Section 3: library functions
NAME clascl2.f – SYNOPSIS Functions/Subroutines subroutine clascl2 (M, N, D, X, LDX) CLASCL2 performs diagonal scaling on a vector. Function/Subroutine Documentation subroutine clascl2 (integerM, integerN, real, dimension( * )D, complex, dimension( ldx, * )X, integerLDX) CLASCL2 performs diagonal scaling on a vector. Purpose: CLASCL2 performs a diagonal scaling on a vector: x <– D *…
NAME clascl.f – SYNOPSIS Functions/Subroutines subroutine clascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO) CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. Function/Subroutine Documentation subroutine clascl (characterTYPE, integerKL, integerKU, realCFROM, realCTO, integerM, integerN, complex, dimension( lda, * )A, integerLDA, integerINFO) CLASCL multiplies a general rectangular matrix by…
NAME clarzt.f – SYNOPSIS Functions/Subroutines subroutine clarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) CLARZT forms the triangular factor T of a block reflector H = I – vtvH. Function/Subroutine Documentation subroutine clarzt (characterDIRECT, characterSTOREV, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( * )TAU, complex, dimension( ldt, * )T, integerLDT)…
NAME clarzb.f – SYNOPSIS Functions/Subroutines subroutine clarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) CLARZB applies a block reflector or its conjugate-transpose to a general matrix. Function/Subroutine Documentation subroutine clarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, complex, dimension( ldv, * )V, integerLDV, complex, dimension(…
NAME clarz.f – SYNOPSIS Functions/Subroutines subroutine clarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentation subroutine clarz (characterSIDE, integerM, integerN, integerL, complex, dimension( * )V, integerINCV, complexTAU, complex, dimension( ldc, * )C, integerLDC, complex, dimension( * )WORK) CLARZ…
NAME clartv.f – SYNOPSIS Functions/Subroutines subroutine clartv (N, X, INCX, Y, INCY, C, S, INCC) CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors. Function/Subroutine Documentation subroutine clartv (integerN, complex, dimension( * )X, integerINCX, complex, dimension( * )Y, integerINCY, real, dimension( * )C,…
NAME clartg.f – SYNOPSIS Functions/Subroutines subroutine clartg (F, G, CS, SN, R) CLARTG generates a plane rotation with real cosine and complex sine. Function/Subroutine Documentation subroutine clartg (complexF, complexG, realCS, complexSN, complexR) CLARTG generates a plane rotation with real cosine and complex sine. Purpose: CLARTG generates a plane rotation so that [ CS SN ]…
NAME clarscl2.f – SYNOPSIS Functions/Subroutines subroutine clarscl2 (M, N, D, X, LDX) CLARSCL2 performs reciprocal diagonal scaling on a vector. Function/Subroutine Documentation subroutine clarscl2 (integerM, integerN, real, dimension( * )D, complex, dimension( ldx, * )X, integerLDX) CLARSCL2 performs reciprocal diagonal scaling on a vector. Purpose: CLARSCL2 performs a reciprocal diagonal scaling on an vector: x…
NAME clarrv.f – SYNOPSIS Functions/Subroutines subroutine clarrv (N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W, WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO) CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT….
NAME clarnv.f – SYNOPSIS Functions/Subroutines subroutine clarnv (IDIST, ISEED, N, X) CLARNV returns a vector of random numbers from a uniform or normal distribution. Function/Subroutine Documentation subroutine clarnv (integerIDIST, integer, dimension( 4 )ISEED, integerN, complex, dimension( * )X) CLARNV returns a vector of random numbers from a uniform or normal distribution. Purpose: CLARNV returns a…
NAME clargv.f – SYNOPSIS Functions/Subroutines subroutine clargv (N, X, INCX, Y, INCY, C, INCC) CLARGV generates a vector of plane rotations with real cosines and complex sines. Function/Subroutine Documentation subroutine clargv (integerN, complex, dimension( * )X, integerINCX, complex, dimension( * )Y, integerINCY, real, dimension( * )C, integerINCC) CLARGV generates a vector of plane rotations with…
NAME clarfx.f – SYNOPSIS Functions/Subroutines subroutine clarfx (SIDE, M, N, V, TAU, C, LDC, WORK) CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. Function/Subroutine Documentation subroutine clarfx (characterSIDE, integerM, integerN, complex, dimension( * )V, complexTAU, complex, dimension( ldc, * )C, integerLDC, complex, dimension(…
NAME clarft.f – SYNOPSIS Functions/Subroutines subroutine clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) CLARFT forms the triangular factor T of a block reflector H = I – vtvH Function/Subroutine Documentation subroutine clarft (characterDIRECT, characterSTOREV, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( * )TAU, complex, dimension( ldt, * )T, integerLDT)…
NAME clarfgp.f – SYNOPSIS Functions/Subroutines subroutine clarfgp (N, ALPHA, X, INCX, TAU) CLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Function/Subroutine Documentation subroutine clarfgp (integerN, complexALPHA, complex, dimension( * )X, integerINCX, complexTAU) CLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta. Purpose: CLARFGP generates a complex elementary reflector H of order n,…
NAME clarfg.f – SYNOPSIS Functions/Subroutines subroutine clarfg (N, ALPHA, X, INCX, TAU) CLARFG generates an elementary reflector (Householder matrix). Function/Subroutine Documentation subroutine clarfg (integerN, complexALPHA, complex, dimension( * )X, integerINCX, complexTAU) CLARFG generates an elementary reflector (Householder matrix). Purpose: CLARFG generates a complex elementary reflector H of order n, such that H**H * ( alpha…
NAME clarfb.f – SYNOPSIS Functions/Subroutines subroutine clarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. Function/Subroutine Documentation subroutine clarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt,…
NAME clarf.f – SYNOPSIS Functions/Subroutines subroutine clarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK) CLARF applies an elementary reflector to a general rectangular matrix. Function/Subroutine Documentation subroutine clarf (characterSIDE, integerM, integerN, complex, dimension( * )V, integerINCV, complexTAU, complex, dimension( ldc, * )C, integerLDC, complex, dimension( * )WORK) CLARF applies an elementary reflector to…
NAME clarcm.f – SYNOPSIS Functions/Subroutines subroutine clarcm (M, N, A, LDA, B, LDB, C, LDC, RWORK) CLARCM copies all or part of a real two-dimensional array to a complex array. Function/Subroutine Documentation subroutine clarcm (integerM, integerN, real, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldc, * )C, integerLDC, real,…
NAME clar2v.f – SYNOPSIS Functions/Subroutines subroutine clar2v (N, X, Y, Z, INCX, C, S, INCC) CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. Function/Subroutine Documentation subroutine clar2v (integerN, complex, dimension( * )X, complex, dimension( * )Y, complex, dimension( * )Z,…
NAME clar1v.f – SYNOPSIS Functions/Subroutines subroutine clar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK) CLAR1V 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…