## netlib/lapack/double/index

```--------------------------------------------------------
Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
--------------------------------------------------------
```
• file: lapack/double/dgesv.f
• prec: double
• for: Solves a general system of linear equations AX=B.
• gams: d2a1
• file: lapack/double/dgbsv.f
• prec: double
• for: Solves a general banded system of linear equations AX=B.
• gams: d2a2
• file: lapack/double/dgtsv.f
• prec: double
• for: Solves a general tridiagonal system of linear equations AX=B.
• gams: d2a2a
• file: lapack/double/dposv.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B.
• gams: d2b1b
• file: lapack/double/dppsv.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage.
• gams: d2b1b
• file: lapack/double/dpbsv.f
• prec: double
• for: Solves a symmetric positive definite banded system , of linear equations AX=B.
• gams: d2b2
• file: lapack/double/dptsv.f
• prec: double
• for: Solves a symmetric positive definite tridiagonal system , of linear equations AX=B.
• gams: d2b2a
• file: lapack/double/dsysv.f
• prec: double
• for: Solves a real symmetric indefinite system of linear equations AX=B.
• gams: d2b1a
• file: lapack/double/dspsv.f
• prec: double
• for: Solves a real symmetric indefinite system of linear equations AX=B, , where A is held in packed storage.
• gams: d2b1a
• file: lapack/double/dgels.f
• prec: double
• for: Computes the least squares solution to an over-determined system , of linear equations, A X=B or A**H X=B, or the minimum norm , solution of an under-determined system, where A is a general , rectangular matrix of full rank, using a QR or LQ factorization , of A.
• gams: d9a1
• file: lapack/double/dgelsd.f
• prec: double
• for: Computes the least squares solution to an over-determined system , of linear equations, A X=B or A**H X=B, or the minimum norm , solution of an under-determined system, using a divide and conquer , method, where A is a general rectangular matrix of full rank, , using a QR or LQ factorization of A.
• gams: d9a1
• file: lapack/double/dgglse.f
• prec: double
• for: Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization
• gams: d9b1
• file: lapack/double/dggglm.f
• prec: double
• for: Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization
• file: lapack/double/dsyev.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix.
• gams: d4a1
• file: lapack/double/dsyevd.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. If eigenvectors are desired, it uses a divide , and conquer algorithm.
• gams: d4a1
• file: lapack/double/dspev.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage.
• gams: d4a1
• file: lapack/double/dspevd.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. If eigenvectors are desired, , it uses a divide and conquer algorithm.
• gams: d4a1
• file: lapack/double/dsbev.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix.
• gams: d4a1, d4a6
• file: lapack/double/dsbevd.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. If eigenvectors are desired, it uses a , divide and conquer algorithm.
• gams: d4a1, d4a6
• file: lapack/double/dstev.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix.
• gams: d4a1, d4a5
• file: lapack/double/dstevd.f
• prec: double
• for: Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. If eigenvectors are desired, it uses , a divide and conquer algorithm.
• gams: d4a1, d4a5
• file: lapack/double/dgees.f
• prec: double
• for: Computes the eigenvalues and Schur factorization of a general , matrix, and orders the factorization so that selected eigenvalues , are at the top left of the Schur form.
• gams: d4a2
• file: lapack/double/dgeev.f
• prec: double
• for: Computes the eigenvalues and left and right eigenvectors of , a general matrix.
• gams: d4a2
• file: lapack/double/dgesvd.f
• prec: double
• for: Computes the singular value decomposition (SVD) of a general , rectangular matrix.
• gams: d6
• file: lapack/double/dgesdd.f
• prec: double
• for: Computes the singular value decomposition (SVD) of a general , rectangular matrix using divide-and-conquer.
• gams: d6
• file: lapack/double/dsygv.f
• prec: double
• for: Computes all eigenvalues and the eigenvectors of a generalized , symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
• gams: d4b1
• file: lapack/double/dsygvd.f
• prec: double
• for: Computes all eigenvalues and the eigenvectors of a generalized , symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. , If eigenvectors are desired, it uses a divide and conquer algorithm.
