Auxiliary Routines

Conjugates a complex vector.

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).

Finds the element with maximum real part absolute value and its corresponding global index.

Forms the 1-norm of a complex vector similar to Level 1 PBLAS p?asum, but using the true absolute value.

Computes an LU factorization of a general tridiagonal matrix with no pivoting. The routine is called by p?dbtrs.

Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges. The routine is called by p?dttrs.

Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/unitary transformation (unblocked algorithm).

Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation (unblocked algorithm).

Computes an LQ factorization of a general rectangular matrix (unblocked algorithm).

Computes a QL factorization of a general rectangular matrix (unblocked algorithm).

Computes a QR factorization of a general rectangular matrix (unblocked algorithm).

Computes an RQ factorization of a general rectangular matrix (unblocked algorithm).

Computes an LU factorization of a general matrix, using partial pivoting with row interchanges (local blocked algorithm).

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.

Estimates the 1-norm of a square matrix, using the reverse communication for evaluating matrix-vector products.

Looks for two consecutive small subdiagonal elements.

Copies all or part of a distributed matrix to another distributed matrix.

Copies from a global parallel array into a local replicated array or vice versa.

Copies all or part of one two-dimensional array to another.

Moves the eigenvectors from where they are computed to ScaLAPACK standard block cyclic array.

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.

Exploits IEEE arithmetic to accelerate the computations of eigenvalues. (C interface function).

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of a general rectangular matrix.

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of an upper Hessenberg matrix.

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.

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of a triangular matrix.

Applies a permutation matrix to a general distributed matrix, resulting in row or column pivoting.

Scales a general rectangular matrix, using row and column scaling factors computed by p?geequ.

Scales a symmetric/Hermitian matrix, using scaling factors computed by p?poequ.

Redistributes an array assuming that the input array bycol is distributed across rows and that all process columns contain the same copy of bycol.

Redistributes an array assuming that the input array byrow is distributed across columns and that all process rows contain the same copy of byrow .

Applies an elementary reflector to a general rectangular matrix.

Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.

Applies the conjugate transpose of an elementary reflector to a general matrix.

Generates an elementary reflector (Householder matrix).

Forms the triangular vector T of a block reflector H=I-VTV^H

Applies an elementary reflector as returned by p?tzrzf to a general matrix.

Applies a block reflector or its transpose/conjugate-transpose as returned by p?tzrzf to a general matrix.

Applies (multiplies by) the conjugate transpose of an elementary reflector as returned by p?tzrzf to a general matrix.

Forms the triangular factor T of a block reflector H=I-VTV^H as returned by p?tzrzf.

Multiplies a general rectangular matrix by a real scalar defined as C_to/C_from.

Initializes the off-diagonal elements of a matrix to α and the diagonal elements to β.

Looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero.

Updates a sum of squares represented in scaled form.

Performs a series of row interchanges on a general rectangular matrix.

Computes the trace of a general square distributed matrix.

Reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal/unitary similarity transformation.

Reduces an upper trapezoidal matrix to upper triangular form by means of orthogonal/unitary transformations.

Computes the product UU^H or L^HL, where U and L are upper or lower triangular matrices (local unblocked algorithm).

Computes the product UU^H or L^HL, where U and L are upper or lower triangular matrices.

Forms the Wilkinson transform.

Generates all or part of the orthogonal/unitary matrix Q from a QL factorization determined by p?geqlf (unblocked algorithm).

Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by p?geqrf (unblocked algorithm).

Generates all or part of the orthogonal/unitary matrix Q from an LQ factorization determined by p?gelqf (unblocked algorithm).

Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by p?gerqf (unblocked algorithm).

Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by p?geqlf (unblocked algorithm).

Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by p?geqrf (unblocked algorithm).

Multiplies a general matrix by the orthogonal/unitary matrix from an LQ factorization determined by p?gelqf (unblocked algorithm).

Multiplies a general matrix by the orthogonal/unitary matrix from an RQ factorization determined by p?gerqf (unblocked algorithm).

Solves a single triangular linear system via frontsolve or backsolve where the triangular matrix is a factor of a banded matrix computed by p?pbtrf.

Solves a single triangular linear system via frontsolve or backsolve where the triangular matrix is a factor of a tridiagonal matrix computed by p?pttrf.

Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (local unblocked algorithm).

Multiplies a vector by the reciprocal of a real scalar.

Reduces a symmetric/Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from p?potrf (local unblocked algorithm).

Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation (local unblocked algorithm).

Computes the inverse of a triangular matrix (local unblocked algorithm).

Sends multiple shifts through a small (single node) matrix to maximize the number of bulges that can be sent through.

Applies Householder reflectors to matrices on either their rows or columns.

Sorts eigenpairs by real and complex data types.

Sorts numbers in increasing or decreasing order.

Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix, using inverse iteration.

Computes an LU factorization of a general band matrix with no pivoting (local unblocked algorithm).

Computes an LU factorization of a general band matrix with no pivoting (local blocked algorithm).

Computes an LU factorization of a general tridiagonal matrix with no pivoting (local blocked algorithm).

Solves a general tridiagonal system of linear equations using the LU factorization computed by ?dttrf.

Solves a symmetric (Hermitian) positive-definite tridiagonal system of linear equations, using the LDL^H factorization computed by ?pttrf.

Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.