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# -------------------------------------------------------- # Available SIMPLE and DIVIDE AND CONQUER DRIVER routines: # -------------------------------------------------------- file sgesv.f sgesv.f plus dependencies prec single for Solves a general system of linear equations AX=B. gams d2a1 file sgbsv.f sgbsv.f plus dependencies prec single for Solves a general banded system of linear equations AX=B. gams d2a2 file sgtsv.f sgtsv.f plus dependencies prec single for Solves a general tridiagonal system of linear equations AX=B. gams d2a2a file sposv.f sposv.f plus dependencies prec single for Solves a symmetric positive definite system of linear , equations AX=B. gams d2b1b file sppsv.f sppsv.f plus dependencies prec single for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage. gams d2b1b file spbsv.f spbsv.f plus dependencies prec single for Solves a symmetric positive definite banded system , of linear equations AX=B. gams d2b2 file sptsv.f sptsv.f plus dependencies prec single for Solves a symmetric positive definite tridiagonal system , of linear equations AX=B. gams d2b2a file ssysv.f ssysv.f plus dependencies prec single for Solves a real symmetric indefinite system of linear equations AX=B. gams d2b1a file sspsv.f sspsv.f plus dependencies prec single for Solves a real symmetric indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2b1a file sgels.f sgels.f plus dependencies prec single 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 sgelsd.f sgelsd.f plus dependencies prec single 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 sgglse.f sgglse.f plus dependencies prec single for Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization gams d9b1 file sggglm.f sggglm.f plus dependencies prec single for Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization file ssyev.f ssyev.f plus dependencies prec single for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. gams d4a1 file ssyevd.f ssyevd.f plus dependencies prec single 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 sspev.f sspev.f plus dependencies prec single for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. gams d4a1 file sspevd.f sspevd.f plus dependencies prec single 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 ssbev.f ssbev.f plus dependencies prec single for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. gams d4a1, d4a6 file ssbevd.f ssbevd.f plus dependencies prec single 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 sstev.f sstev.f plus dependencies prec single for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file sstevd.f sstevd.f plus dependencies prec single 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 sgees.f sgees.f plus dependencies prec single 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 sgeev.f sgeev.f plus dependencies prec single for Computes the eigenvalues and left and right eigenvectors of , a general matrix. gams d4a2 file sgesvd.f sgesvd.f plus dependencies prec single for Computes the singular value decomposition (SVD) of a general , rectangular matrix. gams d6 file sgesdd.f sgesdd.f plus dependencies prec single for Computes the singular value decomposition (SVD) of a general , rectangular matrix using divide-and-conquer. gams d6 file ssygv.f ssygv.f plus dependencies prec single 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 ssygvd.f ssygvd.f plus dependencies prec single 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 sspgv.f sspgv.f plus dependencies prec single 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 sspgvd.f sspgvd.f plus dependencies prec single 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 ssbgv.f ssbgv.f plus dependencies prec single 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 ssbgvd.f ssbgvd.f plus dependencies prec single 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 sgegs.f sgegs.f plus dependencies prec single for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file sgges.f sgges.f plus dependencies prec single for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file sgegv.f sgegv.f plus dependencies prec single for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file sggev.f sggev.f plus dependencies prec single for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file sggsvd.f sggsvd.f plus dependencies prec single for Computes the Generalized Singular Value Decomposition # ----------------------------------------- # Available EXPERT and RRR DRIVER routines: # ----------------------------------------- file sgesvx.f sgesvx.f plus dependencies prec single 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 sgbsvx.f sgbsvx.f plus dependencies prec single 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 sgtsvx.f sgtsvx.f plus dependencies prec single 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 sposvx.f sposvx.f plus dependencies prec single 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 sppsvx.f sppsvx.f plus