• gams: d4b1
• file: lapack/double/dspgv.f
• prec: double
• for: Computes all eigenvalues and eigenvectors of a generalized , symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage.
• gams: d4b1
• file: lapack/double/dspgvd.f
• prec: double
• for: Computes all eigenvalues and eigenvectors of a generalized , symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. , If eigenvectors are desired, it uses a divide and conquer algorithm.
• gams: d4b1
• file: lapack/double/dsbgv.f
• prec: double
• for: Computes all the eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite.
• file: lapack/double/dsbgvd.f
• prec: double
• for: Computes all the eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite. , If eigenvectors are desired, it uses a divide and conquer algorithm.
• file: lapack/double/dgegs.f
• prec: double
• for: Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices
• file: lapack/double/dgges.f
• prec: double
• for: Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices
• file: lapack/double/dgegv.f
• prec: double
• for: Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices
• file: lapack/double/dggev.f
• prec: double
• for: Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices
• file: lapack/double/dggsvd.f
• prec: double
• for: Computes the Generalized Singular Value Decomposition
• ```-----------------------------------------
Available EXPERT and RRR DRIVER routines:
-----------------------------------------
```
• file: lapack/double/dgesvx.f
• prec: double
• for: Solves a general system of linear equations AX=B, A**T X=B , or A**H X=B, and provides an estimate of the condition number , and error bounds on the solution.
• gams: d2a1
• file: lapack/double/dgbsvx.f
• prec: double
• for: Solves a general banded system of linear equations AX=B, , A**T X=B or A**H X=B, and provides an estimate of the condition , number and error bounds on the solution.
• gams: d2a2
• file: lapack/double/dgtsvx.f
• prec: double
• for: Solves a general tridiagonal system of linear equations AX=B, , A**T X=B or A**H X=B, and provides an estimate of the condition , number and error bounds on the solution.
• gams: d2a2a
• file: lapack/double/dposvx.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B, and provides an estimate of the condition number , and error bounds on the solution.
• gams: d2b1b
• file: lapack/double/dppsvx.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage, and provides , an estimate of the condition number and error bounds on the , solution.
• gams: d2b1b
• file: lapack/double/dpbsvx.f
• prec: double
• for: Solves a symmetric positive definite banded system , of linear equations AX=B, and provides an estimate of the condition , number and error bounds on the solution.
• gams: d2b2
• file: lapack/double/dptsvx.f
• prec: double
• for: Solves a symmetric positive definite tridiagonal , system of linear equations AX=B, and provides an estimate of , the condition number and error bounds on the solution.
• gams: d2b2a
• file: lapack/double/dsysvx.f
• prec: double
• for: Solves a real symmetric , indefinite system of linear equations AX=B, and provides an , estimate of the condition number and error bounds on the solution.
• gams: d2b1a
• file: lapack/double/dspsvx.f
• prec: double
• for: Solves a real symmetric , indefinite system of linear equations AX=B, where A is held , in packed storage, and provides an estimate of the condition , number and error bounds on the solution.
• gams: d2b1a
• file: lapack/double/dgelsx.f
• prec: double
• for: Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using a , complete orthogonal factorization of A.
• gams: d9a1
• file: lapack/double/dgelsy.f
• prec: double
• for: Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using a , complete orthogonal factorization of A.
• gams: d9a1
• file: lapack/double/dgelss.f
• prec: double
• for: Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using , the singular value decomposition of A.
• gams: d9a1
• file: lapack/double/dsyevx.f
• prec: double
• for: Computes selected eigenvalues and eigenvectors of a symmetric matrix.
• gams: d4a1
• file: lapack/double/dsyevr.f
• prec: double
• for: Computes selected eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. Eigenvalues are computed by the dqds , algorithm, and eigenvectors are computed from various "good" LDL^T , representations (also known as Relatively Robust Representations).
