Bidiagonal Matrix
|
SBDSDC or DBDSDC
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Computes the singular value decomposition (SVD) of a bidirectional matrix, using a divide and conquer method.
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xBDSQR
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Computes SVD of real upper or lower bidiagonal matrix, using the bidirectional QR algorithm.
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Diagonal Matrix
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SDISNA or DDISNA
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Computes the reciprocal condition numbers for eigenvectors of real symmetric or complex Hermitian matrix.
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General Band Matrix
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xGBBRD
|
Reduces real or complex general band matrix to upper bidiagonal form.
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xGBCON
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Estimates the reciprocal of the condition number of general band matrix using LU factorization.
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xGBEQU
|
Computes row and column scalings to equilibrate a general band matrix and reduce its condition number.
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xGBRFS
|
Refines solution to general banded system of linear equations.
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xGBSV
|
Solves a general banded system of linear equations (simple driver).
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xGBSVX
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Solves a general banded system of linear equations (expert driver).
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xGBTRF
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LU factorization of a general band matrix using partial pivoting with row interchanges.
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xGBTRS (P)
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Solves a general banded system of linear equations, using the factorization computed by xGBTRF.
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General Matrix (Unsymmetric or Rectangular)
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xGEBAK
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Forms the right or left eigenvectors of a general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by xGEBAL.
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xGEBAL
|
Balances a general matrix.
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xGEBRD
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Reduces a general matrix to upper or lower bidiagonal form by an orthogonal transformation.
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xGECON
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Estimates the reciprocal of the condition number of a general matrix, using the factorization computed by xGETRF.
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xGEEQU
|
Computes row and column scalings intended to equilibrate a general rectangular matrix and reduce its condition number.
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xGEES
|
Computes the eigenvalues and Schur factorization of a general matrix (simple driver).
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xGEESX
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Computes the eigenvalues and Schur factorization of a general matrix (expert driver).
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xGEEV
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Computes the eigenvalues and left and right eigenvectors of a general matrix (simple driver).
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xGEEVX
|
Computes the eigenvalues and left and right eigenvectors of a general matrix (expert driver).
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xGEGS
|
Depreciated routine replaced by xGGES.
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xGEGV
|
Depreciated routine replaced by xGGEV.
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xGEHRD
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Reduces a general matrix to upper Hessenberg form by an orthogonal similarity transformation.
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xGELQF (P)
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Computes LQ factorization of a general rectangular matrix.
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xGELS
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Computes the least squares solution to an over-determined system of linear equations using a QR or LQ factorization of A.
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xGELSD
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Computes the least squares solution to an over-determined system of linear equations using a divide and conquer method using a QR or LQ factorization of A.
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xGELSS
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Computes the minimum-norm solution to a linear least squares problem by using the SVD of a general rectangular matrix (simple driver).
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xGELSX
|
Depreciated routine replaced by xSELSY.
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xGELSY
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Computes the minimum-norm solution to a linear least squares problem using a complete orthogonal factorization.
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xGEQLF (P)
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Computes QL factorization of a general rectangular matrix.
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xGEQP3
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Computes QR factorization of general rectangular matrix using Level 3 BLAS.
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xGEQPF
|
Depreciated routine replaced by xGEQP3.
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xGEQRF (P)
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Computes QR factorization of a general rectangular matrix.
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xGERFS
|
Refines solution to a system of linear equations.
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xGERQF (P)
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Computes RQ factorization of a general rectangular matrix.
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xGESDD
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Computes SVD of general rectangular matrix using a divide and conquer method.
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xGESV
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Solves a general system of linear equations (simple driver).
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xGESVX
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Solves a general system of linear equations (expert driver).
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xGESVD
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Computes SVD of general rectangular matrix.
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xGETRF (P)
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Computes an LU factorization of a general rectangular matrix using partial pivoting with row interchanges.
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xGETRI
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Computes inverse of a general matrix using the factorization computed by xGETRF.
