Section 3: library functions
NAME slarfx.f – SYNOPSIS Functions/Subroutines subroutine slarfx (SIDE, M, N, V, TAU, C, LDC, WORK) SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. Function/Subroutine Documentation subroutine slarfx (characterSIDE, integerM, integerN, real, dimension( * )V, realTAU, real, dimension( ldc, * )C, integerLDC, real, dimension(…
slarft.f – Synopsis Functions/Subroutines subroutine slarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) SLARFT forms the triangular factor T of a block reflector H = I – vtvH Function/Subroutine Documentation subroutine slarft (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT) SLARFT…
NAME slarfgp.f – SYNOPSIS Functions/Subroutines subroutine slarfgp (N, ALPHA, X, INCX, TAU) SLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Function/Subroutine Documentation subroutine slarfgp (integerN, realALPHA, real, dimension( * )X, integerINCX, realTAU) SLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Purpose: SLARFGP generates a real elementary reflector H of order n,…
NAME slarfg.f – SYNOPSIS Functions/Subroutines subroutine slarfg (N, ALPHA, X, INCX, TAU) SLARFG generates an elementary reflector (Householder matrix). Function/Subroutine Documentation subroutine slarfg (integerN, realALPHA, real, dimension( * )X, integerINCX, realTAU) SLARFG generates an elementary reflector (Householder matrix). Purpose: SLARFG generates a real elementary reflector H of order n, such that H * ( alpha…
NAME slarfb.f – SYNOPSIS Functions/Subroutines subroutine slarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARFB applies a block reflector or its transpose to a general rectangular matrix. Function/Subroutine Documentation subroutine slarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt,…
NAME slarf.f – SYNOPSIS Functions/Subroutines subroutine slarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK) SLARF applies an elementary reflector to a general rectangular matrix. Function/Subroutine Documentation subroutine slarf (characterSIDE, integerM, integerN, real, dimension( * )V, integerINCV, realTAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK) SLARF applies an elementary reflector to…
NAME slar2v.f – SYNOPSIS Functions/Subroutines subroutine slar2v (N, X, Y, Z, INCX, C, S, INCC) SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. Function/Subroutine Documentation subroutine slar2v (integerN, real, dimension( * )X, real, dimension( * )Y, real, dimension( * )Z,…
NAME slar1v.f – SYNOPSIS Functions/Subroutines subroutine slar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK) SLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT – λI. Function/Subroutine Documentation subroutine…
NAME slaqtr.f – SYNOPSIS Functions/Subroutines subroutine slaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO) SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. Function/Subroutine Documentation subroutine slaqtr (logicalLTRAN, logicalLREAL, integerN, real, dimension( ldt, * )T, integerLDT, real, dimension( * )B, realW,…
NAME slaqsy.f – SYNOPSIS Functions/Subroutines subroutine slaqsy (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED) SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ. Function/Subroutine Documentation subroutine slaqsy (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, characterEQUED) SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by…
NAME slaqsp.f – SYNOPSIS Functions/Subroutines subroutine slaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED) SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. Function/Subroutine Documentation subroutine slaqsp (characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )S, realSCOND, realAMAX, characterEQUED) SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling…
NAME slaqsb.f – SYNOPSIS Functions/Subroutines subroutine slaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED) SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. Function/Subroutine Documentation subroutine slaqsb (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, characterEQUED) SLAQSB scales a symmetric/Hermitian band matrix, using…
NAME slaqr5.f – SYNOPSIS Functions/Subroutines subroutine slaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH) SLAQR5 performs a single small-bulge multi-shift QR sweep. Function/Subroutine Documentation subroutine slaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, real, dimension( * )SR,…
NAME slaqr4.f – SYNOPSIS Functions/Subroutines subroutine slaqr4 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) SLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. Function/Subroutine Documentation subroutine slaqr4 (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, real, dimension( ldh, * )H, integerLDH, real,…
NAME slaqr3.f – SYNOPSIS Functions/Subroutines subroutine slaqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK) SLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix…
NAME slaqr2.f – SYNOPSIS Functions/Subroutines subroutine slaqr2 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK) SLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix…
NAME slaqr1.f – SYNOPSIS Functions/Subroutines subroutine slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V) SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. Function/Subroutine Documentation subroutine slaqr1 (integerN, real, dimension( ldh, * )H, integerLDH, realSR1, realSI1, realSR2, realSI2, real, dimension( * )V)…
NAME slaqr0.f – SYNOPSIS Functions/Subroutines subroutine slaqr0 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) SLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. Function/Subroutine Documentation subroutine slaqr0 (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, real, dimension( ldh, * )H, integerLDH, real,…
NAME slaqps.f – SYNOPSIS Functions/Subroutines subroutine slaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF) SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. Function/Subroutine Documentation subroutine slaqps (integerM, integerN, integerOFFSET, integerNB, integerKB, real, dimension( lda, *…
NAME slaqp2.f – SYNOPSIS Functions/Subroutines subroutine slaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK) SLAQP2 computes a QR factorization with column pivoting of the matrix block. Function/Subroutine Documentation subroutine slaqp2 (integerM, integerN, integerOFFSET, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )VN1, real,…