• gams: d4a1, d4a5
• file: lapack/double/dsygvx.f
• prec: double
• for: Computes selected eigenvalues, and optionally, the eigenvectors of , a generalized symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
• gams: d4b1
• file: lapack/double/dspevx.f
• prec: double
• for: Computes selected eigenvalues and eigenvectors of a , symmetric matrix in packed storage.
• gams: d4a1
• file: lapack/double/dspgvx.f
• prec: double
• for: Computes selected eigenvalues, and optionally, eigenvectors of , a generalized symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage.
• gams: d4b1
• file: lapack/double/dsbevx.f
• prec: double
• for: Computes selected eigenvalues and eigenvectors of a , symmetric band matrix.
• gams: d4a1, d4a6
• file: lapack/double/dsbgvx.f
• prec: double
• for: Computes selected eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite.
• file: lapack/double/dstevx.f
• prec: double
• for: Computes selected eigenvalues and eigenvectors of a real , symmetric tridiagonal matrix.
• gams: d4a1, d4a5
• file: lapack/double/dstevr.f
• prec: double
• for: Computes selected eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. Eigenvalues are computed by the dqds , algorithm, and eigenvectors are computed from various "good" LDL^T , representations (also known as Relatively Robust Representations).
• gams: d4a1, d4a5
• file: lapack/double/dgeesx.f
• prec: double
• for: Computes the eigenvalues and Schur factorization of a general , matrix, orders the factorization so that selected eigenvalues , are at the top left of the Schur form, and computes reciprocal , condition numbers for the average of the selected eigenvalues, , and for the associated right invariant subspace.
• gams: d4a2
• file: lapack/double/dggesx.f
• prec: double
• for: Computes the generalized eigenvalues, the real Schur form, and, , optionally, the left and/or right matrices of Schur vectors.
• file: lapack/double/dgeevx.f
• prec: double
• for: Computes the eigenvalues and left and right eigenvectors of , a general matrix, with preliminary balancing of the matrix, , and computes reciprocal condition numbers for the eigenvalues , and right eigenvectors.
• gams: d4a2
• file: lapack/double/dggevx.f
• prec: double
• for: Computes the generalized eigenvalues, and optionally, the left , and/or right generalized eigenvectors.
• ```---------------------------------
Available COMPUTATIONAL routines:
---------------------------------
```
• file: lapack/double/dbdsdc.f
• prec: double
• for: Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using a divide and conquer method.
• gams: d6
• file: lapack/double/dbdsqr.f
• prec: double
• for: Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm.
• gams: d6
• file: lapack/double/ddisna.f
• prec: double
• for: Computes the reciprocal condition numbers for the eigenvectors of a , real symmetric or complex Hermitian matrix or for the left or right , singular vectors of a general matrix.
• file: lapack/double/dgbbrd.f
• prec: double , Reduces a general band matrix to real upper bidiagonal form , by an orthogonal transformation.
• file: lapack/double/dgbcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a general , band matrix, in either the 1-norm or the infinity-norm, using , the LU factorization computed by DGBTRF.
• gams: d2a2
• file: lapack/double/dgbequ.f
• prec: double
• for: Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number.
• gams: d2a2
• file: lapack/double/dgbrfs.f
• prec: double
• for: Improves the computed solution to a general banded system of , linear equations AX=B, A**T X=B or A**H X=B, and provides forward , and backward error bounds for the solution.
• gams: d2a2
• file: lapack/double/dgbtrf.f
• prec: double
• for: Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges.
• gams: d2a2
• file: lapack/double/dgbtrs.f
• prec: double
• for: Solves a general banded system of linear equations AX=B, , A**T X=B or A**H X=B, using the LU factorization computed , by DGBTRF.
• gams: d2a2
• file: lapack/double/dgebak.f
• prec: double
• for: Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to DGEBAL.
• gams: d4c4
• file: lapack/double/dgebal.f
• prec: double
• for: Balances a general matrix in order to improve the accuracy , of computed eigenvalues.
