Section 3: library functions
NAME dlartgp.f – SYNOPSIS Functions/Subroutines subroutine dlartgp (F, G, CS, SN, R) DLARTGP generates a plane rotation so that the diagonal is nonnegative. Function/Subroutine Documentation subroutine dlartgp (double precisionF, double precisionG, double precisionCS, double precisionSN, double precisionR) DLARTGP generates a plane rotation so that the diagonal is nonnegative. Purpose: DLARTGP generates a plane rotation so…
NAME dlartg.f – SYNOPSIS Functions/Subroutines subroutine dlartg (F, G, CS, SN, R) DLARTG generates a plane rotation with real cosine and real sine. Function/Subroutine Documentation subroutine dlartg (double precisionF, double precisionG, double precisionCS, double precisionSN, double precisionR) DLARTG generates a plane rotation with real cosine and real sine. Purpose: DLARTG generate a plane rotation so…
NAME dlarscl2.f – SYNOPSIS Functions/Subroutines subroutine dlarscl2 (M, N, D, X, LDX) DLARSCL2 performs reciprocal diagonal scaling on a vector. Function/Subroutine Documentation subroutine dlarscl2 (integerM, integerN, double precision, dimension( * )D, double precision, dimension( ldx, * )X, integerLDX) DLARSCL2 performs reciprocal diagonal scaling on a vector. Purpose: DLARSCL2 performs a reciprocal diagonal scaling on an…
NAME dlarrv.f – SYNOPSIS Functions/Subroutines subroutine dlarrv (N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W, WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO) DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT….
NAME dlarrr.f – SYNOPSIS Functions/Subroutines subroutine dlarrr (N, D, E, INFO) DLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues. Function/Subroutine Documentation subroutine dlarrr (integerN, double precision, dimension( * )D, double precision, dimension( * )E, integerINFO) DLARRR performs tests to decide whether…
NAME dlarrk.f – SYNOPSIS Functions/Subroutines subroutine dlarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO) DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. Function/Subroutine Documentation subroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN, double precisionRELTOL,…
NAME dlarrj.f – SYNOPSIS Functions/Subroutines subroutine dlarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO) DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T. Function/Subroutine Documentation subroutine dlarrj (integerN, double precision, dimension( * )D, double precision, dimension( * )E2, integerIFIRST, integerILAST, double precisionRTOL, integerOFFSET,…
NAME dlarrf.f – SYNOPSIS Functions/Subroutines subroutine dlarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO) DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. Function/Subroutine Documentation subroutine dlarrf (integerN, double precision, dimension( * )D, double precision,…
NAME dlarre.f – SYNOPSIS Functions/Subroutines subroutine dlarre (RANGE, N, VL, VU, IL, IU, D, E, E2, RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, WORK, IWORK, INFO) DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues….
NAME dlarrd.f – SYNOPSIS Functions/Subroutines subroutine dlarrd (RANGE, ORDER, N, VL, VU, IL, IU, GERS, RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, M, W, WERR, WL, WU, IBLOCK, INDEXW, WORK, IWORK, INFO) DLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy. Function/Subroutine Documentation subroutine dlarrd (characterRANGE, characterORDER, integerN, double precisionVL, double precisionVU,…
NAME dlarrc.f – SYNOPSIS Functions/Subroutines subroutine dlarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO) DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. Function/Subroutine Documentation subroutine dlarrc (characterJOBT, integerN, double precisionVL, double precisionVU, double precision, dimension( * )D, double precision, dimension( * )E, double precisionPIVMIN, integerEIGCNT, integerLCNT, integerRCNT, integerINFO)…
NAME dlarrb.f – SYNOPSIS Functions/Subroutines subroutine dlarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO) DLARRB provides limited bisection to locate eigenvalues for more accuracy. Function/Subroutine Documentation subroutine dlarrb (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, integerIFIRST, integerILAST, double precisionRTOL1, double precisionRTOL2,…
NAME dlarra.f – SYNOPSIS Functions/Subroutines subroutine dlarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) DLARRA computes the splitting points with the specified threshold. Function/Subroutine Documentation subroutine dlarra (integerN, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )E2, double precisionSPLTOL, double precisionTNRM, integerNSPLIT, integer, dimension( * )ISPLIT, integerINFO)…
NAME dlarnv.f – SYNOPSIS Functions/Subroutines subroutine dlarnv (IDIST, ISEED, N, X) DLARNV returns a vector of random numbers from a uniform or normal distribution. Function/Subroutine Documentation subroutine dlarnv (integerIDIST, integer, dimension( 4 )ISEED, integerN, double precision, dimension( * )X) DLARNV returns a vector of random numbers from a uniform or normal distribution. Purpose: DLARNV returns…
NAME dlargv.f – SYNOPSIS Functions/Subroutines subroutine dlargv (N, X, INCX, Y, INCY, C, INCC) DLARGV generates a vector of plane rotations with real cosines and real sines. Function/Subroutine Documentation subroutine dlargv (integerN, double precision, dimension( * )X, integerINCX, double precision, dimension( * )Y, integerINCY, double precision, dimension( * )C, integerINCC) DLARGV generates a vector of…
NAME dlarfx.f – SYNOPSIS Functions/Subroutines subroutine dlarfx (SIDE, M, N, V, TAU, C, LDC, WORK) DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. Function/Subroutine Documentation subroutine dlarfx (characterSIDE, integerM, integerN, double precision, dimension( * )V, double precisionTAU, double precision, dimension( ldc, * )C,…
NAME dlarft.f – SYNOPSIS Functions/Subroutines subroutine dlarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) DLARFT forms the triangular factor T of a block reflector H = I – vtvH Function/Subroutine Documentation subroutine dlarft (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt,…
NAME dlarfgp.f – SYNOPSIS Functions/Subroutines subroutine dlarfgp (N, ALPHA, X, INCX, TAU) DLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Function/Subroutine Documentation subroutine dlarfgp (integerN, double precisionALPHA, double precision, dimension( * )X, integerINCX, double precisionTAU) DLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Purpose: DLARFGP generates a real elementary reflector H…
NAME dlarfg.f – SYNOPSIS Functions/Subroutines subroutine dlarfg (N, ALPHA, X, INCX, TAU) DLARFG generates an elementary reflector (Householder matrix). Function/Subroutine Documentation subroutine dlarfg (integerN, double precisionALPHA, double precision, dimension( * )X, integerINCX, double precisionTAU) DLARFG generates an elementary reflector (Householder matrix). Purpose: DLARFG generates a real elementary reflector H of order n, such that H…
NAME dlarfb.f – SYNOPSIS Functions/Subroutines subroutine dlarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) DLARFB applies a block reflector or its transpose to a general rectangular matrix. Function/Subroutine Documentation subroutine dlarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision,…