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# ------------------------------------------------------- # Available SIMPLE and DIVIDE AND CONQUER DRIVER routines: # ------------------------------------------------------- file cgesv.f cgesv.f plus dependencies prec complex for Solves a general system of linear equations AX=B. gams d2c1 file cgbsv.f cgbsv.f plus dependencies prec complex for Solves a general banded system of linear equations AX=B. gams d2c2 file cgtsv.f cgtsv.f plus dependencies prec complex for Solves a general tridiagonal system of linear equations AX=B. gams d2c2a file cposv.f cposv.f plus dependencies prec complex for Solves a Hermitian positive definite system of linear , equations AX=B. gams d2d1b file cppsv.f cppsv.f plus dependencies prec complex for Solves a Hermitian positive definite system of linear , equations AX=B, where A is in packed storage. gams d2d1b file cpbsv.f cpbsv.f plus dependencies prec complex for Solves a Hermitian positive definite banded system , of linear equations AX=B. gams d2d2 file cptsv.f cptsv.f plus dependencies prec complex for Solves a Hermitian positive definite tridiagonal system , of linear equations AX=B. gams d2d2a file csysv.f csysv.f plus dependencies prec complex for Solves a complex symmetric indefinite system of linear equations AX=B. gams d2c1 file chesv.f chesv.f plus dependencies prec complex for Solves a complex Hermitian indefinite system of linear equations AX=B. gams d2d1a file cspsv.f cspsv.f plus dependencies prec complex for Solves a complex symmetric indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2c1 file chpsv.f chpsv.f plus dependencies prec complex for Solves a complex Hermitian indefinite system of linear equations AX=B, , where A is held in packed storage. gams d2d1a file cgels.f cgels.f plus dependencies prec complex 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 cgelsd.f cgelsd.f plus dependencies prec complex 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 cgglse.f cgglse.f plus dependencies prec complex for Solves the LSE (Constrained Linear Least Squares Problem) using , the GRQ (Generalized RQ) factorization gams d9b1 file cggglm.f cggglm.f plus dependencies prec complex for Solves the GLM (Generalized Linear Regression Model) using , the GQR (Generalized QR) factorization file cheev.f cheev.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian matrix. gams d4a3 file cheevd.f cheevd.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian matrix. If eigenvectors are desired, it uses a divide , and conquer algorithm. gams d4a3 file cheevr.f cheevr.f plus dependencies prec complex for Computes selected eigenvalues, and optionally, eigenvectors of a complex , Hermitian 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 chpev.f chpev.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian matrix in packed storage. gams d4a3 file chpevd.f chpevd.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian matrix in packed storage. If eigenvectors are desired, it , uses a divide and conquer algorithm. gams d4a3 file chbev.f chbev.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian band matrix. gams d4a3, d4a6 file chbevd.f chbevd.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a complex , Hermitian band matrix. If eigenvectors are desired, it uses a divide , and conquer algorithm. gams d4a3, d4a6 file cgees.f cgees.f plus dependencies prec complex 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 d4a4 file cgeev.f cgeev.f plus dependencies prec complex for Computes the eigenvalues and left and right eigenvectors of , a general matrix. gams d4a4 file cgesvd.f cgesvd.f plus dependencies prec complex for Computes the singular value decomposition (SVD) of a general , rectangular matrix. gams d6 file cgesdd.f cgesdd.f plus dependencies prec complex for Computes the singular value decomposition (SVD) of a general , rectangular matrix using divide-and-conquer. gams d6 file chegv.f chegv.f plus dependencies prec complex for Computes all eigenvalues and the eigenvectors of a generalized , Hermitian-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. gams d4b3 file chegvd.f chegvd.f plus dependencies prec complex for Computes all eigenvalues and the eigenvectors of a generalized , Hermitian-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 d4b3 file chpgv.f chpgv.f plus dependencies prec complex for Computes all eigenvalues and eigenvectors of a generalized , Hermitian-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. gams d4b3 file chpgvd.f chpgvd.f plus dependencies prec complex for Computes all eigenvalues and eigenvectors of a generalized , Hermitian-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 d4b3 file chbgv.f chbgv.f plus dependencies prec complex for Computes all the