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xGETRS (P)
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Solves a general system of linear equations using the factorization computed by xGETRF.
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General Matrix-Generalized Problem (Pair of General Matrices)
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xGGBAK
|
Forms the right or left eigenvectors of a generalized eigenvalue problem based on the output by xGGBAL.
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xGGBAL
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Balances a pair of general matrices for the generalized eigenvalue problem.
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xGGES
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Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for two nonsymmetric matrices.
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xGGESX
|
Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors.
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xGGEV
|
Computes the generalized eigenvalues and the left and/or right generalized eigenvalues for two nonsymmetric matrices.
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xGGEVX
|
Computes the generalized eigenvalues and the left and/or right generalized eigenvectors.
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xGGGLM
|
Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization.
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xGGHRD
|
Reduces two matrices to generalized upper Hessenberg form using orthogonal transformations.
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xGGLSE
|
Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization.
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xGGQRF
|
Computes generalized QR factorization of two matrices.
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xGGRQF
|
Computes generalized RQ factorization of two matrices.
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xGGSVD
|
Computes the generalized singular value decomposition.
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xGGSVP
|
Computes an orthogonal or unitary matrix as a preprocessing step for calculating the generalized singular value decomposition.
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General Tridiagonal Matrix
|
xGTCON
|
Estimates the reciprocal of the condition number of a tridiagonal matrix, using the LU factorization as computed by xGTTRF.
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xGTRFS
|
Refines solution to a general tridiagonal system of linear equations.
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xGTSV
|
Solves a general tridiagonal system of linear equations (simple driver).
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xGTSVX
|
Solves a general tridiagonal system of linear equations (expert driver).
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xGTTRF
|
Computes an LU factorization of a general tridiagonal matrix using partial pivoting and row exchanges.
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xGTTRS (P)
|
Solves general tridiagonal system of linear equations using the factorization computed by x.
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Hermitian Band Matrix
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CHBEV or ZHBEV
|
(Replacement with newer version CHBEVD or ZHBEVD suggested) Computes all eigenvalues and eigenvectors of a Hermitian band matrix.
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CHBEVD or ZHBEVD
|
Computes all eigenvalues and eigenvectors of a Hermitian band matrix and uses a divide and conquer method to calculate eigenvectors.
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CHBEVX or ZHBEVX
|
Computes selected eigenvalues and eigenvectors of a Hermitian band matrix.
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CHBGST or ZHBGST
|
Reduces Hermitian-definite banded generalized eigenproblem to standard form.
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CHBGV or ZHBGV
|
(Replacement with newer version CHBGVD or ZHBGVD suggested) Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.
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CHBGVD or ZHBGVD
|
Computes all eigenvalues and eigenvectors of generalized Hermitian-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.
|
CHBGVX or ZHBGVX
|
Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.
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CHBTRD or ZHBTRD
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Reduces Hermitian band matrix to real symmetric tridiagonal form by using a unitary similarity transform.
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Hermitian Matrix
|
CHECON or ZHECON
|
Estimates the reciprocal of the condition number of a Hermitian matrix using the factorization computed by CHETRF or ZHETRF.
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CHEEV or ZHEEV
|
(Replacement with newer version CHEEVR or ZHEEVR suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix (simple driver).
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CHEEVD or ZHEEVD
|
(Replacement with newer version CHEEVR or ZHEEVR suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix and uses a divide and conquer method to calculate eigenvectors.
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CHEEVR or ZHEEVR
|
Computes selected eigenvalues and the eigenvectors of a complex Hermitian matrix.
|
CHEEVX or ZHEEVX
|
Computes selected eigenvalues and eigenvectors of a Hermitian matrix (expert driver).
|
CHEGST or ZHEGST
|
Reduces a Hermitian-definite generalized eigenproblem to standard form using the factorization computed by CPOTRF or ZPOTRF.
|
CHEGV or ZHEGV
|
(Replacement with newer version CHEGVD or ZHEGVD suggested) Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.
|
CHEGVD or ZHEGVD
|
Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.
