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# -------------------------------------------------------- # Available SIMPLE and DIVIDE AND CONQUER DRIVER routines: # -------------------------------------------------------- file dgesv.f dgesv.f plus dependencies prec double for Solves a general system of linear equations AX=B. gams d2a1 file dsgesv.f dsgesv.f plus dependencies prec double / single for Solves a general system of linear equations AX=B using iterativement refinement. file dgbsv.f dgbsv.f plus dependencies prec double for Solves a general banded system of linear equations AX=B. gams d2a2 file dgtsv.f dgtsv.f plus dependencies prec double for Solves a general tridiagonal system of linear equations AX=B. gams d2a2a file dposv.f dposv.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B. gams d2b1b file dppsv.f dppsv.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage. gams d2b1b file dpbsv.f dpbsv.f plus dependencies prec double for Solves a symmetric positive definite banded system , of linear equations AX=B. gams d2b2 file dptsv.f dptsv.f plus dependencies prec double for Solves a symmetric positive definite tridiagonal system , of linear equations AX=B. gams d2b2a file dsysv.f dsysv.f plus dependencies prec double for Solves a real symmetric indefinite system of linear equations AX=B. gams d2b1a file dspsv.f dspsv.f plus dependencies prec double for Solves a real symmetric indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2b1a file dgels.f dgels.f plus dependencies prec double for Computes the least squares solution to an over-determined system , of linear equations, A X=B or A**H X=B, or the minimum norm , solution of an under-determined system, where A is a general , rectangular matrix of full rank, using a QR or LQ factorization , of A. gams d9a1 file dgelsd.f dgelsd.f plus dependencies prec double for Computes the least squares solution to an over-determined system , of linear equations, A X=B or A**H X=B, or the minimum norm , solution of an under-determined system, using a divide and conquer , method, where A is a general rectangular matrix of full rank, , using a QR or LQ factorization of A. gams d9a1 file dgglse.f dgglse.f plus dependencies prec double for Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization gams d9b1 file dggglm.f dggglm.f plus dependencies prec double for Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization file dsyev.f dsyev.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. gams d4a1 file dsyevd.f dsyevd.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. If eigenvectors are desired, it uses a divide , and conquer algorithm. gams d4a1 file dspev.f dspev.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. gams d4a1 file dspevd.f dspevd.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric matrix in packed storage. If eigenvectors are desired, , it uses a divide and conquer algorithm. gams d4a1 file dsbev.f dsbev.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. gams d4a1, d4a6 file dsbevd.f dsbevd.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric band matrix. If eigenvectors are desired, it uses a , divide and conquer algorithm. gams d4a1, d4a6 file dstev.f dstev.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file dstevd.f dstevd.f plus dependencies prec double for Computes all eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. If eigenvectors are desired, it uses , a divide and conquer algorithm. gams d4a1, d4a5 file dgees.f dgees.f plus dependencies prec double for Computes the eigenvalues and Schur factorization of a general , matrix, and orders the factorization so that selected eigenvalues , are at the top left of the Schur form. gams d4a2 file dgeev.f dgeev.f plus dependencies prec double for Computes the eigenvalues and left and right eigenvectors of , a general matrix. gams d4a2 file dgesvd.f dgesvd.f plus dependencies prec double for Computes the singular value decomposition (SVD) of a general , rectangular matrix. gams d6 file dgesdd.f dgesdd.f plus dependencies prec double for Computes the singular value decomposition (SVD) of a general , rectangular matrix using divide-and-conquer. gams d6 file dsygv.f dsygv.f plus dependencies prec double for Computes all eigenvalues and the eigenvectors of a generalized , symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. gams d4b1 file dsygvd.f dsygvd.f plus dependencies prec double for Computes all eigenvalues and the eigenvectors of a generalized , symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. , If eigenvectors are desired, it uses a divide and conquer algorithm. gams d4b1 file dspgv.f dspgv.f plus dependencies prec double for Computes all eigenvalues and eigenvectors of a generalized , symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. gams d4b1 file dspgvd.f dspgvd.f plus dependencies prec double for Computes all eigenvalues and