dependencies prec single 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 spbsvx.f spbsvx.f plus dependencies prec single 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 sptsvx.f sptsvx.f plus dependencies prec single 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 ssysvx.f ssysvx.f plus dependencies prec single 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 sspsvx.f sspsvx.f plus dependencies prec single 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 sgelsx.f sgelsx.f plus dependencies prec single 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 sgelsy.f sgelsy.f plus dependencies prec single 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 sgelss.f sgelss.f plus dependencies prec single 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 ssyevx.f ssyevx.f plus dependencies prec single for Computes selected eigenvalues and eigenvectors of a symmetric matrix. gams d4a1 file ssyevr.f ssyevr.f plus dependencies prec single 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 ssygvx.f ssygvx.f plus dependencies prec single 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 sspevx.f sspevx.f plus dependencies prec single for Computes selected eigenvalues and eigenvectors of a , symmetric matrix in packed storage. gams d4a1 file sspgvx.f sspgvx.f plus dependencies prec single 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 ssbevx.f ssbevx.f plus dependencies prec single for Computes selected eigenvalues and eigenvectors of a , symmetric band matrix. gams d4a1, d4a6 file ssbgvx.f ssbgvx.f plus dependencies prec single 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 sstevx.f sstevx.f plus dependencies prec single for Computes selected eigenvalues and eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file sstevr.f sstevr.f plus dependencies prec single 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 sgeesx.f sgeesx.f plus dependencies prec single 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 sggesx.f sggesx.f plus dependencies prec single for Computes the generalized eigenvalues, the real Schur form, and, , optionally, the left and/or right matrices of Schur vectors. file sgeevx.f sgeevx.f plus dependencies prec single 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 sggevx.f sggevx.f plus dependencies prec single for Computes the generalized eigenvalues, and optionally, the left , and/or right generalized eigenvectors. # --------------------------------- # Available COMPUTATIONAL routines: # --------------------------------- file sbdsdc.f sbdsdc.f plus dependencies prec single for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using a divide and conquer method. gams d6 file sbdsqr.f sbdsqr.f plus dependencies prec single for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm. gams d6 file sdisna.f sdisna.f plus dependencies prec single 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 sgbbrd.f sgbbrd.f plus dependencies prec single , Reduces a general band matrix to real upper bidiagonal form , by an orthogonal transformation. file sgbcon.f sgbcon.f plus dependencies prec single 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 sgbequ.f sgbequ.f plus dependencies prec single for Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number. gams d2a2 file sgbrfs.f sgbrfs.f plus dependencies prec single 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 sgbtrf.f sgbtrf.f plus dependencies prec single for Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges. gams d2a2 file sgbtrs.f sgbtrs.f plus dependencies prec single 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 sgebak.f sgebak.f plus dependencies prec single for Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to SGEBAL. gams d4c4 file sgebal.f sgebal.f plus dependencies prec single for Balances a general matrix in order to improve the accuracy , of computed eigenvalues. gams d4c1a file sgebrd.f sgebrd.f plus dependencies prec single for Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal transformation. gams d6 file sgecon.f sgecon.f plus dependencies prec single 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 sgeequ.f sgeequ.f plus dependencies prec single for Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number. gams d2a1 file sgehrd.f sgehrd.f plus dependencies prec single for Reduces a general matrix to upper Hessenberg form by an , orthogonal similarity transformation. gams d4c1b2 file sgelqf.f sgelqf.f plus dependencies prec single for Computes an LQ factorization of a general rectangular matrix. gams d5 file sgeqlf.f sgeqlf.f plus dependencies prec single for Computes a QL factorization of a general rectangular matrix. gams d5 file sgeqp3.f sgeqp3.f plus dependencies prec single for Computes a QR factorization with column pivoting of a general , rectangular matrix using Level 3 BLAS. gams d5 file sgeqpf.f sgeqpf.f plus dependencies prec single for Computes a QR factorization with column pivoting of a general , rectangular matrix. gams d5 file sgeqrf.f