Section 3: library functions
NAME dlarf.f – SYNOPSIS Functions/Subroutines subroutine dlarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK) DLARF applies an elementary reflector to a general rectangular matrix. Function/Subroutine Documentation subroutine dlarf (characterSIDE, integerM, integerN, double precision, dimension( * )V, integerINCV, double precisionTAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK) DLARF applies…
NAME dlar2v.f – SYNOPSIS Functions/Subroutines subroutine dlar2v (N, X, Y, Z, INCX, C, S, INCC) DLAR2V 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 dlar2v (integerN, double precision, dimension( * )X, double precision, dimension( * )Y, double precision,…
NAME dlar1v.f – SYNOPSIS Functions/Subroutines subroutine dlar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK) DLAR1V 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 dlaqtr.f – SYNOPSIS Functions/Subroutines subroutine dlaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO) DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. Function/Subroutine Documentation subroutine dlaqtr (logicalLTRAN, logicalLREAL, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( *…
NAME dlaqsy.f – SYNOPSIS Functions/Subroutines subroutine dlaqsy (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED) DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ. Function/Subroutine Documentation subroutine dlaqsy (characterUPLO, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED) DLAQSY scales a symmetric/Hermitian matrix, using…
NAME dlaqsp.f – SYNOPSIS Functions/Subroutines subroutine dlaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED) DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. Function/Subroutine Documentation subroutine dlaqsp (characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED) DLAQSP scales a symmetric/Hermitian matrix in…
NAME dlaqsb.f – SYNOPSIS Functions/Subroutines subroutine dlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED) DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. Function/Subroutine Documentation subroutine dlaqsb (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED) DLAQSB scales a…
NAME dlaqr5.f – SYNOPSIS Functions/Subroutines subroutine dlaqr5 (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) DLAQR5 performs a single small-bulge multi-shift QR sweep. Function/Subroutine Documentation subroutine dlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, double precision, dimension( *…
NAME dlaqr4.f – SYNOPSIS Functions/Subroutines subroutine dlaqr4 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) DLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. Function/Subroutine Documentation subroutine dlaqr4 (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, double precision, dimension( ldh, * )H, integerLDH,…
NAME dlaqr3.f – SYNOPSIS Functions/Subroutines subroutine dlaqr3 (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) DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix…
NAME dlaqr2.f – SYNOPSIS Functions/Subroutines subroutine dlaqr2 (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) DLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix…
NAME dlaqr1.f – SYNOPSIS Functions/Subroutines subroutine dlaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V) DLAQR1 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 dlaqr1 (integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionSR1, double precisionSI1, double precisionSR2, double…
NAME dlaqr0.f – SYNOPSIS Functions/Subroutines subroutine dlaqr0 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) DLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. Function/Subroutine Documentation subroutine dlaqr0 (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, double precision, dimension( ldh, * )H, integerLDH,…
NAME dlaqps.f – SYNOPSIS Functions/Subroutines subroutine dlaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF) DLAQPS 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 dlaqps (integerM, integerN, integerOFFSET, integerNB, integerKB, double precision, dimension( lda,…
NAME dlaqp2.f – SYNOPSIS Functions/Subroutines subroutine dlaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK) DLAQP2 computes a QR factorization with column pivoting of the matrix block. Function/Subroutine Documentation subroutine dlaqp2 (integerM, integerN, integerOFFSET, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension(…
NAME dlaqge.f – SYNOPSIS Functions/Subroutines subroutine dlaqge (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED) DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. Function/Subroutine Documentation subroutine dlaqge (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )R, double precision, dimension( * )C,…
NAME dlaqgb.f – SYNOPSIS Functions/Subroutines subroutine dlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. Function/Subroutine Documentation subroutine dlaqgb (integerM, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double…
NAME dlapy3.f – SYNOPSIS Functions/Subroutines DOUBLE PRECISION function dlapy3 (X, Y, Z) DLAPY3 returns sqrt(x2+y2+z2). Function/Subroutine Documentation DOUBLE PRECISION function dlapy3 (double precisionX, double precisionY, double precisionZ) DLAPY3 returns sqrt(x2+y2+z2). Purpose: DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow. Parameters: X X is DOUBLE PRECISION Y Y is DOUBLE PRECISION Z Z…
NAME dlapy2.f – SYNOPSIS Functions/Subroutines DOUBLE PRECISION function dlapy2 (X, Y) DLAPY2 returns sqrt(x2+y2). Function/Subroutine Documentation DOUBLE PRECISION function dlapy2 (double precisionX, double precisionY) DLAPY2 returns sqrt(x2+y2). Purpose: DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary overflow. Parameters: X X is DOUBLE PRECISION Y Y is DOUBLE PRECISION X and Y specify the…
NAME dlapmt.f – SYNOPSIS Functions/Subroutines subroutine dlapmt (FORWRD, M, N, X, LDX, K) DLAPMT performs a forward or backward permutation of the columns of a matrix. Function/Subroutine Documentation subroutine dlapmt (logicalFORWRD, integerM, integerN, double precision, dimension( ldx, * )X, integerLDX, integer, dimension( * )K) DLAPMT performs a forward or backward permutation of the columns of…