# -------------------------------------------------------- # Available SIMPLE and DIVIDE AND CONQUER DRIVER routines: # -------------------------------------------------------- file clapack/double/dgesv.c for Solves a general system of linear equations AX=B. gams d2a1 file clapack/double/dgbsv.c for Solves a general banded system of linear equations AX=B. gams d2a2 file clapack/double/dgtsv.c for Solves a general tridiagonal system of linear equations AX=B. gams d2a2a file clapack/double/dposv.c for Solves a symmetric positive definite system of linear , equations AX=B. gams d2b1b file clapack/double/dppsv.c for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage. gams d2b1b file clapack/double/dpbsv.c for Solves a symmetric positive definite banded system , of linear equations AX=B. gams d2b2 file clapack/double/dptsv.c for Solves a symmetric positive definite tridiagonal system , of linear equations AX=B. gams d2b2a file clapack/double/dsysv.c for Solves a real symmetric indefinite system of linear equations AX=B. gams d2b1a file clapack/double/dspsv.c for Solves a real symmetric indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2b1a file clapack/double/dgels.c 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 clapack/double/dgglse.c for Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization gams d9b1 file clapack/double/dggglm.c for Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization file clapack/double/dsyev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. gams d4a1 file clapack/double/dsyevd.c 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 clapack/double/dspev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. gams d4a1 file clapack/double/dspevd.c 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 clapack/double/dsbev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. gams d4a1, d4a6 file clapack/double/dsbevd.c 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 clapack/double/dstev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file clapack/double/dstevd.c 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 clapack/double/dgees.c 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 clapack/double/dgeev.c for Computes the eigenvalues and left and right eigenvectors of , a general matrix. gams d4a2 file clapack/double/dgesvd.c for Computes the singular value decomposition (SVD) of a general , rectangular matrix. gams d6 file clapack/double/dsygv.c 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 clapack/double/dspgv.c 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 clapack/double/dsbgv.c 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 clapack/double/dgegs.c for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file clapack/double/dgegv.c for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file clapack/double/dggsvd.c for Computes the Generalized Singular Value Decomposition # --------------------------------- # Available EXPERT DRIVER routines: # --------------------------------- file clapack/double/dgesvx.c 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 clapack/double/dgbsvx.c 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 clapack/double/dgtsvx.c 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 clapack/double/dposvx.c 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 clapack/double/dppsvx.c 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 clapack/double/dpbsvx.c 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 clapack/double/dptsvx.c 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 clapack/double/dsysvx.c 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 clapack/double/dspsvx.c 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 clapack/double/dgelsx.c 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 clapack/double/dgelss.c 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 clapack/double/dsyevx.c for Computes selected eigenvalues and eigenvectors of a symmetric matrix. gams d4a1 file clapack/double/dspevx.c for Computes selected eigenvalues and eigenvectors of a , symmetric matrix in packed storage. gams d4a1 file clapack/double/dsbevx.c for Computes selected eigenvalues and eigenvectors of a , symmetric band matrix. gams d4a1, d4a6 file clapack/double/dstevx.c for Computes selected eigenvalues and eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file clapack/double/dgeesx.c 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 clapack/double/dgeevx.c 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 # --------------------------------- # Available COMPUTATIONAL routines: # --------------------------------- file clapack/double/dbdsqr.c for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm. gams d6 file clapack/double/ddisna.c 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 clapack/double/dgbbrd.c , Reduces a general band matrix to real upper bidiagonal form , by an orthogonal transformation. file clapack/double/dgbcon.c 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 clapack/double/dgbequ.c for Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number. gams d2a2 file clapack/double/dgbrfs.c 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 clapack/double/dgbtrf.c for Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges. gams d2a2 file clapack/double/dgbtrs.c 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 clapack/double/dgebak.c for Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to DGEBAL. gams d4c4 file clapack/double/dgebal.c for Balances a general matrix in order to improve the accuracy , of computed eigenvalues. gams d4c1a file clapack/double/dgebrd.c for Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal transformation. gams d6 file clapack/double/dgecon.c 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 clapack/double/dgeequ.c for Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number. gams d2a1 file clapack/double/dgehrd.c