eigenvalues, and optionally, the eigenvectors , of a complex generalized Hermitian-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian , and banded, and B is also positive definite. file chbgvd.f chbgvd.f plus dependencies prec complex for Computes all the eigenvalues, and optionally, the eigenvectors , of a complex generalized Hermitian-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian , and banded, and B is also positive definite. , If eigenvectors are desired, it uses a divide and conquer algorithm. file cgegs.f cgegs.f plus dependencies prec complex for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file cgges.f cgges.f plus dependencies prec complex for Computes the generalized eigenvalues, Schur form, and left and/or , right Schur vectors for a pair of nonsymmetric matrices file cgegv.f cgegv.f plus dependencies prec complex for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file cggev.f cggev.f plus dependencies prec complex for Computes the generalized eigenvalues, and left and/or right , generalized eigenvectors for a pair of nonsymmetric matrices file cggsvd.f cggsvd.f plus dependencies prec complex for Computes the Generalized Singular Value Decomposition # ----------------------------------------- # Available EXPERT and RRR DRIVER routines: # ----------------------------------------- file cgesvx.f cgesvx.f plus dependencies prec complex 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 d2c1 file cgbsvx.f cgbsvx.f plus dependencies prec complex 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 d2c2 file cgtsvx.f cgtsvx.f plus dependencies prec complex 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 d2c2a file cposvx.f cposvx.f plus dependencies prec complex for Solves a Hermitian positive definite system of linear , equations AX=B, and provides an estimate of the condition number , and error bounds on the solution. gams d2d1b file cppsvx.f cppsvx.f plus dependencies prec complex for Solves a Hermitian 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 d2d1b file cpbsvx.f cpbsvx.f plus dependencies prec complex for Solves a Hermitian positive definite banded system , of linear equations AX=B, and provides an estimate of the condition , number and error bounds on the solution. gams d2d2 file cptsvx.f cptsvx.f plus dependencies prec complex for Solves a Hermitian positive definite tridiagonal , system of linear equations AX=B, and provides an estimate of , the condition number and error bounds on the solution. gams d2d2a file csysvx.f csysvx.f plus dependencies prec complex for Solves a complex symmetric , indefinite system of linear equations AX=B, and provides an , estimate of the condition number and error bounds on the solution. gams d2c1 file chesvx.f chesvx.f plus dependencies prec complex for Solves a complex Hermitian , indefinite system of linear equations AX=B, and provides an , estimate of the condition number and error bounds on the solution. gams d2d1a file cspsvx.f cspsvx.f plus dependencies prec complex for Solves a complex 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 d2c1 file chpsvx.f chpsvx.f plus dependencies prec complex for Solves a complex Hermitian , 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 d2d1a file cgelsx.f cgelsx.f plus dependencies prec complex 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 cgelsy.f cgelsy.f plus dependencies prec complex 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 cgelss.f cgelss.f plus dependencies prec complex 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 cheevx.f cheevx.f plus dependencies prec complex for Computes selected eigenvalues and eigenvectors of a Hermitian matrix. gams d4a3 file cheevr.f cheevr.f plus dependencies prec complex for Computes selected eigenvalues, and optionally, eigenvectors of a complex , Hermitian 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 chegvx.f chegvx.f plus dependencies prec complex for Computes selected eigenvalues, and optionally, the eigenvectors of , a generalized Hermitian-definite generalized eigenproblem, , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. gams d4b3 file chpevx.f chpevx.f plus dependencies prec complex for Computes selected eigenvalues and eigenvectors of a , Hermitian matrix in packed storage. gams d4a3 file chpgvx.f chpgvx.f plus dependencies prec complex for Computes selected eigenvalues, and optionally, the eigenvectors of , a generalized Hermitian-definite generalized eigenproblem, Ax= lambda , Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed , storage. gams d4b3 file chbevx.f chbevx.f plus dependencies prec complex for Computes selected eigenvalues and eigenvectors of a , Hermitian band matrix. gams d4a3, d4a6 file chbgvx.f chbgvx.f plus dependencies prec complex for Computes selected eigenvalues, and