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CHEGVX or ZHEGVX
|
Computes selected eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.
|
CHERFS or ZHERFS
|
Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite.
|
CHESV or ZHESV
|
Solves a complex Hermitian indefinite system of linear equations (simple driver).
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CHESVX or ZHESVX
|
Solves a complex Hermitian indefinite system of linear equations (simple driver).
|
CHETRD or ZHETRD
|
Reduces a Hermitian matrix to real symmetric tridiagonal form by using a unitary similarity transformation.
|
CHETRF or ZHERTF
|
Computes the factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.
|
CHETRI or ZHETRI
|
Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF or ZHETRF.
|
CHETRS (P) or ZHETRS (P)
|
Solves a complex Hermitian indefinite matrix, using the factorization computed by CHETRF or ZHETRF.
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Hermitian Matrix in Packed Storage
|
CHPCON or ZHPCON
|
Estimates the reciprocal of the condition number of a Hermitian indefinite matrix in packed storage using the factorization computed by CHPTRF or ZHPTRF.
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CHPEV or ZHPEV
|
(Replacement with newer version CHPEVD or ZHPEVD suggested) Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage (simple driver).
|
CHPEVX or ZHPEVX
|
Computes selected eigenvalues and eigenvectors of a Hermitian matrix in packed storage (expert driver).
|
CHPEVD or ZHPEVD
|
Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.
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CHPGST or ZHPGST
|
Reduces a Hermitian-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by CPPTRF or ZPPTRF.
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CHPGV or ZHPGV
|
(Replacement with newer version CHPGVD or ZHPGVD suggested) Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).
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CHPGVX or ZHPGVX
|
Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).
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CHPGVD or ZHPGVD
|
Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.
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CHPRFS or ZHPRFS
|
Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite in packed storage.
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CHPSV or ZHPSV
|
Computes the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (simple driver).
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CHPSVX or ZHPSVX
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Uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (expert driver).
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CHPTRD or ZHPTRD
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Reduces a complex Hermitian matrix stored in packed form to real symmetric tridiagonal form.
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CHPTRF or ZHPTRF
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Computes the factorization of a complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method.
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CHPTRI or ZHPTRI
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Computes the inverse of a complex Hermitian indefinite matrix in packed storage using the factorization computed by CHPTRF or ZHPTRF.
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CHPTRS (P) or ZHPTRS (P)
|
Solves a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF or ZHPTRF.
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Upper Hessenberg Matrix
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xHSEIN
|
Computes right and/or left eigenvectors of upper Hessenberg matrix using inverse iteration.
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xHSEQR
|
Computes eigenvectors and Shur factorization of upper Hessenberg matrix using multishift QR algorithm.
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Upper Hessenberg Matrix-Generalized Problem (Hessenberg and Triangular Matrix)
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xHGEQZ
|
Implements single-/double-shift version of QZ method for finding the generalized eigenvalues of the equation det(A - w(i) * B) = 0.
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Real Orthogonal Matrix in Packed Storage
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SOPGTR or DOPGTR
|
Generates an orthogonal transformation matrix from a tridiagonal matrix determined by SSPTRD or DSPTRD.
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SOPMTR or DOPMTR
|
Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by SSPTRD or DSPTRD.
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Real Orthogonal Matrix
|
SORGBR or DORGBR
|
Generates the orthogonal transformation matrices from reduction to bidiagonal form, as determined by SGEBRD or DGEBRD.
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SORGHR or DORGHR
|
Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by SGEHRD or DGEHRD.
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SORGLQ or DORGLQ
|
Generates an orthogonal matrix Q from an LQ factorization, as returned by SGELQF or DGELQF.
|
SORGQL or DORGQL
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Generates an orthogonal matrix Q from a QL factorization, as returned by SGEQLF or DGEQLF.
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SORGQR or DORGQR
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Generates an orthogonal matrix Q from a QR factorization, as returned by SGEQRF or DGEQRF.
