unm22 - {un,or}m22: multiply by banded Q, step in gghd3

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subroutinecunm22(characterside,charactertrans,integerm,integern,integern1,integern2,complex,dimension(ldq,*)q,integerldq,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerlwork,integerinfo)CUNM22 multiplies a general matrix by a banded unitary matrix. Purpose CUNM22 overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'. The unitary matrix Q processes a 2-by-2 block structure [ Q11 Q12 ] Q = [ ] [ Q21 Q22 ], where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': apply Q (No transpose); = 'C': apply Q**H (Conjugate transpose). M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. N1N2 N1 is INTEGER N2 is INTEGER The dimension of Q12 and Q21, respectively. N1, N2 >= 0. The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'. Q Q is COMPLEX array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R' LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). 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. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= M*N. 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. subroutinedorm22(characterside,charactertrans,integerm,integern,integern1,integern2,doubleprecision,dimension(ldq,*)q,integerldq,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORM22 multiplies a general matrix by a banded orthogonal matrix. Purpose DORM22 overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'. The orthogonal matrix Q processes a 2-by-2 block structure [ Q11 Q12 ] Q = [ ] [ Q21 Q22 ], where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': apply Q (No transpose); = 'C': apply Q**T (Conjugate transpose). M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. N1N2 N1 is INTEGER N2 is INTEGER The dimension of Q12 and Q21, respectively. N1, N2 >= 0. The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'. Q Q is DOUBLE PRECISION array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R' LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'. C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). 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. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= M*N. 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. subroutinesorm22(characterside,charactertrans,integerm,integern,integern1,integern2,real,dimension(ldq,*)q,integerldq,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerlwork,integerinfo)SORM22 multiplies a general matrix by a banded orthogonal matrix. Purpose SORM22 overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'. The orthogonal matrix Q processes a 2-by-2 block structure [ Q11 Q12 ] Q = [ ] [ Q21 Q22 ], where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': apply Q (No transpose); = 'C': apply Q**T (Conjugate transpose). M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. N1N2 N1 is INTEGER N2 is INTEGER The dimension of Q12 and Q21, respectively. N1, N2 >= 0. The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'. Q Q is REAL array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R' LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). 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. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= M*N. 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. subroutinezunm22(characterside,charactertrans,integerm,integern,integern1,integern2,complex*16,dimension(ldq,*)q,integerldq,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNM22 multiplies a general matrix by a banded unitary matrix. Purpose ZUNM22 overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'. The unitary matrix Q processes a 2-by-2 block structure [ Q11 Q12 ] Q = [ ] [ Q21 Q22 ], where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': apply Q (No transpose); = 'C': apply Q**H (Conjugate transpose). M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. N1N2 N1 is INTEGER N2 is INTEGER The dimension of Q12 and Q21, respectively. N1, N2 >= 0. The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'. Q Q is COMPLEX*16 array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R' LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'. C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). 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. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= M*N. 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.

unm22 - {un,or}m22: multiply by banded Q, step in gghd3

Functions subroutine cunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info) CUNM22 multiplies a general matrix by a banded unitary matrix. subroutine dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info) DORM22 multiplies a general matrix by a banded orthogonal matrix. subroutine sorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info) SORM22 multiplies a general matrix by a banded orthogonal matrix. subroutine zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info) ZUNM22 multiplies a general matrix by a banded unitary matrix.