• gams: d4c1a
• file: lapack/double/dgebrd.f
• prec: double
• for: Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal transformation.
• gams: d6
• file: lapack/double/dgecon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a general , matrix, in either the 1-norm or the infinity-norm, using the , LU factorization computed by DGETRF.
• gams: d2a1
• file: lapack/double/dgeequ.f
• prec: double
• for: Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number.
• gams: d2a1
• file: lapack/double/dgehrd.f
• prec: double
• for: Reduces a general matrix to upper Hessenberg form by an , orthogonal similarity transformation.
• gams: d4c1b2
• file: lapack/double/dgelqf.f
• prec: double
• for: Computes an LQ factorization of a general rectangular matrix.
• gams: d5
• file: lapack/double/dgeqlf.f
• prec: double
• for: Computes a QL factorization of a general rectangular matrix.
• gams: d5
• file: lapack/double/dgeqp3.f
• prec: double
• for: Computes a QR factorization with column pivoting of a general , rectangular matrix using Level 3 BLAS.
• gams: d5
• file: lapack/double/dgeqpf.f
• prec: double
• for: Computes a QR factorization with column pivoting of a general , rectangular matrix.
• gams: d5
• file: lapack/double/dgeqrf.f
• prec: double
• for: Computes a QR factorization of a general rectangular matrix.
• gams: d5
• file: lapack/double/dgerfs.f
• prec: double
• for: Improves the computed solution to a general system of linear , equations AX=B, A**T X=B or A**H X=B, and provides forward and , backward error bounds for the solution.
• gams: d2a1
• file: lapack/double/dgerqf.f
• prec: double
• for: Computes an RQ factorization of a general rectangular matrix.
• gams: d5
• file: lapack/double/dgetrf.f
• prec: double
• for: Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges.
• gams: d2a1
• file: lapack/double/dgetri.f
• prec: double
• for: Computes the inverse of a general matrix, using the LU factorization , computed by DGETRF.
• gams: d2a1
• file: lapack/double/dgetrs.f
• prec: double
• for: Solves a general system of linear equations AX=B, A**T X=B , or A**H X=B, using the LU factorization computed by DGETRF.
• gams: d2a1
• file: lapack/double/dggbak.f
• prec: double
• For: Forms the right or left eigenvectors of the generalized eigenvalue , problem by backward transformation on the computed eigenvectors of , the balanced pair of matrices output by DGGBAL.
• file: lapack/double/dggbal.f
• prec: double
• For: Balances a pair of general real matrices for the generalized , eigenvalue problem A x = lambda B x.
• file: lapack/double/dgghrd.f
• prec: double
• for: Reduces a pair of real matrices to generalized upper , Hessenberg form using orthogonal transformations
• file: lapack/double/dggqrf.f
• prec: double
• for: Computes a generalized QR factorization of a pair of matrices.
• file: lapack/double/dggrqf.f
• prec: double
• for: Computes a generalized RQ factorization of a pair of matrices.
• file: lapack/double/dggsvp.f
• prec: double
• for: Computes orthogonal matrices as a preprocessing step , for computing the generalized singular value decomposition
• file: lapack/double/dgtcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a general , tridiagonal matrix, in either the 1-norm or the infinity-norm, , using the LU factorization computed by DGTTRF.
• gams: d2a2a
• file: lapack/double/dgtrfs.f
• prec: double
• for: Improves the computed solution to a general tridiagonal system , of linear equations AX=B, A**T X=B or A**H X=B, and provides , forward and backward error bounds for the solution.
• gams: d2a2a
• file: lapack/double/dgttrf.f
• prec: double
• for: Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges.
• gams: d2a2a
• file: lapack/double/dgttrs.f
• prec: double
• for: Solves a general tridiagonal system of linear equations AX=B, , A**T X=B or A**H X=B, using the LU factorization computed by , DGTTRF.
