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IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) NNNNAAAAMMMMEEEE IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK - Introduction to LAPACK solvers for dense linear systems IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN See individual man pages for implementation details These routines are part of the SCSL Scientific Library and can be loaded using either the ----llllssssccccssss or the ----llllssssccccssss____mmmmpppp option. The ----llllssssccccssss____mmmmpppp option directs the linker to use the multi-processor version of the library. When linking to SCSL with ----llllssssccccssss or ----llllssssccccssss____mmmmpppp, the default integer size is 4 bytes (32 bits). Another version of SCSL is available in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using the ----llllssssccccssss____iiii8888 option or the ----llllssssccccssss____iiii8888____mmmmpppp option. A program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN The preferred solvers for dense linear systems are those parts of the LAPACK package that are included in the current version of the SGI Scientific Computing Software Library (SCSL). LLLLAAAAPPPPAAAACCCCKKKK RRRRoooouuuuttttiiiinnnneeeessss LAPACK is a public domain library of subroutines for solving dense linear algebra problems, including the following: * Systems of linear equations * Linear least squares problems * Eigenvalue problems * Singular value decomposition (SVD) problems For details about which routines are supported, see "LAPACK Routines Contained in the Scientific Library," which follows. The LAPACK package is designed to be the successor to the older LINPACK and EISPACK packages. It uses today's high-performance computers more efficiently than the older packages. It also extends the functionality of these packages by including equilibration, iterative refinement, error bounds, and driver routines for linear systems, routines for computing and reordering the Schur factorization, and condition estimation routines for eigenvalue problems. Performance issues are addressed by implementing the most computationally-intensive algorithms by using the Level 2 and 3 Basic Linear Algebra Subprograms (BLAS). Because most of the BLAS were optimized in single- and multiple-processor environments, these algorithms give near optimal performance. PPPPaaaaggggeeee 1111 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) The original Fortran programs are described in the _L_A_P_A_C_K _U_s_e_r'_s _G_u_i_d_e by E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, published by the Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1992. The manual is also available online at hhhhttttttttpppp::::////////wwwwwwwwwwww....nnnneeeettttlllliiiibbbb....oooorrrrgggg////llllaaaappppaaaacccckkkk////lllluuuugggg////iiiinnnnddddeeeexxxx....hhhhttttmmmmllll. LLLLAAAAPPPPAAAACCCCKKKK RRRRoooouuuuttttiiiinnnneeeessss CCCCoooonnnnttttaaaaiiiinnnneeeedddd iiiinnnn tttthhhheeee SSSScccciiiieeeennnnttttiiiiffffiiiicccc LLLLiiiibbbbrrrraaaarrrryyyy All of the real and complex routines from LAPACK 3.0 are supported in SCSL. This includes driver routines and computational routines for solving linear systems, least squares problems, and eigenvalue and singular value problems. Selected auxiliary routines for generating and manipulating elementary orthogonal transformations are also supported. The LAPACK routines in SCSL are described online in man pages. For example, to see a description of the arguments to the expert driver routine for solving a general system of equations, enter the following command: % man sgesvx The user interface to all supported LAPACK routines is exactly the same as the standard LAPACK interface. Tuning parameters for the block algorithms provided in the SCSL are set within the LAPACK routine IIIILLLLAAAAEEEENNNNVVVV(3S). IIIILLLLAAAAEEEENNNNVVVV(3S) is an integer function subprogram that accepts information about the problem type and dimensions, and it returns one integer parameter, such as the optimal block size, the minimum block size for which a block algorithm should be used, or the crossover point (the problem size at which it becomes more efficient to switch to an unblocked algorithm). The setting of tuning parameters occurs without user intervention, but users may call IIIILLLLAAAAEEEENNNNVVVV(3S) directly to discover the values that will be used (for example, to determine how much workspace to provide). CCCCaaaalllllllliiiinnnngggg LLLLAAAAPPPPAAAACCCCKKKK RRRRoooouuuuttttiiiinnnneeeessss ffffrrrroooommmm CCCC Although LAPACK is a library of Fortran 77 subroutines, C and C++ users have full access to LAPACK functionality provided that they follow conventions documented in Chapter 8 of the MMMMIIIIPPPPSSSSpppprrrroooo 7777 FFFFoooorrrrttttrrrraaaannnn 99990000 CCCCoooommmmmmmmaaaannnnddddssss aaaannnndddd DDDDiiiirrrreeeeccccttttiiiivvvveeeessss RRRReeeeffffeeeerrrreeeennnncccceeee MMMMaaaannnnuuuuaaaallll, "Interlanguage Calling" (available from hhhhttttttttpppp::::////////tttteeeecccchhhhppppuuuubbbbssss....ssssggggiiii....ccccoooommmm////). The large majority of LAPACK routines can be called from C/C++ using the following four rules: * The name of the LAPACK subprogram must be declared in the C/C++ program using all lowercase letters, appended with a trailing underscore. * The correspondence between Fortran and C data types is as follows: Fortran C/C++ ------- ----- PPPPaaaaggggeeee 2222 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) INTEGER int (32-bit integer library) long long (64-bit integer library) LOGICAL int (32-bit integer library) long long (64-bit integer library) REAL float DOUBLE PRECISION double COMPLEX struct{float real, imag;}; DOUBLE COMPLEX struct{double real, imag;}; CHARACTER char * All subroutine arguments should be passed by reference. * The LAPACK routines expect multidimensional arrays to be stored in column-major format in a contiguous region of memory. Note that the list above represents a subset of the general set of interlanguage calling conventions described in the Fortran 90 reference manual. Character strings, in particular, require special handling when passed as subroutine arguments or when returned from a function: if a string is longer than one character in extent, its length must be passed as an additional argument. Since most LAPACK subprograms employ character strings of length one, however, this special case can usually be ignored. Two important exceptions, IIIILLLLAAAAEEEENNNNVVVV(3S) and XXXXEEEERRRRBBBBLLLLAAAA(3S), are discussed more fully below. To call the double precision Cholesky factorization routine DDDDPPPPOOOOTTTTRRRRFFFF(3S), for example, the following prototype and code might apply: void dpotrf_(char *, int *, double *, int *, int *); char uplo; int info, lda, n; double a[1000][1001]; uplo = 'U'; lda = 1001; n = 1000; dpotrf_(&uplo, &n, (double *) a, &lda, &info); Or, to calculate the eigenvalues and eigenvectors of a double complex Hermitian matrix using ZZZZHHHHEEEEEEEEVVVVDDDD(3S) from the 64-bit integer version of SCSL, one might have: typedef struct {double real, imag;} zomplex; void zheevd_(char *, char *, long long *, zomplex *, long long *, double *, zomplex *, long long *, double *, long long *, long long *, long long *, long long *); char jobz, uplo; PPPPaaaaggggeeee 3333 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) long long info, lda, liwork, lrwork, lwork, n; long long *iwork; double *rwork, *w; zomplex *a, *work; ... (array allocations and variable assignments) ... zheevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, rwork, &lrwork iwork, &liwork, &info); Two LAPACK routines involving character string arguments are XXXXEEEERRRRBBBBLLLLAAAA(3S) and IIIILLLLAAAAEEEENNNNVVVV(3S). The corresponding C/C++ prototypes, assuming 32-bit integers in the former case and 64-bit integers in the latter, would be void xerbla_(char *, int *, const int); long long ilaenv_(long long *, char *str1, char *str2, long long *, long long *, long long *, long long *, const int len_str1, const int len_str2); Here the lengths of the strings are passed as implicit arguments, in order of use, following the explicit argument list. Note that, regardless