eigenvectors of a generalized , symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. , If eigenvectors are desired, it uses a divide and conquer algorithm. gams d4b1 file dsbgv.f dsbgv.f plus dependencies prec double for Computes all the eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite. file dsbgvd.f dsbgvd.f plus dependencies prec double for Computes all the eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite. , If eigenvectors are desired, it uses a divide and conquer algorithm. file dgegs.f dgegs.f plus dependencies prec double for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file dgges.f dgges.f plus dependencies prec double for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file dgegv.f dgegv.f plus dependencies prec double for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file dggev.f dggev.f plus dependencies prec double for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file dggsvd.f dggsvd.f plus dependencies prec double for Computes the Generalized Singular Value Decomposition # ----------------------------------------- # Available EXPERT and RRR DRIVER routines: # ----------------------------------------- file dgesvx.f dgesvx.f plus dependencies prec double for Solves a general system of linear equations AX=B, A**T X=B , or A**H X=B, and provides an estimate of the condition number , and error bounds on the solution. gams d2a1 file dgbsvx.f dgbsvx.f plus dependencies prec double for Solves a general banded system of linear equations AX=B, , A**T X=B or A**H X=B, and provides an estimate of the condition , number and error bounds on the solution. gams d2a2 file dgtsvx.f dgtsvx.f plus dependencies prec double for Solves a general tridiagonal system of linear equations AX=B, , A**T X=B or A**H X=B, and provides an estimate of the condition , number and error bounds on the solution. gams d2a2a file dposvx.f dposvx.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B, and provides an estimate of the condition number , and error bounds on the solution. gams d2b1b file dppsvx.f dppsvx.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage, and provides , an estimate of the condition number and error bounds on the , solution. gams d2b1b file dpbsvx.f dpbsvx.f plus dependencies prec double for Solves a symmetric positive definite banded system , of linear equations AX=B, and provides an estimate of the condition , number and error bounds on the solution. gams d2b2 file dptsvx.f dptsvx.f plus dependencies prec double for Solves a symmetric positive definite tridiagonal , system of linear equations AX=B, and provides an estimate of , the condition number and error bounds on the solution. gams d2b2a file dsysvx.f dsysvx.f plus dependencies prec double for Solves a real symmetric , indefinite system of linear equations AX=B, and provides an , estimate of the condition number and error bounds on the solution. gams d2b1a file dspsvx.f dspsvx.f plus dependencies prec double for Solves a real symmetric , indefinite system of linear equations AX=B, where A is held , in packed storage, and provides an estimate of the condition , number and error bounds on the solution. gams d2b1a file dgelsx.f dgelsx.f plus dependencies prec double for Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using a , complete orthogonal factorization of A. gams d9a1 file dgelsy.f dgelsy.f plus dependencies prec double for Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using a , complete orthogonal factorization of A. gams d9a1 file dgelss.f dgelss.f plus dependencies prec double for Computes the minimum norm least squares solution to an over- , or under-determined system of linear equations A X=B, using , the singular value decomposition of A. gams d9a1 file dsyevx.f dsyevx.f plus dependencies prec double for Computes selected eigenvalues and eigenvectors of a symmetric matrix. gams d4a1 file dsyevr.f dsyevr.f plus dependencies prec double for Computes selected eigenvalues, and optionally, eigenvectors of a real , symmetric matrix. Eigenvalues are computed by the dqds , algorithm, and eigenvectors are computed from various "good" LDL^T , representations (also known as Relatively Robust Representations). gams d4a1, d4a5 file dsygvx.f dsygvx.f plus dependencies prec double for Computes selected eigenvalues, and optionally, the eigenvectors of , a generalized symmetric-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. gams d4b1 file dspevx.f dspevx.f plus dependencies prec double for Computes selected eigenvalues and eigenvectors of a , symmetric matrix in packed storage. gams d4a1 file dspgvx.f dspgvx.f plus dependencies prec double for Computes selected eigenvalues, and optionally, eigenvectors of , a generalized symmetric-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. gams d4b1 file dsbevx.f dsbevx.f plus dependencies prec double for Computes selected eigenvalues and eigenvectors