• gams: d2a2a
• file: lapack/double/dhgeqz.f
• prec: double
• for: Implements a single-/double-shift version of the QZ method for , finding the generalized eigenvalues of the equation , det(A - w(i) B) = 0
• file: lapack/double/dhsein.f
• prec: double
• for: Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration.
• gams: d4c3
• file: lapack/double/dhseqr.f
• prec: double
• for: Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm.
• gams: d4c2b
• file: lapack/double/dopgtr.f
• prec: double
• for: Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by DSPTRD.
• gams: d4c1b1
• file: lapack/double/dopmtr.f
• prec: double
• for: Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSPTRD.
• gams: d4c4
• file: lapack/double/dorgbr.f
• prec: double
• for: Generates the orthogonal transformation matrices from , a reduction to bidiagonal form determined by DGEBRD.
• gams: d6
• file: lapack/double/dorghr.f
• prec: double
• for: Generates the orthogonal transformation matrix from , a reduction to Hessenberg form determined by DGEHRD.
• gams: d4c1b2
• file: lapack/double/dorglq.f
• prec: double
• for: Generates all or part of the orthogonal matrix Q from , an LQ factorization determined by DGELQF.
• gams: d5
• file: lapack/double/dorgql.f
• prec: double
• for: Generates all or part of the orthogonal matrix Q from , a QL factorization determined by DGEQLF.
• gams: d5
• file: lapack/double/dorgqr.f
• prec: double
• for: Generates all or part of the orthogonal matrix Q from , a QR factorization determined by DGEQRF.
• gams: d5
• file: lapack/double/dorgrq.f
• prec: double
• for: Generates all or part of the orthogonal matrix Q from , an RQ factorization determined by DGERQF.
• gams: d5
• file: lapack/double/dorgtr.f
• prec: double
• for: Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by DSYTRD.
• gams: d4c1b1
• file: lapack/double/dormbr.f
• prec: double
• for: Multiplies a general matrix by one of the orthogonal , transformation matrices from a reduction to bidiagonal form , determined by DGEBRD.
• gams: d6
• file: lapack/double/dormhr.f
• prec: double
• for: Multiplies a general matrix by the orthogonal transformation , matrix from a reduction to Hessenberg form determined by DGEHRD.
• gams: d4c4
• file: lapack/double/dormlq.f
• prec: double
• for: Multiplies a general matrix by the orthogonal matrix , from an LQ factorization determined by DGELQF.
• gams: d5
• file: lapack/double/dormql.f
• prec: double
• for: Multiplies a general matrix by the orthogonal matrix , from a QL factorization determined by DGEQLF.
• gams: d5
• file: lapack/double/dormqr.f
• prec: double
• for: Multiplies a general matrix by the orthogonal matrix , from a QR factorization determined by DGEQRF.
• gams: d5
• file: lapack/double/dormr3.f
• prec: double
• for: Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by DTZRZF.
• file: lapack/double/dormrq.f
• prec: double
• for: Multiplies a general matrix by the orthogonal matrix , from an RQ factorization determined by DGERQF.
• gams: d5
• file: lapack/double/dormrz.f
• prec: double
• for: Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by DTZRZF.
• file: lapack/double/dormtr.f
• prec: double
• for: Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSYTRD.
• gams: d4c4
• file: lapack/double/dpbcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a , symmetric positive definite band matrix, using the , Cholesky factorization computed by DPBTRF.
• gams: d2b2
• file: lapack/double/dpbequ.f
• prec: double
• for: Computes row and column scalings to equilibrate a symmetric , positive definite band matrix and reduce its condition number.
• gams: d2b2
• file: lapack/double/dpbrfs.f
• prec: double
• for: Improves the computed solution to a symmetric positive , definite banded system of linear equations AX=B, and provides , forward and backward error bounds for the solution.
• gams: d2b2
• file: lapack/double/dpbstf.f
• prec: double
• for: Computes a split Cholesky factorization of a real symmetric positive , definite band matrix.
