# -------------------------------------------------------- # Available SIMPLE and DIVIDE AND CONQUER DRIVER routines: # -------------------------------------------------------- file clapack/single/sgesv.c for Solves a general system of linear equations AX=B. gams d2a1 file clapack/single/sgbsv.c for Solves a general banded system of linear equations AX=B. gams d2a2 file clapack/single/sgtsv.c for Solves a general tridiagonal system of linear equations AX=B. gams d2a2a file clapack/single/sposv.c for Solves a symmetric positive definite system of linear , equations AX=B. gams d2b1b file clapack/single/sppsv.c for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage. gams d2b1b file clapack/single/spbsv.c for Solves a symmetric positive definite banded system , of linear equations AX=B. gams d2b2 file clapack/single/sptsv.c for Solves a symmetric positive definite tridiagonal system , of linear equations AX=B. gams d2b2a file clapack/single/ssysv.c for Solves a real symmetric indefinite system of linear equations AX=B. gams d2b1a file clapack/single/sspsv.c for Solves a real symmetric indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2b1a file clapack/single/sgels.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/single/sgglse.c for Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization gams d9b1 file clapack/single/sggglm.c for Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization file clapack/single/ssyev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. gams d4a1 file clapack/single/ssyevd.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/single/sspev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. gams d4a1 file clapack/single/sspevd.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/single/ssbev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. gams d4a1, d4a6 file clapack/single/ssbevd.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/single/sstev.c for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file clapack/single/sstevd.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/single/sgees.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/single/sgeev.c for Computes the eigenvalues and left and right eigenvectors of , a general matrix. gams d4a2 file clapack/single/sgesvd.c for Computes the singular value decomposition (SVD) of a general , rectangular matrix. gams d6 file clapack/single/ssygv.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/single/sspgv.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/single/ssbgv.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/single/sgegs.c for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file clapack/single/sgegv.c for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file clapack/single/sggsvd.c for Computes the Generalized Singular Value Decomposition # --------------------------------- # Available EXPERT DRIVER routines: # --------------------------------- file clapack/single/sgesvx.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/single/sgbsvx.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/single/sgtsvx.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/single/sposvx.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/single/sppsvx.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/single/spbsvx.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/single/sptsvx.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/single/ssysvx.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/single/sspsvx.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/single/sgelsx.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/single/sgelss.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/single/ssyevx.c for Computes selected eigenvalues and eigenvectors of a symmetric matrix. gams d4a1 file clapack/single/sspevx.c for Computes selected eigenvalues and eigenvectors of a , symmetric matrix in packed storage. gams d4a1 file clapack/single/ssbevx.c for Computes selected eigenvalues and eigenvectors of a , symmetric band matrix. gams d4a1, d4a6 file clapack/single/sstevx.c for Computes selected eigenvalues and eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file clapack/single/sgeesx.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/single/sgeevx.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/single/sbdsqr.c for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm. gams d6 file clapack/single/sdisna.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/single/sgbbrd.c , Reduces a general band matrix to real upper bidiagonal form , by an orthogonal transformation. file clapack/single/sgbcon.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 SGBTRF. gams d2a2 file clapack/single/sgbequ.c for Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number. gams d2a2 file clapack/single/sgbrfs.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/single/sgbtrf.c for Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges. gams d2a2 file clapack/single/sgbtrs.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 SGBTRF. gams d2a2 file clapack/single/sgebak.c for Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to SGEBAL. gams d4c4 file clapack/single/sgebal.c for Balances a general matrix in order to improve the accuracy , of computed eigenvalues. gams d4c1a file clapack/single/sgebrd.c for Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal transformation. gams d6 file clapack/single/sgecon.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 SGETRF. gams d2a1 file clapack/single/sgeequ.c for Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number. gams d2a1 file clapack/single/sgehrd.c for Reduces a general matrix to upper Hessenberg form by an , orthogonal similarity transformation. gams d4c1b2 file clapack/single/sgelqf.c for Computes an LQ factorization of a general rectangular matrix. gams d5 file clapack/single/sgeqlf.c for Computes a QL factorization of a general rectangular matrix. gams d5 file clapack/single/sgeqpf.c for Computes a QR factorization with column pivoting of a general , rectangular matrix. gams d5 file clapack/single/sgeqrf.c for Computes a QR factorization of a general rectangular matrix. gams d5 file clapack/single/sgerfs.