Section 3: library functions
dlag2.f – Synopsis Functions/Subroutines subroutine dlag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI) DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. Function/Subroutine Documentation subroutine dlag2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precisionSAFMIN, double precisionSCALE1,…
dlaexc.f – Synopsis Functions/Subroutines subroutine dlaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO) DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. Function/Subroutine Documentation subroutine dlaexc (logicalWANTQ, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( ldq, *…
dlaev2.f – Synopsis Functions/Subroutines subroutine dlaev2 (A, B, C, RT1, RT2, CS1, SN1) DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine dlaev2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2, double precisionCS1, double precisionSN1) DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: DLAEV2…
dlaein.f – Synopsis Functions/Subroutines subroutine dlaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO) DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentation subroutine dlaein (logicalRIGHTV, logicalNOINIT, integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionWR, double…
dlaeda.f – Synopsis Functions/Subroutines subroutine dlaeda (N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO) DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. Function/Subroutine Documentation subroutine dlaeda (integerN, integerTLVLS, integerCURLVL, integerCURPBM, integer, dimension( * )PRMPTR,…
dlaed9.f – Synopsis Functions/Subroutines subroutine dlaed9 (K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO) DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. Function/Subroutine Documentation subroutine dlaed9 (integerK, integerKSTART, integerKSTOP, integerN, double precision, dimension( * )D, double…
dlaed8.f – Synopsis Functions/Subroutines subroutine dlaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO) DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. Function/Subroutine Documentation subroutine dlaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, double precision,…
dlaed7.f – Synopsis Functions/Subroutines subroutine dlaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO) DLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. Function/Subroutine…
dlaed6.f – Synopsis Functions/Subroutines subroutine dlaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO) DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. Function/Subroutine Documentation subroutine dlaed6 (integerKNITER, logicalORGATI, double precisionRHO, double precision, dimension( 3 )D, double precision, dimension( 3 )Z, double precisionFINIT, double precisionTAU, integerINFO) DLAED6 used by sstedc….
dlaed5.f – Synopsis Functions/Subroutines subroutine dlaed5 (I, D, Z, DELTA, RHO, DLAM) DLAED5 used by sstedc. Solves the 2-by-2 secular equation. Function/Subroutine Documentation subroutine dlaed5 (integerI, double precision, dimension( 2 )D, double precision, dimension( 2 )Z, double precision, dimension( 2 )DELTA, double precisionRHO, double precisionDLAM) DLAED5 used by sstedc. Solves the 2-by-2 secular equation. Purpose:…
dlaed4.f – Synopsis Functions/Subroutines subroutine dlaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) DLAED4 used by sstedc. Finds a single root of the secular equation. Function/Subroutine Documentation subroutine dlaed4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension( * )DELTA, double precisionRHO, double precisionDLAM, integerINFO) DLAED4 used by…
dlaed3.f – Synopsis Functions/Subroutines subroutine dlaed3 (K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO) DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. Function/Subroutine Documentation subroutine dlaed3 (integerK, integerN, integerN1, double precision, dimension( * )D, double…
dlaed2.f – Synopsis Functions/Subroutines subroutine dlaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO) DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. Function/Subroutine Documentation subroutine dlaed2 (integerK, integerN, integerN1, double precision, dimension( * )D, double precision, dimension(…
dlaed1.f – Synopsis Functions/Subroutines subroutine dlaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) DLAED1 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. Function/Subroutine Documentation subroutine dlaed1 (integerN, double precision, dimension( * )D, double precision, dimension(…
dlaed0.f – Synopsis Functions/Subroutines subroutine dlaed0 (ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Function/Subroutine Documentation subroutine dlaed0 (integerICOMPQ, integerQSIZ, integerN, double precision, dimension( * )D, double precision, dimension(…
dlaebz.f – Synopsis Functions/Subroutines subroutine dlaebz (IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, NAB, WORK, IWORK, INFO) DLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the…
dlae2.f – Synopsis Functions/Subroutines subroutine dlae2 (A, B, C, RT1, RT2) DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. Function/Subroutine Documentation subroutine dlae2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2) DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. Purpose: DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix [ A…
NAME dladiv.f – SYNOPSIS Functions/Subroutines subroutine dladiv (A, B, C, D, P, Q) DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. subroutine dladiv1 (A, B, C, D, P, Q) DOUBLE PRECISION function dladiv2 (A, B, C, D, R, T) Function/Subroutine Documentation subroutine dladiv (double precisionA, double precisionB, double precisionC, double precisionD, double precisionP,…
NAME dladiv.f – SYNOPSIS Functions/Subroutines subroutine dladiv (A, B, C, D, P, Q) DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. subroutine dladiv1 (A, B, C, D, P, Q) DOUBLE PRECISION function dladiv2 (A, B, C, D, R, T) Function/Subroutine Documentation subroutine dladiv (double precisionA, double precisionB, double precisionC, double precisionD, double precisionP,…
dladiv.f – Synopsis Functions/Subroutines subroutine dladiv (A, B, C, D, P, Q) DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Function/Subroutine Documentation subroutine dladiv (double precisionA, double precisionB, double precisionC, double precisionD, double precisionP, double precisionQ) DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Purpose: DLADIV performs complex division in real…