optionally, the eigenvectors , of a complex generalized Hermitian-definite banded eigenproblem, of , the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian , and banded, and B is also positive definite. file cgeesx.f cgeesx.f plus dependencies prec complex 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 d4a4 file cggesx.f cggesx.f plus dependencies prec complex for Computes the generalized eigenvalues, the real Schur form, and, , optionally, the left and/or right matrices of Schur vectors. file cgeevx.f cgeevx.f plus dependencies prec complex 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 d4a4 file cggevx.f cggevx.f plus dependencies prec complex for Computes the generalized eigenvalues, and optionally, the left , and/or right generalized eigenvectors. # --------------------------------- # Available COMPUTATIONAL routines: # --------------------------------- file cbdsdc.f cbdsdc.f plus dependencies prec complex for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using a divide and conquer method. gams d6 file cbdsqr.f cbdsqr.f plus dependencies prec complex for Computes the singular value decomposition (SVD) of a real bidiagonal , matrix, using the bidiagonal QR algorithm. gams d6 file cgbbrd.f cgbbrd.f plus dependencies prec complex , Reduces a complex general band matrix to real upper bidiagonal form , by a unitary transformation. file cgbcon.f cgbcon.f plus dependencies prec complex 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 CGBTRF. gams d2c2 file cgbequ.f cgbequ.f plus dependencies prec complex for Computes row and column scalings to equilibrate a general band , matrix and reduce its condition number. gams d2c2 file cgbrfs.f cgbrfs.f plus dependencies prec complex 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 d2c2 file cgbtrf.f cgbtrf.f plus dependencies prec complex for Computes an LU factorization of a general band matrix, using , partial pivoting with row interchanges. gams d2c2 file cgbtrs.f cgbtrs.f plus dependencies prec complex 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 CGBTRF. gams d2c2 file cgebak.f cgebak.f plus dependencies prec complex for Transforms eigenvectors of a balanced matrix to those of the , original matrix supplied to CGEBAL. gams d4c4 file cgebal.f cgebal.f plus dependencies prec complex for Balances a general matrix in order to improve the accuracy , of computed eigenvalues. gams d4c1a file cgebrd.f cgebrd.f plus dependencies prec complex for Reduces a general rectangular matrix to real bidiagonal form , by an orthogonal/unitary transformation. gams d6 file cgecon.f cgecon.f plus dependencies prec complex 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 CGETRF. gams d2c1 file cgeequ.f cgeequ.f plus dependencies prec complex for Computes row and column scalings to equilibrate a general , rectangular matrix and reduce its condition number. gams d2c1 file cgehrd.f cgehrd.f plus dependencies prec complex for Reduces a general matrix to upper Hessenberg form by an , unitary similarity transformation. gams d4c1b2 file cgelqf.f cgelqf.f plus dependencies prec complex for Computes an LQ factorization of a general rectangular matrix. gams d5 file cgeqlf.f cgeqlf.f plus dependencies prec complex for Computes a QL factorization of a general rectangular matrix. gams d5 file cgeqp3.f cgeqp3.f plus dependencies prec complex for Computes a QR factorization with column pivoting of a general , rectangular matrix using Level 3 BLAS. gams d5 file cgeqpf.f cgeqpf.f plus dependencies prec complex for Computes a QR factorization with column pivoting of a general , rectangular matrix. gams d5 file cgeqrf.f cgeqrf.f plus dependencies prec complex for Computes a QR factorization of a general rectangular matrix. gams d5 file cgerfs.f cgerfs.f plus dependencies prec complex 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 d2c1 file cgerqf.f cgerqf.f plus dependencies prec complex for Computes an RQ factorization of a general rectangular matrix. gams d5 file cgetrf.f cgetrf.f plus dependencies prec complex for Computes an LU factorization of a general matrix, using partial , pivoting with row interchanges. gams d2c1 file cgetri.f cgetri.f plus dependencies prec complex for Computes the inverse of a general matrix, using the LU factorization , computed by CGETRF. gams d2c1 file cgetrs.f cgetrs.f plus dependencies prec complex 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 CGETRF. gams d2c1 file cggbak.f cggbak.f plus dependencies prec complex 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 CGGBAL. file cggbal.f cggbal.f plus dependencies prec complex For Balances a pair of general complex matrices for the generalized , eigenvalue problem A x = lambda B x. file cgghrd.f cgghrd.f plus dependencies prec complex for Reduces a pair of complex matrices to generalized upper , Hessenberg form using unitary similarity transformations. file cggqrf.f cggqrf.f plus dependencies prec complex for Computes a generalized QR factorization of a pair of matrices. file cggrqf.f cggrqf.f plus dependencies prec complex for Computes a generalized RQ factorization of a pair of matrices. file cggsvp.f cggsvp.f plus dependencies prec complex for Computes unitary matrices as a preprocessing step , for computing the generalized singular value decomposition file cgtcon.f cgtcon.f plus dependencies prec complex 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 CGTTRF. gams d2c2a file cgtrfs.f cgtrfs.f plus dependencies prec complex 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 d2c2a file cgttrf.f cgttrf.f plus dependencies prec complex for Computes an LU factorization of a general tridiagonal matrix, , using partial pivoting with row interchanges. gams d2c2a file cgttrs.f cgttrs.f plus dependencies prec complex 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 , CGTTRF. gams d2c2a file chgeqz.f chgeqz.f plus dependencies prec complex 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 chsein.f chsein.f plus dependencies prec complex for Computes specified right and/or left eigenvectors of an upper , Hessenberg matrix by inverse iteration. gams d4c3 file chseqr.f chseqr.f plus dependencies prec complex for Computes the eigenvalues and Schur factorization of an upper , Hessenberg matrix, using the multishift QR algorithm. gams d4c2b file cupgtr.f cupgtr.f plus dependencies prec complex for Generates the unitary transformation matrix from , a reduction to tridiagonal form determined by CHPTRD. gams d4c1b1 file cupmtr.f cupmtr.f plus dependencies prec complex for Multiplies a general matrix by the unitary , transformation matrix from a reduction to tridiagonal form , determined by CHPTRD. gams d4c4 file cuncsd.f cuncsd.f plus dependencies prec complex for Compute the CS decomposition of a block-partitioned , orthogonal/unitary matrix. file cungbr.f cungbr.f plus dependencies prec complex for Generates the unitary transformation matrices from , a reduction to bidiagonal form determined by CGEBRD. gams d6 file cunghr.f cunghr.f plus dependencies prec complex for Generates the unitary transformation matrix from , a reduction to Hessenberg form determined by CGEHRD. gams d4c1b2 file cunglq.f cunglq.f plus dependencies prec complex for Generates all or part of the unitary matrix Q from , an LQ factorization determined by CGELQF. gams d5 file cungql.f cungql.f plus dependencies prec complex for Generates all or part of the unitary matrix Q from , a QL factorization determined by CGEQLF. gams d5 file cungqr.f cungqr.f plus dependencies prec complex for Generates all or part of the unitary matrix Q from , a QR factorization determined by CGEQRF. gams d5 file cungrq.f cungrq.f plus dependencies prec complex for Generates all or part of the unitary matrix Q from , an RQ factorization determined by CGERQF. gams d5 file cungtr.f cungtr.f plus dependencies prec complex for Generates the unitary transformation matrix from , a reduction to tridiagonal form determined by CHETRD. gams d4c1b1 file cunmbr.f cunmbr.f plus dependencies prec complex for Multiplies a general matrix by one of the unitary , transformation matrices from a reduction to bidiagonal form , determined by CGEBRD. gams d6 file cunmhr.f cunmhr.f plus dependencies prec complex for Multiplies a general matrix by the unitary transformation , matrix from a reduction to Hessenberg form determined by CGEHRD. gams d4c4 file cunmlq.f cunmlq.f plus dependencies prec complex for Multiplies a general matrix by the unitary matrix , from an LQ factorization determined by CGELQF. gams d5 file cunmql.f cunmql.f plus dependencies prec complex for Multiplies a general matrix by the unitary matrix , from a QL factorization determined by CGEQLF. gams d5 file cunmqr.f cunmqr.f plus dependencies prec complex for Multiplies a general matrix by the unitary matrix , from a QR factorization determined by CGEQRF. gams d5 file cunmr3.f cunmr3.f plus dependencies prec complex for Multiples a general matrix by the unitary matrix , from an RZ factorization determined by CTZRZF. file cunmrq.f cunmrq.f plus dependencies prec complex for Multiplies a general matrix by the unitary matrix , from an RQ factorization determined by CGERQF. gams d5 file cunmrz.f cunmrz.f plus dependencies prec complex for Multiples a general matrix by the unitary matrix , from an RZ factorization determined by CTZRZF. file cunmtr.f cunmtr.f plus dependencies prec complex for Multiplies a general matrix by the unitary , transformation matrix from a reduction to tridiagonal form , determined by CHETRD. gams d4c4 file cpbcon.f cpbcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , Hermitian