matrix in RFP format.
?hfrk	c , z	Performs a Hermitian rank-k operation for matrix in RFP format.
?tfsm	s , d , c , z	Solves a matrix equation (one operand is a triangular matrix in RFP format).
?tfttp	s , d , c , z	Copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
?tfttr	s , d , c , z	Copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
?tpqrt2	s , d , c , z	Computes a QR factorization of a real or complex “triangular-pentagonal” matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
?tprfb	s , d , c , z	Applies a real or complex “triangular-pentagonal” blocked reflector to a real or complex matrix, which is composed of two blocks.
?tpttf	s , d , c , z	Copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
?tpttr	s , d , c , z	Copies a triangular matrix from the standard packed format (TP) to the standard full format (TR).
?trttf	s , d , c , z	Copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
?trttp	s , d , c , z	Copies a triangular matrix from the standard full format (TR) to the standard packed format (TP).
?lacp2	c , z	Copies all or part of a real two-dimensional array to a complex array.
?larcm	c , z	Copies all or part of a real two-dimensional array to a complex array.
mkl_?tppack	s , d , c , z	Copies a triangular/symmetric matrix or submatrix from standard full format to standard packed format.
mkl_?tpunpack	s , d , c , z	Copies a triangular/symmetric matrix or submatrix from standard packed format to full format.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

LAPACK Auxiliary Routines