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SORGRQ or DORGRQ
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Generates orthogonal matrix Q from an RQ factorization, as returned by SGERQF or DGERQF.
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SORGTR or DORGTR
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Generates an orthogonal matrix reduced to tridiagonal form by SSYTRD or DSYTRD.
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SORMBR or DORMBR
|
Multiplies a general matrix with the orthogonal matrix reduced to bidiagonal form, as determined by SGEBRD or DGEBRD.
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SORMHR or DORMHR
|
Multiplies a general matrix by the orthogonal matrix reduced to Hessenberg form by SGEHRD or DGEHRD.
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SORMLQ (P) or DORMLQ (P)
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Multiplies a general matrix by the orthogonal matrix from an LQ factorization, as returned by SGELQF or DGELQF.
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SORMQL (P) or DORMQL (P)
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Multiplies a general matrix by the orthogonal matrix from a QL factorization, as returned by SGEQLF or DGEQLF.
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SORMQR (P) or DORMQR (P)
|
Multiplies a general matrix by the orthogonal matrix from a QR factorization, as returned by SGEQRF or DGEQRF.
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SORMR3 or DORMR3
|
Multiplies a general matrix by the orthogonal matrix returned by STZRZF or DTZRZF.
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SORMRQ (P) or DORMRQ (P)
|
Multiplies a general matrix by the orthogonal matrix from an RQ factorization returned by SGERQF or DGERQF.
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SORMRZ or DORMRZ
|
Multiplies a general matrix by the orthogonal matrix from an RZ factorization, as returned by STZRZF or DTZRZF.
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SORMTR or DORMTR
|
Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by SSYTRD or DSYTRD.
|
Symmetric or Hermitian Positive Definite Band Matrix
|
xPBCON
|
Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite band matrix, using the Cholesky factorization returned by xPBTRF.
|
xPBEQU
|
Computes equilibration scale factors for a symmetric or Hermitian positive definite band matrix.
|
xPBRFS
|
Refines solution to a symmetric or Hermitian positive definite banded system of linear equations.
|
xPBSTF
|
Computes a split Cholesky factorization of a real symmetric positive definite band matrix.
|
xPBSV
|
Solves a symmetric or Hermitian positive definite banded system of linear equations (simple driver).
|
xPBSVX
|
Solves a symmetric or Hermitian positive definite banded system of linear equations (expert driver).
|
xPBTRF
|
Computes Cholesky factorization of a symmetric or Hermitian positive definite band matrix.
|
xPBTRS (P)
|
Solves symmetric positive definite banded matrix, using the Cholesky factorization computed by xPBTRF.
|
Symmetric or Hermitian Positive Definite Matrix
|
xPOCON
|
Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite matrix, using the Cholesky factorization returned by xPOTRF.
|
xPOEQU
|
Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix.
|
xPORFS
|
Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix.
|
xPOSV
|
Solves a symmetric or Hermitian positive definite system of linear equations (simple driver).
|
xPOSVX
|
Solves a symmetric or Hermitian positive definite system of linear equations (expert driver).
|
xPOTRF (P)
|
Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix.
|
xPOTRI
|
Computes the inverse of a symmetric or Hermitian positive definite matrix using the Cholesky-factorization returned by xPOTRF.
|
xPOTRS (P)
|
Solves a symmetric or Hermitian positive definite system of linear equations, using the Cholesky factorization returned by xPOTRF.
|
Symmetric or Hermitian Positive Definite Matrix in Packed Storage
|
xPPCON
|
Reciprocal condition number of a Cholesky-factored symmetric positive definite matrix in packed storage.
|
xPPEQU
|
Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix in packed storage.
|
xPPRFS
|
Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix in packed storage.
|
xPPSV
|
Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (simple driver).
|
xPPSVX
|
Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (expert driver).
|
xPPTRF
|
Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix in packed storage.