• file: lapack/double/dpbtrf.f
• prec: double
• for: Computes the Cholesky factorization of a symmetric , positive definite band matrix.
• gams: d2b2
• file: lapack/double/dpbtrs.f
• prec: double
• for: Solves a symmetric positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by DPBTRF.
• gams: d2b2
• file: lapack/double/dpocon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a , symmetric positive definite matrix, using the , Cholesky factorization computed by DPOTRF.
• gams: d2b1b
• file: lapack/double/dpoequ.f
• prec: double
• for: Computes row and column scalings to equilibrate a symmetric , positive definite matrix and reduce its condition number.
• gams: d2b1b
• file: lapack/double/dporfs.f
• prec: double
• for: Improves the computed solution to a symmetric positive , definite system of linear equations AX=B, and provides forward , and backward error bounds for the solution.
• gams: d2b1b
• file: lapack/double/dpotrf.f
• prec: double
• for: Computes the Cholesky factorization of a symmetric , positive definite matrix.
• gams: d2b1b
• file: lapack/double/dpotri.f
• prec: double
• for: Computes the inverse of a symmetric positive definite , matrix, using the Cholesky factorization computed by DPOTRF.
• gams: d2b1b
• file: lapack/double/dpotrs.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , DPOTRF.
• gams: d2b1b
• file: lapack/double/dppcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a , symmetric positive definite matrix in packed storage, , using the Cholesky factorization computed by DPPTRF.
• gams: d2b1b
• file: lapack/double/dppequ.f
• prec: double
• for: Computes row and column scalings to equilibrate a symmetric , positive definite matrix in packed storage and reduce its condition , number.
• gams: d2b1b
• file: lapack/double/dpprfs.f
• prec: double
• for: Improves the computed solution to a symmetric positive , definite system of linear equations AX=B, where A is held in , packed storage, and provides forward and backward error bounds , for the solution.
• gams: d2b1b
• file: lapack/double/dpptrf.f
• prec: double
• for: Computes the Cholesky factorization of a symmetric , positive definite matrix in packed storage.
• gams: d2b1b
• file: lapack/double/dpptri.f
• prec: double
• for: Computes the inverse of a symmetric positive definite , matrix in packed storage, using the Cholesky factorization computed , by DPPTRF.
• gams: d2b1b
• file: lapack/double/dpptrs.f
• prec: double
• for: Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage, using the , Cholesky factorization computed by DPPTRF.
• gams: d2b1b
• file: lapack/double/dptcon.f
• prec: double
• for: Computes the reciprocal of the condition number of a , symmetric positive definite tridiagonal matrix, , using the LDL**H factorization computed by DPTTRF.
• gams: d2b2a
• file: lapack/double/dpteqr.f
• prec: double
• for: Computes all eigenvalues and eigenvectors of a real symmetric , positive definite tridiagonal matrix, by computing the SVD of , its bidiagonal Cholesky factor.
• gams: d4c2a
• file: lapack/double/dptrfs.f
• prec: double
• for: Improves the computed solution to a symmetric positive , definite tridiagonal system of linear equations AX=B, and provides , forward and backward error bounds for the solution.
• gams: d2b2a
• file: lapack/double/dpttrf.f
• prec: double
• for: Computes the LDL**H factorization of a symmetric , positive definite tridiagonal matrix.
• gams: d2b2a
• file: lapack/double/dpttrs.f
• prec: double
• for: Solves a symmetric positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by DPTTRF.
• gams: d2b2a
• file: lapack/double/dsbgst.f
• prec: double
• for: Reduces a real symmetric-definite banded generalized eigenproblem , A x = lambda B x to standard form, where B has been factorized by , DPBSTF (Crawford's algorithm).
• file: lapack/double/dsbtrd.f
• prec: double
• for: Reduces a symmetric band matrix to real symmetric , tridiagonal form by an orthogonal similarity transformation.
• gams: d4c1b1
• file: lapack/double/dspcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a , real symmetric indefinite , matrix in packed storage, using the factorization computed , by DSPTRF.
