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---
:name: sggsvp
:md5sum: 8f9fa51bd57835c14e5543a88bb2b821
:category: :subroutine
:arguments:
- jobu:
:type: char
:intent: input
- jobv:
:type: char
:intent: input
- jobq:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- p:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: real
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- tola:
:type: real
:intent: input
- tolb:
:type: real
:intent: input
- k:
:type: integer
:intent: output
- l:
:type: integer
:intent: output
- u:
:type: real
:intent: output
:dims:
- ldu
- m
- ldu:
:type: integer
:intent: input
- v:
:type: real
:intent: output
:dims:
- ldv
- p
- ldv:
:type: integer
:intent: input
- q:
:type: real
:intent: output
:dims:
- ldq
- n
- ldq:
:type: integer
:intent: input
- iwork:
:type: integer
:intent: workspace
:dims:
- n
- tau:
:type: real
:intent: workspace
:dims:
- n
- work:
:type: real
:intent: workspace
:dims:
- MAX(MAX(3*n,m),p)
- info:
:type: integer
:intent: output
:substitutions:
m: lda
p: ldb
ldq: "lsame_(&jobq,\"Q\") ? MAX(1,n) : 1"
ldu: "lsame_(&jobu,\"U\") ? MAX(1,m) : 1"
ldv: "lsame_(&jobv,\"V\") ? MAX(1,p) : 1"
:fortran_help: " SUBROUTINE SGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGGSVP computes orthogonal matrices U, V and Q such that\n\
*\n\
* N-K-L K L\n\
* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;\n\
* L ( 0 0 A23 )\n\
* M-K-L ( 0 0 0 )\n\
*\n\
* N-K-L K L\n\
* = K ( 0 A12 A13 ) if M-K-L < 0;\n\
* M-K ( 0 0 A23 )\n\
*\n\
* N-K-L K L\n\
* V'*B*Q = L ( 0 0 B13 )\n\
* P-L ( 0 0 0 )\n\
*\n\
* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular\n\
* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,\n\
* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective\n\
* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the\n\
* transpose of Z.\n\
*\n\
* This decomposition is the preprocessing step for computing the\n\
* Generalized Singular Value Decomposition (GSVD), see subroutine\n\
* SGGSVD.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBU (input) CHARACTER*1\n\
* = 'U': Orthogonal matrix U is computed;\n\
* = 'N': U is not computed.\n\
*\n\
* JOBV (input) CHARACTER*1\n\
* = 'V': Orthogonal matrix V is computed;\n\
* = 'N': V is not computed.\n\
*\n\
* JOBQ (input) CHARACTER*1\n\
* = 'Q': Orthogonal matrix Q is computed;\n\
* = 'N': Q is not computed.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* P (input) INTEGER\n\
* The number of rows of the matrix B. P >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrices A and B. N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit, A contains the triangular (or trapezoidal) matrix\n\
* described in the Purpose section.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* B (input/output) REAL array, dimension (LDB,N)\n\
* On entry, the P-by-N matrix B.\n\
* On exit, B contains the triangular matrix described in\n\
* the Purpose section.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,P).\n\
*\n\
* TOLA (input) REAL\n\
* TOLB (input) REAL\n\
* TOLA and TOLB are the thresholds to determine the effective\n\
* numerical rank of matrix B and a subblock of A. Generally,\n\
* they are set to\n\
* TOLA = MAX(M,N)*norm(A)*MACHEPS,\n\
* TOLB = MAX(P,N)*norm(B)*MACHEPS.\n\
* The size of TOLA and TOLB may affect the size of backward\n\
* errors of the decomposition.\n\
*\n\
* K (output) INTEGER\n\
* L (output) INTEGER\n\
* On exit, K and L specify the dimension of the subblocks\n\
* described in Purpose.\n\
* K + L = effective numerical rank of (A',B')'.\n\
*\n\
* U (output) REAL array, dimension (LDU,M)\n\
* If JOBU = 'U', U contains the orthogonal matrix U.\n\
* If JOBU = 'N', U is not referenced.\n\
*\n\
* LDU (input) INTEGER\n\
* The leading dimension of the array U. LDU >= max(1,M) if\n\
* JOBU = 'U'; LDU >= 1 otherwise.\n\
*\n\
* V (output) REAL array, dimension (LDV,P)\n\
* If JOBV = 'V', V contains the orthogonal matrix V.\n\
* If JOBV = 'N', V is not referenced.\n\
*\n\
* LDV (input) INTEGER\n\
* The leading dimension of the array V. LDV >= max(1,P) if\n\
* JOBV = 'V'; LDV >= 1 otherwise.\n\
*\n\
* Q (output) REAL array, dimension (LDQ,N)\n\
* If JOBQ = 'Q', Q contains the orthogonal matrix Q.\n\
* If JOBQ = 'N', Q is not referenced.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= max(1,N) if\n\
* JOBQ = 'Q'; LDQ >= 1 otherwise.\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (N)\n\
*\n\
* TAU (workspace) REAL array, dimension (N)\n\
*\n\
* WORK (workspace) REAL array, dimension (max(3*N,M,P))\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The subroutine uses LAPACK subroutine SGEQPF for the QR factorization\n\
* with column pivoting to detect the effective numerical rank of the\n\
* a matrix. It may be replaced by a better rank determination strategy.\n\
*\n\
* =====================================================================\n\
*\n"
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