|
xPPTRI
|
Computes the inverse of a symmetric or Hermitian positive definite matrix in packed storage using the Cholesky-factorization returned by xPPTRF.
|
xPPTRS (P)
|
Solves a symmetric or Hermitian positive definite system of linear equations where the coefficient matrix is in packed storage, using the Cholesky factorization returned by xPPTRF.
|
Symmetric or Hermitian Positive Definite Tridiagonal Matrix
|
xPTCON
|
Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite tridiagonal matrix using the Cholesky factorization returned by xPTTRF.
|
xPTEQR
|
Computes all eigenvectors and eigenvalues of a real symmetric or Hermitian positive definite system of linear equations.
|
xPTRFS
|
Refines solution to a symmetric or Hermitian positive definite tridiagonal system of linear equations.
|
xPTSV
|
Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (simple driver).
|
xPTSVX
|
Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (expert driver).
|
xPTTRF
|
Computes the LDLH factorization of a symmetric or Hermitian positive definite tridiagonal matrix.
|
xPTTRS (P)
|
Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations using the LDLH factorization returned by xPTTRF.
|
Real Symmetric Band Matrix
|
SSBEV or DSBEV
|
(Replacement with newer version SSBEVD or DSBEVD suggested) Computes all eigenvalues and eigenvectors of a symmetric band matrix.
|
SSBEVD or DSBEVD
|
Computes all eigenvalues and eigenvectors of a symmetric band matrix and uses a divide and conquer method to calculate eigenvectors.
|
SSBEVX or DSBEVX
|
Computes selected eigenvalues and eigenvectors of a symmetric band matrix.
|
SSBGST or DSBGST
|
Reduces symmetric-definite banded generalized eigenproblem to standard form.
|
SSBGV or DSBGV
|
(Replacement with newer version SSBGVD or DSBGVD suggested) Computes all eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.
|
SSBGVD or DSBGVD
|
Computes all eigenvalues and eigenvectors of generalized symmetric-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.
|
SSBGVX or DSBGVX
|
Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.
|
SSBTRD or DSBTRD
|
Reduces symmetric band matrix to real symmetric tridiagonal form by using an orthogonal similarity transform.
|
Symmetric Matrix in Packed Storage
|
xSPCON
|
Estimates the reciprocal of the condition number of a symmetric packed matrix using the factorization computed by xSPTRF.
|
SSPEV or DSPEV
|
(Replacement with newer version SSPEVD or DSPEVD suggested) Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage (simple driver).
|
SSPEVX or DSPEVX
|
Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage (expert driver).
|
SSPEVD or DSPEVD
|
Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.
|
SSPGST or DSPGST
|
Reduces a real symmetric-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by SPPTRF or DPPTRF.
|
SSPGVD or DSPGVD
|
Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.
|
SSPGV or DSPGV
|
(Replacement with newer version SSPGVD or DSPGVD suggested) Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).
|
SSPGVX or DSPGVX
|
Computes selected eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).
|
xSPRFS
|
Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite in packed storage.
|
xSPSV
|
Computes the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (simple driver).
|
xSPSVX
|
Uses the diagonal pivoting factorization to compute the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (expert driver).
|
SSPTRD or DSPTRD
|
Reduces a real symmetric matrix stored in packed form to real symmetric tridiagonal form using an orthogonal similarity transform.
|
xSPTRF
|
Computes the factorization of a symmetric packed matrix using the Bunch-Kaufman diagonal pivoting method.
|
xSPTRI
|
Computes the inverse of a symmetric indefinite matrix in packed storage using the factorization computed by xSPTRF.
|
xSPTRS (P)
|
Solves a system of linear equations by the symmetric matrix stored in packed format using the factorization computed by xSPTRF.
|
Real Symmetric Tridiagonal Matrix
|
SSTEBZ or DSTEBZ
|
Computes the eigenvalues of a real symmetric tridiagonal matrix.
|
xSTEDC
|
Computes all the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using a divide and conquer method.