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/single/sgerqf.c for Computes an RQ factorization of a general rectangular matrix. gams d5 file clapack/single/sgetrf.c for Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges. gams d2a1 file clapack/single/sgetri.c for Computes the inverse of a general matrix, using the LU factorization , computed by SGETRF. gams d2a1 file clapack/single/sgetrs.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 SGETRF. gams d2a1 file clapack/single/sggbak.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 SGGBAL. file clapack/single/sggbal.c For Balances a pair of general real matrices for the generalized , eigenvalue problem A x = lambda B x. file clapack/single/sgghrd.c for Reduces a pair of real matrices to generalized upper , Hessenberg form using orthogonal transformations file clapack/single/sggqrf.c for Computes a generalized QR factorization of a pair of matrices. file clapack/single/sggrqf.c for Computes a generalized RQ factorization of a pair of matrices. file clapack/single/sggsvp.c for Computes orthogonal matrices as a preprocessing step , for computing the generalized singular value decomposition file clapack/single/sgtcon.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 SGTTRF. gams d2a2a file clapack/single/sgtrfs.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/single/sgttrf.c for Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges. gams d2a2a file clapack/single/sgttrs.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 , SGTTRF. gams d2a2a file clapack/single/shgeqz.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/single/shsein.c for Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration. gams d4c3 file clapack/single/shseqr.c for Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm. gams d4c2b file clapack/single/sopgtr.c for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by SSPTRD. gams d4c1b1 file clapack/single/sopmtr.c for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by SSPTRD. gams d4c4 file clapack/single/sorgbr.c for Generates the orthogonal transformation matrices from , a reduction to bidiagonal form determined by SGEBRD. gams d6 file clapack/single/sorghr.c for Generates the orthogonal transformation matrix from , a reduction to Hessenberg form determined by SGEHRD. gams d4c1b2 file clapack/single/sorglq.c for Generates all or part of the orthogonal matrix Q from , an LQ factorization determined by SGELQF. gams d5 file clapack/single/sorgql.c for Generates all or part of the orthogonal matrix Q from , a QL factorization determined by SGEQLF. gams d5 file clapack/single/sorgqr.c for Generates all or part of the orthogonal matrix Q from , a QR factorization determined by SGEQRF. gams d5 file clapack/single/sorgrq.c for Generates all or part of the orthogonal matrix Q from , an RQ factorization determined by SGERQF. gams d5 file clapack/single/sorgtr.c for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by SSYTRD. gams d4c1b1 file clapack/single/sormbr.c for Multiplies a general matrix by one of the orthogonal , transformation matrices from a reduction to bidiagonal form , determined by SGEBRD. gams d6 file clapack/single/sormhr.c for Multiplies a general matrix by the orthogonal transformation , matrix from a reduction to Hessenberg form determined by SGEHRD. gams d4c4 file clapack/single/sormlq.c for Multiplies a general matrix by the orthogonal matrix , from an LQ factorization determined by SGELQF. gams d5 file clapack/single/sormql.c for Multiplies a general matrix by the orthogonal matrix , from a QL factorization determined by SGEQLF. gams d5 file clapack/single/sormqr.c for Multiplies a general matrix by the orthogonal matrix , from a QR factorization determined by SGEQRF. gams d5 file clapack/single/sormrq.c for Multiplies a general matrix by the orthogonal matrix , from an RQ factorization determined by SGERQF. gams d5 file clapack/single/sormtr.c for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by SSYTRD. gams d4c4 file clapack/single/spbcon.c for Estimates the reciprocal of the condition number of a , symmetric positive definite band matrix, using the , Cholesky factorization computed by SPBTRF. gams d2b2 file clapack/single/spbequ.c for Computes row and column scalings to equilibrate a symmetric , positive definite band matrix and reduce its condition number. gams d2b2 file clapack/single/spbrfs.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/single/spbstf.c for Computes a split Cholesky factorization of a real symmetric positive , definite band matrix. file clapack/single/spbtrf.c for Computes the Cholesky factorization of a symmetric , positive definite band matrix. gams d2b2 file clapack/single/spbtrs.c for Solves a symmetric positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by SPBTRF. gams d2b2 file clapack/single/spocon.c for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix, using the , Cholesky factorization computed by SPOTRF. gams d2b1b file clapack/single/spoequ.c for Computes row and column scalings to equilibrate a symmetric , positive definite matrix and reduce its condition number. gams d2b1b file clapack/single/sporfs.