of a , symmetric band matrix. gams d4a1, d4a6 file dsbgvx.f dsbgvx.f plus dependencies prec double for Computes selected eigenvalues, and optionally, the eigenvectors , of a real generalized symmetric-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be symmetric , and banded, and B is also positive definite. file dstevx.f dstevx.f plus dependencies prec double for Computes selected eigenvalues and eigenvectors of a real , symmetric tridiagonal matrix. gams d4a1, d4a5 file dstevr.f dstevr.f plus dependencies prec double for Computes selected eigenvalues, and optionally, eigenvectors of a real , symmetric tridiagonal matrix. Eigenvalues are computed by the dqds , algorithm, and eigenvectors are computed from various "good" LDL^T , representations (also known as Relatively Robust Representations). gams d4a1, d4a5 file dgeesx.f dgeesx.f plus dependencies prec double for Computes the eigenvalues and Schur factorization of a general , matrix, orders the factorization so that selected eigenvalues , are at the top left of the Schur form, and computes reciprocal , condition numbers for the average of the selected eigenvalues, , and for the associated right invariant subspace. gams d4a2 file dggesx.f dggesx.f plus dependencies prec double for Computes the generalized eigenvalues, the real Schur form, and, , optionally, the left and/or right matrices of Schur vectors. file dgeevx.f dgeevx.f plus dependencies prec double for Computes the eigenvalues and left and right eigenvectors of , a general matrix, with preliminary balancing of the matrix, , and computes reciprocal condition numbers for the eigenvalues , and right eigenvectors. gams d4a2 file dggevx.f dggevx.f plus dependencies prec double for Computes the generalized eigenvalues, and optionally, the left , and/or right generalized eigenvectors. # --------------------------------- # Available COMPUTATIONAL routines: # --------------------------------- file dbdsdc.f dbdsdc.f plus dependencies prec double for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using a divide and conquer method. gams d6 file dbdsqr.f dbdsqr.f plus dependencies prec double for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm. gams d6 file ddisna.f ddisna.f plus dependencies prec double for Computes the reciprocal condition numbers for the eigenvectors of a , real symmetric or complex Hermitian matrix or for the left or right , singular vectors of a general matrix. file dgbbrd.f dgbbrd.f plus dependencies prec double , Reduces a general band matrix to real upper bidiagonal form , by an orthogonal transformation. file dgbcon.f dgbcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a general , band matrix, in either the 1-norm or the infinity-norm, using , the LU factorization computed by DGBTRF. gams d2a2 file dgbequ.f dgbequ.f plus dependencies prec double for Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number. gams d2a2 file dgbrfs.f dgbrfs.f plus dependencies prec double for Improves the computed solution to a general banded system of , linear equations AX=B, A**T X=B or A**H X=B, and provides forward , and backward error bounds for the solution. gams d2a2 file dgbtrf.f dgbtrf.f plus dependencies prec double for Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges. gams d2a2 file dgbtrs.f dgbtrs.f plus dependencies prec double for Solves a general banded system of linear equations AX=B, , A**T X=B or A**H X=B, using the LU factorization computed , by DGBTRF. gams d2a2 file dgebak.f dgebak.f plus dependencies prec double for Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to DGEBAL. gams d4c4 file dgebal.f dgebal.f plus dependencies prec double for Balances a general matrix in order to improve the accuracy , of computed eigenvalues. gams d4c1a file dgebrd.f dgebrd.f plus dependencies prec double for Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal transformation. gams d6 file dgecon.f dgecon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a general , matrix, in either the 1-norm or the infinity-norm, using the , LU factorization computed by DGETRF. gams d2a1 file dgeequ.f dgeequ.f plus dependencies prec double for Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number. gams d2a1 file dgehrd.f dgehrd.f plus dependencies prec double for Reduces a general matrix to upper Hessenberg form by an , orthogonal similarity transformation. gams d4c1b2 file dgelqf.f dgelqf.f plus dependencies prec double for Computes an LQ factorization of a general rectangular matrix. gams d5 file dgeqlf.f dgeqlf.f plus dependencies prec double for Computes a QL factorization of a general rectangular matrix. gams d5 file dgeqp3.f dgeqp3.f plus dependencies prec double for Computes a QR factorization with column pivoting of a general , rectangular matrix using Level 3 BLAS. gams d5 file dgeqpf.f dgeqpf.f plus dependencies prec double for Computes a QR factorization with column pivoting