slahrd.f – Synopsis Functions/Subroutines subroutine slahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) SLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. Function/Subroutine…
NAME slahrd.f – SYNOPSIS Functions/Subroutines subroutine slahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) SLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A….
NAME slagv2.f – SYNOPSIS Functions/Subroutines subroutine slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. Function/Subroutine Documentation subroutine slagv2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( 2…
NAME slagts.f – SYNOPSIS Functions/Subroutines subroutine slagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO) SLAGTS 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 Documentation subroutine slagts (integerJOB, integerN, real, dimension(…
slagtm.f – Synopsis Functions/Subroutines subroutine slagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) SLAGTM 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…
NAME slagtf.f – SYNOPSIS Functions/Subroutines subroutine slagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO) SLAGTF 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 Documentation subroutine slagtf (integerN, real, dimension( * )A, realLAMBDA, real, dimension( *…
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,…