for Reduces a general matrix to upper Hessenberg form by an , orthogonal similarity transformation. gams d4c1b2 file clapack/double/dgelqf.c for Computes an LQ factorization of a general rectangular matrix. gams d5 file clapack/double/dgeqlf.c for Computes a QL factorization of a general rectangular matrix. gams d5 file clapack/double/dgeqpf.c for Computes a QR factorization with column pivoting of a general , rectangular matrix. gams d5 file clapack/double/dgeqrf.c for Computes a QR factorization of a general rectangular matrix. gams d5 file clapack/double/dgerfs.c 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 clapack/double/dgerqf.c for Computes an RQ factorization of a general rectangular matrix. gams d5 file clapack/double/dgetrf.c for Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges. gams d2a1 file clapack/double/dgetri.c for Computes the inverse of a general matrix, using the LU factorization , computed by DGETRF. gams d2a1 file clapack/double/dgetrs.c 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 clapack/double/dggbak.c 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 clapack/double/dggbal.c For Balances a pair of general real matrices for the generalized , eigenvalue problem A x = lambda B x. file clapack/double/dgghrd.c for Reduces a pair of real matrices to generalized upper , Hessenberg form using orthogonal transformations file clapack/double/dggqrf.c for Computes a generalized QR factorization of a pair of matrices. file clapack/double/dggrqf.c for Computes a generalized RQ factorization of a pair of matrices. file clapack/double/dggsvp.c for Computes orthogonal matrices as a preprocessing step , for computing the generalized singular value decomposition file clapack/double/dgtcon.c 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 clapack/double/dgtrfs.c 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 clapack/double/dgttrf.c for Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges. gams d2a2a file clapack/double/dgttrs.c 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 clapack/double/dhgeqz.c 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 clapack/double/dhsein.c for Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration. gams d4c3 file clapack/double/dhseqr.c for Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm. gams d4c2b file clapack/double/dopgtr.c for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by SSPTRD. gams d4c1b1 file clapack/double/dopmtr.c for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSPTRD. gams d4c4 file clapack/double/dorgbr.c for Generates the orthogonal transformation matrices from , a reduction to bidiagonal form determined by DGEBRD. gams d6 file clapack/double/dorghr.c for Generates the orthogonal transformation matrix from , a reduction to Hessenberg form determined by DGEHRD. gams d4c1b2 file clapack/double/dorglq.c for Generates all or part of the orthogonal matrix Q from , an LQ factorization determined by DGELQF. gams d5 file clapack/double/dorgql.c for Generates all or part of the orthogonal matrix Q from , a QL factorization determined by DGEQLF. gams d5 file clapack/double/dorgqr.c for Generates all or part of the orthogonal matrix Q from , a QR factorization determined by DGEQRF. gams d5 file clapack/double/dorgrq.c for Generates all or part of the orthogonal matrix Q from , an RQ factorization determined by DGERQF. gams d5 file clapack/double/dorgtr.c for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by DSYTRD. gams d4c1b1 file clapack/double/dormbr.c for Multiplies a general matrix by one of the orthogonal , transformation matrices from a reduction to bidiagonal form , determined by DGEBRD. gams d6 file clapack/double/dormhr.c for Multiplies a general matrix by the orthogonal transformation , matrix from a reduction to Hessenberg form determined by DGEHRD. gams d4c4 file clapack/double/dormlq.c for Multiplies a general matrix by the orthogonal matrix , from an LQ factorization determined by DGELQF. gams d5 file clapack/double/dormql.c for Multiplies a general matrix by the orthogonal matrix , from a QL factorization determined by DGEQLF. gams d5 file clapack/double/dormqr.c for Multiplies a general matrix by the orthogonal matrix , from a QR factorization determined by DGEQRF. gams d5 file clapack/double/dormrq.c for Multiplies a general matrix by the orthogonal matrix , from an RQ factorization determined by DGERQF. gams d5 file clapack/double/dormtr.c for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSYTRD. gams d4c4 file clapack/double/dpbcon.c 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 clapack/double/dpbequ.c for Computes row and column scalings to equilibrate a symmetric , positive definite band matrix and reduce its condition number. gams d2b2 file clapack/double/dpbrfs.c 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 clapack/double/dpbstf.c for Computes a split Cholesky factorization of a real symmetric positive , definite band matrix. file clapack/double/dpbtrf.c for Computes the Cholesky factorization of a symmetric , positive definite band matrix. gams d2b2 file clapack/double/dpbtrs.c for Solves a symmetric positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by DPBTRF. gams d2b2 file clapack/double/dpocon.c for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix, using the , Cholesky factorization computed by DPOTRF. gams d2b1b file clapack/double/dpoequ.c for Computes row and column scalings to equilibrate a symmetric , positive definite matrix and reduce its condition number. gams d2b1b file clapack/double/dporfs.c 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 clapack/double/dpotrf.c for Computes the Cholesky factorization of a symmetric , positive definite matrix. gams d2b1b file clapack/double/dpotri.c for Computes the inverse of a symmetric positive definite , matrix, using the Cholesky factorization computed by DPOTRF. gams