Section 3: library functions
dlartgs.f – SynopsisFunctions/Subroutinessubroutine dlartgs (X, Y, SIGMA, CS, SN) DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. Function/Subroutine Documentationsubroutine dlartgs (double precisionX, double precisionY, double precisionSIGMA, double precisionCS, double precisionSN)DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for…
dlartgp.f – SynopsisFunctions/Subroutinessubroutine dlartgp (F, G, CS, SN, R) DLARTGP generates a plane rotation so that the diagonal is nonnegative. Function/Subroutine Documentationsubroutine 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 that [ CS SN ]…
dlartg.f – SynopsisFunctions/Subroutinessubroutine dlartg (F, G, CS, SN, R) DLARTG generates a plane rotation with real cosine and real sine. Function/Subroutine Documentationsubroutine 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 that [ CS SN ]…
dlarscl2.f – SynopsisFunctions/Subroutinessubroutine dlarscl2 (M, N, D, X, LDX) DLARSCL2 performs reciprocal diagonal scaling on a vector. Function/Subroutine Documentationsubroutine 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 vector: x <– inv(D) *…
dlarrv.f – SynopsisFunctions/Subroutinessubroutine 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. Function/Subroutine Documentationsubroutine dlarrv…
dlarrr.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrr (integerN, double precision, dimension( * )D, double precision, dimension( * )E, integerINFO)DLARRR performs tests to decide whether the symmetric tridiagonal matrix T…
dlarrk.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN, double precisionRELTOL, double precisionW, double precisionWERR,…
dlarrj.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrj (integerN, double precision, dimension( * )D, double precision, dimension( * )E2, integerIFIRST, integerILAST, double precisionRTOL, integerOFFSET, double precision, dimension( *…
dlarrf.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrf (integerN, double precision, dimension( * )D, double precision, dimension( * )L, double…
dlarre.f – SynopsisFunctions/Subroutinessubroutine 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. Function/Subroutine Documentationsubroutine dlarre…
dlarrd.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrd (characterRANGE, characterORDER, integerN, double precisionVL, double precisionVU, integerIL, integerIU, double precision,…
dlarrc.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrc (characterJOBT, integerN, double precisionVL, double precisionVU, double precision, dimension( * )D, double precision, dimension( * )E, double precisionPIVMIN, integerEIGCNT, integerLCNT, integerRCNT, integerINFO)DLARRC computes the number of…
dlarrb.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarrb (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, integerIFIRST, integerILAST, double precisionRTOL1, double precisionRTOL2, integerOFFSET, double precision, dimension(…
dlarra.f – SynopsisFunctions/Subroutinessubroutine dlarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) DLARRA computes the splitting points with the specified threshold. Function/Subroutine Documentationsubroutine dlarra (integerN, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )E2, double precisionSPLTOL, double precisionTNRM, integerNSPLIT, integer, dimension( * )ISPLIT, integerINFO)DLARRA computes the splitting points…
dlarnv.f – SynopsisFunctions/Subroutinessubroutine dlarnv (IDIST, ISEED, N, X) DLARNV returns a vector of random numbers from a uniform or normal distribution. Function/Subroutine Documentationsubroutine 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 a vector of n random…
dlargv.f – SynopsisFunctions/Subroutinessubroutine dlargv (N, X, INCX, Y, INCY, C, INCC) DLARGV generates a vector of plane rotations with real cosines and real sines. Function/Subroutine Documentationsubroutine dlargv (integerN, double precision, dimension( * )X, integerINCX, double precision, dimension( * )Y, integerINCY, double precision, dimension( * )C, integerINCC)DLARGV generates a vector of plane rotations with real cosines…
dlarfx.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarfx (characterSIDE, integerM, integerN, double precision, dimension( * )V, double precisionTAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension(…
dlarft.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarft (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt, * )T, integerLDT)DLARFT forms…
dlarfgp.f – SynopsisFunctions/Subroutinessubroutine dlarfgp (N, ALPHA, X, INCX, TAU) DLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Function/Subroutine Documentationsubroutine 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 of order n, such that…
dlarfg.f – SynopsisFunctions/Subroutinessubroutine dlarfg (N, ALPHA, X, INCX, TAU) DLARFG generates an elementary reflector (Householder matrix). Function/Subroutine Documentationsubroutine 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 * ( alpha ) =…