positive definite band matrix, using the , Cholesky factorization computed by CPBTRF. gams d2d2 file cpbequ.f cpbequ.f plus dependencies prec complex for Computes row and column scalings to equilibrate a Hermitian , positive definite band matrix and reduce its condition number. gams d2d2 file cpbrfs.f cpbrfs.f plus dependencies prec complex for Improves the computed solution to a Hermitian positive , definite banded system of linear equations AX=B, and provides , forward and backward error bounds for the solution. gams d2d2 file cpbstf.f cpbstf.f plus dependencies prec complex for Computes a split Cholesky factorization of a complex Hermitian , positive definite band matrix. file cpbtrf.f cpbtrf.f plus dependencies prec complex for Computes the Cholesky factorization of a Hermitian , positive definite band matrix. gams d2d2 file cpbtrs.f cpbtrs.f plus dependencies prec complex for Solves a Hermitian positive definite banded system , of linear equations AX=B, using the Cholesky factorization , computed by CPBTRF. gams d2d2 file cpocon.f cpocon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , Hermitian positive definite matrix, using the , Cholesky factorization computed by CPOTRF. gams d2d1b file cpoequ.f cpoequ.f plus dependencies prec complex for Computes row and column scalings to equilibrate a Hermitian , positive definite matrix and reduce its condition number. gams d2d1b file cporfs.f cporfs.f plus dependencies prec complex for Improves the computed solution to a Hermitian positive , definite system of linear equations AX=B, and provides forward , and backward error bounds for the solution. gams d2d1b file cpotrf.f cpotrf.f plus dependencies prec complex for Computes the Cholesky factorization of a Hermitian , positive definite matrix. gams d2d1b file cpotri.f cpotri.f plus dependencies prec complex for Computes the inverse of a Hermitian positive definite , matrix, using the Cholesky factorization computed by CPOTRF. gams d2d1b file cpotrs.f cpotrs.f plus dependencies prec complex for Solves a Hermitian positive definite system of linear , equations AX=B, using the Cholesky factorization computed by , CPOTRF. gams d2d1b file cppcon.f cppcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , Hermitian positive definite matrix in packed storage, , using the Cholesky factorization computed by CPPTRF. gams d2d1b file cppequ.f cppequ.f plus dependencies prec complex for Computes row and column scalings to equilibrate a Hermitian , positive definite matrix in packed storage and reduce its condition , number. gams d2d1b file cpprfs.f cpprfs.f plus dependencies prec complex for Improves the computed solution to a Hermitian 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 d2d1b file cpptrf.f cpptrf.f plus dependencies prec complex for Computes the Cholesky factorization of a Hermitian , positive definite matrix in packed storage. gams d2d1b file cpptri.f cpptri.f plus dependencies prec complex for Computes the inverse of a Hermitian positive definite , matrix in packed storage, using the Cholesky factorization computed , by CPPTRF. gams d2d1b file cpptrs.f cpptrs.f plus dependencies prec complex for Solves a Hermitian positive definite system of linear , equations AX=B, where A is held in packed storage, using the , Cholesky factorization computed by CPPTRF. gams d2d1b file cptcon.f cptcon.f plus dependencies prec complex for Computes the reciprocal of the condition number of a , Hermitian positive definite tridiagonal matrix, , using the LDL**H factorization computed by CPTTRF. gams d2d2a file cpteqr.f cpteqr.f plus dependencies prec complex for Computes all eigenvalues and eigenvectors of a complex symmetric , positive definite tridiagonal matrix, by computing the SVD of , its bidiagonal Cholesky factor. gams d4c2a file cptrfs.f cptrfs.f plus dependencies prec complex for Improves the computed solution to a Hermitian positive , definite tridiagonal system of linear equations AX=B, and provides , forward and backward error bounds for the solution. gams d2d2a file cpttrf.f cpttrf.f plus dependencies prec complex for Computes the LDL**H factorization of a Hermitian , positive definite tridiagonal matrix. gams d2d2a file cpttrs.f cpttrs.f plus dependencies prec complex for Solves a Hermitian positive definite tridiagonal , system of linear equations, using the LDL**H factorization , computed by CPTTRF. gams d2d2a file chbgst.f chbgst.f plus dependencies prec complex for Reduces a complex Hermitian-definite banded generalized eigenproblem , A x = lambda B x to standard form, where B has been factorized by , CPBSTF (Crawford's algorithm). file chbtrd.f chbtrd.f plus dependencies prec complex for Reduces a Hermitian band matrix to real symmetric , tridiagonal form by a unitary similarity