d2b1b file clapack/double/dpotrs.c for Solves a symmetric positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , DPOTRF. gams d2b1b file clapack/double/dppcon.c 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 clapack/double/dppequ.c for Computes row and column scalings to equilibrate a symmetric , positive definite matrix in packed storage and reduce its condition , number. gams d2b1b file clapack/double/dpprfs.c 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 clapack/double/dpptrf.c for Computes the Cholesky factorization of a symmetric , positive definite matrix in packed storage. gams d2b1b file clapack/double/dpptri.c for Computes the inverse of a symmetric positive definite , matrix in packed storage, using the Cholesky factorization computed , by DPPTRF. gams d2b1b file clapack/double/dpptrs.c 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 clapack/double/dptcon.c 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 clapack/double/dpteqr.c 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 clapack/double/dptrfs.c 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 clapack/double/dpttrf.c for Computes the LDL**H factorization of a symmetric , positive definite tridiagonal matrix. gams d2b2a file clapack/double/dpttrs.c for Solves a symmetric positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by DPTTRF. gams d2b2a file clapack/double/dsbgst.c 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 clapack/double/dsbtrd.c for Reduces a symmetric band matrix to real symmetric , tridiagonal form by an orthogonal similarity transformation. gams d4c1b1 file clapack/double/dspcon.c 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 clapack/double/dspgst.c 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 clapack/double/dsprfs.c 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 clapack/double/dsptrd.c for Reduces a symmetric matrix in packed storage to real , symmetric tridiagonal form by an orthogonal similarity , transformation. gams d4c1b1 file clapack/double/dsptrf.c for Computes the factorization of a real , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2b1a file clapack/double/dsptri.c for Computes the inverse of a real symmetric , indefinite matrix in packed storage, using the factorization , computed by DSPTRF. gams d2b1a file clapack/double/dsptrs.c 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 clapack/double/dstebz.c for Computes selected eigenvalues of a real symmetric tridiagonal , matrix by bisection. gams d4c2a file clapack/double/dstedc.c for Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm. file clapack/double/dstein.c for Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration. gams d4c3 file clapack/double/dsteqr.c for Computes all eigenvalues and eigenvectors of a real symmetric , tridiagonal matrix, using the implicit QL or QR algorithm. gams d4a1, d4a5, d4c2a file clapack/double/dsterf.c for Computes all eigenvalues of a real symmetric tridiagonal matrix, , using a root-free variant of the QL or QR algorithm. gams d4c2a file clapack/double/dsycon.c for Estimates the reciprocal of the condition number of a , real symmetric indefinite matrix, , using the factorization computed by DSYTRF. gams d2b1a file clapack/double/dsygst.c 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 clapack/double/dsyrfs.c 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 clapack/double/dsytrd.c for Reduces a symmetric matrix to real symmetric tridiagonal , form by an orthogonal similarity transformation. gams d4c1b1 file clapack/double/dsytrf.c for Computes the factorization of a real symmetric-indefinite matrix, , using the diagonal pivoting method. gams d2b1a file clapack/double/dsytri.c for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by DSYTRF. gams d2b1a file clapack/double/dsytrs.c for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by DSPTRF. gams d2b1a file clapack/double/dtbcon.c 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 clapack/double/dtbrfs.c 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 clapack/double/dtbtrs.c for Solves a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a2, d2a3 file clapack/double/dtgevc.c for Computes some or all of the right and/or left generalized eigenvectors , of a pair of upper triangular matrices. gams d4b2 file clapack/double/dtgsja.c for Computes the generalized singular value decomposition of two real , upper triangular (or trapezoidal) matrices as output by DGGSVP. gams d6 file clapack/double/dtpcon.c 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 clapack/double/dtprfs.c 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 clapack/double/dtptri.c for Computes the inverse of a triangular matrix in packed storage. gams d2a3 file clapack/double/dtptrs.c 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 clapack/double/dtrcon.c for Estimates the reciprocal of the condition number of a triangular , matrix, in either the 1-norm or the infinity-norm. gams d2a3 file clapack/double/dtrevc.c for Computes some or all of the right and/or left eigenvectors of , an upper quasi-triangular matrix. gams d4c3 file clapack/double/dtrexc.c for Reorders the Schur factorization of a matrix by an orthogonal , similarity transformation. gams d4c file clapack/double/dtrrfs.c 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 clapack/double/dtrsen.c 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 clapack/double/dtrsna.c for Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of an upper , quasi-triangular matrix. gams d4c file clapack/double/dtrsyl.c 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 clapack/double/dtrtri.c for Computes the inverse of a triangular matrix. gams d2a3 file clapack/double/dtrtrs.c for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a3 file clapack/double/dtzrqf.c for Computes an RQ factorization of an upper trapezoidal matrix. gams d5 .