Section 3: library functions
NAME clahqr.f – SYNOPSIS Functions/Subroutines subroutine clahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO) CLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. Function/Subroutine Documentation subroutine clahqr (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, complex, dimension( ldh, * )H, integerLDH, complex, dimension( *…
NAME clahef.f – SYNOPSIS Functions/Subroutines subroutine clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). Function/Subroutine Documentation subroutine clahef (characterUPLO, integerN, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer,…
NAME clagtm.f – SYNOPSIS Functions/Subroutines subroutine clagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) CLAGTM 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….
NAME clags2.f – SYNOPSIS Functions/Subroutines subroutine clags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) CLAGS2 Function/Subroutine Documentation subroutine clags2 (logicalUPPER, realA1, complexA2, realA3, realB1, complexB2, realB3, realCSU, complexSNU, realCSV, complexSNV, realCSQ, complexSNQ) CLAGS2 Purpose: CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER )…
NAME clag2z.f – SYNOPSIS Functions/Subroutines subroutine clag2z (M, N, SA, LDSA, A, LDA, INFO) CLAG2Z converts a complex single precision matrix to a complex double precision matrix. Function/Subroutine Documentation subroutine clag2z (integerM, integerN, complex, dimension( ldsa, * )SA, integerLDSA, complex*16, dimension( lda, * )A, integerLDA, integerINFO) CLAG2Z converts a complex single precision matrix to a…
NAME claev2.f – SYNOPSIS Functions/Subroutines subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: CLAEV2 computes the eigendecomposition of a 2-by-2…
NAME claesy.f – SYNOPSIS Functions/Subroutines subroutine claesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1) CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. Function/Subroutine Documentation subroutine claesy (complexA, complexB, complexC, complexRT1, complexRT2, complexEVSCAL, complexCS1, complexSN1) CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. Purpose: CLAESY computes the…
NAME claein.f – SYNOPSIS Functions/Subroutines subroutine claein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO) CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentation subroutine claein (logicalRIGHTV, logicalNOINIT, integerN, complex, dimension( ldh, * )H, integerLDH, complexW, complex, dimension( * )V, complex,…
NAME claed8.f – SYNOPSIS Functions/Subroutines subroutine claed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) CLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. Function/Subroutine Documentation subroutine claed8 (integerK, integerN, integerQSIZ, complex, dimension( ldq,…
NAME claed7.f – SYNOPSIS Functions/Subroutines subroutine claed7 (N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) CLAED7 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 claed0.f – SYNOPSIS Functions/Subroutines subroutine claed0 (QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, IWORK, INFO) CLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Function/Subroutine Documentation subroutine claed0 (integerQSIZ, integerN, real, dimension( * )D, real, dimension( * )E, complex,…
NAME cladiv.f – SYNOPSIS Functions/Subroutines COMPLEX function cladiv (X, Y) CLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Function/Subroutine Documentation COMPLEX function cladiv (complexX, complexY) CLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Purpose: CLADIV := X / Y, where X and Y are complex. The computation of X / Y…
NAME clacrt.f – SYNOPSIS Functions/Subroutines subroutine clacrt (N, CX, INCX, CY, INCY, C, S) CLACRT performs a linear transformation of a pair of complex vectors. Function/Subroutine Documentation subroutine clacrt (integerN, complex, dimension( * )CX, integerINCX, complex, dimension( * )CY, integerINCY, complexC, complexS) CLACRT performs a linear transformation of a pair of complex vectors. Purpose: CLACRT…
NAME clacrm.f – SYNOPSIS Functions/Subroutines subroutine clacrm (M, N, A, LDA, B, LDB, C, LDC, RWORK) CLACRM multiplies a complex matrix by a square real matrix. Function/Subroutine Documentation subroutine clacrm (integerM, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, complex, dimension( ldc, * )C, integerLDC, real, dimension( * )RWORK) CLACRM…
NAME clacpy.f – SYNOPSIS Functions/Subroutines subroutine clacpy (UPLO, M, N, A, LDA, B, LDB) CLACPY copies all or part of one two-dimensional array to another. Function/Subroutine Documentation subroutine clacpy (characterUPLO, integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB) CLACPY copies all or part of one two-dimensional array to another….
NAME clacp2.f – SYNOPSIS Functions/Subroutines subroutine clacp2 (UPLO, M, N, A, LDA, B, LDB) CLACP2 copies all or part of a real two-dimensional array to a complex array. Function/Subroutine Documentation subroutine clacp2 (characterUPLO, integerM, integerN, real, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB) CLACP2 copies all or part of a real…
NAME clacon.f – SYNOPSIS Functions/Subroutines subroutine clacon (N, V, X, EST, KASE) CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. Function/Subroutine Documentation subroutine clacon (integerN, complex, dimension( n )V, complex, dimension( n )X, realEST, integerKASE) CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating…
NAME clacn2.f – SYNOPSIS Functions/Subroutines subroutine clacn2 (N, V, X, EST, KASE, ISAVE) CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. Function/Subroutine Documentation subroutine clacn2 (integerN, complex, dimension( * )V, complex, dimension( * )X, realEST, integerKASE, integer, dimension( 3 )ISAVE) CLACN2 estimates the 1-norm of a square matrix,…
NAME clacgv.f – SYNOPSIS Functions/Subroutines subroutine clacgv (N, X, INCX) CLACGV conjugates a complex vector. Function/Subroutine Documentation subroutine clacgv (integerN, complex, dimension( * )X, integerINCX) CLACGV conjugates a complex vector. Purpose: CLACGV conjugates a complex vector of length N. Parameters: N N is INTEGER The length of the vector X. N >= 0. X…
NAME clabrd.f – SYNOPSIS Functions/Subroutines subroutine clabrd (M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY) CLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. Function/Subroutine Documentation subroutine clabrd (integerM, integerN, integerNB, complex, dimension( lda, * )A, integerLDA, real, dimension( * )D, real, dimension(…