of the default integer size in the version of SCSL one uses, the length of the character string is always passed as type int. NNNNaaaammmmiiiinnnngggg SSSScccchhhheeeemmmmeeee The name of each LAPACK routine is a coded specification of its function (within the limits of the FORTRAN 77 standard for six-character names). All driver and computational routines have five- or six-character names of the form _X_Y_Y_Z_Z or _X_Y_Y_Z_Z_Z. The first letter in each name, _X, indicates the data type, as follows: SSSS RRRREEEEAAAALLLL DDDD DDDDOOOOUUUUBBBBLLLLEEEE PPPPRRRREEEECCCCIIIISSSSIIIIOOOONNNN CCCC CCCCOOOOMMMMPPPPLLLLEEEEXXXX ZZZZ DDDDOOOOUUUUBBBBLLLLEEEE CCCCOOOOMMMMPPPPLLLLEEEEXXXX The next two letters, _Y_Y, indicate the type of matrix (or the most-significant matrix). Most of these two-letter codes apply to both real and complex matrices, but a few apply specifically to only one or the other. The matrix types are as follows: BBBBDDDD BiDiagonal PPPPaaaaggggeeee 4444 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) DDDDIIII Diagonal GGGGBBBB General Band GGGGEEEE GEneral (nonsymmetric) GGGGGGGG General matrices, Generalized problem GGGGTTTT General Tridiagonal HHHHBBBB Hermitian Band (complex only) HHHHEEEE HErmitian (possibly indefinite) (complex only) HHHHGGGG Hessenberg matrix, Generalized problem HHHHPPPP Hermitian Packed (possibly indefinite) (complex only) HHHHSSSS upper HeSsenberg OOOOPPPP Orthogonal Packed (real only) OOOORRRR ORthogonal (real only) PPPPBBBB Positive definite Band (symmetric or Hermitian) PPPPOOOO POsitive definite (symmetric or Hermitian) PPPPPPPP Positive definite Packed (symmetric or Hermitian) PPPPTTTT Positive definite Tridiagonal (symmetric or Hermitian) SSSSBBBB Symmetric Band (real only) SSSSPPPP Symmetric Packed (possibly indefinite) SSSSTTTT Symmetric Tridiagonal SSSSYYYY SYmmetric (possibly indefinite) TTTTBBBB Triangular Band TTTTGGGG Triangular matrices, Generalized problem TTTTPPPP Triangular Packed TTTTRRRR TRiangular TTTTZZZZ TrapeZoidal PPPPaaaaggggeeee 5555 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) UUUUNNNN UNitary (complex only) UUUUPPPP Unitary Packed (complex only) The last two or three letters, _Z_Z or _Z_Z_Z, indicate the computation performed. For example, SSSSGGGGEEEETTTTRRRRFFFF performs a TTTTRRRRiangular FFFFactorization of a SSSSingle-precision (real) GGGGEEEEneral matrix; CCCCGGGGEEEETTTTRRRRFFFF performs the factorization of a CCCComplex GGGGEEEEneral matrix. LLLLiiiissssttttssss ooooffff AAAAvvvvaaaaiiiillllaaaabbbblllleeee LLLLAAAAPPPPAAAACCCCKKKK RRRRoooouuuuttttiiiinnnneeeessss The following pages contain lists of driver and computational routines from LAPACK available in the SCSL Scientific Library. For details about the argument lists and usage of these routines, see the individual online man pages or the _L_A_P_A_C_K _U_s_e_r'_s _G_u_i_d_e. These routines are listed in alphabetical order. * CCCCHHHHEEEESSSSVVVV, ZZZZHHHHEEEESSSSVVVV: Solves a complex Hermitian indefinite system of linear equations _A_X = _B. * CCCCHHHHEEEESSSSVVVVXXXX, ZZZZHHHHEEEESSSSVVVVXXXX: Solves a complex Hermitian indefinite system of linear equations _A_X = _B and provides an estimate of the condition number and error bounds on the solution. * CCCCHHHHPPPPSSSSVVVV, ZZZZHHHHPPPPSSSSVVVV: Solves a complex Hermitian indefinite system of linear equations _A_X = _B; _A is held in packed storage. * CCCCHHHHPPPPSSSSVVVVXXXX, ZZZZHHHHPPPPSSSSVVVVXXXX: Solves a complex Hermitian indefinite system of linear equations _A_X = _B (_A is held in packed storage) and provides an estimate of the condition number and error bounds on the solution. * SSSSGGGGBBBBSSSSVVVV, DDDDGGGGBBBBSSSSVVVV, CCCCGGGGBBBBSSSSVVVV, ZZZZGGGGBBBBSSSSVVVV: Solves a general banded system of linear equations _A_X = _B. * SSSSGGGGBBBBSSSSVVVVXXXX, DDDDGGGGBBBBSSSSVVVVXXXX, CCCCGGGGBBBBSSSSVVVVXXXX, ZZZZGGGGBBBBSSSSVVVVXXXX: Solves any of the following general banded systems of linear equations and provides an estimate of the condition number and error bounds on the solution. A X = B T A = B H A X = B * SSSSGGGGEEEEEEEESSSS, DDDDGGGGEEEEEEEESSSS, CCCCGGGGEEEEEEEESSSS, ZZZZGGGGEEEEEEEESSSS: Computes eigenvalues, Schur form, and Schur vectors of a general matrix. PPPPaaaaggggeeee 6666 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSGGGGEEEEEEEESSSSXXXX, DDDDGGGGEEEEEEEESSSSXXXX, CCCCGGGGEEEEEEEESSSSXXXX, ZZZZGGGGEEEEEEEESSSSXXXX: Computes eigenvalues, Schur form, Schur vectors, and condition numbers of a general matrix. * SSSSGGGGEEEEEEEEVVVV, DDDDGGGGEEEEEEEEVVVV, CCCCGGGGEEEEEEEEVVVV, ZZZZGGGGEEEEEEEEVVVV: Computes eigenvalues and eigenvectors of a general matrix. * SSSSGGGGEEEEEEEEVVVVXXXX, DDDDGGGGEEEEEEEEVVVVXXXX, CCCCGGGGEEEEEEEEVVVVXXXX, ZZZZGGGGEEEEEEEEVVVVXXXX: Compute eigenvalues, eigenvectors, and condition numbers of a general matrix. * SSSSGGGGEEEEGGGGSSSS, DDDDGGGGEEEEGGGGSSSS, CCCCGGGGEEEEGGGGSSSS, ZZZZGGGGEEEEGGGGSSSS: Computes the generalized Schur factorization of a matrix pair (A,B). * SSSSGGGGEEEEGGGGVVVV, DDDDGGGGEEEEGGGGVVVV, CCCCGGGGEEEEGGGGVVVV, ZZZZGGGGEEEEGGGGVVVV: Computes the eigenvalues and eigenvectors of a matrix pair (A,B). * SSSSGGGGEEEELLLLSSSS, DDDDGGGGEEEELLLLSSSS, CCCCGGGGEEEELLLLSSSS, ZZZZGGGGEEEELLLLSSSS: Finds a least squares or minimum norm solution of an overdetermined or underdetermined linear. system. * SSSSGGGGEEEELLLLSSSSDDDD, DDDDGGGGEEEELLLLSSSSDDDD, CCCCGGGGEEEELLLLSSSSDDDD, ZZZZGGGGEEEELLLLSSSSDDDD: Solves linear least squares problem using divide-and-conquer. * SSSSGGGGEEEELLLLSSSSSSSS, DDDDGGGGEEEELLLLSSSSSSSS, CCCCGGGGEEEELLLLSSSSSSSS, ZZZZGGGGEEEELLLLSSSSSSSS: Solves linear least squares problem using SVD. * SSSSGGGGEEEELLLLSSSSYYYY, DDDDGGGGEEEELLLLSSSSYYYY, CCCCGGGGEEEELLLLSSSSYYYY, ZZZZGGGGEEEELLLLSSSSYYYY: Computes a minimum norm solution of a linear least squares problem using a complete orthogonal factorization. * SSSSGGGGEEEESSSSDDDDDDDD, DDDDGGGGEEEESSSSDDDDDDDD, CCCCGGGGEEEESSSSDDDDDDDD, ZZZZGGGGEEEESSSSDDDDDDDD: Computes the singular value decomposition (SVD) of a general matrix using divide-and-conquer. * SSSSGGGGEEEESSSSVVVV, DDDDGGGGEEEESSSSVVVV, CCCCGGGGEEEESSSSVVVV, ZZZZGGGGEEEESSSSVVVV: Solves a general system of linear equations _A_X = _B. * SSSSGGGGEEEESSSSVVVVDDDD, DDDDGGGGEEEESSSSVVVVDDDD, CCCCGGGGEEEESSSSVVVVDDDD, ZZZZGGGGEEEESSSSVVVVDDDD: Computes the singular value decomposition (SVD) of a general matrix. * SSSSGGGGEEEESSSSVVVVXXXX, DDDDGGGGEEEESSSSVVVVXXXX, CCCCGGGGEEEESSSSVVVVXXXX, ZZZZGGGGEEEESSSSVVVVXXXX: Solves any of the following general systems of linear equations and provides an estimate of the condition number and error bounds on the solution. A X = B T A X = B H A X = B PPPPaaaaggggeeee 7777 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSGGGGGGGGEEEESSSS, DDDDGGGGGGGGEEEESSSS, CCCCGGGGGGGGEEEESSSS, ZZZZGGGGGGGGEEEESSSS: Computes the generalized Schur factorization of a matrix pair (A,B). * SSSSGGGGGGGGEEEESSSSXXXX, DDDDGGGGGGGGEEEESSSSXXXX, CCCCGGGGGGGGEEEESSSSXXXX, ZZZZGGGGGGGGEEEESSSSXXXX: Computes the generalized Schur factorization of a matrix pair (A,B), expert driver. * SSSSGGGGGGGGEEEEVVVV, DDDDGGGGGGGGEEEEVVVV, CCCCGGGGGGGGEEEEVVVV, ZZZZGGGGGGGGEEEEVVVV: Computes the eigenvalues and eigenvectors of a matrix pair (A,B). * SSSSGGGGGGGGEEEEVVVVXXXX, DDDDGGGGGGGGEEEEVVVVXXXX, CCCCGGGGGGGGEEEEVVVVXXXX, ZZZZGGGGGGGGEEEEVVVVXXXX: Computes the eigenvalues and eigenvectors of a matrix pair (A,B), expert driver. * SSSSGGGGGGGGLLLLSSSSEEEE, DDDDGGGGGGGGLLLLSSSSEEEE, CCCCGGGGGGGGLLLLSSSSEEEE, ZZZZGGGGGGGGLLLLSSSSEEEE: Solves a linear equality-constrained least squares problem (LSE) using GRQ. * SSSSGGGGGGGGGGGGLLLLMMMM, DDDDGGGGGGGGGGGGLLLLMMMM, CCCCGGGGGGGGGGGGLLLLMMMM, ZZZZGGGGGGGGGGGGLLLLMMMM: Solves a general (Gauss-Markov) linear model problem (GLM) using GQR. * SSSSGGGGGGGGSSSSVVVVDDDD, DDDDGGGGGGGGSSSSVVVVDDDD, CCCCGGGGGGGGSSSSVVVVDDDD, ZZZZGGGGGGGGSSSSVVVVDDDD: Computes the generalized singular value decomposition (SVD) of a matrix pair (A,B). * SSSSGGGGTTTTSSSSVVVV, DDDDGGGGTTTTSSSSVVVV, CCCCGGGGTTTTSSSSVVVV, ZZZZGGGGTTTTSSSSVVVV: Solves a general tridiagonal system of linear equations _A_X = _B. * SSSSGGGGTTTTSSSSVVVVXXXX, DDDDGGGGTTTTSSSSVVVVXXXX, CCCCGGGGTTTTSSSSVVVVXXXX, ZZZZGGGGTTTTSSSSVVVVXXXX: Solves any of the following general tridiagonal systems of linear equations and provides an estimate of the condition number and error bounds on the solution. A X = B T A = B H A X = B * SSSSPPPPBBBBSSSSVVVV, DDDDPPPPBBBBSSSSVVVV, CCCCPPPPBBBBSSSSVVVV, ZZZZPPPPBBBBSSSSVVVV: Solves a symmetric or Hermitian positive definite banded system of linear equations _A_X = _B. * SSSSPPPPBBBBSSSSVVVVXXXX, DDDDPPPPBBBBSSSSVVVVXXXX, CCCCPPPPBBBBSSSSVVVVXXXX, ZZZZPPPPBBBBSSSSVVVVXXXX: Solves a symmetric or Hermitian positive definite banded system of linear equations _A_X = _B and provides an estimate of the condition number and error bounds on the solution. * SSSSPPPPOOOOSSSSVVVV, DDDDPPPPOOOOSSSSVVVV, CCCCPPPPOOOOSSSSVVVV, ZZZZPPPPOOOOSSSSVVVV: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B. * SSSSPPPPOOOOSSSSVVVVXXXX, DDDDPPPPOOOOSSSSVVVVXXXX, CCCCPPPPOOOOSSSSVVVVXXXX, ZZZZPPPPOOOOSSSSVVVVXXXX: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B and provides an estimate of the condition number and error bounds on the solution. PPPPaaaaggggeeee 8888 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSPPPPPPPPSSSSVVVV, DDDDPPPPPPPPSSSSVVVV, CCCCPPPPPPPPSSSSVVVV, ZZZZPPPPPPPPSSSSVVVV: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B; _A is held in packed storage. * SSSSPPPPPPPPSSSSVVVVXXXX, DDDDPPPPPPPPSSSSVVVVXXXX, CCCCPPPPPPPPSSSSVVVVXXXX, ZZZZPPPPPPPPSSSSVVVVXXXX: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B (_A is held in packed storage) and provides an estimate of the condition number and error bounds on the solution. * SSSSPPPPTTTTSSSSVVVV, DDDDPPPPTTTTSSSSVVVV, CCCCPPPPTTTTSSSSVVVV, ZZZZPPPPTTTTSSSSVVVV: Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations _A_X = _B. * SSSSPPPPTTTTSSSSVVVVXXXX, DDDDPPPPTTTTSSSSVVVVXXXX, CCCCPPPPTTTTSSSSVVVVXXXX, ZZZZPPPPTTTTSSSSVVVVXXXX: Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations _A_X = _B and provides an estimate of the condition number and error bounds on the solution. * SSSSSSSSBBBBEEEEVVVV, DDDDSSSSBBBBEEEEVVVV, CCCCHHHHBBBBEEEEVVVV, ZZZZHHHHBBBBEEEEVVVV: Compute all eigenvalues and eigenvectors of a symmetric or Hermitian band matrix. * SSSSSSSSBBBBEEEEVVVVDDDD, DDDDSSSSBBBBEEEEVVVVDDDD, CCCCHHHHBBBBEEEEVVVVDDDD, ZZZZHHHHBBBBEEEEVVVVDDDD: Compute all eigenvalues and eigenvectors of a symmetric or Hermitian band matrix using divide- and-conquer. * SSSSSSSSBBBBEEEEVVVVXXXX, DDDDSSSSBBBBEEEEVVVVXXXX, CCCCHHHHBBBBEEEEVVVVXXXX, ZZZZHHHHBBBBEEEEVVVVXXXX: Compute selected eigenvalues and eigenvectors of a symmetric or Hermitian band matrix. * SSSSSSSSBBBBGGGGVVVV, DDDDSSSSBBBBGGGGVVVV, CCCCHHHHBBBBGGGGVVVV, ZZZZHHHHBBBBGGGGVVVV: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian- definite banded eigenproblem. * SSSSSSSSBBBBGGGGVVVVDDDD, DDDDSSSSBBBBGGGGVVVVDDDD, CCCCHHHHBBBBGGGGVVVVDDDD, ZZZZHHHHBBBBGGGGVVVVDDDD: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian- definite banded eigenproblem using divide-and-conquer. * SSSSSSSSBBBBGGGGVVVVXXXX, DDDDSSSSBBBBGGGGVVVVXXXX, CCCCHHHHBBBBGGGGVVVVXXXX, ZZZZHHHHBBBBGGGGVVVVXXXX: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian- definite banded eigenproblem expert driver. * SSSSSSSSPPPPEEEEVVVV, DDDDSSSSPPPPEEEEVVVV, CCCCHHHHPPPPEEEEVVVV, ZZZZHHHHPPPPEEEEVVVV: Computes all eigenvalues and eigenvectors of a symmetric or Hermitian packed matrix. * SSSSSSSSPPPPEEEEVVVVDDDD, DDDDSSSSPPPPEEEEVVVVDDDD, CCCCHHHHPPPPEEEEVVVVDDDD, ZZZZHHHHPPPPEEEEVVVVDDDD: Computes all eigenvalues and eigenvectors of a symmetric or Hermitian packed matrix using divide- and-conquer. * SSSSSSSSPPPPEEEEVVVVXXXX, DDDDSSSSPPPPEEEEVVVVXXXX, CCCCHHHHPPPPEEEEVVVVXXXX, ZZZZHHHHPPPPEEEEVVVVXXXX: Computes selected eigenvalues and eigenvectors of a symmetric or Hermitian packed matrix. * SSSSSSSSPPPPGGGGVVVV, DDDDSSSSPPPPGGGGVVVV, CCCCHHHHPPPPGGGGVVVV, ZZZZHHHHPPPPGGGGVVVV: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian-definite packed eigenproblem. PPPPaaaaggggeeee 9999 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSSSSSPPPPSSSSVVVV, DDDDSSSSPPPPSSSSVVVV, CCCCSSSSPPPPSSSSVVVV, ZZZZSSSSPPPPSSSSVVVV: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B; _A is held in packed storage. * SSSSSSSSPPPPSSSSVVVVXXXX, DDDDSSSSPPPPSSSSVVVVXXXX, CCCCSSSSPPPPSSSSVVVVXXXX, ZZZZSSSSPPPPSSSSVVVVXXXX: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B (_A is held in packed storage) and provides an estimate of the condition number and error bounds on the solution. * SSSSSSSSTTTTEEEEVVVV, DDDDSSSSTTTTEEEEVVVV: Compute all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. * SSSSSSSSTTTTEEEEVVVVDDDD, DDDDSSSSTTTTEEEEVVVVDDDD: Compute all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using divide-and-conquer. * SSSSSSSSTTTTEEEEVVVVRRRR, DDDDSSSSTTTTEEEEVVVVRRRR: Compute all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using RRR (relatively robust representation). * SSSSSSSSTTTTEEEEVVVVXXXX, DDDDSSSSTTTTEEEEVVVVXXXX: Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. * SSSSSSSSYYYYEEEEVVVV, DDDDSSSSYYYYEEEEVVVV, CCCCHHHHEEEEEEEEVVVV, ZZZZHHHHEEEEEEEEVVVV: Computes all eigenvalues and eigenvectors of a symmetric or Hermitian matrix. * SSSSSSSSYYYYEEEEVVVVDDDD, DDDDSSSSYYYYEEEEVVVVDDDD, CCCCHHHHEEEEEEEEVVVVDDDD, ZZZZHHHHEEEEEEEEVVVVDDDD: Computes all eigenvalues and eigenvectors of a symmetric or Hermitian matrix using divide-and- conquer. * SSSSSSSSYYYYEEEEVVVVRRRR, DDDDSSSSYYYYEEEEVVVVRRRR, CCCCHHHHEEEEEEEEVVVVRRRR, ZZZZHHHHEEEEEEEEVVVVRRRR: Computes all eigenvalues and eigenvectors of a symmetric or Hermitian matrix using RRR (relatively robust representation). * SSSSSSSSYYYYEEEEVVVVXXXX, DDDDSSSSYYYYEEEEVVVVXXXX, CCCCHHHHEEEEEEEEVVVVXXXX, ZZZZHHHHEEEEEEEEVVVVXXXX: Computes selected eigenvalues and eigenvectors of a symmetric or Hermitian matrix. * SSSSSSSSYYYYGGGGVVVV, DDDDSSSSYYYYGGGGVVVV, CCCCHHHHEEEEGGGGVVVV, ZZZZHHHHEEEEGGGGVVVV: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian-definite eigenproblem. * SSSSSSSSYYYYGGGGVVVVDDDD, DDDDSSSSYYYYGGGGVVVVDDDD, CCCCHHHHEEEEGGGGVVVVDDDD, ZZZZHHHHEEEEGGGGVVVVDDDD: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian- definite eigenproblem using divide-and-conquer. * SSSSSSSSYYYYGGGGVVVVXXXX, DDDDSSSSYYYYGGGGVVVVXXXX, CCCCHHHHEEEEGGGGVVVVXXXX, ZZZZHHHHEEEEGGGGVVVVXXXX: Computes all eigenvalues and eigenvectors of a generalized symmetric-definite or Hermitian- definite eigenproblem expert driver. * SSSSSSSSYYYYSSSSVVVV, DDDDSSSSYYYYSSSSVVVV, CCCCSSSSYYYYSSSSVVVV, ZZZZSSSSYYYYSSSSVVVV: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B. PPPPaaaaggggeeee 11110000 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSSSSSYYYYSSSSVVVVXXXX, DDDDSSSSYYYYSSSSVVVVXXXX, CCCCSSSSYYYYSSSSVVVVXXXX, ZZZZSSSSYYYYSSSSVVVVXXXX: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B and provides an estimate of the condition number and error bounds on the solution. These computational routines are listed in alphabetical order, with real matrix routines and complex matrix routines grouped together as appropriate. * CCCCHHHHEEEECCCCOOOONNNN, ZZZZHHHHEEEECCCCOOOONNNN: Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix, using the factorization computed by CCCCHHHHEEEETTTTRRRRFFFF. * CCCCHHHHEEEERRRRFFFFSSSS, ZZZZHHHHEEEERRRRFFFFSSSS: Improves the computed solution to a complex Hermitian indefinite system of linear equations _A_X = _B and provides error bounds for the solution. * CCCCHHHHEEEETTTTRRRRFFFF, ZZZZHHHHEEEETTTTRRRRFFFF: Computes the factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method. * CCCCHHHHEEEETTTTRRRRIIII, ZZZZHHHHEEEETTTTRRRRIIII: Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by CCCCHHHHEEEETTTTRRRRFFFF. * CCCCHHHHEEEETTTTRRRRSSSS, ZZZZHHHHEEEETTTTRRRRSSSS: Solves a complex Hermitian indefinite system of linear equations _A_X = _B, using the factorization computed by CCCCHHHHEEEETTTTRRRRFFFF. * CCCCHHHHPPPPCCCCOOOONNNN, ZZZZHHHHPPPPCCCCOOOONNNN: Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CCCCHHHHPPPPTTTTRRRRFFFF. * CCCCHHHHPPPPRRRRFFFFSSSS, ZZZZHHHHPPPPRRRRFFFFSSSS: Improves the computed solution to a complex Hermitian indefinite system of linear equations _A_X = _B (_A is held in packed storage) and provides error bounds for the solution. * CCCCHHHHPPPPTTTTRRRRFFFF, ZZZZHHHHPPPPTTTTRRRRFFFF: Computes the factorization