sgeqrf.f plus dependencies prec single for Computes a QR factorization of a general rectangular matrix. gams d5 file sgerfs.f sgerfs.f plus dependencies prec single 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 sgerqf.f sgerqf.f plus dependencies prec single for Computes an RQ factorization of a general rectangular matrix. gams d5 file sgetrf.f sgetrf.f plus dependencies prec single for Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges. gams d2a1 file sgetri.f sgetri.f plus dependencies prec single for Computes the inverse of a general matrix, using the LU factorization , computed by SGETRF. gams d2a1 file sgetrs.f sgetrs.f plus dependencies prec single 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 sggbak.f sggbak.f plus dependencies prec single 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 sggbal.f sggbal.f plus dependencies prec single For Balances a pair of general real matrices for the generalized , eigenvalue problem A x = lambda B x. file sgghrd.f sgghrd.f plus dependencies prec single for Reduces a pair of real matrices to generalized upper , Hessenberg form using orthogonal transformations file sggqrf.f sggqrf.f plus dependencies prec single for Computes a generalized QR factorization of a pair of matrices. file sggrqf.f sggrqf.f plus dependencies prec single for Computes a generalized RQ factorization of a pair of matrices. file sggsvp.f sggsvp.f plus dependencies prec single for Computes orthogonal matrices as a preprocessing step , for computing the generalized singular value decomposition file sgtcon.f sgtcon.f plus dependencies prec single 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 sgtrfs.f sgtrfs.f plus dependencies prec single 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 sgttrf.f sgttrf.f plus dependencies prec single for Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges. gams d2a2a file sgttrs.f sgttrs.f plus dependencies prec single 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 shgeqz.f shgeqz.f plus dependencies prec single 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 shsein.f shsein.f plus dependencies prec single for Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration. gams d4c3 file shseqr.f shseqr.f plus dependencies prec single for Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm. gams d4c2b file sopgtr.f sopgtr.f plus dependencies prec single for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by SSPTRD. gams d4c1b1 file sopmtr.f sopmtr.f plus dependencies prec single for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by SSPTRD. gams d4c4 file sorcsd.f sorcsd.f plus dependencies prec single for Compute the CS decomposition of an orthogonal/unitary , matrix in bidiagonal-block form. file sorgbr.f sorgbr.f plus dependencies prec single for Generates the orthogonal transformation matrices from , a reduction to bidiagonal form determined by SGEBRD. gams d6 file sorghr.f sorghr.f plus dependencies prec single for Generates the orthogonal transformation matrix from , a reduction to Hessenberg form determined by SGEHRD. gams d4c1b2 file sorglq.f sorglq.f plus dependencies prec single for Generates all or part of the orthogonal matrix Q from , an LQ factorization determined by SGELQF. gams d5 file sorgql.f sorgql.f plus dependencies prec single for Generates all or part of the orthogonal matrix Q from , a QL factorization determined by SGEQLF. gams d5 file sorgqr.f sorgqr.f plus dependencies prec single for Generates all or part of the orthogonal matrix Q from , a QR factorization determined by SGEQRF. gams d5 file sorgrq.f sorgrq.f plus dependencies prec single for Generates all or part of the orthogonal matrix Q from , an RQ factorization determined by SGERQF. gams d5 file sorgtr.f sorgtr.f plus dependencies prec single for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by SSYTRD. gams d4c1b1 file sormbr.f sormbr.f plus dependencies prec single for Multiplies a general matrix by one of the orthogonal , transformation matrices from a reduction to bidiagonal form , determined by SGEBRD. gams d6 file sormhr.f sormhr.f plus dependencies prec single for Multiplies a general matrix by the orthogonal transformation , matrix from a reduction to Hessenberg form determined by SGEHRD. gams d4c4 file sormlq.f sormlq.f plus dependencies prec single for Multiplies a general matrix by the orthogonal matrix , from an LQ factorization determined by SGELQF. gams d5 file sormql.f sormql.f plus dependencies prec single for Multiplies a general matrix by the orthogonal matrix , from a QL factorization determined by SGEQLF. gams d5 file sormqr.f sormqr.f plus dependencies prec single for Multiplies a general matrix by the orthogonal matrix , from a QR factorization determined by SGEQRF. gams d5 file sormr3.f sormr3.f plus dependencies prec single for Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by STZRZF. file sormrq.f sormrq.f plus dependencies prec single for Multiplies a general matrix by the orthogonal matrix , from an RQ factorization determined by SGERQF. gams d5 file sormrz.f sormrz.f plus dependencies prec single for Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by STZRZF. file sormtr.f sormtr.f plus dependencies prec single for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by SSYTRD. gams d4c4 file spbcon.f spbcon.f plus dependencies prec single 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 spbequ.f spbequ.f plus dependencies prec single for Computes row and column scalings to equilibrate a symmetric , positive definite band matrix and reduce its condition number. gams d2b2 file spbrfs.f spbrfs.f plus dependencies prec single 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 spbstf.f spbstf.f plus dependencies prec single for Computes a split Cholesky factorization of a real symmetric positive , definite band matrix. file spbtrf.f spbtrf.f plus dependencies prec single for Computes the Cholesky factorization of a symmetric , positive definite band matrix. gams d2b2 file spbtrs.f spbtrs.f plus dependencies prec single for Solves a symmetric positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by SPBTRF. gams d2b2 file spocon.f spocon.f plus dependencies prec single for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix, using the , Cholesky factorization computed by SPOTRF. gams d2b1b file spoequ.f spoequ.f plus dependencies prec single for Computes row and column scalings to equilibrate a symmetric , positive definite matrix and reduce its condition number. gams d2b1b file sporfs.f sporfs.f plus dependencies prec single 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 spotrf.f spotrf.f plus dependencies prec single for Computes the Cholesky factorization of a symmetric , positive definite matrix. gams d2b1b file spotri.f spotri.f plus dependencies prec single for Computes the inverse of a symmetric positive definite , matrix, using the Cholesky factorization computed by SPOTRF. gams d2b1b file spotrs.f spotrs.f plus dependencies prec single for Solves a symmetric positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , SPOTRF. gams d2b1b file sppcon.f sppcon.f plus dependencies prec single 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 sppequ.f sppequ.f plus dependencies prec single for Computes row and column scalings to equilibrate a symmetric , positive definite matrix in packed storage and reduce its condition , number. gams d2b1b file spprfs.f spprfs.f plus dependencies prec single 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 spptrf.f spptrf.f plus dependencies prec single for Computes the Cholesky factorization of a symmetric , positive definite matrix in packed storage. gams d2b1b file spptri.f spptri.f plus dependencies prec single for Computes the inverse of a symmetric positive definite , matrix in packed storage, using the Cholesky factorization computed , by SPPTRF. gams d2b1b file spptrs.f spptrs.f plus dependencies prec single 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 sptcon.f sptcon.f plus dependencies prec single 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 spteqr.f spteqr.f plus dependencies prec single 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 sptrfs.f sptrfs.f plus dependencies prec single 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 spttrf.f spttrf.f plus dependencies prec single for Computes the LDL**H factorization of a symmetric , positive definite tridiagonal matrix. gams d2b2a file spttrs.f spttrs.f plus dependencies prec single for Solves a symmetric positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by SPTTRF. gams d2b2a file ssbgst.f ssbgst.f plus dependencies prec single 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 ssbtrd.f ssbtrd.f plus dependencies prec single for Reduces a symmetric band matrix to real symmetric , tridiagonal form by an orthogonal similarity transformation. gams d4c1b1 file sspcon.f sspcon.f plus dependencies prec single 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 sspgst.f sspgst.f plus dependencies prec single 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 ssprfs.f ssprfs.f plus dependencies prec single 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 ssptrd.f ssptrd.f plus dependencies prec single for Reduces a symmetric matrix in packed storage to real , symmetric tridiagonal form by an orthogonal similarity , transformation. gams d4c1b1 file ssptrf.f ssptrf.f plus dependencies prec single for Computes the factorization of a real , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2b1a file ssptri.f ssptri.f plus dependencies prec single for Computes the inverse of a real symmetric , indefinite matrix in packed storage, using the factorization , computed by SSPTRF. gams d2b1a file ssptrs.f ssptrs.f plus dependencies prec single 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 sstebz.f sstebz.f plus dependencies prec single for Computes selected eigenvalues of a real symmetric tridiagonal , matrix by bisection. gams d4c2a file sstedc.f sstedc.f plus dependencies