|
xSTEGR
|
Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.
|
xSTEIN
|
Computes selected eigenvectors of a real symmetric tridiagonal matrix using inverse iteration.
|
xSTEQR
|
Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using the implicit QL or QR algorithm.
|
SSTERF or DSTERF
|
Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a root-free QL or QR algorithm variant.
|
SSTEV or DSTEV
|
(Replacement with newer version SSTEVR or DSTEVR suggested) Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (simple driver).
|
SSTEVX or DSTEVX
|
Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (expert driver).
|
SSTEVD or DSTEVD
|
(Replacement with newer version SSTEVR or DSTEVR suggested) Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a divide and conquer method.
|
SSTEVR or DSTEVR
|
Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.
|
xSTSV
|
Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.
|
xSTTRF
|
Computes the factorization of a symmetric tridiagonal matrix.
|
xSTTRS (P)
|
Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.
|
Symmetric Matrix
|
xSYCON
|
Estimates the reciprocal of the condition number of a symmetric matrix using the factorization computed by SSYTRF or DSYTRF.
|
SSYEV or DSYEV
|
(Replacement with newer version SSYEVR or DSYEVR suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix.
|
SSYEVX or DSYEVX
|
Computes eigenvalues and eigenvectors of a symmetric matrix (expert driver).
|
SSYEVD or DSYEVD
|
(Replacement with newer version SSYEVR or DSYEVR suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix and uses a divide and conquer method to calculate eigenvectors.
|
SSYEVR or DSYEVR
|
Computes selected eigenvalues and eigenvectors of a symmetric tridiagonal matrix.
|
SSYGST or DSYGST
|
Reduces a symmetric-definite generalized eigenproblem to standard form using the factorization computed by SPOTRF or DPOTRF.
|
SSYGV or DSYGV
|
(Replacement with newer version SSYGVD or DSYGVD suggested) Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.
|
SSYGVX or DSYGVX
|
Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.
|
SSYGVD or DSYGVD
|
Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.
|
xSYRFS
|
Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite.
|
xSYSV
|
Solves a real symmetric indefinite system of linear equations (simple driver).
|
xSYSVX
|
Solves a real symmetric indefinite system of linear equations (expert driver).
|
SSYTRD or DSYTRD
|
Reduces a symmetric matrix to real symmetric tridiagonal form by using a orthogonal similarity transformation.
|
xSYTRF
|
Computes the factorization of a real symmetric indefinite matrix using the diagonal pivoting method.
|
xSYTRI
|
Computes the inverse of a symmetric indefinite matrix using the factorization computed by xSYTRF.
|
xSYTRS (P)
|
Solves a system of linear equations by the symmetric matrix using the factorization computed by xSYTRF.
|
Triangular Band Matrix
|
xTBCON
|
Estimates the reciprocal condition number of a triangular band matrix.
|
xTBRFS
|
Determines error bounds and estimates for solving a triangular banded system of linear equations.
|
xTBTRS (P)
|
Solves a triangular banded system of linear equations.
|
Triangular Matrix-Generalized Problem (Pair of Triangular Matrices)
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xTGEVC
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Computes right and/or left generalized eigenvectors of two upper triangular matrices.
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xTGEXC
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Reorders the generalized Schur decomposition of a real or complex matrix pair using an orthogonal or unitary equivalence transformation.
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xTGSEN
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Reorders the generalized real-Schur or Schur decomposition of two matrixes and computes the generalized eigenvalues.
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xTGSJA
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Computes the generalized SVD from two upper triangular matrices obtained from xGGSVP.
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xTGSNA
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Estimates reciprocal condition numbers for specified eigenvalues and eigenvectors of two matrices in real-Schur or Schur canonical form.
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xTGSYL
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Solves the generalized Sylvester equation.
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Triangular Matrix in Packed Storage
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xTPCON
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Estimates the reciprocal or the condition number of a triangular matrix in packed storage.
