Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

ScaLAPACK Auxiliary Routines

ScaLAPACK Auxiliary Routines
Routine Name
Data Types
Description
c,z
Conjugates a complex vector.
c,z
Finds the index of the element whose real part has maximum absolute value (similar to the Level 1 PBLAS
p?amax
, but using the absolute value to the real part).
s,d
Finds the collaborators of a process.
s,d
Computes the eigenpair range assignments for all processes.
c,z
Finds the element with maximum real part absolute value and its corresponding global index.
sc,dz
Forms the 1-norm of a complex vector similar to Level 1 PBLAS
p?asum
, but using the true absolute value.
s,d,c,z
Computes an
LU
 factorization of a general tridiagonal matrix with no pivoting. The routine is called by
p?dbtrs
.
s,d,c,z
Computes an
LU
 factorization of a general band matrix, using partial pivoting with row interchanges. The routine is called by
p?dttrs
.
s,d
Balances a general real/complex matrix.
s,d,c,z
Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/unitary transformation (unblocked algorithm).
s,d,c,z
Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation (unblocked algorithm).
s,d,c,z
Computes an
LQ
 factorization of a general rectangular matrix (unblocked algorithm).
s,d,c,z
Computes a
QL
 factorization of a general rectangular matrix (unblocked algorithm).
s,d,c,z
Computes a
QR
 factorization of a general rectangular matrix (unblocked algorithm).
s,d,c,z
Computes an
RQ
 factorization of a general rectangular matrix (unblocked algorithm).
s,d,c,z
Computes an
LU
 factorization of a general matrix, using partial pivoting with row interchanges (local blocked algorithm).
s,d,c,z
Reduces the first
nb
 rows and columns of a general rectangular matrix A to real bidiagonal form by an orthogonal/unitary transformation, and returns auxiliary matrices that are needed to apply the transformation to the unreduced part of A.
s,d,c,z
Estimates the 1-norm of a square matrix, using the reverse communication for evaluating matrix-vector products.
s,d
Looks for two consecutive small subdiagonal elements.
s,d,c,z
Copies all or part of a distributed matrix to another distributed matrix.
s,d
Copies from a global parallel array into a local replicated array or vice versa.
s,d,c,z
Copies all or part of one two-dimensional array to another.
s,d,c,z
Moves the eigenvectors from where they are computed to ScaLAPACK standard block cyclic array.
s,d,c,z
Reduces the first
nb
 columns of a general rectangular matrix A so that elements below the
k
th
 subdiagonal are zero, by an orthogonal/unitary transformation, and returns auxiliary matrices that are needed to apply the transformation to the unreduced part of A.
s,d,c,z
Exploits IEEE arithmetic to accelerate the computations of eigenvalues.
s, d
Copies all or part of one two-dimensional distributed array to another.
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.
s,d,c,z
Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of an upper Hessenberg matrix.
s,d,c,z/c,z
Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a real symmetric or complex Hermitian matrix.
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 triangular matrix.
s,d,c,z
Applies a permutation matrix to a general distributed matrix, resulting in row or column pivoting.
s,d,c,z
Scales a general rectangular matrix, using row and column scaling factors computed by
p?geequ
.
s,d
Computes the eigenvalues of a Hessenberg matrix and optionally returns the matrices from the Schur decomposition.
s,d
Sets a scalar multiple of the first column of the product of a 2-by-2 or 3-by-3 matrix and specified shifts.
s,d
Performs the orthogonal/unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
s,d
Performs the orthogonal/unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
s,d
Performs a single small-bulge multi-shift QR sweep.
s,d,c,z
Scales a symmetric/Hermitian matrix, using scaling factors computed by
p?poequ
.
s,d
Redistributes an array assuming that the input array
bycol
 is distributed across rows and that all process columns contain the same copy of
bycol
.
s,d
Redistributes an array assuming that the input array
byrow
 is distributed across columns and that all process rows contain the same copy of
byrow
 .
s,d,c,z
Applies an elementary reflector to a general rectangular matrix.
s,d,c,z
Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.
c,z
Applies the conjugate transpose of an elementary reflector to a general matrix.
s,d,c,z
Generates an elementary reflector (Householder matrix).
s,d,c,z
Forms the triangular vector
T
 of a block reflector
H
=
I
-
VTV
H
s,d,c,z
Applies an elementary reflector as returned by
p?tzrzf
 to a general matrix.
s,d,c,z
Applies a block reflector or its transpose/conjugate-transpose as returned by
p?tzrzf
 to a general matrix.
c,z
Applies (multiplies by) the conjugate transpose of an elementary reflector as returned by
p?tzrzf
 to a general matrix.
s,d,c,z
Forms the triangular factor
T
 of a block reflector
H
=
I
-
VTV
H
 as returned by
p?tzrzf
.
s,d,c,z
Multiplies a general rectangular matrix by a real scalar defined as
C
to
/
C
from
.
s,d,c,z
Initializes the off-diagonal elements of a matrix to
α
 and the diagonal elements to
β
.
s,d
Looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero.
s,d,c,z
Updates a sum of squares represented in scaled form.
s,d,c,z
Performs a series of row interchanges on a general rectangular matrix.
s,d,c,z
Computes the trace of a general square distributed matrix.
s,d,c,z
Reduces the first
nb
 rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal/unitary similarity transformation.
s,d,c,z
Reduces an upper trapezoidal matrix to upper triangular form by means of orthogonal/unitary transformations.
s,d,c,z
Computes the product
UU
H
 or
L
H
L
, where
U
 and
L
 are upper or lower triangular matrices (local unblocked algorithm).
s,d,c,z
Computes the product
UU
H
 or
L
H
L
, where
U
 and
L
 are upper or lower triangular matrices.
s,d
Forms the Wilkinson transform.
s,d,c,z
Generates all or part of the orthogonal/unitary matrix
Q
 from a
QL
 factorization determined by
p?geqlf
 (unblocked algorithm).