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/single/spotrf.c for Computes the Cholesky factorization of a symmetric , positive definite matrix. gams d2b1b file clapack/single/spotri.c for Computes the inverse of a symmetric positive definite , matrix, using the Cholesky factorization computed by SPOTRF. gams d2b1b file clapack/single/spotrs.c for Solves a symmetric positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , SPOTRF. gams d2b1b file clapack/single/sppcon.c for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix in packed storage, , using the Cholesky factorization computed by SPPTRF. gams d2b1b file clapack/single/sppequ.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/single/spprfs.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/single/spptrf.c for Computes the Cholesky factorization of a symmetric , positive definite matrix in packed storage. gams d2b1b file clapack/single/spptri.c for Computes the inverse of a symmetric positive definite , matrix in packed storage, using the Cholesky factorization computed , by SPPTRF. gams d2b1b file clapack/single/spptrs.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 SPPTRF. gams d2b1b file clapack/single/sptcon.c for Computes the reciprocal of the condition number of a , symmetric positive definite tridiagonal matrix, , using the LDL**H factorization computed by SPTTRF. gams d2b2a file clapack/single/spteqr.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/single/sptrfs.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/single/spttrf.c for Computes the LDL**H factorization of a symmetric , positive definite tridiagonal matrix. gams d2b2a file clapack/single/spttrs.c for Solves a symmetric positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by SPTTRF. gams d2b2a file clapack/single/ssbgst.c for Reduces a real symmetric-definite banded generalized eigenproblem , A x = lambda B x to standard form, where B has been factorized by , SPBSTF (Crawford's algorithm). file clapack/single/ssbtrd.c for Reduces a symmetric band matrix to real symmetric , tridiagonal form by an orthogonal similarity transformation. gams d4c1b1 file clapack/single/sspcon.c for Estimates the reciprocal of the condition number of a , real symmetric indefinite , matrix in packed storage, using the factorization computed , by SSPTRF. gams d2b1a file clapack/single/sspgst.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 SPPTRF. gams d4c1c file clapack/single/ssprfs.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/single/ssptrd.c for Reduces a symmetric matrix in packed storage to real , symmetric tridiagonal form by an orthogonal similarity , transformation. gams d4c1b1 file clapack/single/ssptrf.c for Computes the factorization of a real , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2b1a file clapack/single/ssptri.c for Computes the inverse of a real symmetric , indefinite matrix in packed storage, using the factorization , computed by SSPTRF. gams d2b1a file clapack/single/ssptrs.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 SSPTRF. gams d2b1a file clapack/single/sstebz.c for Computes selected eigenvalues of a real symmetric tridiagonal , matrix by bisection. gams d4c2a file clapack/single/sstedc.c for Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm. file clapack/single/sstein.c for Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration. gams d4c3 file clapack/single/ssteqr.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/single/ssterf.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/single/ssycon.c for Estimates the reciprocal of the condition number of a , real symmetric indefinite matrix, , using the factorization computed by SSYTRF. gams d2b1a file clapack/single/ssygst.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 SPOTRF. gams d4c1c file clapack/single/ssyrfs.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/single/ssytrd.c for Reduces a symmetric matrix to real symmetric tridiagonal , form by an orthogonal similarity transformation. gams d4c1b1 file clapack/single/ssytrf.c for Computes the factorization of a real symmetric-indefinite matrix, , using the diagonal pivoting method. gams d2b1a file clapack/single/ssytri.c for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by SSYTRF. gams d2b1a file clapack/single/ssytrs.c for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by SSPTRF. gams d2b1a file clapack/single/stbcon.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/single/stbrfs.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/single/stbtrs.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/single/stgevc.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/single/stgsja.c for Computes the generalized singular value decomposition of two real , upper triangular (or trapezoidal) matrices as output by SGGSVP. gams d6 file clapack/single/stpcon.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/single/stprfs.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/single/stptri.c for Computes the inverse of a triangular matrix in packed storage. gams d2a3 file clapack/single/stptrs.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/single/strcon.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/single/strevc.c for Computes some or all of the right and/or left eigenvectors of , an upper quasi-triangular matrix. gams d4c3 file clapack/single/strexc.c for Reorders the Schur factorization of a matrix by an orthogonal , similarity transformation. gams d4c file clapack/single/strrfs.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/single/strsen.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/single/strsna.c for Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of an upper , quasi-triangular matrix. gams d4c file clapack/single/strsyl.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/single/strtri.c for Computes the inverse of a triangular matrix. gams d2a3 file clapack/single/strtrs.c for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a3 file clapack/single/stzrqf.c for Computes an RQ factorization of an upper trapezoidal matrix. gams d5 .