Section 3: library functions
NAME slags2.f – SYNOPSIS Functions/Subroutines subroutine slags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel. Function/Subroutine Documentation subroutine slags2 (logicalUPPER, realA1,…
NAME slag2d.f – SYNOPSIS Functions/Subroutines subroutine slag2d (M, N, SA, LDSA, A, LDA, INFO) SLAG2D converts a single precision matrix to a double precision matrix. Function/Subroutine Documentation subroutine slag2d (integerM, integerN, real, dimension( ldsa, * )SA, integerLDSA, double precision, dimension( lda, * )A, integerLDA, integerINFO) SLAG2D converts a single precision matrix to a double precision…
NAME slag2.f – SYNOPSIS Functions/Subroutines subroutine slag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI) SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. Function/Subroutine Documentation subroutine slag2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realSAFMIN, realSCALE1, realSCALE2, realWR1, realWR2,…
NAME slaexc.f – SYNOPSIS Functions/Subroutines subroutine slaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO) SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. Function/Subroutine Documentation subroutine slaexc (logicalWANTQ, integerN, real, dimension( ldt, * )T, integerLDT, real, dimension( ldq, * )Q,…
NAME slaev2.f – SYNOPSIS Functions/Subroutines subroutine slaev2 (A, B, C, RT1, RT2, CS1, SN1) SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1) SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: SLAEV2 computes the eigendecomposition of a 2-by-2…
NAME slaein.f – SYNOPSIS Functions/Subroutines subroutine slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO) SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentation subroutine slaein (logicalRIGHTV, logicalNOINIT, integerN, real, dimension( ldh, * )H, integerLDH, realWR, realWI, real,…
NAME slaeda.f – SYNOPSIS Functions/Subroutines subroutine slaeda (N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO) SLAEDA 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 slaeda (integerN, integerTLVLS, integerCURLVL, integerCURPBM, integer, dimension( *…
NAME slaed9.f – SYNOPSIS Functions/Subroutines subroutine slaed9 (K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO) SLAED9 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 slaed9 (integerK, integerKSTART, integerKSTOP, integerN, real, dimension( * )D, real,…
NAME slaed8.f – SYNOPSIS Functions/Subroutines subroutine slaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO) SLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. Function/Subroutine Documentation subroutine slaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, real,…
NAME slaed7.f – SYNOPSIS Functions/Subroutines subroutine slaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO) SLAED7 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….
NAME slaed6.f – SYNOPSIS Functions/Subroutines subroutine slaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO) SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. Function/Subroutine Documentation subroutine slaed6 (integerKNITER, logicalORGATI, realRHO, real, dimension( 3 )D, real, dimension( 3 )Z, realFINIT, realTAU, integerINFO) SLAED6 used by sstedc. Computes one Newton step…
NAME slaed5.f – SYNOPSIS Functions/Subroutines subroutine slaed5 (I, D, Z, DELTA, RHO, DLAM) SLAED5 used by sstedc. Solves the 2-by-2 secular equation. Function/Subroutine Documentation subroutine slaed5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDLAM) SLAED5 used by sstedc. Solves the 2-by-2 secular equation. Purpose: This subroutine computes the…
NAME slaed4.f – SYNOPSIS Functions/Subroutines subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) SLAED4 used by sstedc. Finds a single root of the secular equation. Function/Subroutine Documentation subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO) SLAED4 used by sstedc. Finds a single…
NAME slaed3.f – SYNOPSIS Functions/Subroutines subroutine slaed3 (K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO) SLAED3 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 slaed3 (integerK, integerN, integerN1, real, dimension( * )D, real,…
NAME slaed2.f – SYNOPSIS Functions/Subroutines subroutine slaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO) SLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. Function/Subroutine Documentation subroutine slaed2 (integerK, integerN, integerN1, real, dimension( * )D, real, dimension( ldq,…
NAME slaed1.f – SYNOPSIS Functions/Subroutines subroutine slaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) SLAED1 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 slaed1 (integerN, real, dimension( * )D, real, dimension( ldq,…
NAME slaed0.f – SYNOPSIS Functions/Subroutines subroutine slaed0 (ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) SLAED0 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 slaed0 (integerICOMPQ, integerQSIZ, integerN, real, dimension( * )D, real, dimension( *…
NAME slaebz.f – SYNOPSIS Functions/Subroutines subroutine slaebz (IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, NAB, WORK, IWORK, INFO) SLAEBZ 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…
NAME slae2.f – SYNOPSIS Functions/Subroutines subroutine slae2 (A, B, C, RT1, RT2) SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. Function/Subroutine Documentation subroutine slae2 (realA, realB, realC, realRT1, realRT2) SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. Purpose: SLAE2 computes the eigenvalues of a 2 – by – 2 symmetric matrix[A B][B C].On…
NAME sladiv.f – SYNOPSIS Functions/Subroutines subroutine sladiv (A, B, C, D, P, Q) SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. subroutine sladiv1 (A, B, C, D, P, Q) REAL function sladiv2 (A, B, C, D, R, T) Function/Subroutine Documentation subroutine sladiv (realA, realB, realC, realD, realP, realQ) SLADIV performs complex division in…