prec single for Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm. file sstegr.f sstegr.f plus dependencies prec single 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 sstein.f sstein.f plus dependencies prec single for Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration. gams d4c3 file ssteqr.f ssteqr.f plus dependencies prec single for Computes all eigenvalues and eigenvectors of a real symmetric , tridiagonal matrix, using the implicit QL or QR algorithm. gams d4a1, d4a5, d4c2a file ssterf.f ssterf.f plus dependencies prec single for Computes all eigenvalues of a real symmetric tridiagonal matrix, , using a root-free variant of the QL or QR algorithm. gams d4c2a file ssycon.f ssycon.f plus dependencies prec single for Estimates the reciprocal of the condition number of a , real symmetric indefinite matrix, , using the factorization computed by SSYTRF. gams d2b1a file ssygst.f ssygst.f plus dependencies prec single 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 ssyrfs.f ssyrfs.f plus dependencies prec single 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 ssytrd.f ssytrd.f plus dependencies prec single for Reduces a symmetric matrix to real symmetric tridiagonal , form by an orthogonal similarity transformation. gams d4c1b1 file ssytrf.f ssytrf.f plus dependencies prec single for Computes the factorization of a real symmetric-indefinite matrix, , using the diagonal pivoting method. gams d2b1a file ssytri2.f ssytri2.f plus dependencies prec single for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by SSYTRF using LEVEL 3 Blas. file ssytri.f ssytri.f plus dependencies prec single for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by SSYTRF. gams d2b1a file ssytrs2.f ssytrs2.f plus dependencies prec single for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by SSPTRF using LEVEL 3 Blas. file ssytrs.f ssytrs.f plus dependencies prec single for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by SSPTRF. gams d2b1a file stbcon.f stbcon.f plus dependencies prec single 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 stbrfs.f stbrfs.f plus dependencies prec single 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 stbtrs.f stbtrs.f plus dependencies prec single for Solves a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a2, d2a3 file stgevc.f stgevc.f plus dependencies prec single for Computes some or all of the right and/or left generalized eigenvectors , of a pair of upper triangular matrices. gams d4b2 file stgexc.f stgexc.f plus dependencies prec single 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 stgsen.f stgsen.f plus dependencies prec single 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 stgsja.f stgsja.f plus dependencies prec single for Computes the generalized singular value decomposition of two real , upper triangular (or trapezoidal) matrices as output by SGGSVP. gams d6 file stgsna.f stgsna.f plus dependencies prec single 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 SGGES. file stgsyl.f stgsyl.f plus dependencies prec single for Solves the generalized Sylvester equation. file stpcon.f stpcon.f plus dependencies prec single 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 stprfs.f stprfs.f plus dependencies prec single 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 stptri.f stptri.f plus dependencies prec single for Computes the inverse of a triangular matrix in packed storage. gams d2a3 file stptrs.f stptrs.f plus dependencies prec single 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 strcon.f strcon.f plus dependencies prec single for Estimates the reciprocal of the condition number of a triangular , matrix, in either the 1-norm or the infinity-norm. gams d2a3 file strevc.f strevc.f plus dependencies prec single for Computes some or all of the right and/or left eigenvectors of , an upper quasi-triangular matrix. gams d4c3 file strexc.f strexc.f plus dependencies prec single for Reorders the Schur factorization of a matrix by an orthogonal , similarity transformation. gams d4c file strrfs.f strrfs.f plus dependencies prec single 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 strsen.f strsen.f plus dependencies prec single 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 strsna.f strsna.f plus dependencies prec single for Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of an upper , quasi-triangular matrix. gams d4c file strsyl.f strsyl.f plus dependencies prec single 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 strtri.f strtri.f plus dependencies prec single for Computes the inverse of a triangular matrix. gams d2a3 file strtrs.f strtrs.f plus dependencies prec single for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a3 file stzrqf.f stzrqf.f plus dependencies prec single for Computes an RQ factorization of an upper trapezoidal matrix. gams d5 file stzrzf.f stzrzf.f plus dependencies prec single for Computes an RZ factorization of an upper trapezoidal matrix , (blocked version of STZRQF).