LAPACK Auxiliary Routines

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 11/07/2023

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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.

Parent topic: LAPACK Routines

?lacgv
Conjugates a complex vector.
?lacrm
Multiplies a complex matrix by a square real matrix.
?syconv
Converts a symmetric matrix given by a triangular matrix factorization into two matrices and vice versa.
?syr
Performs the symmetric rank-1 update of a complex symmetric matrix.
i?max1
Finds the index of the vector element whose real part has maximum absolute value.
?sum1
Forms the 1-norm of the complex vector using the true absolute value.
?gelq2
Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
?geqr2
Computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
?geqrt2
Computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
?geqrt3
Recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
?getf2
Computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).
?lacn2
Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
?lacpy
Copies all or part of one two-dimensional array to another.
?lakf2
Forms a matrix containing Kronecker products between the given matrices.
?lange
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
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
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
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_set_nancheck
Turns NaN checking off or on
LAPACKE_get_nancheck
Gets the current NaN checking flag, which indicates whether NaN checking has been turned off or on.
?lapmr
Rearranges rows of a matrix as specified by a permutation vector.
?lapmt
Performs a forward or backward permutation of the columns of a matrix.
?lapy2
Returns sqrt(x²+y²).
?lapy3
Returns sqrt(x²+y²+z²).
?laran
Returns a random real number from a uniform distribution.
?larfb
Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.
?larfg
Generates an elementary reflector (Householder matrix).
?larft
Forms the triangular factor T of a block reflector H = I - V*T*V**H.
?larfx
Applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order less than or equal to 10.
?large
Pre- and post-multiplies a real general matrix with a random orthogonal matrix.
?larnd
Returns a random real number from a uniform or normal distribution.
?larnv
Returns a vector of random numbers from a uniform or normal distribution.
?laror
Pre- or post-multiplies an m-by-n matrix by a random orthogonal/unitary matrix.
?larot
Applies a Givens rotation to two adjacent rows or columns.
?lartgp
Generates a plane rotation.
?lartgs
Generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.
?lascl
Multiplies a general rectangular matrix by a real scalar defined as c_to/c_from.
?lasd0
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
Computes the SVD of an upper bidiagonal matrix B of the specified size. Used by ?bdsdc.
?lasd2
Merges the two sets of singular values together into a single sorted set. Used by ?bdsdc.
?lasd3
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
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
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
Computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by ?bdsdc.
?lasd7
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
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.
?lasd9
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
Computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by ?bdsdc.
?lasdq
Computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by ?bdsdc.
?lasdt
Creates a tree of subproblems for bidiagonal divide and conquer. Used by ?bdsdc.
?laset
Initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
?lasrt
Sorts numbers in increasing or decreasing order.
?laswp
Performs a series of row interchanges on a general rectangular matrix.
?latm1
Computes the entries of a matrix as specified.
?latm2
Returns an entry of a random matrix.
?latm3
Returns set entry of a random matrix.
?latm5
Generates matrices involved in the Generalized Sylvester equation.
?latm6
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
Generates random non-symmetric square matrices with specified eigenvalues.
?latmr
Generates random matrices of various types.
?lauum
Computes the product U*U^T(U*U^H) or L^T*L (L^H*L), where U and L are upper or lower triangular matrices (blocked algorithm).
?syswapr
Applies an elementary permutation on the rows and columns of a symmetric matrix.
?heswapr
Applies an elementary permutation on the rows and columns of a Hermitian matrix.
?sfrk
Performs a symmetric rank-k operation for matrix in RFP format.
?hfrk
Performs a Hermitian rank-k operation for matrix in RFP format.
?tfsm
Solves a matrix equation (one operand is a triangular matrix in RFP format).
?tfttp
Copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP) .
?tfttr
Copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR) .
?tpqrt2
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
Applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks.
?tpttf
Copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
?tpttr
Copies a triangular matrix from the standard packed format (TP) to the standard full format (TR) .
?trttf
Copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
?trttp
Copies a triangular matrix from the standard full format (TR) to the standard packed format (TP) .
?lacp2
Copies all or part of a real two-dimensional array to a complex array.
?larcm
Multiplies a square real matrix by a complex matrix.
mkl_?tppack
Copies a triangular/symmetric matrix or submatrix from standard full format to standard packed format.
mkl_?tpunpack
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