of a complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method. * CCCCHHHHPPPPTTTTRRRRIIII, ZZZZHHHHPPPPTTTTRRRRIIII: Computes the inverse of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CCCCHHHHPPPPTTTTRRRRFFFF. * CCCCHHHHPPPPTTTTRRRRSSSS, ZZZZHHHHPPPPTTTTRRRRSSSS: Solves a complex Hermitian indefinite system of linear equations _A_X = _B (_A is held in packed storage) using the factorization computed by CCCCHHHHPPPPTTTTRRRRFFFF. * IIIILLLLAAAAEEEENNNNVVVV: Determines tuning parameters (such as the block size). * SSSSBBBBDDDDSSSSDDDDCCCC, DDDDBBBBDDDDSSSSDDDDCCCC, CCCCBBBBDDDDSSSSDDDDCCCC, ZZZZBBBBDDDDSSSSDDDDCCCC: Compute the singular value decomposition of a general matrix reduced to bidiagonal form using divide-and-conquer. PPPPaaaaggggeeee 11111111 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSBBBBDDDDSSSSQQQQRRRR, DDDDBBBBDDDDSSSSQQQQRRRR, CCCCBBBBDDDDSSSSQQQQRRRR, ZZZZBBBBDDDDSSSSQQQQRRRR: Compute the singular value decomposition of a general matrix reduced to bidiagonal form * SSSSDDDDIIIISSSSNNNNAAAA, DDDDDDDDIIIISSSSNNNNAAAA, CCCCDDDDIIIISSSSNNNNAAAA, ZZZZDDDDIIIISSSSNNNNAAAA: 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. * SSSSGGGGBBBBBBBBRRRRDDDD, DDDDGGGGBBBBBBBBRRRRDDDD, CCCCGGGGBBBBBBBBRRRRDDDD, ZZZZGGGGBBBBBBBBRRRRDDDD: Reduces a general band matrix to real upper bidiagonal form by an orthogonal/unitary transformation. * SSSSGGGGBBBBCCCCOOOONNNN, DDDDGGGGBBBBCCCCOOOONNNN, CCCCGGGGBBBBCCCCOOOONNNN, ZZZZGGGGBBBBCCCCOOOONNNN: Estimates the reciprocal of the condition number of a general band matrix, in either the 1-norm or the infinity-norm, using the _L_U factorization computed by SSSSGGGGBBBBTTTTRRRRFFFF or CCCCGGGGBBBBTTTTRRRRFFFF. * SSSSGGGGBBBBEEEEQQQQUUUU, DDDDGGGGBBBBEEEEQQQQUUUU, CCCCGGGGBBBBEEEEQQQQUUUU, ZZZZGGGGBBBBEEEEQQQQUUUU: Computes row and column scalings to equilibrate a general band matrix and reduce its condition number. Does not multiprocess or call any multiprocessing routines. * SSSSGGGGBBBBRRRRFFFFSSSS, DDDDGGGGBBBBRRRRFFFFSSSS, CCCCGGGGBBBBRRRRFFFFSSSS, ZZZZGGGGBBBBRRRRFFFFSSSS: Improves the computed solution to any of the following general banded systems of linear equations and provides error bounds for the solution. A X = B T A X = B H A X = B * SSSSGGGGBBBBTTTTRRRRFFFF, DDDDGGGGBBBBTTTTRRRRFFFF, CCCCGGGGBBBBTTTTRRRRFFFF, ZZZZGGGGBBBBTTTTRRRRFFFF: Computes an _L_U factorization of a general band matrix, using partial pivoting with row interchanges. * SSSSGGGGBBBBTTTTRRRRSSSS, DDDDGGGGBBBBTTTTRRRRSSSS, CCCCGGGGBBBBTTTTRRRRSSSS, ZZZZGGGGBBBBTTTTRRRRSSSS: Solves any of the following general banded systems of linear equations using the _L_U factorization computed by SSSSGGGGBBBBTTTTRRRRFFFF or CCCCGGGGBBBBTTTTRRRRFFFF. A X = B T A X = B H A X = B * SSSSGGGGEEEEBBBBAAAAKKKK, DDDDGGGGEEEEBBBBAAAAKKKK, CCCCGGGGEEEEBBBBAAAAKKKK, ZZZZGGGGEEEEBBBBAAAAKKKK: Back transform the eigenvectors of a matrix transformed by SSSSGGGGEEEEBBBBAAAALLLL/CCCCGGGGEEEEBBBBAAAALLLL. PPPPaaaaggggeeee 11112222 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSGGGGEEEEBBBBAAAALLLL, DDDDGGGGEEEEBBBBAAAALLLL, CCCCGGGGEEEEBBBBAAAALLLL, ZZZZGGGGEEEEBBBBAAAALLLL: Balances a general matrix _A. * SSSSGGGGEEEEBBBBRRRRDDDD, DDDDGGGGEEEEBBBBRRRRDDDD, CCCCGGGGEEEEBBBBRRRRDDDD, ZZZZGGGGEEEEBBBBRRRRDDDD: Reduces a general matrix to upper or lower bidiagonal form by an orthogonal/unitary transformation. * SSSSGGGGEEEECCCCOOOONNNN, DDDDGGGGEEEECCCCOOOONNNN, CCCCGGGGEEEECCCCOOOONNNN, ZZZZGGGGEEEECCCCOOOONNNN: Estimates the reciprocal of the condition number of a general matrix, in either the 1-norm or the infinity-norm, using the _L_U factorization computed by SSSSGGGGEEEETTTTRRRRFFFF or CCCCGGGGEEEETTTTRRRRFFFF. * SSSSGGGGEEEEEEEEQQQQUUUU, DDDDGGGGEEEEEEEEQQQQUUUU, CCCCGGGGEEEEEEEEQQQQUUUU, ZZZZGGGGEEEEEEEEQQQQUUUU: Computes row and column scalings to equilibrate a general rectangular matrix and to reduce its condition number. * SSSSGGGGEEEEHHHHRRRRDDDD, DDDDGGGGEEEEHHHHRRRRDDDD, CCCCGGGGEEEEHHHHRRRRDDDD, ZZZZGGGGEEEEHHHHRRRRDDDD: Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary transformation. * SSSSGGGGEEEELLLLQQQQFFFF, DDDDGGGGEEEELLLLQQQQFFFF, CCCCGGGGEEEELLLLQQQQFFFF, ZZZZGGGGEEEELLLLQQQQFFFF: Computes an _L_Q factorization of a general rectangular matrix. * SSSSGGGGEEEEQQQQLLLLFFFF, DDDDGGGGEEEEQQQQLLLLFFFF, CCCCGGGGEEEEQQQQLLLLFFFF, ZZZZGGGGEEEEQQQQLLLLFFFF: Computes a _Q_L factorization of a general rectangular matrix. * SSSSGGGGEEEEQQQQPPPP3333, DDDDGGGGEEEEQQQQPPPP3333, CCCCGGGGEEEEQQQQPPPP3333, ZZZZGGGGEEEEQQQQPPPP3333: Computes a QR factorization with column pivoting of a general rectangular matrix using level-3 BLAS. * SSSSGGGGEEEEQQQQPPPPFFFF, DDDDGGGGEEEEQQQQPPPPFFFF, CCCCGGGGEEEEQQQQPPPPFFFF, ZZZZGGGGEEEEQQQQPPPPFFFF: Computes a QQQQRRRR factorization with column pivoting of a general rectangular matrix. * SSSSGGGGEEEEQQQQRRRRFFFF, DDDDGGGGEEEEQQQQRRRRFFFF, CCCCGGGGEEEEQQQQRRRRFFFF, ZZZZGGGGEEEEQQQQRRRRFFFF: Computes a _Q_R factorization of a general rectangular matrix. * SSSSGGGGEEEERRRRFFFFSSSS, DDDDGGGGEEEERRRRFFFFSSSS, CCCCGGGGEEEERRRRFFFFSSSS, ZZZZGGGGEEEERRRRFFFFSSSS: Improves the computed solution to any of the following general systems of linear equations and provides error bounds for the solution. A X = B T A X = B H A X = B * SSSSGGGGEEEERRRRQQQQFFFF, DDDDGGGGEEEERRRRQQQQFFFF, CCCCGGGGEEEERRRRQQQQFFFF, ZZZZGGGGEEEERRRRQQQQFFFF: Computes an _R_Q factorization of a general rectangular matrix. * SSSSGGGGEEEETTTTRRRRFFFF, DDDDGGGGEEEETTTTRRRRFFFF, CCCCGGGGEEEETTTTRRRRFFFF, ZZZZGGGGEEEETTTTRRRRFFFF: Computes an _L_U factorization of a general matrix, using partial pivoting with row interchanges. PPPPaaaaggggeeee 11113333 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSGGGGEEEETTTTRRRRIIII, DDDDGGGGEEEETTTTRRRRIIII, CCCCGGGGEEEETTTTRRRRIIII, ZZZZGGGGEEEETTTTRRRRIIII: Computes the inverse of a general matrix, using the _L_U factorization computed by SSSSGGGGEEEETTTTRRRRFFFF or CCCCGGGGEEEETTTTRRRRFFFF. * SSSSGGGGEEEETTTTRRRRSSSS, DDDDGGGGEEEETTTTRRRRSSSS, CCCCGGGGEEEETTTTRRRRSSSS, ZZZZGGGGEEEETTTTRRRRSSSS: Solves any of the following general systems of linear equations using the _L_U factorization computed by SSSSGGGGEEEETTTTRRRRFFFF or CCCCGGGGEEEETTTTRRRRFFFF. A X = B T A X = B H A X = B * SSSSGGGGGGGGBBBBAAAAKKKK, DDDDGGGGGGGGBBBBAAAAKKKK, CCCCGGGGGGGGBBBBAAAAKKKK, ZZZZGGGGGGGGBBBBAAAAKKKK: Back transform the eigenvectors of a generalized eigenvalue problem transformed by SSSSGGGGGGGGBBBBAAAALLLL * SSSSGGGGGGGGBBBBAAAALLLL, DDDDGGGGGGGGBBBBAAAALLLL, CCCCGGGGGGGGBBBBAAAALLLL, ZZZZGGGGGGGGBBBBAAAALLLL: Balance a pair of general matrices (A,B) * SSSSGGGGGGGGHHHHRRRRDDDD, DDDDGGGGGGGGHHHHRRRRDDDD, CCCCGGGGGGGGHHHHRRRRDDDD, ZZZZGGGGGGGGHHHHRRRRDDDD: Reduce a pair of matrices (A,B) to generalized upper Hessenberg form * SSSSGGGGGGGGQQQQRRRRFFFF, DDDDGGGGGGGGQQQQRRRRFFFF, CCCCGGGGGGGGQQQQRRRRFFFF, ZZZZGGGGGGGGQQQQRRRRFFFF: Computes a generalized QR factorization of a pair of matrices (A,B). * SSSSGGGGGGGGRRRRQQQQFFFF, DDDDGGGGGGGGRRRRQQQQFFFF, CCCCGGGGGGGGRRRRQQQQFFFF, ZZZZGGGGGGGGRRRRQQQQFFFF: Computes a generalized RQ factorization of a pair of matrices (A,B). * SSSSGGGGGGGGSSSSVVVVPPPP, DDDDGGGGGGGGSSSSVVVVPPPP, CCCCGGGGGGGGSSSSVVVVPPPP, ZZZZGGGGGGGGSSSSVVVVPPPP: Computes orthogonal/unitary matrices U, V, and Q as the preprocessing step for computing the generalized singular value decomposition (GSVD). * SSSSGGGGTTTTCCCCOOOONNNN, DDDDGGGGTTTTCCCCOOOONNNN, CCCCGGGGTTTTCCCCOOOONNNN, ZZZZGGGGTTTTCCCCOOOONNNN: Estimates the reciprocal of the condition number of a general tridiagonal matrix, in either the 1- norm or the infinity-norm, using the _L_U factorization computed by SSSSGGGGTTTTTTTTRRRRFFFF or CCCCGGGGTTTTTTTTRRRRFFFF. * SSSSGGGGTTTTRRRRFFFFSSSS, DDDDGGGGTTTTRRRRFFFFSSSS, CCCCGGGGTTTTRRRRFFFFSSSS, ZZZZGGGGTTTTRRRRFFFFSSSS: Improves the computed solution to any of the following general tridiagonal systems of linear equations and provides error bounds for the solution. A X = B T A X = B H A X = B PPPPaaaaggggeeee 11114444 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSGGGGTTTTTTTTRRRRFFFF, DDDDGGGGTTTTTTTTRRRRFFFF, CCCCGGGGTTTTTTTTRRRRFFFF, ZZZZGGGGTTTTTTTTRRRRFFFF: Computes an _L_U factorization of a general tridiagonal matrix, using partial pivoting