Section 3: library functions
dlagv2.f – SynopsisFunctions/Subroutinessubroutine dlagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. Function/Subroutine Documentationsubroutine dlagv2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( 2 )ALPHAR,…
dlagts.f – SynopsisFunctions/Subroutinessubroutine dlagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO) DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf. Function/Subroutine Documentationsubroutine dlagts (integerJOB, integerN, double precision, dimension( * )A, double…
dlagtm.f – SynopsisFunctions/Subroutinessubroutine dlagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. Function/Subroutine Documentationsubroutine dlagtm…
dlagtf.f – SynopsisFunctions/Subroutinessubroutine dlagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO) DLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges. Function/Subroutine Documentationsubroutine dlagtf (integerN, double precision, dimension( * )A, double precisionLAMBDA, double precision, dimension( * )B,…
dlags2.f – SynopsisFunctions/Subroutinessubroutine dlags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) DLAGS2 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 Documentationsubroutine dlags2 (logicalUPPER, double precisionA1, double precisionA2, double…
dlag2s.f – SynopsisFunctions/Subroutinessubroutine dlag2s (M, N, A, LDA, SA, LDSA, INFO) DLAG2S converts a double precision matrix to a single precision matrix. Function/Subroutine Documentationsubroutine dlag2s (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, real, dimension( ldsa, * )SA, integerLDSA, integerINFO)DLAG2S converts a double precision matrix to a single precision matrix. Purpose: DLAG2S converts a…
dlag2.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlag2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precisionSAFMIN, double precisionSCALE1, double precisionSCALE2, double…
dlaexc.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaexc (logicalWANTQ, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( ldq, * )Q, integerLDQ, integerJ1,…
dlaev2.f – SynopsisFunctions/Subroutinessubroutine dlaev2 (A, B, C, RT1, RT2, CS1, SN1) DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentationsubroutine 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 computes the eigendecomposition of…
dlaein.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaein (logicalRIGHTV, logicalNOINIT, integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionWR, double precisionWI, double precision,…
dlaeda.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaeda (integerN, integerTLVLS, integerCURLVL, integerCURPBM, integer, dimension( * )PRMPTR, integer, dimension( *…
dlaed9.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed9 (integerK, integerKSTART, integerKSTOP, integerN, double precision, dimension( * )D, double precision, dimension( ldq,…
dlaed8.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, double precision, dimension( * )D,…
dlaed7.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed7…
dlaed6.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed6 (integerKNITER, logicalORGATI, double precisionRHO, double precision, dimension( 3 )D, double precision, dimension( 3 )Z, double precisionFINIT, double precisionTAU, integerINFO)DLAED6 used by sstedc. Computes one Newton step…
dlaed5.f – SynopsisFunctions/Subroutinessubroutine dlaed5 (I, D, Z, DELTA, RHO, DLAM) DLAED5 used by sstedc. Solves the 2-by-2 secular equation. Function/Subroutine Documentationsubroutine 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: This subroutine computes the…
dlaed4.f – SynopsisFunctions/Subroutinessubroutine dlaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) DLAED4 used by sstedc. Finds a single root of the secular equation. Function/Subroutine Documentationsubroutine dlaed4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension( * )DELTA, double precisionRHO, double precisionDLAM, integerINFO)DLAED4 used by sstedc. Finds a single…
dlaed3.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed3 (integerK, integerN, integerN1, double precision, dimension( * )D, double precision, dimension( ldq,…
dlaed2.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed2 (integerK, integerN, integerN1, double precision, dimension( * )D, double precision, dimension( ldq, * )Q,…
dlaed1.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlaed1 (integerN, double precision, dimension( * )D, double precision, dimension( ldq, * )Q,…