Section 3: library functions
dlas2.f – SynopsisFunctions/Subroutinessubroutine dlas2 (F, G, H, SSMIN, SSMAX) DLAS2 computes singular values of a 2-by-2 triangular matrix. Function/Subroutine Documentationsubroutine dlas2 (double precisionF, double precisionG, double precisionH, double precisionSSMIN, double precisionSSMAX)DLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: DLAS2 computes the singular values of the 2-by-2 matrix [ F G ] [ 0…
dlarzt.f – SynopsisFunctions/Subroutinessubroutine dlarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) DLARZT forms the triangular factor T of a block reflector H = I – vtvH. Function/Subroutine Documentationsubroutine dlarzt (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt, * )T, integerLDT)DLARZT forms…
dlarzb.f – SynopsisFunctions/Subroutinessubroutine dlarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) DLARZB applies a block reflector or its transpose to a general matrix. Function/Subroutine Documentationsubroutine dlarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldt, *…
dlarz.f – SynopsisFunctions/Subroutinessubroutine dlarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentationsubroutine dlarz (characterSIDE, integerM, integerN, integerL, double precision, dimension( * )V, integerINCV, double precisionTAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK)DLARZ applies…
dlaruv.f – SynopsisFunctions/Subroutinessubroutine dlaruv (ISEED, N, X) DLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentationsubroutine dlaruv (integer, dimension( 4 )ISEED, integerN, double precision, dimension( n )X)DLARUV returns a vector of n random real numbers from a uniform distribution. Purpose: DLARUV returns a vector of n random real numbers…
dlartv.f – SynopsisFunctions/Subroutinessubroutine dlartv (N, X, INCX, Y, INCY, C, S, INCC) DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. Function/Subroutine Documentationsubroutine dlartv (integerN, double precision, dimension( * )X, integerINCX, double precision, dimension( * )Y, integerINCY, double precision, dimension( * )C, double…
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…