with row interchanges. * SSSSGGGGTTTTTTTTRRRRSSSS, DDDDGGGGTTTTTTTTRRRRSSSS, CCCCGGGGTTTTTTTTRRRRSSSS, ZZZZGGGGTTTTTTTTRRRRSSSS: Solves a general tridiagonal system of linear equations using the _L_U factorization computed by SSSSGGGGTTTTTTTTRRRRFFFF or CCCCGGGGTTTTTTTTRRRRFFFF. A X = B T A X = B H A X = B * SSSSHHHHGGGGEEEEQQQQZZZZ, DDDDHHHHGGGGEEEEQQQQZZZZ, CCCCHHHHGGGGEEEEQQQQZZZZ, ZZZZHHHHGGGGEEEEQQQQZZZZ: Compute the eigenvalues of a matrix pair (A,B) in generalized upper Hessenberg form using the QZ method * SSSSHHHHSSSSEEEEIIIINNNN, DDDDHHHHSSSSEEEEIIIINNNN, CCCCHHHHSSSSEEEEIIIINNNN, ZZZZHHHHSSSSEEEEIIIINNNN: Compute eigenvectors of a upper Hessenberg matrix by inverse iteration * SSSSHHHHSSSSEEEEQQQQRRRR, DDDDHHHHSSSSEEEEQQQQRRRR, CCCCHHHHSSSSEEEEQQQQRRRR, ZZZZHHHHSSSSEEEEQQQQRRRR: Compute eigenvalues, Schur form, and Schur vectors of a upper Hessenberg matrix * SSSSLLLLAAAAMMMMCCCCHHHH, DDDDLLLLAAAAMMMMCCCCHHHH: Computes machine-specific constants. * SSSSLLLLAAAARRRRFFFF, DDDDLLLLAAAARRRRFFFF, CCCCLLLLAAAARRRRFFFF, ZZZZLLLLAAAARRRRFFFF: Applies an elementary reflector. * SSSSLLLLAAAARRRRFFFFBBBB, DDDDLLLLAAAARRRRFFFFBBBB, CCCCLLLLAAAARRRRFFFFBBBB, ZZZZLLLLAAAARRRRFFFFBBBB: Applies a block reflector. * SSSSLLLLAAAARRRRFFFFGGGG, DDDDLLLLAAAARRRRFFFFGGGG, CCCCLLLLAAAARRRRFFFFGGGG, ZZZZLLLLAAAARRRRFFFFGGGG: Generates an elementary reflector. * SSSSLLLLAAAARRRRFFFFTTTT, DDDDLLLLAAAARRRRFFFFTTTT, CCCCLLLLAAAARRRRFFFFTTTT, ZZZZLLLLAAAARRRRFFFFTTTT: Forms the triangular factor of a block reflector. * SSSSLLLLAAAARRRRGGGGVVVV, DDDDLLLLAAAARRRRGGGGVVVV, CCCCLLLLAAAARRRRGGGGVVVV, ZZZZLLLLAAAARRRRGGGGVVVV: Generate a vector of real or complex plane rotations * SSSSLLLLAAAARRRRNNNNVVVV, DDDDLLLLAAAARRRRNNNNVVVV, CCCCLLLLAAAARRRRNNNNVVVV, ZZZZLLLLAAAARRRRNNNNVVVV: Generates a vector of random numbers. * SSSSLLLLAAAARRRRTTTTGGGG, DDDDLLLLAAAARRRRTTTTGGGG, CCCCLLLLAAAARRRRTTTTGGGG, ZZZZLLLLAAAARRRRTTTTGGGG: Generates a plane rotation. * SSSSLLLLAAAARRRRTTTTVVVV, DDDDLLLLAAAARRRRTTTTVVVV, CCCCLLLLAAAARRRRTTTTVVVV, ZZZZLLLLAAAARRRRTTTTVVVV: Apply a vector of real or complex plane rotations to two vectors * SSSSLLLLAAAASSSSRRRR, DDDDLLLLAAAASSSSRRRR, CCCCLLLLAAAASSSSRRRR, ZZZZLLLLAAAASSSSRRRR: Apply a sequence of real plane rotations to a matrix PPPPaaaaggggeeee 11115555 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSOOOOPPPPGGGGTTTTRRRR, DDDDOOOOPPPPGGGGTTTTRRRR, CCCCUUUUPPPPGGGGTTTTRRRR, ZZZZUUUUPPPPGGGGTTTTRRRR: Generates the orthogonal/unitary matrix _Q from SSSSSSSSPPPPTTTTRRRRDDDD/CCCCHHHHPPPPTTTTRRRRDDDD. * SSSSOOOOPPPPMMMMTTTTRRRR, DDDDOOOOPPPPMMMMTTTTRRRR, CCCCUUUUPPPPMMMMTTTTRRRR, ZZZZUUUUPPPPMMMMTTTTRRRR: Multiplies by the orthogonal/unitary matrix _Q from SSSSSSSSPPPPTTTTRRRRDDDD/CCCCHHHHPPPPTTTTRRRRDDDD. * SSSSOOOORRRRGGGGBBBBRRRR, DDDDOOOORRRRGGGGBBBBRRRR, CCCCUUUUNNNNGGGGBBBBRRRR, ZZZZUUUUNNNNGGGGBBBBRRRR: Generates one of the orghogonal/unitary matrices: H Q or P from SSSSGGGGEEEEBBBBRRRRDDDD/CCCCGGGGEEEEBBBBRRRRDDDD. * SSSSOOOORRRRGGGGHHHHRRRR, DDDDOOOORRRRGGGGHHHHRRRR, CCCCUUUUNNNNGGGGHHHHRRRR, ZZZZUUUUNNNNGGGGHHHHRRRR: Generates the orthogonal/unitary matrix _Q from SSSSGGGGEEEEHHHHRRRRDDDD/CCCCGGGGEEEEHHHHRRRRDDDD. * SSSSOOOORRRRGGGGLLLLQQQQ, DDDDOOOORRRRGGGGLLLLQQQQ, CCCCUUUUNNNNGGGGLLLLQQQQ, ZZZZUUUUNNNNGGGGLLLLQQQQ: Generates all or part of the orthogonal or unitary matrix _Q from an _L_Q factorization determined by SSSSGGGGEEEELLLLQQQQFFFF or CCCCGGGGEEEELLLLQQQQFFFF. * SSSSOOOORRRRGGGGQQQQLLLL, DDDDOOOORRRRGGGGQQQQLLLL, CCCCUUUUNNNNGGGGQQQQLLLL, ZZZZUUUUNNNNGGGGQQQQLLLL: Generates all or part of the orthogonal or unitary matrix _Q from a _Q_L factorization determined by SSSSGGGGEEEEQQQQLLLLFFFF or CCCCGGGGEEEEQQQQLLLLFFFF. * SSSSOOOORRRRGGGGQQQQRRRR, DDDDOOOORRRRGGGGQQQQRRRR, CCCCUUUUNNNNGGGGQQQQRRRR, ZZZZUUUUNNNNGGGGQQQQRRRR: Generates all or part of the orthogonal or unitary matrix _Q from a _Q_R factorization determined by SSSSGGGGEEEEQQQQRRRRFFFF or CCCCGGGGEEEEQQQQRRRRFFFF. * SSSSOOOORRRRGGGGRRRRQQQQ, DDDDOOOORRRRGGGGRRRRQQQQ, CCCCUUUUNNNNGGGGRRRRQQQQ, ZZZZUUUUNNNNGGGGRRRRQQQQ: Generates all or part of the orthogonal or unitary matrix _Q from an _R_Q factorization determined by SSSSGGGGEEEERRRRQQQQFFFF or CCCCGGGGEEEERRRRQQQQFFFF. * SSSSOOOORRRRGGGGTTTTRRRR, DDDDOOOORRRRGGGGTTTTRRRR, CCCCUUUUNNNNGGGGTTTTRRRR, ZZZZUUUUNNNNGGGGTTTTRRRR: Generates the orthogonal/unitary matrix _Q from SSSSSSSSYYYYTTTTRRRRDDDD/CCCCHHHHEEEETTTTRRRRDDDD. * SSSSOOOORRRRMMMMBBBBRRRR, DDDDOOOORRRRMMMMBBBBRRRR, CCCCUUUUNNNNMMMMBBBBRRRR, ZZZZUUUUNNNNMMMMBBBBRRRR: Multiplies by one of the orthogonal/unitary matrices _Q or _P from SSSSGGGGEEEEBBBBRRRRDDDD/CCCCGGGGEEEEBBBBRRRRDDDD. * SSSSOOOORRRRMMMMHHHHRRRR, DDDDOOOORRRRMMMMHHHHRRRR, CCCCUUUUNNNNMMMMHHHHRRRR, ZZZZUUUUNNNNMMMMHHHHRRRR: Multiplies by the orthogonal/unitary matrix _Q from SSSSGGGGEEEEHHHHRRRRDDDD/CCCCGGGGEEEEHHHHRRRRDDDD. * SSSSOOOORRRRMMMMLLLLQQQQ, DDDDOOOORRRRMMMMLLLLQQQQ, CCCCUUUUNNNNMMMMLLLLQQQQ, ZZZZUUUUNNNNMMMMLLLLQQQQ: Multiplies a general matrix by the orthogonal or unitary matrix from an _L_Q factorization determined by SSSSGGGGEEEELLLLQQQQFFFF or CCCCGGGGEEEELLLLQQQQFFFF. * SSSSOOOORRRRMMMMQQQQLLLL, DDDDOOOORRRRMMMMQQQQLLLL, CCCCUUUUNNNNMMMMQQQQLLLL, ZZZZUUUUNNNNMMMMQQQQLLLL: Multiplies a general matrix by the orthogonal or unitary matrix from a _Q_L factorization determined by SSSSGGGGEEEEQQQQLLLLFFFF or CCCCGGGGEEEEQQQQLLLLFFFF. PPPPaaaaggggeeee 11116666 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSOOOORRRRMMMMQQQQRRRR, DDDDOOOORRRRMMMMQQQQRRRR, CCCCUUUUNNNNMMMMQQQQRRRR, ZZZZUUUUNNNNMMMMQQQQRRRR: Multiplies a general matrix by the orthogonal or unitary matrix from a _Q_R factorization determined by SSSSGGGGEEEEQQQQRRRRFFFF or CCCCGGGGEEEEQQQQRRRRFFFF. * SSSSOOOORRRRMMMMRRRRQQQQ, DDDDOOOORRRRMMMMRRRRQQQQ, CCCCUUUUNNNNMMMMRRRRQQQQ, ZZZZUUUUNNNNMMMMRRRRQQQQ: Multiplies a general matrix by the orthogonal or unitary matrix from an _R_Q factorization determined by SSSSGGGGEEEERRRRQQQQFFFF or CCCCGGGGEEEERRRRQQQQFFFF. * SSSSOOOORRRRMMMMRRRRZZZZ, DDDDOOOORRRRMMMMRRRRZZZZ, CCCCUUUUNNNNMMMMRRRRZZZZ, ZZZZUUUUNNNNMMMMRRRRZZZZ: Multiplies a general matrix by the orthogonal or unitary matrix from an RZ factorization determined by SSSSTTTTZZZZRRRRZZZZFFFF or CCCCTTTTZZZZRRRRZZZZFFFF. * SSSSOOOORRRRMMMMTTTTRRRR, DDDDOOOORRRRMMMMTTTTRRRR, CCCCUUUUNNNNMMMMTTTTRRRR, ZZZZUUUUNNNNMMMMTTTTRRRR: Multiplies by the orthogonal/unitary matrix _Q from SSSSSSSSYYYYTTTTRRRRDDDD/CCCCHHHHEEEETTTTRRRRDDDD. * SSSSPPPPBBBBCCCCOOOONNNN, DDDDPPPPBBBBCCCCOOOONNNN, CCCCPPPPBBBBCCCCOOOONNNN, ZZZZPPPPBBBBCCCCOOOONNNN: Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite band matrix, using the Cholesky factorization computed by SSSSPPPPBBBBTTTTRRRRFFFF or CCCCPPPPBBBBTTTTRRRRFFFF. * SSSSPPPPBBBBEEEEQQQQUUUU, DDDDPPPPBBBBEEEEQQQQUUUU, CCCCPPPPBBBBEEEEQQQQUUUU, ZZZZPPPPBBBBEEEEQQQQUUUU: Computes row and column scalings to equilibrate a symmetric or Hermitian positive definite band matrix and to reduce its condition number. * SSSSPPPPBBBBRRRRFFFFSSSS, DDDDPPPPBBBBRRRRFFFFSSSS, CCCCPPPPBBBBRRRRFFFFSSSS, ZZZZPPPPBBBBRRRRFFFFSSSS: Improves the computed solution to a symmetric or Hermitian positive definite banded system of linear equations _A_X = _B and provides error bounds for the solution. * SSSSPPPPBBBBSSSSTTTTFFFF, DDDDPPPPBBBBSSSSTTTTFFFF, CCCCPPPPBBBBSSSSTTTTFFFF, ZZZZPPPPBBBBSSSSTTTTFFFF: Compute a split Cholesky factorization of a symmetric or Hermitian positive definite band matrix. * SSSSPPPPBBBBTTTTRRRRFFFF, DDDDPPPPBBBBTTTTRRRRFFFF, CCCCPPPPBBBBTTTTRRRRFFFF, ZZZZPPPPBBBBTTTTRRRRFFFF: Computes the Cholesky factorization of a symmetric or Hermitian positive definite band matrix. * SSSSPPPPBBBBTTTTRRRRSSSS, DDDDPPPPBBBBTTTTRRRRSSSS, CCCCPPPPBBBBTTTTRRRRSSSS, ZZZZPPPPBBBBTTTTRRRRSSSS: Solves a symmetric or Hermitian positive definite banded system of linear equations _A_X = _B, using the Cholesky factorization computed by SSSSPPPPBBBBTTTTRRRRFFFF or CCCCPPPPBBBBTTTTRRRRFFFF. * SSSSPPPPOOOOCCCCOOOONNNN, DDDDPPPPOOOOCCCCOOOONNNN, CCCCPPPPOOOOCCCCOOOONNNN, ZZZZPPPPOOOOCCCCOOOONNNN: Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite matrix, using the Cholesky factorization computed by SSSSPPPPOOOOTTTTRRRRFFFF or