of a general , rectangular matrix. gams d5 file dgeqrf.f dgeqrf.f plus dependencies prec double for Computes a QR factorization of a general rectangular matrix. gams d5 file dgerfs.f dgerfs.f plus dependencies prec double for Improves the computed solution to a general system of linear , equations AX=B, A**T X=B or A**H X=B, and provides forward and , backward error bounds for the solution. gams d2a1 file dgerqf.f dgerqf.f plus dependencies prec double for Computes an RQ factorization of a general rectangular matrix. gams d5 file dgetrf.f dgetrf.f plus dependencies prec double for Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges. gams d2a1 file dgetri.f dgetri.f plus dependencies prec double for Computes the inverse of a general matrix, using the LU factorization , computed by DGETRF. gams d2a1 file dgetrs.f dgetrs.f plus dependencies prec double for Solves a general system of linear equations AX=B, A**T X=B , or A**H X=B, using the LU factorization computed by DGETRF. gams d2a1 file dggbak.f dggbak.f plus dependencies prec double For Forms the right or left eigenvectors of the generalized eigenvalue , problem by backward transformation on the computed eigenvectors of , the balanced pair of matrices output by DGGBAL. file dggbal.f dggbal.f plus dependencies prec double For Balances a pair of general real matrices for the generalized , eigenvalue problem A x = lambda B x. file dgghrd.f dgghrd.f plus dependencies prec double for Reduces a pair of real matrices to generalized upper , Hessenberg form using orthogonal transformations file dggqrf.f dggqrf.f plus dependencies prec double for Computes a generalized QR factorization of a pair of matrices. file dggrqf.f dggrqf.f plus dependencies prec double for Computes a generalized RQ factorization of a pair of matrices. file dggsvp.f dggsvp.f plus dependencies prec double for Computes orthogonal matrices as a preprocessing step , for computing the generalized singular value decomposition file dgtcon.f dgtcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a general , tridiagonal matrix, in either the 1-norm or the infinity-norm, , using the LU factorization computed by DGTTRF. gams d2a2a file dgtrfs.f dgtrfs.f plus dependencies prec double for Improves the computed solution to a general tridiagonal system , of linear equations AX=B, A**T X=B or A**H X=B, and provides , forward and backward error bounds for the solution. gams d2a2a file dgttrf.f dgttrf.f plus dependencies prec double for Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges. gams d2a2a file dgttrs.f dgttrs.f plus dependencies prec double for Solves a general tridiagonal system of linear equations AX=B, , A**T X=B or A**H X=B, using the LU factorization computed by , DGTTRF. gams d2a2a file dhgeqz.f dhgeqz.f plus dependencies prec double for Implements a single-/double-shift version of the QZ method for , finding the generalized eigenvalues of the equation , det(A - w(i) B) = 0 file dhsein.f dhsein.f plus dependencies prec double for Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration. gams d4c3 file dhseqr.f dhseqr.f plus dependencies prec double for Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm. gams d4c2b file dopgtr.f dopgtr.f plus dependencies prec double for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by DSPTRD. gams d4c1b1 file dopmtr.f dopmtr.f plus dependencies prec double for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSPTRD. gams d4c4 file dorcsd.f dorcsd.f plus dependencies prec double for Compute the CS decomposition of a block-partitioned , orthogonal/unitary matrix. file dorgbr.f dorgbr.f plus dependencies prec double for Generates the orthogonal transformation matrices from , a reduction to bidiagonal form determined by DGEBRD. gams d6 file dorghr.f dorghr.f plus dependencies prec double for Generates the orthogonal transformation matrix from , a reduction to Hessenberg form determined by DGEHRD. gams d4c1b2 file dorglq.f dorglq.f plus dependencies prec double for Generates all or part of the orthogonal matrix Q from , an LQ factorization determined by DGELQF. gams d5 file dorgql.f dorgql.f plus dependencies prec double for Generates all or part of the orthogonal matrix Q from , a QL factorization determined by DGEQLF. gams d5 file dorgqr.f dorgqr.f plus dependencies prec double for Generates all or part of the orthogonal matrix Q from , a QR factorization determined by DGEQRF. gams d5 file dorgrq.f dorgrq.f plus dependencies prec double for Generates all or part of the orthogonal matrix Q from , an RQ factorization determined by DGERQF. gams d5 file dorgtr.f dorgtr.f plus dependencies prec double for Generates the orthogonal transformation matrix from , a reduction to tridiagonal form determined by DSYTRD. gams d4c1b1 file dormbr.f dormbr.f plus dependencies prec double for Multiplies a general matrix by one of the orthogonal , transformation