Section 3: library functions
NAME slarzb.f – SYNOPSIS Functions/Subroutines subroutine slarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARZB applies a block reflector or its transpose to a general matrix. Function/Subroutine Documentation subroutine slarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension(…
NAME slarz.f – SYNOPSIS Functions/Subroutines subroutine slarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentation subroutine slarz (characterSIDE, integerM, integerN, integerL, real, dimension( * )V, integerINCV, realTAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK) SLARZ…
NAME slaruv.f – SYNOPSIS Functions/Subroutines subroutine slaruv (ISEED, N, X) SLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentation subroutine slaruv (integer, dimension( 4 )ISEED, integerN, real, dimension( n )X) SLARUV returns a vector of n random real numbers from a uniform distribution. Purpose: SLARUV returns a vector of…
NAME slartv.f – SYNOPSIS Functions/Subroutines subroutine slartv (N, X, INCX, Y, INCY, C, S, INCC) SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. Function/Subroutine Documentation subroutine slartv (integerN, real, dimension( * )X, integerINCX, real, dimension( * )Y, integerINCY, real, dimension( * )C,…
NAME slartgs.f – SYNOPSIS Functions/Subroutines subroutine slartgs (X, Y, SIGMA, CS, SN) SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. Function/Subroutine Documentation subroutine slartgs (realX, realY, realSIGMA, realCS, realSN) SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for…
NAME slartgp.f – SYNOPSIS Functions/Subroutines subroutine slartgp (F, G, CS, SN, R) SLARTGP generates a plane rotation so that the diagonal is nonnegative. Function/Subroutine Documentation subroutine slartgp (realF, realG, realCS, realSN, realR) SLARTGP generates a plane rotation so that the diagonal is nonnegative. Purpose: SLARTGP generates a plane rotation so that [CS SN] .[F] =…
NAME slartg.f – SYNOPSIS Functions/Subroutines subroutine slartg (F, G, CS, SN, R) SLARTG generates a plane rotation with real cosine and real sine. Function/Subroutine Documentation subroutine slartg (realF, realG, realCS, realSN, realR) SLARTG generates a plane rotation with real cosine and real sine. Purpose: SLARTG generate a plane rotation so that [CS SN] .[F] =…
NAME slarscl2.f – SYNOPSIS Functions/Subroutines subroutine slarscl2 (M, N, D, X, LDX) SLARSCL2 performs reciprocal diagonal scaling on a vector. Function/Subroutine Documentation subroutine slarscl2 (integerM, integerN, real, dimension( * )D, real, dimension( ldx, * )X, integerLDX) SLARSCL2 performs reciprocal diagonal scaling on a vector. Purpose: SLARSCL2 performs a reciprocal diagonal scaling on an vector: x…
slarrv.f – Synopsis Functions/Subroutines subroutine slarrv (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) SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. Function/Subroutine…
NAME slarrr.f – SYNOPSIS Functions/Subroutines subroutine slarrr (N, D, E, INFO) SLARRR 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 slarrr (integerN, real, dimension( * )D, real, dimension( * )E, integerINFO) SLARRR performs tests to decide whether the symmetric…
NAME slarrk.f – SYNOPSIS Functions/Subroutines subroutine slarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO) SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. Function/Subroutine Documentation subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real, dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR, integerINFO) SLARRK computes one…
NAME slarrj.f – SYNOPSIS Functions/Subroutines subroutine slarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO) SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T. Function/Subroutine Documentation subroutine slarrj (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( *…
NAME slarrf.f – SYNOPSIS Functions/Subroutines subroutine slarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO) SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. Function/Subroutine Documentation subroutine slarrf (integerN, real, dimension( * )D, real, dimension( *…
NAME slarre.f – SYNOPSIS Functions/Subroutines subroutine slarre (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) SLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues….
NAME slarrd.f – SYNOPSIS Functions/Subroutines subroutine slarrd (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) SLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy. Function/Subroutine Documentation subroutine slarrd (characterRANGE, characterORDER, integerN, realVL, realVU, integerIL, integerIU,…
NAME slarrc.f – SYNOPSIS Functions/Subroutines subroutine slarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO) SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. Function/Subroutine Documentation subroutine slarrc (characterJOBT, integerN, realVL, realVU, real, dimension( * )D, real, dimension( * )E, realPIVMIN, integerEIGCNT, integerLCNT, integerRCNT, integerINFO) SLARRC computes the number of…
NAME slarrb.f – SYNOPSIS Functions/Subroutines subroutine slarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO) SLARRB provides limited bisection to locate eigenvalues for more accuracy. Function/Subroutine Documentation subroutine slarrb (integerN, real, dimension( * )D, real, dimension( * )LLD, integerIFIRST, integerILAST, realRTOL1, realRTOL2, integerOFFSET, real, dimension( *…
NAME slarra.f – SYNOPSIS Functions/Subroutines subroutine slarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) SLARRA computes the splitting points with the specified threshold. Function/Subroutine Documentation subroutine slarra (integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( * )E2, realSPLTOL, realTNRM, integerNSPLIT, integer, dimension( * )ISPLIT, integerINFO) SLARRA computes the splitting points…
NAME slarnv.f – SYNOPSIS Functions/Subroutines subroutine slarnv (IDIST, ISEED, N, X) SLARNV returns a vector of random numbers from a uniform or normal distribution. Function/Subroutine Documentation subroutine slarnv (integerIDIST, integer, dimension( 4 )ISEED, integerN, real, dimension( * )X) SLARNV returns a vector of random numbers from a uniform or normal distribution. Purpose: SLARNV returns a…
NAME slargv.f – SYNOPSIS Functions/Subroutines subroutine slargv (N, X, INCX, Y, INCY, C, INCC) SLARGV generates a vector of plane rotations with real cosines and real sines. Function/Subroutine Documentation subroutine slargv (integerN, real, dimension( * )X, integerINCX, real, dimension( * )Y, integerINCY, real, dimension( * )C, integerINCC) SLARGV generates a vector of plane rotations with…