transformation. gams d4c1b1 file cspcon.f cspcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , complex symmetric indefinite , matrix in packed storage, using the factorization computed , by CSPTRF. gams d2c1 file chpcon.f chpcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , complex Hermitian indefinite , matrix in packed storage, using the factorization computed , by CHPTRF. gams d2d1a file chpgst.f chpgst.f plus dependencies prec complex for Reduces a Hermitian-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 CPPTRF. gams d4c1c file csprfs.f csprfs.f plus dependencies prec complex for Improves the computed solution to a complex , 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 d2c1 file chprfs.f chprfs.f plus dependencies prec complex for Improves the computed solution to a complex , Hermitian 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 d2d1a file chptrd.f chptrd.f plus dependencies prec complex for Reduces a Hermitian matrix in packed storage to real , symmetric tridiagonal form by a unitary similarity , transformation. gams d4c1b1 file csptrf.f csptrf.f plus dependencies prec complex for Computes the factorization of a complex , symmetric-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2c1 file chptrf.f chptrf.f plus dependencies prec complex for Computes the factorization of a complex , Hermitian-indefinite matrix in packed storage, , using the diagonal pivoting method. gams d2d1a file csptri.f csptri.f plus dependencies prec complex for Computes the inverse of a complex symmetric , indefinite matrix in packed storage, using the factorization , computed by CSPTRF. gams d2c1 file chptri.f chptri.f plus dependencies prec complex for Computes the inverse of a complex , Hermitian indefinite matrix in packed storage, using the factorization , computed by CHPTRF. gams d2d1a file csptrs.f csptrs.f plus dependencies prec complex for Solves a complex symmetric , indefinite system of linear equations AX=B, where A is held , in packed storage, using the factorization computed , by CSPTRF. gams d2c1 file chptrs.f chptrs.f plus dependencies prec complex for Solves a complex Hermitian , indefinite system of linear equations AX=B, where A is held , in packed storage, using the factorization computed , by CHPTRF. gams d2d1a file cstedc.f cstedc.f plus dependencies prec complex for Computes all eigenvalues and, optionally, eigenvectors of a , symmetric tridiagonal matrix using the divide and conquer algorithm. file cstegr.f cstegr.f plus dependencies prec complex 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 cstein.f cstein.f plus dependencies prec complex for Computes selected eigenvectors of a real symmetric tridiagonal , matrix by inverse iteration. gams d4c3 file csteqr.f csteqr.f plus dependencies prec complex for Computes all eigenvalues and eigenvectors of a real symmetric , tridiagonal matrix, using the implicit QL or QR algorithm. gams d4a1, d4a5, d4c2a file csycon.f csycon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , complex symmetric indefinite matrix, , using the factorization computed by CSYTRF. gams d2c1 file checon.f checon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a , complex Hermitian indefinite matrix, , using the factorization computed by CHETRF. gams d2d1a file chegst.f chegst.f plus dependencies prec complex for Reduces a Hermitian-definite generalized eigenproblem , Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard , form, where B has been factorized by CPOTRF. gams d4c1c file csyrfs.f csyrfs.f plus dependencies prec complex for Improves the computed solution to a complex , symmetric indefinite system of linear equations , AX=B, and provides forward and backward error bounds for the , solution. gams d2c1 file cherfs.f cherfs.f plus dependencies prec complex for Improves the computed solution to a complex , Hermitian indefinite system of linear equations , AX=B, and provides forward and backward error bounds for the , solution. gams d2d1a file chetrd.f chetrd.f plus dependencies prec complex for Reduces a Hermitian matrix to real symmetric tridiagonal , form by an orthogonal/unitary similarity transformation. gams d4c1b1 file csytrf.f csytrf.f plus dependencies prec complex for Computes the factorization of a complex symmetric-indefinite matrix, , using the diagonal pivoting method. gams d2c1 file chetrf.f chetrf.f plus dependencies prec complex for Computes the factorization of a complex Hermitian-indefinite matrix, , using the diagonal pivoting method. gams d2d1a file csytri.f csytri.f plus dependencies prec complex for Computes the inverse of a complex symmetric indefinite matrix, , using the factorization computed by CSYTRF. gams d2c1 file csytri2.f csytri2.f plus dependencies prec complex for Computes the inverse of a complex symmetric