matrices from a reduction to bidiagonal form , determined by DGEBRD. gams d6 file dormhr.f dormhr.f plus dependencies prec double for Multiplies a general matrix by the orthogonal transformation , matrix from a reduction to Hessenberg form determined by DGEHRD. gams d4c4 file dormlq.f dormlq.f plus dependencies prec double for Multiplies a general matrix by the orthogonal matrix , from an LQ factorization determined by DGELQF. gams d5 file dormql.f dormql.f plus dependencies prec double for Multiplies a general matrix by the orthogonal matrix , from a QL factorization determined by DGEQLF. gams d5 file dormqr.f dormqr.f plus dependencies prec double for Multiplies a general matrix by the orthogonal matrix , from a QR factorization determined by DGEQRF. gams d5 file dormr3.f dormr3.f plus dependencies prec double for Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by DTZRZF. file dormrq.f dormrq.f plus dependencies prec double for Multiplies a general matrix by the orthogonal matrix , from an RQ factorization determined by DGERQF. gams d5 file dormrz.f dormrz.f plus dependencies prec double for Multiples a general matrix by the orthogonal matrix , from an RZ factorization determined by DTZRZF. file dormtr.f dormtr.f plus dependencies prec double for Multiplies a general matrix by the orthogonal , transformation matrix from a reduction to tridiagonal form , determined by DSYTRD. gams d4c4 file dpbcon.f dpbcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a , symmetric positive definite band matrix, using the , Cholesky factorization computed by DPBTRF. gams d2b2 file dpbequ.f dpbequ.f plus dependencies prec double for Computes row and column scalings to equilibrate a symmetric , positive definite band matrix and reduce its condition number. gams d2b2 file dpbrfs.f dpbrfs.f plus dependencies prec double for Improves the computed solution to a symmetric positive , definite banded system of linear equations AX=B, and provides , forward and backward error bounds for the solution. gams d2b2 file dpbstf.f dpbstf.f plus dependencies prec double for Computes a split Cholesky factorization of a real symmetric positive , definite band matrix. file dpbtrf.f dpbtrf.f plus dependencies prec double for Computes the Cholesky factorization of a symmetric , positive definite band matrix. gams d2b2 file dpbtrs.f dpbtrs.f plus dependencies prec double for Solves a symmetric positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by DPBTRF. gams d2b2 file dpocon.f dpocon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix, using the , Cholesky factorization computed by DPOTRF. gams d2b1b file dpoequ.f dpoequ.f plus dependencies prec double for Computes row and column scalings to equilibrate a symmetric , positive definite matrix and reduce its condition number. gams d2b1b file dporfs.f dporfs.f plus dependencies prec double for Improves the computed solution to a symmetric positive , definite system of linear equations AX=B, and provides forward , and backward error bounds for the solution. gams d2b1b file dpotrf.f dpotrf.f plus dependencies prec double for Computes the Cholesky factorization of a symmetric , positive definite matrix. gams d2b1b file dpotri.f dpotri.f plus dependencies prec double for Computes the inverse of a symmetric positive definite , matrix, using the Cholesky factorization computed by DPOTRF. gams d2b1b file dpotrs.f dpotrs.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , DPOTRF. gams d2b1b file dppcon.f dppcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a , symmetric positive definite matrix in packed storage, , using the Cholesky factorization computed by DPPTRF. gams d2b1b file dppequ.f dppequ.f plus dependencies prec double for Computes row and column scalings to equilibrate a symmetric , positive definite matrix in packed storage and reduce its condition , number. gams d2b1b file dpprfs.f dpprfs.f plus dependencies prec double for Improves the computed solution to a symmetric positive , definite system of linear equations AX=B, where A is held in , packed storage, and provides forward and backward error bounds , for the solution. gams d2b1b file dpptrf.f dpptrf.f plus dependencies prec double for Computes the Cholesky factorization of a symmetric , positive definite matrix in packed storage. gams d2b1b file dpptri.f dpptri.f plus dependencies prec double for Computes the inverse of a symmetric positive definite , matrix in packed storage, using the Cholesky factorization computed , by DPPTRF. gams d2b1b file dpptrs.f dpptrs.f plus dependencies prec double for Solves a symmetric positive definite system of linear , equations AX=B, where A is held in packed storage, using the , Cholesky factorization computed by DPPTRF. gams d2b1b file dptcon.f dptcon.f plus dependencies prec double for Computes the reciprocal of the condition number of a , symmetric positive definite tridiagonal