CCCCPPPPOOOOTTTTRRRRFFFF. * SSSSPPPPOOOOEEEEQQQQUUUU, DDDDPPPPOOOOEEEEQQQQUUUU, CCCCPPPPOOOOEEEEQQQQUUUU, ZZZZPPPPOOOOEEEEQQQQUUUU: Computes row and column scalings to equilibrate a symmetric or Hermitian positive definite matrix and reduces its condition number. * SSSSPPPPOOOORRRRFFFFSSSS, DDDDPPPPOOOORRRRFFFFSSSS, CCCCPPPPOOOORRRRFFFFSSSS, ZZZZPPPPOOOORRRRFFFFSSSS: Improves the computed solution to a symmetric or Hermitian positive definite system of linear equations _A_X = _B and provides error bounds for the solution. PPPPaaaaggggeeee 11117777 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSPPPPOOOOTTTTRRRRFFFF, DDDDPPPPOOOOTTTTRRRRFFFF, CCCCPPPPOOOOTTTTRRRRFFFF, ZZZZPPPPOOOOTTTTRRRRFFFF: Computes the Cholesky factorization of a symmetric or Hermitian positive definite matrix. * SSSSPPPPOOOOTTTTRRRRIIII, DDDDPPPPOOOOTTTTRRRRIIII, CCCCPPPPOOOOTTTTRRRRIIII, ZZZZPPPPOOOOTTTTRRRRIIII: Computes the inverse of a symmetric or Hermitian positive definite matrix, using the Cholesky factorization computed by SSSSPPPPOOOOTTTTRRRRFFFF or CCCCPPPPOOOOTTTTRRRRFFFF. * SSSSPPPPOOOOTTTTRRRRSSSS, DDDDPPPPOOOOTTTTRRRRSSSS, CCCCPPPPOOOOTTTTRRRRSSSS, ZZZZPPPPOOOOTTTTRRRRSSSS: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B, using the Cholesky factorization computed by SSSSPPPPOOOOTTTTRRRRFFFF or CCCCPPPPOOOOTTTTRRRRFFFF. * SSSSPPPPPPPPCCCCOOOONNNN, DDDDPPPPPPPPCCCCOOOONNNN, CCCCPPPPPPPPCCCCOOOONNNN, ZZZZPPPPPPPPCCCCOOOONNNN: Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SSSSPPPPPPPPTTTTRRRRFFFF or CCCCPPPPPPPPTTTTRRRRFFFF. * SSSSPPPPPPPPEEEEQQQQUUUU, DDDDPPPPPPPPEEEEQQQQUUUU, CCCCPPPPPPPPEEEEQQQQUUUU, ZZZZPPPPPPPPEEEEQQQQUUUU: Computes row and column scalings to equilibrate a symmetric or Hermitian positive definite matrix in packed storage and reduces its condition number. * SSSSPPPPPPPPRRRRFFFFSSSS, DDDDPPPPPPPPRRRRFFFFSSSS, CCCCPPPPPPPPRRRRFFFFSSSS, ZZZZPPPPPPPPRRRRFFFFSSSS: Improves the computed solution to a symmetric or Hermitian positive definite system of linear equations _A_X = _B (_A is held in packed storage) and provides error bounds for the solution. * SSSSPPPPPPPPTTTTRRRRFFFF, DDDDPPPPPPPPTTTTRRRRFFFF, CCCCPPPPPPPPTTTTRRRRFFFF, ZZZZPPPPPPPPTTTTRRRRFFFF: Computes the Cholesky factorization of a symmetric or Hermitian positive definite matrix in packed storage. * SSSSPPPPPPPPTTTTRRRRIIII, DDDDPPPPPPPPTTTTRRRRIIII, CCCCPPPPPPPPTTTTRRRRIIII, ZZZZPPPPPPPPTTTTRRRRIIII: Computes the inverse of a symmetric or Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SSSSPPPPPPPPTTTTRRRRFFFF or CCCCPPPPPPPPTTTTRRRRFFFF. * SSSSPPPPPPPPTTTTRRRRSSSS, DDDDPPPPPPPPTTTTRRRRSSSS, CCCCPPPPPPPPTTTTRRRRSSSS, ZZZZPPPPPPPPTTTTRRRRSSSS: Solves a symmetric or Hermitian positive definite system of linear equations _A_X = _B (_A is held in packed storage) using the Cholesky factorization computed by SSSSPPPPPPPPTTTTRRRRFFFF or CCCCPPPPPPPPTTTTRRRRFFFF. * SSSSPPPPTTTTCCCCOOOONNNN, DDDDPPPPTTTTCCCCOOOONNNN, CCCCPPPPTTTTCCCCOOOONNNN, ZZZZPPPPTTTTCCCCOOOONNNN: Uses the LDLH factorization computed by SSSSPPPPTTTTTTTTRRRRFFFF or CCCCPPPPTTTTTTTTRRRRFFFF to compute the reciprocal of the condition number of a symmetric or Hermitian positive definite tridiagonal matrix. * SSSSPPPPTTTTEEEEQQQQRRRR, DDDDPPPPTTTTEEEEQQQQRRRR, CCCCPPPPTTTTEEEEQQQQRRRR, ZZZZPPPPTTTTEEEEQQQQRRRR: Compute eigenvalues and eigenvectors of a symmetric or Hermitian positive definite tridiagonal matrix. * SSSSPPPPTTTTRRRRFFFFSSSS, DDDDPPPPTTTTRRRRFFFFSSSS, CCCCPPPPTTTTRRRRFFFFSSSS, ZZZZPPPPTTTTRRRRFFFFSSSS: Improves the computed solution to a symmetric or Hermitian positive definite tridiagonal system of linear equations _A_X = _B and provides error bounds for the solution. * SSSSPPPPTTTTTTTTRRRRFFFF, DDDDPPPPTTTTTTTTRRRRFFFF, CCCCPPPPTTTTTTTTRRRRFFFF, ZZZZPPPPTTTTTTTTRRRRFFFF: Computes the LDLH factorization of a symmetric or Hermitian positive definite tridiagonal matrix. PPPPaaaaggggeeee 11118888 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSPPPPTTTTTTTTRRRRSSSS, DDDDPPPPTTTTTTTTRRRRSSSS, CCCCPPPPTTTTTTTTRRRRSSSS, ZZZZPPPPTTTTTTTTRRRRSSSS: Uses the LDLH factorization computed by SSSSPPPPTTTTTTTTRRRRFFFF or CCCCPPPPTTTTTTTTRRRRFFFF to solve a symmetric or Hermitian positive definite tridiagonal system of linear equations. * SSSSSSSSBBBBGGGGSSSSTTTT, DDDDSSSSBBBBGGGGSSSSTTTT, CCCCHHHHBBBBGGGGSSSSTTTT, ZZZZHHHHBBBBGGGGSSSSTTTT: Reduce a symmetric or Hermitian definite banded generalized eigenproblem to standard form. * SSSSSSSSBBBBTTTTRRRRDDDD, DDDDSSSSBBBBTTTTRRRRDDDD, CCCCHHHHBBBBTTTTRRRRDDDD, ZZZZHHHHBBBBTTTTRRRRDDDD: Reduce a symmetric or Hermitian band matrix to real symmetric tridiagonal form by an orthogonal/unitary transformation. * SSSSSSSSPPPPCCCCOOOONNNN, DDDDSSSSPPPPCCCCOOOONNNN, CCCCSSSSPPPPCCCCOOOONNNN, ZZZZSSSSPPPPCCCCOOOONNNN: Estimates the reciprocal of the condition number of a real or complex symmetric indefinite matrix in packed storage, using the factorization computed by SSSSSSSSPPPPTTTTRRRRFFFF or CCCCSSSSPPPPTTTTRRRRFFFF. * SSSSSSSSPPPPGGGGSSSSTTTT, DDDDSSSSPPPPGGGGSSSSTTTT, CCCCHHHHPPPPGGGGSSSSTTTT, ZZZZHHHHPPPPGGGGSSSSTTTT: Reduce a symmetric or Hermitian definite generalized eigenproblem to standard form, using packed storage. * SSSSSSSSPPPPRRRRFFFFSSSS, DDDDSSSSPPPPRRRRFFFFSSSS, CCCCSSSSPPPPRRRRFFFFSSSS, ZZZZSSSSPPPPRRRRFFFFSSSS: Improves the computed solution to a real or complex symmetric indefinite system of linear equations _A_X = _B (_A is held in packed storage) and provides error bounds for the solution. * SSSSSSSSPPPPTTTTRRRRDDDD, DDDDSSSSPPPPTTTTRRRRDDDD, CCCCHHHHPPPPTTTTRRRRDDDD, ZZZZHHHHPPPPTTTTRRRRDDDD: Reduces a symmetric/Hermitian packed matrix A to real symmetric tridiagonal form by an orthogonal/unitary transformation. * SSSSSSSSPPPPTTTTRRRRFFFF, DDDDSSSSPPPPTTTTRRRRFFFF, CCCCSSSSPPPPTTTTRRRRFFFF, ZZZZSSSSPPPPTTTTRRRRFFFF: Computes the factorization of a real or complex symmetric indefinite matrix in packed storage, using the diagonal pivoting method. * SSSSSSSSPPPPTTTTRRRRIIII, DDDDSSSSPPPPTTTTRRRRIIII, CCCCSSSSPPPPTTTTRRRRIIII, ZZZZSSSSPPPPTTTTRRRRIIII: Computes the inverse of a real or complex symmetric indefinite matrix in packed storage, using the factorization computed by SSSSSSSSPPPPTTTTRRRRFFFF or CCCCSSSSPPPPTTTTRRRRFFFF. * SSSSSSSSPPPPTTTTRRRRSSSS, DDDDSSSSPPPPTTTTRRRRSSSS, CCCCSSSSPPPPTTTTRRRRSSSS, ZZZZSSSSPPPPTTTTRRRRSSSS: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B (_A is held in packed storage) using the factorization computed by SSSSSSSSPPPPTTTTRRRRFFFF or CCCCSSSSPPPPTTTTRRRRFFFF. * SSSSSSSSTTTTEEEEBBBBZZZZ, DDDDSSSSTTTTEEEEBBBBZZZZ: Compute eigenvalues of a symmetric tridiagonal matrix by bisection. * SSSSSSSSTTTTEEEEDDDDCCCC, DDDDSSSSTTTTEEEEDDDDCCCC, CCCCSSSSTTTTEEEEDDDDCCCC, ZZZZSSSSTTTTEEEEDDDDCCCC: Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer algorithm. * SSSSSSSSTTTTEEEEGGGGRRRR, DDDDSSSSTTTTEEEEGGGGRRRR, CCCCSSSSTTTTEEEEGGGGRRRR, ZZZZSSSSTTTTEEEEGGGGRRRR: Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representations. PPPPaaaaggggeeee 11119999 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSSSSSTTTTEEEEIIIINNNN, DDDDSSSSTTTTEEEEIIIINNNN, CCCCSSSSTTTTEEEEIIIINNNN, ZZZZSSSSTTTTEEEEIIIINNNN: Compute eigenvectors of a real symmetric tridiagonal matrix by inverse iteration. * SSSSSSSSTTTTEEEEQQQQRRRR, DDDDSSSSTTTTEEEEQQQQRRRR, CCCCSSSSTTTTEEEEQQQQRRRR, ZZZZSSSSTTTTEEEEQQQQRRRR: Compute eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using the implicit QL or QR method. * SSSSSSSSTTTTEEEERRRRFFFF, DDDDSSSSTTTTEEEERRRRFFFF: Compute all eigenvalues of a symmetric tridiagonal matrix using the root-free variant of the QL or QR algorithm. * SSSSSSSSYYYYCCCCOOOONNNN, DDDDSSSSYYYYCCCCOOOONNNN, CCCCSSSSYYYYCCCCOOOONNNN, ZZZZSSSSYYYYCCCCOOOONNNN: Estimates the reciprocal of the condition number of a real or complex symmetric indefinite matrix, using the factorization computed by SSSSSSSSYYYYTTTTRRRRFFFF or CCCCSSSSYYYYTTTTRRRRFFFF. * SSSSSSSSYYYYGGGGSSSSTTTT, DDDDSSSSYYYYGGGGSSSSTTTT, CCCCHHHHEEEEGGGGSSSSTTTT, ZZZZHHHHEEEEGGGGSSSSTTTT: Reduce a symmetric or Hermitian definite generalized eigenproblem to standard form. * SSSSSSSSYYYYRRRRFFFFSSSS, DDDDSSSSYYYYRRRRFFFFSSSS, CCCCSSSSYYYYRRRRFFFFSSSS, ZZZZSSSSYYYYRRRRFFFFSSSS: Improves the computed solution to a real or complex symmetric indefinite system of linear equations _A_X = _B and provides error bounds for the solution. * SSSSSSSSYYYYTTTTRRRRDDDD, DDDDSSSSYYYYTTTTRRRRDDDD, CCCCHHHHEEEETTTTRRRRDDDD, ZZZZHHHHEEEETTTTRRRRDDDD: Reduces a symmetric/Hermitian matrix _A to real symmetric tridiagonal form by an orthogonal/unitary transformation. * SSSSSSSSYYYYTTTTRRRRFFFF, DDDDSSSSYYYYTTTTRRRRFFFF, CCCCSSSSYYYYTTTTRRRRFFFF, ZZZZSSSSYYYYTTTTRRRRFFFF: Computes the factorization of a real complex symmetric indefinite matrix, using the diagonal pivoting method. * SSSSSSSSYYYYTTTTRRRRIIII, DDDDSSSSYYYYTTTTRRRRIIII, CCCCSSSSYYYYTTTTRRRRIIII, ZZZZSSSSYYYYTTTTRRRRIIII: Computes the inverse of a real or complex symmetric indefinite matrix, using the factorization computed by SSSSSSSSYYYYTTTTRRRRFFFF or CCCCSSSSYYYYTTTTRRRRFFFF. * SSSSSSSSYYYYTTTTRRRRSSSS, DDDDSSSSYYYYTTTTRRRRSSSS, CCCCSSSSYYYYTTTTRRRRSSSS, ZZZZSSSSYYYYTTTTRRRRSSSS: Solves a real or complex symmetric indefinite system of linear equations _A_X = _B, using the factorization computed by SSSSSSSSYYYYTTTTRRRRFFFF or CCCCSSSSYYYYTTTTRRRRFFFF. * SSSSTTTTBBBBCCCCOOOONNNN, DDDDTTTTBBBBCCCCOOOONNNN, CCCCTTTTBBBBCCCCOOOONNNN, ZZZZTTTTBBBBCCCCOOOONNNN: Estimates the reciprocal of the condition number of a triangular band matrix, in either the 1-norm or the infinity-norm. * SSSSTTTTBBBBRRRRFFFFSSSS, DDDDTTTTBBBBRRRRFFFFSSSS, CCCCTTTTBBBBRRRRFFFFSSSS, ZZZZTTTTBBBBRRRRFFFFSSSS: Provides error bounds for the solution of any of the following triangular banded systems of linear equations: A X = B T A X = B H A X = B PPPPaaaaggggeeee 22220000 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSTTTTBBBBTTTTRRRRSSSS, DDDDTTTTBBBBTTTTRRRRSSSS, CCCCTTTTBBBBTTTTRRRRSSSS, ZZZZTTTTBBBBTTTTRRRRSSSS: Solves any of the following triangular banded systems of linear equations: A X = B T A X = B H A X = B * SSSSTTTTGGGGEEEEVVVVCCCC, DDDDTTTTGGGGEEEEVVVVCCCC, CCCCTTTTGGGGEEEEVVVVCCCC, ZZZZTTTTGGGGEEEEVVVVCCCC: Compute eigenvectors of a pair of matrices (A,B) in generalized Schur form. * SSSSTTTTGGGGEEEEXXXXCCCC, DDDDTTTTGGGGEEEEXXXXCCCC, CCCCTTTTGGGGEEEEXXXXCCCC, ZZZZTTTTGGGGEEEEXXXXCCCC: Reorders the generalized real- Schur/Schur decomposition of a matrix pair (A,B) using an orthogonal/unitary equivalence transformation so that the diagonal block of (A,B) with row index IFST is moved to row ILST. * SSSSTTTTGGGGSSSSEEEENNNN, DDDDTTTTGGGGSSSSEEEENNNN, CCCCTTTTGGGGSSSSEEEENNNN, ZZZZTTTTGGGGSSSSEEEENNNN: Reorders the generalized real- Schur/Schur decomposition of a matrix pair (A,B), computes the generalized eigenvalues of the reordered matrix pair, and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces. * SSSSTTTTGGGGSSSSJJJJAAAA, DDDDTTTTGGGGSSSSJJJJAAAA, CCCCTTTTGGGGSSSSJJJJAAAA, ZZZZTTTTGGGGSSSSJJJJAAAA: Computes the generalized singular value decomposition (GSVD) of a pair of upper triangular (or trapezoidal) matrices, which may be obtained by the preprocessing subroutine SSSSGGGGGGGGSSSSVVVVPPPP/CCCCGGGGGGGGSSSSVVVVPPPP. * SSSSTTTTGGGGSSSSNNNNAAAA, DDDDTTTTGGGGSSSSNNNNAAAA, CCCCTTTTGGGGSSSSNNNNAAAA, ZZZZTTTTGGGGSSSSNNNNAAAA: Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A,B) in generalized real-Schur/Schur canonical form. * SSSSTTTTGGGGSSSSYYYYLLLL, DDDDTTTTGGGGSSSSYYYYLLLL, CCCCTTTTGGGGSSSSYYYYLLLL, ZZZZTTTTGGGGSSSSYYYYLLLL: Solves the generalized Sylvester equation. * SSSSTTTTPPPPCCCCOOOONNNN, DDDDTTTTPPPPCCCCOOOONNNN, CCCCTTTTPPPPCCCCOOOONNNN, ZZZZTTTTPPPPCCCCOOOONNNN: Estimates the reciprocal of the condition number of a triangular matrix in packed storage, in either the 1-norm or the infinity-norm. * SSSSTTTTPPPPRRRRFFFFSSSS, DDDDTTTTPPPPRRRRFFFFSSSS, CCCCTTTTPPPPRRRRFFFFSSSS, ZZZZTTTTPPPPRRRRFFFFSSSS: Provides error bounds for the solution of any of the following triangular systems of linear equations where _A is held in packed storage. A X = B T A X = B H PPPPaaaaggggeeee 22221111 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) A X = B * SSSSTTTTPPPPTTTTRRRRIIII, DDDDTTTTPPPPTTTTRRRRIIII, CCCCTTTTPPPPTTTTRRRRIIII, ZZZZTTTTPPPPTTTTRRRRIIII: Computes the inverse of a triangular matrix in packed storage. * SSSSTTTTPPPPTTTTRRRRSSSS, DDDDTTTTPPPPTTTTRRRRSSSS, CCCCTTTTPPPPTTTTRRRRSSSS, ZZZZTTTTPPPPTTTTRRRRSSSS: Solves any of the following triangular systems of linear equations where _A is held in packed storage. A X = B T A X = B H A X = B * SSSSTTTTRRRRCCCCOOOONNNN, DDDDTTTTRRRRCCCCOOOONNNN, CCCCTTTTRRRRCCCCOOOONNNN, ZZZZTTTTRRRRCCCCOOOONNNN: Estimates the reciprocal of the condition number of a triangular matrix, in either the 1-norm or the infinity-norm. * SSSSTTTTRRRREEEEVVVVCCCC, DDDDTTTTRRRREEEEVVVVCCCC, CCCCTTTTRRRREEEEVVVVCCCC, ZZZZTTTTRRRREEEEVVVVCCCC: Compute eigenvectors of a real upper quasi-triangular matrix or a complex triangular matrix. * SSSSTTTTRRRREEEEXXXXCCCC, DDDDTTTTRRRREEEEXXXXCCCC, CCCCTTTTRRRREEEEXXXXCCCC, ZZZZTTTTRRRREEEEXXXXCCCC: Exchange diagonal blocks in the real Schur factorization of a real or complex matrix. * SSSSTTTTRRRRRRRRFFFFSSSS, DDDDTTTTRRRRRRRRFFFFSSSS, CCCCTTTTRRRRRRRRFFFFSSSS, ZZZZTTTTRRRRRRRRFFFFSSSS: Provides error bounds for the solution of any of the following triangular systems of linear equations: A X = B T A X = B H A X = B * SSSSTTTTRRRRSSSSEEEENNNN, DDDDTTTTRRRRSSSSEEEENNNN, CCCCTTTTRRRRSSSSEEEENNNN, ZZZZTTTTRRRRSSSSEEEENNNN: Compute condition numbers to measure the sensitivity of a cluster of eigenvalues and its corresponding invariant subspace. * SSSSTTTTRRRRSSSSNNNNAAAA, DDDDTTTTRRRRSSSSNNNNAAAA, CCCCTTTTRRRRSSSSNNNNAAAA, ZZZZTTTTRRRRSSSSNNNNAAAA: Compute condition numbers for specified eigenvalues and eigenvectors of a real upper quasi- triangular matrix or complex upper triangular matrix. PPPPaaaaggggeeee 22222222 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) * SSSSTTTTRRRRSSSSYYYYLLLL, DDDDTTTTRRRRSSSSYYYYLLLL, CCCCTTTTRRRRSSSSYYYYLLLL, ZZZZTTTTRRRRSSSSYYYYLLLL: Solve the Sylvester matrix equation. * SSSSTTTTRRRRTTTTRRRRIIII, DDDDTTTTRRRRTTTTRRRRIIII, CCCCTTTTRRRRTTTTRRRRIIII, ZZZZTTTTRRRRTTTTRRRRIIII: Computes the inverse of a triangular matrix. * SSSSTTTTRRRRTTTTRRRRSSSS, DDDDTTTTRRRRTTTTRRRRSSSS, CCCCTTTTRRRRTTTTRRRRSSSS, ZZZZTTTTRRRRTTTTRRRRSSSS: Solves any of the following triangular systems of linear equations: A X = B T A X = B H A X = B * SSSSTTTTZZZZRRRRQQQQFFFF, DDDDTTTTZZZZRRRRQQQQFFFF, CCCCTTTTZZZZRRRRQQQQFFFF, ZZZZTTTTZZZZRRRRQQQQFFFF: Reduces an upper trapezoidal matrix to upper triangular form by an orthogonal/unitary transformation. * SSSSTTTTZZZZRRRRZZZZFFFF, DDDDTTTTZZZZRRRRZZZZFFFF, CCCCTTTTZZZZRRRRZZZZFFFF, ZZZZTTTTZZZZRRRRZZZZFFFF: Reduces an upper trapezoidal matrix to upper triangular form by an orthogonal/unitary transformation. In addition to the driver and computational routines, the following auxiliary routines are also available. For information about using these routines, see the individual man pages. CCCCLLLLAAAACCCCGGGGVVVV ZZZZLLLLAAAACCCCGGGGVVVV CCCCLLLLAAAACCCCRRRRMMMM ZZZZLLLLAAAACCCCRRRRMMMM CCCCLLLLAAAACCCCRRRRTTTT ZZZZLLLLAAAACCCCRRRRTTTT CCCCLLLLAAAAEEEESSSSYYYY ZZZZLLLLAAAAEEEESSSSYYYY CCCCRRRROOOOTTTT ZZZZRRRROOOOTTTT CCCCSSSSRRRROOOOTTTT ZZZZDDDDRRRROOOOTTTT CCCCSSSSPPPPMMMMVVVV ZZZZSSSSPPPPMMMMVVVV CCCCSSSSPPPPRRRR ZZZZSSSSPPPPRRRR CCCCSSSSYYYYMMMMVVVV ZZZZSSSSYYYYMMMMVVVV CCCCSSSSYYYYRRRR ZZZZSSSSYYYYRRRR IIIICCCCMMMMAAAAXXXX1111 IIIIZZZZMMMMAAAAXXXX1111 SSSSCCCCSSSSUUUUMMMM1111 DDDDZZZZSSSSUUUUMMMM1111 SSSSGGGGBBBBTTTTFFFF2222 DDDDGGGGBBBBTTTTFFFF2222 CCCCGGGGBBBBTTTTFFFF2222 ZZZZGGGGBBBBTTTTFFFF2222 SSSSGGGGEEEEBBBBDDDD2222 DDDDGGGGEEEEBBBBDDDD2222 CCCCGGGGEEEEBBBBDDDD2222 ZZZZGGGGEEEEBBBBDDDD2222 SSSSGGGGEEEEHHHHDDDD2222 DDDDGGGGEEEEHHHHDDDD2222 CCCCGGGGEEEEHHHHDDDD2222 ZZZZGGGGEEEEHHHHDDDD2222 SSSSGGGGEEEELLLLQQQQ2222 DDDDGGGGEEEELLLLQQQQ2222 CCCCGGGGEEEELLLLQQQQ2222 ZZZZGGGGEEEELLLLQQQQ2222 SSSSGGGGEEEEQQQQLLLL2222 DDDDGGGGEEEEQQQQLLLL2222 CCCCGGGGEEEEQQQQLLLL2222 ZZZZGGGGEEEEQQQQLLLL2222 SSSSGGGGEEEEQQQQRRRR2222 DDDDGGGGEEEEQQQQRRRR2222 CCCCGGGGEEEEQQQQRRRR2222 ZZZZGGGGEEEEQQQQRRRR2222 SSSSGGGGEEEETTTTFFFF2222 DDDDGGGGEEEETTTTFFFF2222 CCCCGGGGEEEETTTTFFFF2222 ZZZZGGGGEEEETTTTFFFF2222 SSSSLLLLAAAABBBBAAAADDDD DDDDLLLLAAAABBBBAAAADDDD SSSSLLLLAAAABBBBRRRRDDDD DDDDLLLLAAAABBBBRRRRDDDD CCCCLLLLAAAABBBBRRRRDDDD ZZZZLLLLAAAABBBBRRRRDDDD SSSSLLLLAAAACCCCOOOONNNN DDDDLLLLAAAACCCCOOOONNNN CCCCLLLLAAAACCCCOOOONNNN ZZZZLLLLAAAACCCCOOOONNNN