• gams: d2b1a
• file: lapack/double/dspgst.f
• prec: double
• for: Reduces a symmetric-definite generalized eigenproblem , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard , form, where A and B are held in packed storage, and B has been , factorized by DPPTRF.
• gams: d4c1c
• file: lapack/double/dsprfs.f
• prec: double
• for: Improves the computed solution to a real , symmetric indefinite system of linear equations , AX=B, where A is held in packed storage, and provides forward , and backward error bounds for the solution.
• gams: d2b1a
• file: lapack/double/dsptrd.f
• prec: double
• for: Reduces a symmetric matrix in packed storage to real , symmetric tridiagonal form by an orthogonal similarity , transformation.
• gams: d4c1b1
• file: lapack/double/dsptrf.f
• prec: double
• for: Computes the factorization of a real , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method.
• gams: d2b1a
• file: lapack/double/dsptri.f
• prec: double
• for: Computes the inverse of a real symmetric , indefinite matrix in packed storage, using the factorization , computed by DSPTRF.
• gams: d2b1a
• file: lapack/double/dsptrs.f
• prec: double
• for: Solves a real symmetric , indefinite system of linear equations AX=B, where A is held , in packed storage, using the factorization computed , by DSPTRF.
• gams: d2b1a
• file: lapack/double/dstebz.f
• prec: double
• for: Computes selected eigenvalues of a real symmetric tridiagonal , matrix by bisection.
• gams: d4c2a
• file: lapack/double/dstedc.f
• prec: double
• for: Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm.
• file: lapack/double/dstegr.f
• prec: double
• for: Computes selected eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix. The eigenvalues are computed by the , dqds algorithm, while eigenvectors are computed from various "good" , LDL^T representations (also known as Relatively Robust Representations.)
• file: lapack/double/dstein.f
• prec: double
• for: Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration.
• gams: d4c3
• file: lapack/double/dsteqr.f
• prec: double
• for: Computes all eigenvalues and eigenvectors of a real symmetric , tridiagonal matrix, using the implicit QL or QR algorithm.
• gams: d4a1, d4a5, d4c2a
• file: lapack/double/dsterf.f
• prec: double
• for: Computes all eigenvalues of a real symmetric tridiagonal matrix, , using a root-free variant of the QL or QR algorithm.
• gams: d4c2a
• file: lapack/double/dsycon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a , real symmetric indefinite matrix, , using the factorization computed by DSYTRF.
• gams: d2b1a
• file: lapack/double/dsygst.f
• prec: double
• for: Reduces a symmetric-definite generalized eigenproblem , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard , form, where B has been factorized by DPOTRF.
• gams: d4c1c
• file: lapack/double/dsyrfs.f
• prec: double
• for: Improves the computed solution to a real , symmetric indefinite system of linear equations , AX=B, and provides forward and backward error bounds for the , solution.
• gams: d2b1a
• file: lapack/double/dsytrd.f
• prec: double
• for: Reduces a symmetric matrix to real symmetric tridiagonal , form by an orthogonal similarity transformation.
• gams: d4c1b1
• file: lapack/double/dsytrf.f
• prec: double
• for: Computes the factorization of a real symmetric-indefinite matrix, , using the diagonal pivoting method.
• gams: d2b1a
• file: lapack/double/dsytri.f
• prec: double
• for: Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by DSYTRF.
• gams: d2b1a
• file: lapack/double/dsytrs.f
• prec: double
• for: Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by DSPTRF.
• gams: d2b1a
• file: lapack/double/dtbcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a triangular , band matrix, in either the 1-norm or the infinity-norm.
• gams: d2a2, d2a3
• file: lapack/double/dtbrfs.f
• prec: double
• for: Provides forward and backward error bounds for the solution , of a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B.
• gams: d2a2, d2a3
• file: lapack/double/dtbtrs.f
• prec: double
• for: Solves a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B.