matrix, , using the LDL**H factorization computed by DPTTRF. gams d2b2a file dpteqr.f dpteqr.f plus dependencies prec double for Computes all eigenvalues and eigenvectors of a real symmetric , positive definite tridiagonal matrix, by computing the SVD of , its bidiagonal Cholesky factor. gams d4c2a file dptrfs.f dptrfs.f plus dependencies prec double for Improves the computed solution to a symmetric positive , definite tridiagonal system of linear equations AX=B, and provides , forward and backward error bounds for the solution. gams d2b2a file dpttrf.f dpttrf.f plus dependencies prec double for Computes the LDL**H factorization of a symmetric , positive definite tridiagonal matrix. gams d2b2a file dpttrs.f dpttrs.f plus dependencies prec double for Solves a symmetric positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by DPTTRF. gams d2b2a file dsbgst.f dsbgst.f plus dependencies prec double for Reduces a real symmetric-definite banded generalized eigenproblem , A x = lambda B x to standard form, where B has been factorized by , DPBSTF (Crawford's algorithm). file dsbtrd.f dsbtrd.f plus dependencies prec double for Reduces a symmetric band matrix to real symmetric , tridiagonal form by an orthogonal similarity transformation. gams d4c1b1 file dspcon.f dspcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a , real symmetric indefinite , matrix in packed storage, using the factorization computed , by DSPTRF. gams d2b1a file dspgst.f dspgst.f plus dependencies prec double for Reduces a symmetric-definite generalized eigenproblem , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard , form, where A and B are held in packed storage, and B has been , factorized by DPPTRF. gams d4c1c file dsprfs.f dsprfs.f plus dependencies prec double for Improves the computed solution to a real , symmetric indefinite system of linear equations , AX=B, where A is held in packed storage, and provides forward , and backward error bounds for the solution. gams d2b1a file dsptrd.f dsptrd.f plus dependencies prec double for Reduces a symmetric matrix in packed storage to real , symmetric tridiagonal form by an orthogonal similarity , transformation. gams d4c1b1 file dsptrf.f dsptrf.f plus dependencies prec double for Computes the factorization of a real , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2b1a file dsptri.f dsptri.f plus dependencies prec double for Computes the inverse of a real symmetric , indefinite matrix in packed storage, using the factorization , computed by DSPTRF. gams d2b1a file dsptrs.f dsptrs.f plus dependencies prec double for Solves a real symmetric , indefinite system of linear equations AX=B, where A is held , in packed storage, using the factorization computed , by DSPTRF. gams d2b1a file dstebz.f dstebz.f plus dependencies prec double for Computes selected eigenvalues of a real symmetric tridiagonal , matrix by bisection. gams d4c2a file dstedc.f dstedc.f plus dependencies prec double for Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm. file dstegr.f dstegr.f plus dependencies prec double for Computes selected eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix. The eigenvalues are computed by the , dqds algorithm, while eigenvectors are computed from various "good" , LDL^T representations (also known as Relatively Robust Representations.) file dstein.f dstein.f plus dependencies prec double for Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration. gams d4c3 file dsteqr.f dsteqr.f plus dependencies prec double for Computes all eigenvalues and eigenvectors of a real symmetric , tridiagonal matrix, using the implicit QL or QR algorithm. gams d4a1, d4a5, d4c2a file dsterf.f dsterf.f plus dependencies prec double for Computes all eigenvalues of a real symmetric tridiagonal matrix, , using a root-free variant of the QL or QR algorithm. gams d4c2a file dsycon.f dsycon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a , real symmetric indefinite matrix, , using the factorization computed by DSYTRF. gams d2b1a file dsygst.f dsygst.f plus dependencies prec double for Reduces a symmetric-definite generalized eigenproblem , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard , form, where B has been factorized by DPOTRF. gams d4c1c file dsyrfs.f dsyrfs.f plus dependencies prec double for Improves the computed solution to a real , symmetric indefinite system of linear equations , AX=B, and provides forward and backward error bounds for the , solution. gams d2b1a file dsytrd.f dsytrd.f plus dependencies prec double for Reduces a symmetric matrix to real symmetric tridiagonal , form by an orthogonal similarity transformation. gams d4c1b1 file dsytrf.f dsytrf.f plus dependencies prec double for Computes the factorization of a real symmetric-indefinite matrix, , using the diagonal pivoting method. gams d2b1a file dsytri.f dsytri.f plus dependencies prec double for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by