SSSSLLLLAAAACCCCPPPPYYYY DDDDLLLLAAAACCCCPPPPYYYY CCCCLLLLAAAACCCCPPPPYYYY ZZZZLLLLAAAACCCCPPPPYYYY SSSSLLLLAAAADDDDIIIIVVVV DDDDLLLLAAAADDDDIIIIVVVV CCCCLLLLAAAADDDDIIIIVVVV ZZZZLLLLAAAADDDDIIIIVVVV SSSSLLLLAAAAEEEE2222 DDDDLLLLAAAAEEEE2222 PPPPaaaaggggeeee 22223333 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) SSSSLLLLAAAAEEEEBBBBZZZZ DDDDLLLLAAAAEEEEBBBBZZZZ SSSSLLLLAAAAEEEEDDDD0000 DDDDLLLLAAAAEEEEDDDD0000 CCCCLLLLAAAAEEEEDDDD0000 ZZZZLLLLAAAAEEEEDDDD0000 SSSSLLLLAAAAEEEEDDDD1111 DDDDLLLLAAAAEEEEDDDD1111 SSSSLLLLAAAAEEEEDDDD2222 DDDDLLLLAAAAEEEEDDDD2222 SSSSLLLLAAAAEEEEDDDD3333 DDDDLLLLAAAAEEEEDDDD3333 SSSSLLLLAAAAEEEEDDDD4444 DDDDLLLLAAAAEEEEDDDD4444 SSSSLLLLAAAAEEEEDDDD5555 DDDDLLLLAAAAEEEEDDDD5555 SSSSLLLLAAAAEEEEDDDD6666 DDDDLLLLAAAAEEEEDDDD6666 SSSSLLLLAAAAEEEEDDDD7777 DDDDLLLLAAAAEEEEDDDD7777 CCCCLLLLAAAAEEEEDDDD7777 ZZZZLLLLAAAAEEEEDDDD7777 SSSSLLLLAAAAEEEEDDDD8888 DDDDLLLLAAAAEEEEDDDD8888 CCCCLLLLAAAAEEEEDDDD8888 ZZZZLLLLAAAAEEEEDDDD8888 SSSSLLLLAAAAEEEEDDDD9999 DDDDLLLLAAAAEEEEDDDD9999 SSSSLLLLAAAAEEEEDDDDAAAA DDDDLLLLAAAAEEEEDDDDAAAA SSSSLLLLAAAAEEEEIIIINNNN DDDDLLLLAAAAEEEEIIIINNNN CCCCLLLLAAAAEEEEIIIINNNN ZZZZLLLLAAAAEEEEIIIINNNN SSSSLLLLAAAAEEEEVVVV2222 DDDDLLLLAAAAEEEEVVVV2222 CCCCLLLLAAAAEEEEVVVV2222 ZZZZLLLLAAAAEEEEVVVV2222 SSSSLLLLAAAAEEEEXXXXCCCC DDDDLLLLAAAAEEEEXXXXCCCC SSSSLLLLAAAAGGGG2222 DDDDLLLLAAAAGGGG2222 SSSSLLLLAAAAGGGGTTTTFFFF DDDDLLLLAAAAGGGGTTTTFFFF SSSSLLLLAAAAGGGGTTTTMMMM DDDDLLLLAAAAGGGGTTTTMMMM CCCCLLLLAAAAGGGGTTTTMMMM ZZZZLLLLAAAAGGGGTTTTMMMM SSSSLLLLAAAAGGGGTTTTSSSS DDDDLLLLAAAAGGGGTTTTSSSS SSSSLLLLAAAAHHHHQQQQRRRR DDDDLLLLAAAAHHHHQQQQRRRR CCCCLLLLAAAAHHHHQQQQRRRR ZZZZLLLLAAAAHHHHQQQQRRRR SSSSLLLLAAAAHHHHRRRRDDDD DDDDLLLLAAAAHHHHRRRRDDDD CCCCLLLLAAAAHHHHRRRRDDDD ZZZZLLLLAAAAHHHHRRRRDDDD SSSSLLLLAAAAIIIICCCC1111 DDDDLLLLAAAAIIIICCCC1111 CCCCLLLLAAAAIIIICCCC1111 ZZZZLLLLAAAAIIIICCCC1111 SSSSLLLLAAAALLLLNNNN2222 DDDDLLLLAAAALLLLNNNN2222 SSSSLLLLAAAAMMMMRRRRGGGG DDDDLLLLAAAAMMMMRRRRGGGG SSSSLLLLAAAANNNNGGGGBBBB DDDDLLLLAAAANNNNGGGGBBBB CCCCLLLLAAAANNNNGGGGBBBB ZZZZLLLLAAAANNNNGGGGBBBB SSSSLLLLAAAANNNNGGGGEEEE DDDDLLLLAAAANNNNGGGGEEEE CCCCLLLLAAAANNNNGGGGEEEE ZZZZLLLLAAAANNNNGGGGEEEE SSSSLLLLAAAANNNNGGGGTTTT DDDDLLLLAAAANNNNGGGGTTTT CCCCLLLLAAAANNNNGGGGTTTT ZZZZLLLLAAAANNNNGGGGTTTT SSSSLLLLAAAANNNNHHHHSSSS DDDDLLLLAAAANNNNHHHHSSSS CCCCLLLLAAAANNNNHHHHSSSS ZZZZLLLLAAAANNNNHHHHSSSS SSSSLLLLAAAANNNNSSSSBBBB DDDDLLLLAAAANNNNSSSSBBBB CCCCLLLLAAAANNNNSSSSBBBB ZZZZLLLLAAAANNNNSSSSBBBB CCCCLLLLAAAANNNNHHHHBBBB ZZZZLLLLAAAANNNNHHHHBBBB SSSSLLLLAAAANNNNSSSSPPPP DDDDLLLLAAAANNNNSSSSPPPP CCCCLLLLAAAANNNNSSSSPPPP ZZZZLLLLAAAANNNNSSSSPPPP CCCCLLLLAAAANNNNHHHHPPPP ZZZZLLLLAAAANNNNHHHHPPPP SSSSLLLLAAAANNNNSSSSTTTT DDDDLLLLAAAANNNNSSSSTTTT CCCCLLLLAAAANNNNSSSSTTTT ZZZZLLLLAAAANNNNSSSSTTTT SSSSLLLLAAAANNNNSSSSYYYY DDDDLLLLAAAANNNNSSSSYYYY CCCCLLLLAAAANNNNSSSSYYYY ZZZZLLLLAAAANNNNSSSSYYYY CCCCLLLLAAAANNNNHHHHEEEE ZZZZLLLLAAAANNNNHHHHEEEE SSSSLLLLAAAANNNNTTTTBBBB DDDDLLLLAAAANNNNTTTTBBBB CCCCLLLLAAAANNNNTTTTBBBB ZZZZLLLLAAAANNNNTTTTBBBB SSSSLLLLAAAANNNNTTTTPPPP DDDDLLLLAAAANNNNTTTTPPPP CCCCLLLLAAAANNNNTTTTPPPP ZZZZLLLLAAAANNNNTTTTPPPP SSSSLLLLAAAANNNNTTTTRRRR DDDDLLLLAAAANNNNTTTTRRRR CCCCLLLLAAAANNNNTTTTRRRR ZZZZLLLLAAAANNNNTTTTRRRR SSSSLLLLAAAANNNNVVVV2222 DDDDLLLLAAAANNNNVVVV2222 SSSSLLLLAAAAPPPPLLLLLLLL DDDDLLLLAAAAPPPPLLLLLLLL CCCCLLLLAAAAPPPPLLLLLLLL ZZZZLLLLAAAAPPPPLLLLLLLL SSSSLLLLAAAAPPPPMMMMTTTT DDDDLLLLAAAAPPPPMMMMTTTT CCCCLLLLAAAAPPPPMMMMTTTT ZZZZLLLLAAAAPPPPMMMMTTTT SSSSLLLLAAAAPPPPYYYY2222 DDDDLLLLAAAAPPPPYYYY2222 SSSSLLLLAAAAPPPPYYYY3333 DDDDLLLLAAAAPPPPYYYY3333 SSSSLLLLAAAAQQQQGGGGBBBB DDDDLLLLAAAAQQQQGGGGBBBB CCCCLLLLAAAAQQQQGGGGBBBB ZZZZLLLLAAAAQQQQGGGGBBBB SSSSLLLLAAAAQQQQGGGGEEEE DDDDLLLLAAAAQQQQGGGGEEEE CCCCLLLLAAAAQQQQGGGGEEEE ZZZZLLLLAAAAQQQQGGGGEEEE SSSSLLLLAAAAQQQQSSSSBBBB DDDDLLLLAAAAQQQQSSSSBBBB CCCCLLLLAAAAQQQQSSSSBBBB ZZZZLLLLAAAAQQQQSSSSBBBB SSSSLLLLAAAAQQQQSSSSPPPP DDDDLLLLAAAAQQQQSSSSPPPP CCCCLLLLAAAAQQQQSSSSPPPP ZZZZLLLLAAAAQQQQSSSSPPPP SSSSLLLLAAAAQQQQSSSSYYYY DDDDLLLLAAAAQQQQSSSSYYYY CCCCLLLLAAAAQQQQSSSSYYYY ZZZZLLLLAAAAQQQQSSSSYYYY SSSSLLLLAAAAQQQQTTTTRRRR DDDDLLLLAAAAQQQQTTTTRRRR SSSSLLLLAAAARRRR2222VVVV DDDDLLLLAAAARRRR2222VVVV CCCCLLLLAAAARRRR2222VVVV ZZZZLLLLAAAARRRR2222VVVV PPPPaaaaggggeeee 22224444 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) SSSSLLLLAAAARRRRFFFFXXXX DDDDLLLLAAAARRRRFFFFXXXX CCCCLLLLAAAARRRRFFFFXXXX ZZZZLLLLAAAARRRRFFFFXXXX SSSSLLLLAAAARRRRUUUUVVVV DDDDLLLLAAAARRRRUUUUVVVV SSSSLLLLAAAASSSS2222 DDDDLLLLAAAASSSS2222 SSSSLLLLAAAASSSSCCCCLLLL DDDDLLLLAAAASSSSCCCCLLLL CCCCLLLLAAAASSSSCCCCLLLL ZZZZLLLLAAAASSSSCCCCLLLL SSSSLLLLAAAASSSSEEEETTTT DDDDLLLLAAAASSSSEEEETTTT CCCCLLLLAAAASSSSEEEETTTT ZZZZLLLLAAAASSSSEEEETTTT SSSSLLLLAAAASSSSQQQQ1111 DDDDLLLLAAAASSSSQQQQ1111 SSSSLLLLAAAASSSSQQQQ2222 DDDDLLLLAAAASSSSQQQQ2222 SSSSLLLLAAAASSSSQQQQ3333 DDDDLLLLAAAASSSSQQQQ3333 SSSSLLLLAAAASSSSQQQQ4444 DDDDLLLLAAAASSSSQQQQ4444 SSSSLLLLAAAASSSSRRRRTTTT DDDDLLLLAAAASSSSRRRRTTTT SSSSLLLLAAAASSSSSSSSQQQQ DDDDLLLLAAAASSSSSSSSQQQQ CCCCLLLLAAAASSSSSSSSQQQQ ZZZZLLLLAAAASSSSSSSSQQQQ SSSSLLLLAAAASSSSVVVV2222 DDDDLLLLAAAASSSSVVVV2222 SSSSLLLLAAAASSSSWWWWPPPP DDDDLLLLAAAASSSSWWWWPPPP CCCCLLLLAAAASSSSWWWWPPPP ZZZZLLLLAAAASSSSWWWWPPPP SSSSLLLLAAAASSSSYYYY2222 DDDDLLLLAAAASSSSYYYY2222 SSSSLLLLAAAASSSSYYYYFFFF DDDDLLLLAAAASSSSYYYYFFFF CCCCLLLLAAAASSSSYYYYFFFF ZZZZLLLLAAAASSSSYYYYFFFF CCCCLLLLAAAAHHHHEEEEFFFF ZZZZLLLLAAAAHHHHEEEEFFFF SSSSLLLLAAAATTTTBBBBSSSS DDDDLLLLAAAATTTTBBBBSSSS CCCCLLLLAAAATTTTBBBBSSSS ZZZZLLLLAAAATTTTBBBBSSSS SSSSLLLLAAAATTTTPPPPSSSS DDDDLLLLAAAATTTTPPPPSSSS CCCCLLLLAAAATTTTPPPPSSSS ZZZZLLLLAAAATTTTPPPPSSSS SSSSLLLLAAAATTTTRRRRDDDD DDDDLLLLAAAATTTTRRRRDDDD CCCCLLLLAAAATTTTRRRRDDDD ZZZZLLLLAAAATTTTRRRRDDDD SSSSLLLLAAAATTTTRRRRSSSS DDDDLLLLAAAATTTTRRRRSSSS CCCCLLLLAAAATTTTRRRRSSSS ZZZZLLLLAAAATTTTRRRRSSSS SSSSLLLLAAAATTTTZZZZMMMM DDDDLLLLAAAATTTTZZZZMMMM CCCCLLLLAAAATTTTZZZZMMMM ZZZZLLLLAAAATTTTZZZZMMMM SSSSLLLLAAAAUUUUUUUU2222 DDDDLLLLAAAAUUUUUUUU2222 CCCCLLLLAAAAUUUUUUUU2222 ZZZZLLLLAAAAUUUUUUUU2222 SSSSLLLLAAAAUUUUUUUUMMMM DDDDLLLLAAAAUUUUUUUUMMMM CCCCLLLLAAAAUUUUUUUUMMMM ZZZZLLLLAAAAUUUUUUUUMMMM SSSSOOOORRRRGGGG2222LLLL DDDDOOOORRRRGGGG2222LLLL CCCCUUUUNNNNGGGG2222LLLL ZZZZUUUUNNNNGGGG2222LLLL SSSSOOOORRRRGGGG2222RRRR DDDDOOOORRRRGGGG2222RRRR CCCCUUUUNNNNGGGG2222RRRR ZZZZUUUUNNNNGGGG2222RRRR SSSSOOOORRRRGGGGLLLL2222 DDDDOOOORRRRGGGGLLLL2222 CCCCUUUUNNNNGGGGLLLL2222 ZZZZUUUUNNNNGGGGLLLL2222 SSSSOOOORRRRGGGGRRRR2222 DDDDOOOORRRRGGGGRRRR2222 CCCCUUUUNNNNGGGGRRRR2222 ZZZZUUUUNNNNGGGGRRRR2222 SSSSOOOORRRRMMMM2222LLLL DDDDOOOORRRRMMMM2222LLLL CCCCUUUUNNNNMMMM2222LLLL ZZZZUUUUNNNNMMMM2222LLLL SSSSOOOORRRRMMMM2222RRRR DDDDOOOORRRRMMMM2222RRRR CCCCUUUUNNNNMMMM2222RRRR ZZZZUUUUNNNNMMMM2222RRRR SSSSOOOORRRRMMMMLLLL2222 DDDDOOOORRRRMMMMLLLL2222 CCCCUUUUNNNNMMMMLLLL2222 ZZZZUUUUNNNNMMMMLLLL2222 SSSSOOOORRRRMMMMRRRR2222 DDDDOOOORRRRMMMMRRRR2222 CCCCUUUUNNNNMMMMRRRR2222 ZZZZUUUUNNNNMMMMRRRR2222 SSSSPPPPBBBBTTTTFFFF2222 DDDDPPPPBBBBTTTTFFFF2222 CCCCPPPPBBBBTTTTFFFF2222 ZZZZPPPPBBBBTTTTFFFF2222 SSSSPPPPOOOOTTTTFFFF2222 DDDDPPPPOOOOTTTTFFFF2222 CCCCPPPPOOOOTTTTFFFF2222 ZZZZPPPPOOOOTTTTFFFF2222 SSSSRRRRSSSSCCCCLLLL DDDDRRRRSSSSCCCCLLLL CCCCSSSSRRRRSSSSCCCCLLLL ZZZZDDDDRRRRSSSSCCCCLLLL SSSSSSSSYYYYGGGGSSSS2222 DDDDSSSSYYYYGGGGSSSS2222 CCCCHHHHEEEEGGGGSSSS2222 ZZZZHHHHEEEEGGGGSSSS2222 SSSSSSSSYYYYTTTTDDDD2222 DDDDSSSSYYYYTTTTDDDD2222 CCCCHHHHEEEETTTTDDDD2222 ZZZZHHHHEEEETTTTDDDD2222 SSSSSSSSYYYYTTTTFFFF2222 DDDDSSSSYYYYTTTTFFFF2222 CCCCSSSSYYYYTTTTFFFF2222 ZZZZSSSSYYYYTTTTFFFF2222 CCCCHHHHEEEETTTTFFFF2222 ZZZZHHHHEEEETTTTFFFF2222 SSSSTTTTRRRRTTTTIIII2222 DDDDTTTTRRRRTTTTIIII2222 CCCCTTTTRRRRTTTTIIII2222 ZZZZTTTTRRRRTTTTIIII2222 LLLLSSSSNNNNAAAAMMMMEEEE LLLLSSSSAAAAMMMMEEEENNNN XXXXEEEERRRRBBBBLLLLAAAA NNNNOOOOTTTTEEEESSSS SCSL does not currently support reshaped arrays. SSSSEEEEEEEE AAAALLLLSSSSOOOO _L_A_P_A_C_K _U_s_e_r'_s _G_u_i_d_e IIIINNNNTTTTRRRROOOO____BBBBLLLLAAAASSSS1111(3S), IIIINNNNTTTTRRRROOOO____BBBBLLLLAAAASSSS2222(3S), IIIINNNNTTTTRRRROOOO____BBBBLLLLAAAASSSS3333(3S), IIIINNNNTTTTRRRROOOO____SSSSCCCCSSSSLLLL(3S), IIIINNNNTTTTRRRROOOO____SSSSOOOOLLLLVVVVEEEERRRRSSSS(3S) PPPPaaaaggggeeee 22225555 IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) IIIINNNNTTTTRRRROOOO____LLLLAAAAPPPPAAAACCCCKKKK((((3333SSSS)))) PPPPaaaaggggeeee 22226666