• gams: d2a2, d2a3
• file: lapack/double/dtgevc.f
• prec: double
• for: Computes some or all of the right and/or left generalized eigenvectors , of a pair of upper triangular matrices.
• gams: d4b2
• file: lapack/double/dtgexc.f
• prec: double
• for: Reorders the generalized real Schur decomposition of a real , matrix pair (A,B) using an orthogonal equivalence transformation , so that the diagonal block of (A,B) with row index IFST is moved , to row ILST.
• file: lapack/double/dtgsen.f
• prec: double
• for: Reorders the generalized real Schur decomposition of a real , matrix pair (A, B) so that a selected cluster of eigenvalues , appears in the leading diagonal blocks of the upper quasi-triangular , matrix A and the upper triangular B.
• file: lapack/double/dtgsja.f
• prec: double
• for: Computes the generalized singular value decomposition of two real , upper triangular (or trapezoidal) matrices as output by DGGSVP.
• gams: d6
• file: lapack/double/dtgsna.f
• prec: double
• for: Estimates reciprocal condition numbers for specified , eigenvalues and/or eigenvectors of a matrix pair (A, B) in , generalized real Schur canonical form, as returned by DGGES.
• file: lapack/double/dtgsyl.f
• prec: double
• for: Solves the generalized Sylvester equation.
• file: lapack/double/dtpcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a triangular , matrix in packed storage, in either the 1-norm or the infinity-norm.
• gams: d2a3
• file: lapack/double/dtprfs.f
• prec: double
• for: Provides forward and backward error bounds for the solution , of a triangular system of linear equations AX=B, A**T X=B or , A**H X=B, where A is held in packed storage.
• gams: d2a3
• file: lapack/double/dtptri.f
• prec: double
• for: Computes the inverse of a triangular matrix in packed storage.
• gams: d2a3
• file: lapack/double/dtptrs.f
• prec: double
• for: Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B, where A is held in packed storage.
• gams: d2a3
• file: lapack/double/dtrcon.f
• prec: double
• for: Estimates the reciprocal of the condition number of a triangular , matrix, in either the 1-norm or the infinity-norm.
• gams: d2a3
• file: lapack/double/dtrevc.f
• prec: double
• for: Computes some or all of the right and/or left eigenvectors of , an upper quasi-triangular matrix.
• gams: d4c3
• file: lapack/double/dtrexc.f
• prec: double
• for: Reorders the Schur factorization of a matrix by an orthogonal , similarity transformation.
• gams: d4c
• file: lapack/double/dtrrfs.f
• prec: double
• for: Provides forward and backward error bounds for the solution , of a triangular system of linear equations A X=B, A**T X=B or , A**H X=B.
• gams: d2a3
• file: lapack/double/dtrsen.f
• prec: double
• for: Reorders the Schur factorization of a matrix in order to find , an orthonormal basis of a right invariant subspace corresponding , to selected eigenvalues, and returns reciprocal condition numbers , (sensitivities) of the average of the cluster of eigenvalues , and of the invariant subspace.
• gams: d4c
• file: lapack/double/dtrsna.f
• prec: double
• for: Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of an upper , quasi-triangular matrix.
• gams: d4c
• file: lapack/double/dtrsyl.f
• prec: double
• for: Solves the Sylvester matrix equation A X +/- X B=C where A , and B are upper quasi-triangular, and may be transposed.
• gams: d8
• file: lapack/double/dtrtri.f
• prec: double
• for: Computes the inverse of a triangular matrix.
• gams: d2a3
• file: lapack/double/dtrtrs.f
• prec: double
• for: Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B.
• gams: d2a3
• file: lapack/double/dtzrqf.f
• prec: double
• for: Computes an RQ factorization of an upper trapezoidal matrix.
• gams: d5
• file: lapack/double/dtzrzf.f
• prec: double
• for: Computes an RZ factorization of an upper trapezoidal matrix , (blocked version of DTZRQF).
• index help

Eric and Jack