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xTPRFS
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Determines error bounds and estimates for solving a triangular system of linear equations where the coefficient matrix is in packed storage.
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xTPTRI
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Computes the inverse of a triangular matrix in packed storage.
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xTPTRS (P)
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Solves a triangular system of linear equations where the coefficient matrix is in packed storage.
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Triangular Matrix
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xTRCON
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Estimates the reciprocal or the condition number of a triangular matrix.
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xTREVC
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Computes right and/or left eigenvectors of an upper triangular matrix.
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xTREXC
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Reorders Schur factorization of matrix using an orthogonal or unitary similarity transformation.
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xTRRFS
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Determines error bounds and estimates for triangular system of a linear equations.
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xTRSEN
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Reorders Schur factorization of matrix to group selected cluster of eigenvalues in the leading positions on the diagonal of the upper triangular matrix T and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.
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xTRSNA
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Estimates the reciprocal condition numbers of selected eigenvalues and eigenvectors of an upper quasi-triangular matrix.
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xTRSYL
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Solves Sylvester matrix equation.
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xTRTRI
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Computes the inverse of a triangular matrix.
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xTRTRS (P)
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Solves a triangular system of linear equations.
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Trapezoidal Matrix
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xTZRQF
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Depreciated routine replaced by routine xTZRZF.
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xTZRZF
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Reduces a rectangular upper trapezoidal matrix to upper triangular form by means of orthogonal transformations.
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Unitary Matrix
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CUNGBR or ZUNGBR
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Generates the unitary transformation matrices from reduction to bidiagonal form, as determined by CGEBRD or ZGEBRD.
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CUNGHR or ZUNGHR
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Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by CGEHRD or ZGEHRD.
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CUNGLQ or ZUNGLQ
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Generates a unitary matrix Q from an LQ factorization, as returned by CGELQF or ZGELQF.
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CUNGQL or ZUNGQL
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Generates a unitary matrix Q from a QL factorization, as returned by CGEQLF or ZGEQLF.
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CUNGQR or ZUNGQR
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Generates a unitary matrix Q from a QR factorization, as returned by CGEQRF or ZGEQRF.
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CUNGRQ or ZUNGRQ
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Generates a unitary matrix Q from an RQ factorization, as returned by CGERQF or ZGERQF.
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CUNGTR or ZUNGTR
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Generates a unitary matrix reduced to tridiagonal form, by CHETRD or ZHETRD.
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CUNMBR or ZUNMBR
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Multiplies a general matrix with the unitary transformation matrix reduced to bidiagonal form, as determined by CGEBRD or ZGEBRD.
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CUNMHR or ZUNMHR
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Multiplies a general matrix by the unitary matrix reduced to Hessenberg form by CGEHRD or ZGEHRD.
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CUNMLQ (P) or ZUNMLQ (P)
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Multiplies a general matrix by the unitary matrix from an LQ factorization, as returned by CGELQF or ZGELQF.
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CUNMQL (P) or ZUNMQL (P)
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Multiplies a general matrix by the unitary matrix from a QL factorization, as returned by CGEQLF or ZGEQLF.
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CUNMQR (P) or ZUNMQR (P)
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Multiplies a general matrix by the unitary matrix from a QR factorization, as returned by CGEQRF or ZGEQRF.
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CUNMRQ (P) or ZUNMRQ (P)
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Multiplies a general matrix by the unitary matrix from an RQ factorization, as returned by CGERQF or ZGERQF.
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CUNMRZ or ZUNMRZ
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Multiplies a general matrix by the unitary matrix from an RZ factorization, as returned by CTZRZF or ZTZRZF.
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CUNMTR or ZUNMTR
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Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by CHETRD or ZHETRD.
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Unitary Matrix in Packed Storage
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CUPGTR or ZUPGTR
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Generates the unitary transformation matrix from a tridiagonal matrix determined by CHPTRD or ZHPTRD.
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CUPMTR or ZUPMTR
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Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by CHPTRD or ZHPTRD.
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