ungtr - {un,or}gtr: generate Q from hetrd

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subroutinecungtr(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerlwork,integerinfo)CUNGTRPurpose: CUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from CHETRD; = 'L': Lower triangle of A contains elementary reflectors from CHETRD. N N is INTEGER The order of the matrix Q. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CHETRD. On exit, the N-by-N unitary matrix Q. LDA LDA is INTEGER The leading dimension of the array A. LDA >= N. TAU TAU is COMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD. WORK WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N-1. For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinedorgtr(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORGTRPurpose: DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD. N N is INTEGER The order of the matrix Q. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DSYTRD. On exit, the N-by-N orthogonal matrix Q. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TAU TAU is DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,N-1). For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinesorgtr(characteruplo,integern,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerlwork,integerinfo)SORGTRPurpose: SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD. N N is INTEGER The order of the matrix Q. N >= 0. A A is REAL array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by SSYTRD. On exit, the N-by-N orthogonal matrix Q. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TAU TAU is REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD. WORK WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,N-1). For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinezungtr(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNGTRPurpose: ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from ZHETRD; = 'L': Lower triangle of A contains elementary reflectors from ZHETRD. N N is INTEGER The order of the matrix Q. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZHETRD. On exit, the N-by-N unitary matrix Q. LDA LDA is INTEGER The leading dimension of the array A. LDA >= N. TAU TAU is COMPLEX*16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD. WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N-1. For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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.

ungtr - {un,or}gtr: generate Q from hetrd

Functions subroutine cungtr (uplo, n, a, lda, tau, work, lwork, info) CUNGTR subroutine dorgtr (uplo, n, a, lda, tau, work, lwork, info) DORGTR subroutine sorgtr (uplo, n, a, lda, tau, work, lwork, info) SORGTR subroutine zungtr (uplo, n, a, lda, tau, work, lwork, info) ZUNGTR