indefinite matrix, , using the factorization computed by CSYTRF using Level 3 BLAS. gams d2c1 file chetri.f chetri.f plus dependencies prec complex for Computes the inverse of a complex Hermitian indefinite matrix, , using the factorization computed by CHETRF. gams d2d1a file csytrs.f csytrs.f plus dependencies prec complex for Solves a complex symmetric indefinite system of linear equations AX=B, , using the factorization computed by CSPTRF. gams d2c1 file csytrs2.f csytrs2.f plus dependencies prec complex for Solves a complex symmetric indefinite system of linear equations AX=B, , using the factorization computed by CSPTRF using Level 3 BLAS. gams d2c1 file chetrs.f chetrs.f plus dependencies prec complex for Solves a complex Hermitian indefinite system of linear equations AX=B, , using the factorization computed by CHPTRF. gams d2d1a file chetrs2.f chetrs2.f plus dependencies prec complex for Solves a complex Hermitian indefinite system of linear equations AX=B, , using the factorization computed by CHPTRF using Level 3 BLAS. gams d2d1a file ctbcon.f ctbcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a triangular , band matrix, in either the 1-norm or the infinity-norm. gams d2c2, d2c3 file ctbrfs.f ctbrfs.f plus dependencies prec complex 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 d2c2, d2c3 file ctbtrs.f ctbtrs.f plus dependencies prec complex for Solves a triangular banded system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2c2, d2c3 file ctgevc.f ctgevc.f plus dependencies prec complex for Computes some or all of the right and/or left generalized eigenvectors , of a pair of complex upper triangular matrices. gams d4b4 file ctgexc.f ctgexc.f plus dependencies prec complex for Reorders the generalized Schur decomposition of a complex , matrix pair (A,B) using a unitary equivalence transformation , so that the diagonal block of (A,B) with row index IFST is moved , to row ILST. file ctgsen.f ctgsen.f plus dependencies prec complex for Reorders the generalized Schur decomposition of a complex , matrix pair (A, B) so that a selected cluster of eigenvalues , appears in the leading diagonal blocks of the pair (A,B). file ctgsja.f ctgsja.f plus dependencies prec complex for Computes the generalized singular value decomposition of two complex , upper triangular (or trapezoidal) matrices as output by CGGSVP. gams d6 file ctgsna.f ctgsna.f plus dependencies prec complex for Estimates reciprocal condition numbers for specified , eigenvalues and/or eigenvectors of a matrix pair (A, B) in , generalized Schur canonical form, as returned by CGGES. file ctgsyl.f ctgsyl.f plus dependencies prec complex for Solves the generalized Sylvester equation. file ctpcon.f ctpcon.f plus dependencies prec complex 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 d2c3 file ctprfs.f ctprfs.f plus dependencies prec complex 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 d2c3 file ctptri.f ctptri.f plus dependencies prec complex for Computes the inverse of a triangular matrix in packed storage. gams d2c3 file ctptrs.f ctptrs.f plus dependencies prec complex 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 d2c3 file ctrcon.f ctrcon.f plus dependencies prec complex for Estimates the reciprocal of the condition number of a triangular , matrix, in either the 1-norm or the infinity-norm. gams d2c3 file ctrevc.f ctrevc.f plus dependencies prec complex for Computes left and right eigenvectors of an complex upper triangular , matrix. gams d4c3 file ctrexc.f ctrexc.f plus dependencies prec complex for Reorders the Schur factorization of a matrix by a unitary , similarity transformation. gams d4c file ctrrfs.f ctrrfs.f plus dependencies prec complex 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 d2c3 file ctrsen.f ctrsen.f plus dependencies prec complex 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 ctrsna.f ctrsna.f plus dependencies prec complex for Estimates the reciprocal condition numbers (sensitivities) , of selected eigenvalues and eigenvectors of a complex upper , triangular matrix. gams d4c file ctrsyl.f ctrsyl.f plus dependencies prec complex for Solves the Sylvester matrix equation A X +/- X B=C where A , and B are complex upper triangular, and may be transposed. gams d8 file ctrtri.f ctrtri.f plus dependencies prec complex for Computes the inverse of a triangular matrix. gams d2c3 file ctrtrs.f ctrtrs.f plus dependencies prec complex for Solves a triangular system of linear equations AX=B, , A**T X=B or A**H X=B. gams d2c3 file ctzrqf.f ctzrqf.f plus dependencies prec complex for Computes an RQ factorization of an upper trapezoidal matrix. gams d5 file ctzrzf.f ctzrzf.f plus dependencies prec complex for Computes an RZ factorization of an upper trapezoidal matrix , (blocked version of CTZRQF).