DSYTRF. gams d2b1a file dsytri2.f dsytri2.f plus dependencies prec double for Computes the inverse of a real symmetric indefinite matrix, , using the factorization computed by DSYTRF using Level BLAS 3. gams d2b1a file dsytrs.f dsytrs.f plus dependencies prec double for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by DSPTRF. gams d2b1a file dsytrs2.f dsytrs2.f plus dependencies prec double for Solves a real symmetric indefinite system of linear equations AX=B, , using the factorization computed by DSPTRF using Level BLAS 3. gams d2b1a file dtbcon.f dtbcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a triangular , band matrix, in either the 1-norm or the infinity-norm. gams d2a2, d2a3 file dtbrfs.f dtbrfs.f plus dependencies prec double for Provides forward and backward error bounds for the solution , of a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a2, d2a3 file dtbtrs.f dtbtrs.f plus dependencies prec double for Solves a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a2, d2a3 file dtgevc.f dtgevc.f plus dependencies prec double for Computes some or all of the right and/or left generalized eigenvectors , of a pair of upper triangular matrices. gams d4b2 file dtgexc.f dtgexc.f plus dependencies prec double for Reorders the generalized real Schur decomposition of a real , matrix pair (A,B) using an orthogonal equivalence transformation , so that the diagonal block of (A,B) with row index IFST is moved , to row ILST. file dtgsen.f dtgsen.f plus dependencies prec double for Reorders the generalized real Schur decomposition of a real , matrix pair (A, B) so that a selected cluster of eigenvalues , appears in the leading diagonal blocks of the upper quasi-triangular , matrix A and the upper triangular B. file dtgsja.f dtgsja.f plus dependencies prec double for Computes the generalized singular value decomposition of two real , upper triangular (or trapezoidal) matrices as output by DGGSVP. gams d6 file dtgsna.f dtgsna.f plus dependencies prec double for Estimates reciprocal condition numbers for specified , eigenvalues and/or eigenvectors of a matrix pair (A, B) in , generalized real Schur canonical form, as returned by DGGES. file dtgsyl.f dtgsyl.f plus dependencies prec double for Solves the generalized Sylvester equation. file dtpcon.f dtpcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a triangular , matrix in packed storage, in either the 1-norm or the infinity-norm. gams d2a3 file dtprfs.f dtprfs.f plus dependencies prec double for Provides forward and backward error bounds for the solution , of a triangular system of linear equations AX=B, A**T X=B or , A**H X=B, where A is held in packed storage. gams d2a3 file dtptri.f dtptri.f plus dependencies prec double for Computes the inverse of a triangular matrix in packed storage. gams d2a3 file dtptrs.f dtptrs.f plus dependencies prec double for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B, where A is held in packed storage. gams d2a3 file dtrcon.f dtrcon.f plus dependencies prec double for Estimates the reciprocal of the condition number of a triangular , matrix, in either the 1-norm or the infinity-norm. gams d2a3 file dtrevc.f dtrevc.f plus dependencies prec double for Computes some or all of the right and/or left eigenvectors of , an upper quasi-triangular matrix. gams d4c3 file dtrexc.f dtrexc.f plus dependencies prec double for Reorders the Schur factorization of a matrix by an orthogonal , similarity transformation. gams d4c file dtrrfs.f dtrrfs.f plus dependencies prec double for Provides forward and backward error bounds for the solution , of a triangular system of linear equations A X=B, A**T X=B or , A**H X=B. gams d2a3 file dtrsen.f dtrsen.f plus dependencies prec double for Reorders the Schur factorization of a matrix in order to find , an orthonormal basis of a right invariant subspace corresponding , to selected eigenvalues, and returns reciprocal condition numbers , (sensitivities) of the average of the cluster of eigenvalues , and of the invariant subspace. gams d4c file dtrsna.f dtrsna.f plus dependencies prec double for Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of an upper , quasi-triangular matrix. gams d4c file dtrsyl.f dtrsyl.f plus dependencies prec double for Solves the Sylvester matrix equation A X +/- X B=C where A , and B are upper quasi-triangular, and may be transposed. gams d8 file dtrtri.f dtrtri.f plus dependencies prec double for Computes the inverse of a triangular matrix. gams d2a3 file dtrtrs.f dtrtrs.f plus dependencies prec double for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2a3 file dtzrqf.f dtzrqf.f plus dependencies prec double for Computes an RQ factorization of an upper trapezoidal matrix. gams d5 file dtzrzf.f dtzrzf.f plus dependencies prec double for Computes an RZ factorization of an upper trapezoidal matrix , (blocked version of DTZRQF).