ssbgst(3) [debian man page]
ssbgst.f(3) LAPACK ssbgst.f(3) NAME
ssbgst.f - SYNOPSIS
Functions/Subroutines subroutine ssbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO) SSBGST Function/Subroutine Documentation subroutine ssbgst (characterVECT, characterUPLO, integerN, integerKA, integerKB, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldbb, * )BB, integerLDBB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )WORK, integerINFO) SSBGST Purpose: SSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**T*S by SPBSTF, using a split Cholesky factorization. A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. Parameters: VECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**T*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is REAL array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by SPBSTF, stored in the first KB+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is REAL array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is REAL array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 159 of file ssbgst.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 ssbgst.f(3)
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dsbgst.f(3) LAPACK dsbgst.f(3) NAME
dsbgst.f - SYNOPSIS
Functions/Subroutines subroutine dsbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO) DSBGST Function/Subroutine Documentation subroutine dsbgst (characterVECT, characterUPLO, integerN, integerKA, integerKB, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldbb, * )BB, integerLDBB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( * )WORK, integerINFO) DSBGST Purpose: DSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**T*S by DPBSTF, using a split Cholesky factorization. A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. Parameters: VECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**T*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is DOUBLE PRECISION array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by DPBSTF, stored in the first KB+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is DOUBLE PRECISION array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is DOUBLE PRECISION array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 159 of file dsbgst.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dsbgst.f(3)